bond cash flows literacy - state treasurer's office · 7/8/2014 · bond cash flows literacy...

48
BOND CASH FLOWS LITERACY INTERMEDIATE BOND MATH (PART 1) For technical issues, contact GoToWebinar (GoToMeeting) at 1-800-263-6317 or http://support.citrixonline.com/gotomeeting/ Presentation slides are available to download at http://www.treasurer.ca.gov/cdiac/webinars/2014/201408 07/description.asp For MCLE credit, email [email protected] Live captioning is available at www.streamtext.net/text.aspx?event=CDIAC August 7, 2014 2:00 PM – 3:30 PM

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Page 1: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

BOND CASH FLOWS LITERACY INTERMEDIATE BOND MATH (PART 1)

bull For technical issues contact GoToWebinar (GoToMeeting) at

1-800-263-6317 or

httpsupportcitrixonlinecomgotomeeting

bull Presentation slides are available to download at

httpwwwtreasurercagovcdiacwebinars2014201408

07descriptionasp

bull For MCLE credit email cdiac_educationtreasurercagov

bull Live captioning is available at

wwwstreamtextnettextaspxevent=CDIAC

August 7 2014 200 PM ndash 330 PM

BOND CASH FLOWS LITERACY INTERMEDIATE BOND MATH (PART 1)

PRESENTED BY LOUIS CHOI

PUBLIC RESOURCES ADVISORY GROUP AN INDEPENDENT REGISTERED MUNICIPAL ADVISOR (IRMA)

Topics presented by

3

Bonds and Loans

How Municipal Bonds are Priced (or Valued)

Understanding Cash Flow Schedules

Debt Amortization

Bonus Using Microsoft Excel Functions

Bonds and Loans

Bond cash flows literacy intermediate bond math (Part 1)

Bonds and Loans

Bonds as Loans presented by

5

ϜϜ

π

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

Bonds and Loans

In Aggregate Bonds in an Issue Are

Equivalent to a Loan presented by

6

$120

$100 Interest

$80 $60 $40 $20 $0

$120

$100

$80

$60

$40

$20

$0

Principal

1

$120

$60

$80

$100 Interest

Principal

$40

$20

$0

5 10 15 20 25 30

$0

$20

$40

$60

$80

$100

$120

Interest

Principal

Interest

Principal

1 5 10 15 20 25 30

= 1 5 10 15 20 25 30 1 5 10 15 20 25 30

Bonds and Loans

A Bond Issue and a Loan Are Mathematically

Similar But Not Identical presented by

77

A Loan

Principal 500 Debt

Date Balance Principal Interest Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

A Bond Issue 200 300 400 450 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375

512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375

512017 31450000 9975000 400 399000 471375 550000 1420375 11395375

512018 21475000 10475000 450 471375 550000 1021375 11496375

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500

Interest on Principal Due

presented by

Bonds and Loans

Differences in Rates Across Maturities Generate a

Yield Curve 8

State Public Works Board of the State of California $152420000 Lease Revenue Bonds

(Department of Corrections and Rehabilitation) 2014 Series C

00

05

10

15

20

25

30

35

40

45

2014 2019 2024 2029 2034

Yie

ld

0

2

4

6

8

10

12$Millions

Pri

nci

pa

l

Principal

Yield

Principal Amounts and Initial Reoffering Yields as of April 10 2014

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 2: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

BOND CASH FLOWS LITERACY INTERMEDIATE BOND MATH (PART 1)

PRESENTED BY LOUIS CHOI

PUBLIC RESOURCES ADVISORY GROUP AN INDEPENDENT REGISTERED MUNICIPAL ADVISOR (IRMA)

Topics presented by

3

Bonds and Loans

How Municipal Bonds are Priced (or Valued)

Understanding Cash Flow Schedules

Debt Amortization

Bonus Using Microsoft Excel Functions

Bonds and Loans

Bond cash flows literacy intermediate bond math (Part 1)

Bonds and Loans

Bonds as Loans presented by

5

ϜϜ

π

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

Bonds and Loans

In Aggregate Bonds in an Issue Are

Equivalent to a Loan presented by

6

$120

$100 Interest

$80 $60 $40 $20 $0

$120

$100

$80

$60

$40

$20

$0

Principal

1

$120

$60

$80

$100 Interest

Principal

$40

$20

$0

5 10 15 20 25 30

$0

$20

$40

$60

$80

$100

$120

Interest

Principal

Interest

Principal

1 5 10 15 20 25 30

= 1 5 10 15 20 25 30 1 5 10 15 20 25 30

Bonds and Loans

A Bond Issue and a Loan Are Mathematically

Similar But Not Identical presented by

77

A Loan

Principal 500 Debt

Date Balance Principal Interest Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

A Bond Issue 200 300 400 450 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375

512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375

512017 31450000 9975000 400 399000 471375 550000 1420375 11395375

512018 21475000 10475000 450 471375 550000 1021375 11496375

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500

Interest on Principal Due

presented by

Bonds and Loans

Differences in Rates Across Maturities Generate a

Yield Curve 8

State Public Works Board of the State of California $152420000 Lease Revenue Bonds

(Department of Corrections and Rehabilitation) 2014 Series C

00

05

10

15

20

25

30

35

40

45

2014 2019 2024 2029 2034

Yie

ld

0

2

4

6

8

10

12$Millions

Pri

nci

pa

l

Principal

Yield

Principal Amounts and Initial Reoffering Yields as of April 10 2014

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 3: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Topics presented by

3

Bonds and Loans

How Municipal Bonds are Priced (or Valued)

Understanding Cash Flow Schedules

Debt Amortization

Bonus Using Microsoft Excel Functions

Bonds and Loans

Bond cash flows literacy intermediate bond math (Part 1)

Bonds and Loans

Bonds as Loans presented by

5

ϜϜ

π

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

Bonds and Loans

In Aggregate Bonds in an Issue Are

Equivalent to a Loan presented by

6

$120

$100 Interest

$80 $60 $40 $20 $0

$120

$100

$80

$60

$40

$20

$0

Principal

1

$120

$60

$80

$100 Interest

Principal

$40

$20

$0

5 10 15 20 25 30

$0

$20

$40

$60

$80

$100

$120

Interest

Principal

Interest

Principal

1 5 10 15 20 25 30

= 1 5 10 15 20 25 30 1 5 10 15 20 25 30

Bonds and Loans

A Bond Issue and a Loan Are Mathematically

Similar But Not Identical presented by

77

A Loan

Principal 500 Debt

Date Balance Principal Interest Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

A Bond Issue 200 300 400 450 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375

512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375

512017 31450000 9975000 400 399000 471375 550000 1420375 11395375

512018 21475000 10475000 450 471375 550000 1021375 11496375

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500

Interest on Principal Due

presented by

Bonds and Loans

Differences in Rates Across Maturities Generate a

Yield Curve 8

State Public Works Board of the State of California $152420000 Lease Revenue Bonds

(Department of Corrections and Rehabilitation) 2014 Series C

00

05

10

15

20

25

30

35

40

45

2014 2019 2024 2029 2034

Yie

ld

0

2

4

6

8

10

12$Millions

Pri

nci

pa

l

Principal

Yield

Principal Amounts and Initial Reoffering Yields as of April 10 2014

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 4: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonds and Loans

Bond cash flows literacy intermediate bond math (Part 1)

Bonds and Loans

Bonds as Loans presented by

5

ϜϜ

π

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

Bonds and Loans

In Aggregate Bonds in an Issue Are

Equivalent to a Loan presented by

6

$120

$100 Interest

$80 $60 $40 $20 $0

$120

$100

$80

$60

$40

$20

$0

Principal

1

$120

$60

$80

$100 Interest

Principal

$40

$20

$0

5 10 15 20 25 30

$0

$20

$40

$60

$80

$100

$120

Interest

Principal

Interest

Principal

1 5 10 15 20 25 30

= 1 5 10 15 20 25 30 1 5 10 15 20 25 30

Bonds and Loans

A Bond Issue and a Loan Are Mathematically

Similar But Not Identical presented by

77

A Loan

Principal 500 Debt

Date Balance Principal Interest Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

A Bond Issue 200 300 400 450 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375

512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375

512017 31450000 9975000 400 399000 471375 550000 1420375 11395375

512018 21475000 10475000 450 471375 550000 1021375 11496375

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500

Interest on Principal Due

presented by

Bonds and Loans

Differences in Rates Across Maturities Generate a

Yield Curve 8

State Public Works Board of the State of California $152420000 Lease Revenue Bonds

(Department of Corrections and Rehabilitation) 2014 Series C

00

05

10

15

20

25

30

35

40

45

2014 2019 2024 2029 2034

Yie

ld

0

2

4

6

8

10

12$Millions

Pri

nci

pa

l

Principal

Yield

Principal Amounts and Initial Reoffering Yields as of April 10 2014

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 5: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonds and Loans

Bonds as Loans presented by

5

ϜϜ

π

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

$120

$100

$80

$60

$40

$20

$0

Interest

Principal

1 5 10 15 20 25 30

Bonds and Loans

In Aggregate Bonds in an Issue Are

Equivalent to a Loan presented by

6

$120

$100 Interest

$80 $60 $40 $20 $0

$120

$100

$80

$60

$40

$20

$0

Principal

1

$120

$60

$80

$100 Interest

Principal

$40

$20

$0

5 10 15 20 25 30

$0

$20

$40

$60

$80

$100

$120

Interest

Principal

Interest

Principal

1 5 10 15 20 25 30

= 1 5 10 15 20 25 30 1 5 10 15 20 25 30

Bonds and Loans

A Bond Issue and a Loan Are Mathematically

Similar But Not Identical presented by

77

A Loan

Principal 500 Debt

Date Balance Principal Interest Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

A Bond Issue 200 300 400 450 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375

512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375

512017 31450000 9975000 400 399000 471375 550000 1420375 11395375

512018 21475000 10475000 450 471375 550000 1021375 11496375

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500

Interest on Principal Due

presented by

Bonds and Loans

Differences in Rates Across Maturities Generate a

Yield Curve 8

State Public Works Board of the State of California $152420000 Lease Revenue Bonds

(Department of Corrections and Rehabilitation) 2014 Series C

00

05

10

15

20

25

30

35

40

45

2014 2019 2024 2029 2034

Yie

ld

0

2

4

6

8

10

12$Millions

Pri

nci

pa

l

Principal

Yield

Principal Amounts and Initial Reoffering Yields as of April 10 2014

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 6: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonds and Loans

In Aggregate Bonds in an Issue Are

Equivalent to a Loan presented by

6

$120

$100 Interest

$80 $60 $40 $20 $0

$120

$100

$80

$60

$40

$20

$0

Principal

1

$120

$60

$80

$100 Interest

Principal

$40

$20

$0

5 10 15 20 25 30

$0

$20

$40

$60

$80

$100

$120

Interest

Principal

Interest

Principal

1 5 10 15 20 25 30

= 1 5 10 15 20 25 30 1 5 10 15 20 25 30

Bonds and Loans

A Bond Issue and a Loan Are Mathematically

Similar But Not Identical presented by

77

A Loan

Principal 500 Debt

Date Balance Principal Interest Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

A Bond Issue 200 300 400 450 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375

512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375

512017 31450000 9975000 400 399000 471375 550000 1420375 11395375

512018 21475000 10475000 450 471375 550000 1021375 11496375

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500

Interest on Principal Due

presented by

Bonds and Loans

Differences in Rates Across Maturities Generate a

Yield Curve 8

State Public Works Board of the State of California $152420000 Lease Revenue Bonds

(Department of Corrections and Rehabilitation) 2014 Series C

00

05

10

15

20

25

30

35

40

45

2014 2019 2024 2029 2034

Yie

ld

0

2

4

6

8

10

12$Millions

Pri

nci

pa

l

Principal

Yield

Principal Amounts and Initial Reoffering Yields as of April 10 2014

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 7: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonds and Loans

A Bond Issue and a Loan Are Mathematically

Similar But Not Identical presented by

77

A Loan

Principal 500 Debt

Date Balance Principal Interest Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

A Bond Issue 200 300 400 450 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375

512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375

512017 31450000 9975000 400 399000 471375 550000 1420375 11395375

512018 21475000 10475000 450 471375 550000 1021375 11496375

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500

Interest on Principal Due

presented by

Bonds and Loans

Differences in Rates Across Maturities Generate a

Yield Curve 8

State Public Works Board of the State of California $152420000 Lease Revenue Bonds

(Department of Corrections and Rehabilitation) 2014 Series C

00

05

10

15

20

25

30

35

40

45

2014 2019 2024 2029 2034

Yie

ld

0

2

4

6

8

10

12$Millions

Pri

nci

pa

l

Principal

Yield

Principal Amounts and Initial Reoffering Yields as of April 10 2014

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 8: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

presented by

Bonds and Loans

Differences in Rates Across Maturities Generate a

Yield Curve 8

State Public Works Board of the State of California $152420000 Lease Revenue Bonds

(Department of Corrections and Rehabilitation) 2014 Series C

00

05

10

15

20

25

30

35

40

45

2014 2019 2024 2029 2034

Yie

ld

0

2

4

6

8

10

12$Millions

Pri

nci

pa

l

Principal

Yield

Principal Amounts and Initial Reoffering Yields as of April 10 2014

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 9: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonds and Loans

Selected Historical Yield Curves presented by

9

AAA GO MMD

0

1

2

3

4

5

6

1 5 10 15 20 25 30

8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today

PercentileDate 25th 50th 75th 82901 121208 22307 12106

1Y vs 5Y MMD 052 088 130 088 201 000 ndash005

1Y vs 10Y MMD 095 155 235 159 326 012 008

1Y vs 30Y MMD 165 250 344 250 486 044 044

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 10: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

Bond cash flows literacy intermediate bond math (Part 1)

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 11: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

Time-Value of Money (TVM) presented by

11

Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for

Opportunity cost

Inflation

Investments

t

p

i

FVPV

1

ldquoPVrdquo = Present Value

ldquoFVrdquo = Future Cash Flows

ldquo i rdquo = Interest Rate

ldquo p rdquo = ompounding Periods Per Year

ldquo t rdquo = Time or Periods

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 12: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

TVM Is the Basis for Calculating Bond Prices presented by

12

A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms

Present Value Formula for Multiple Future Cash Flows

nt

n

tt

p

i

CF

p

i

CF

p

i

CFPV

111

21

21

ldquoPVrdquo = Present Value or Price

ldquoFrdquo = Future Cash Flows which for bonds include

Principal

Semi-Annual Interest

ldquo i rdquo = Interest Rate or Yield

ldquo p rdquo = ompounding Periods Per Year

(Municipal Convention = 2)

ldquo t rdquo = Time or Periods

(Municipal Convention = 180

360

30Days

)

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 13: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

Bond Pricing Formula presented by

13

Municipal Standard Price Formula

RB

A

Y

R

Y

RVP

N

k E

AEk

E

AEN

^^100

21

2100

21

1 11

Principal Component

Interest Component

Accrued Interest

Component

ldquordquo = 30360 days from dated date to settlement date

ldquordquo = Days in the year (usually 360)

ldquoErdquo = Days in semi-annual period (usually 180)

ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage

ldquoPrdquo = Dollar price (as a ) of the principal amount

ldquoRrdquo = nnual coupon (as decimal)

ldquoRVrdquo = Redemption value including premiums if any

ldquoYrdquo = Yield (as decimal)

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 14: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

Prices Can Vary Greatly with Different Coupons

and Maturities presented by

14

10-year bond with a 3 coupon at yield of 315

10-year bond with a 5 coupon at yield of 315

10-year bond with a 5 coupon at yield of 5165

721983360

0100

2

1531

2

3100

2

1531

100 20

1 180

01801

180

0180120

k k^^

7641155360

0100

2

1531

2

5100

2

1531

100 20

1 180

01801^

180

0180120^

k k

721985360

0100

2

16551

2

5100

2

16551

100 20

1 180

01801^

180

0180120^

k k

Terminology

Par Price = 100 Discount Price lt 100 Premium Price gt 100

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 15: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

Bond Prices are Commonly Expressed in Yields

for Ease of Comparison presented by

15

Yields help to inform consistency of pricing as terms vary

7252014 AAA GO MMD

00

05

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Yield gtgt 011 031 054 087 121 145 169 191 207 219

Co

up

on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239

400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176

500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113

C 5 P 109500 Y 0236

C 4 P 109000 Y 0950

C 3 P 108500 Y 0835

C 5 P 124000 Y 2064 C 3

P 108000 Y 1779

C 4 P 116500 Y 1778

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 16: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

Bond Pricing Conventions presented by

16

Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999

Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option

Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked

Bonds where coupon equals yield are priced at 100000 (or par)

Prices are truncated to third place after decimal

E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ

E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά

Yields are rounded to the nearest third place after decimal

E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή

E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ

For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price

Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014

Assumed

Redemption Date

No of interest

periods (N)

Redemption

value (RV) Price (P)

1112024 20 102 110410

1112025 22 101 110406

1112026 24 100 110424

1112028 28 100 111813

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 17: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

Capital Appreciation Bonds (CAB) presented by

17

Also based on TVM formula

Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed

Interest is compounded and paid at maturity

Growth in value of a CAB is expressed as an accreted value

2^

21

n

nY

PRAV

ldquoAVnrdquo = ccreted value at period n

ldquoPRrdquo = Initial price (generally par)

ldquoYrdquo = Yield

Generally not subject to optional redemption

Sold in denominations such that the final accreted value of each denomination is $5000

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 18: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Calculating Bond Prices

Capital Appreciation Bonds (Contrsquod) presented by

18

Solving for an accretion tablehellip

2^

21

nM

n

Y

DNAV

ldquoAVnrdquo = ccreted value at period n

ldquoYrdquo = Yield

ldquoMrdquo = Maturity

Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000

ldquoDNrdquo = ccreted value at maturity (effective denomination)

Date

Accreted

Value

5142014 $420891

1112014 427721

512015 435206

1112015 442822

512016 450571

1112016 458456

512017 466479

1112017 474643

512018 482949

1112018 491400

512019 500000

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 19: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

Bond cash flows literacy intermediate bond math (Part 1)

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 20: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

Describing a Bond Issue with Numbers presented by

20

Goal to understand how the numbers that describe individual bonds and a bond issue work

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 21: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

Start with a Basic Loanhellip presented by

21

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9048740 2500000 11548740

512016 40951260 9501177 2047563 11548740

512017 31450083 9976236 1572504 11548740

512018 21473847 10475048 1073692 11548740

512019 10998800 10998800 549940 11548740

Total 50000000 7743700 57743700

Assumptions ndash

bull $50000000 borrowed

bull Repaid in 5 years

bull Interest rate of 500

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 22: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

hellipRound by Denominationshellip presented by

22

500

Principal Interest on Debt

Date Balance Principal Balance Service

512014 50000000

512015 50000000 9050000 2500000 11550000

512016 40950000 9500000 2047500 11547500

512017 31450000 9975000 1572500 11547500

512018 21475000 10475000 1073750 11548750

512019 11000000 11000000 550000 11550000

Total 50000000 7743750 57743750

Municipal bonds are generally sold (and therefore repaid) in denominations of $5000

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 23: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by

23

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750

512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750

512017 31450000 9975000 400 399000 523750 550000 1472750 11447750

512018 21475000 10475000 500 523750 550000 1073750 11548750

512019 11000000 11000000 500 550000 550000 11550000

Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000

Interest on Principal Due

Or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9050000 200 1938750 10988750

512016 40950000 9500000 300 1757750 11257750

512017 31450000 9975000 400 1472750 11447750

512018 21475000 10475000 500 1073750 11548750

512019 11000000 11000000 500 550000 11550000

Total 50000000 6793000 56793000

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 24: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by

24

200 300 400 500 500

Principal Total Debt

Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service

512014 50000000

512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550

512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250

512017 30980000 9890000 400 395600 514500 540000 1450100 11340100

512018 21090000 10290000 500 514500 540000 1054500 11344500

512019 10800000 10800000 500 540000 540000 11340000

Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400

Interest on Principal Due

Once again or in the more familiar form below

Principal Total Debt

Date Balance Principal Coupon Interest Service

512014 50000000

512015 50000000 9415000 200 1926550 11341550

512016 40585000 9605000 300 1738250 11343250

512017 30980000 9890000 400 1450100 11340100

512018 21090000 10290000 500 1054500 11344500

512019 10800000 10800000 500 540000 11340000

Total 50000000 6709400 56709400

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 25: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

hellipIntroduce Prices Yields and Proceedshellip presented by

25

Principal Total Debt

Date Balance Principal Coupon Interest Service Yield Price Proceeds

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254

512019 10800000 10800000 500 540000 11340000 310 108737 11743596

Total 50000000 6709400 56709400 52642532

Each maturity generates proceeds equal to the product of its price and its principal

Note Prices are calculated following all of the rules discussed above

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 26: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

hellipCalculate Purchase Pricehellip presented by

26

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Principal 50000000

Net Original Issue Premium(Discount) 2642532

Production 52642532

Underwriters Discount -162052

Purchase Price 52480479

Underwriters Discount

Takedown 137240

Underwriters Counsel 15000

CDIAC 3000

CUSIP 600

Day Loan 1462

Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 27: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

hellipAdd in Sources and Uses Componentshellip presented by

27

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415

512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013

512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725

512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588

512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500

Total 50000000 6709400 56709400 52642532 137240

Sources of Funds Principal 50000000

Principal 50000000 Net Original Issue Premium(Discount) 2642532

Net OIP (OID) 2642532 Production 52642532

Funds on Hand 1000000 Underwriters Discount -162052

Total Sources of Funds 53642532 Purchase Price 52480479

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 137240

Reserve Fund 5264253 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 162052 CUSIP 600

Contingency -2023774 Day Loan 1462

Total Uses of Funds 53642532 Dalcomp 3750

Dalnet 500

DTC 500

Total Uses of Funds 162052

Project deposit represents target amount to be borrowed

Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 28: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

hellipand Readjust Principal of Each Maturity to Target Proceeds

presented by

28

Principal Total Debt Takedown Takedown

Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)

512014 50000000

512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820

512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038

512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788

512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238

512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244

Total 52145000 6997350 59142350 54900918 143126

Sources of Funds Principal 52145000

Principal 52145000 Net Original Issue Premium(Discount) 2755918

Net OIP (OID) 2755918 Production 54900918

Funds on Hand 1000000 Underwriters Discount -168162

Total Sources of Funds 55900918 Purchase Price 54732756

Uses of Funds Underwriters Discount

Project Deposit 50000000 Takedown 143126

Reserve Fund 5490092 Underwriters Counsel 15000

Costs of Issuance 240000 CDIAC 3000

Underwriters Discount 168162 CUSIP 600

Contingency 2664 Day Loan 1525

Total Uses of Funds 55900918 Dalcomp 3911

Dalnet 500

DTC 500

Total Uses of Funds 168162

Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 29: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Principal Total Debt

Date Balance Principal Coupon Interest Service 255204 265880 281677

512014 50000000

512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666

512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363

512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168

512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464

512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917

Total 52145000 6997350 59142350 54887069 54718564 54470579

Sources of Funds True All-in True

Principal 52145000 Arbitrage Interest Interest

Net OIP (OID) 2755918 Yield Cost Cost

Funds on Hand 1000000 Proceeds 54900918 54900918 54900918

Total Sources of Funds 55900918 Costs of Issuance -240000

Underwriters Discount -168162 -168162

Uses of Funds Arbitrage Adjustments

Project Deposit 50000000 Target Value 54900918 54732756 54492756

Reserve Fund 5490092

Costs of Issuance 240000

Underwriters Discount 168162

Contingency 2664

Total Uses of Funds 55900918

Present Value of Debt Service at

Cash Flow Schedules

presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29

Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of

Find the rate as the internal rate of return (IRR) of debt service to the target value

Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield

capital for a bond issue

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 30: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Cash Flow Schedules

How to Calculate an ldquoAveragerdquo presented by

30

Principal x

Principal Princpial x Total Debt Years to Years to

Date Balance Principal Coupon Coupon Interest Service Maturity Maturity

512014 50000000

512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000

512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000

512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000

512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000

512019 9120000 11265000 500 563250 563250 11828250 500000 56325000

Total 52145000 2009200 6997350 59142350 160040000

Weighted

Average Average

Coupon Maturity

2009200 160040000

ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash

52145000 52145000

385 306913

In general averages are calculated as weighted averages by principal

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 31: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

Bond cash flows literacy intermediate bond math (Part 1)

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 32: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

32

Level Principal

Ease of calculation

Common for bank product term-out provisions and GOs

Interestprincipal ratio 077 (based on 5 rate)

Level Debt Service

Even distribution of cost

Simplify long-term budget preparation

Interestprincipal ratio 095 (based on 5 rate)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 33: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

33

Deferred Principal

Revenues or operational cost savings become available at the later date (eg upon project completion)

Interestprincipal ratio 099 (based on 5 rate)

Ascending Debt Service

Growing revenues

Cost-recovery mechanism is subject to inflation

Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 34: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

34

Backloaded Principal

Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)

Interestprincipal ratio 125 (based on 5 rate for THIS example)

Wrapped Debt Service

Profile of aggregate debt service is level

Extends useful life of existing debt-funded asset

Interestprincipal ratio 109 (based on 5 rate for THIS example)

presented by Common Amortization Structures

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

InterestPrincipal

0

2

4

6

8

10

12

1 5 10 15 20 25 30

($mm)

Principal Interest Existing

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 35: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

Solving for Amortization Structure presented by

35

Debt Service for a given year Debt service is equal to the sum of

Principal

Interest on principal

1

)1(ni

iinnn CPPCDS

due and ldquoDSn rdquo = Debt service for year n

ldquoP rdquo = Principal amount for maturity n Interest on principal still n

outstanding ldquoC rdquo = oupon for maturity n n

Solving algebraically for principal results in the following

n

ni

iin

n

C

CPDS

P

11

Given target debt service numbers each principal amount can be solved

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 36: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

Solving for Amortization Structure presented by

36

No unknowns egin from the last maturityhellip Example

Target debt service $5000000 Coupon for 2024 (last maturity) 500

000007604$

809047614$0051

0$0000005$

2018

2018

2018

P

P

P

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 238000 238000 4762000

2016 $5000000 300 238000 238000 4762000

2017 $5000000 350 238000 238000 4762000

2018 $5000000 500 238000 238000 4762000

2019 $5000000 500 238000 238000 4762000

2020 $5000000 500 238000 238000 4762000

2021 $5000000 500 238000 238000 4762000

2022 $5000000 475 238000 238000 4762000

2023 $5000000 475 238000 238000 4762000

2024 $5000000 4760000 500 238000 4998000 2000

Total $50000000 4760000 2380000 7140000 42860000

Rounding based on

denomination

or round down to

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 37: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

37

΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example

Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 300 $453888 $453888 $4546113

2016 $5000000 300 $453888 $453888 $4546113

2017 $5000000 350 $453888 $453888 $4546113

2018 $5000000 500 $453888 $453888 $4546113

2019 $5000000 500 $453888 $453888 $4546113

2020 $5000000 500 $453888 $453888 $4546113

2021 $5000000 500 $453888 $453888 $4546113

2022 $5000000 475 $453888 $453888 $4546113

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $9305000 $4322988 $13627988 $36372013

000005454$

050625464$7541

0050007604$0000005$

2017

2017

2017

P

P

P

or round down to

Ϳώ Ϳπ ͳ ϜϘ in the last step

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 38: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

Solving for Amortization Structure (Contrsquod) presented by

38

Remaining unknowns hellipnd so forth will be solved just in time as well

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 39: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

Adjusting for Target Proceeds presented by

39

If there is too much principal (or if there are too many proceeds) reduce target debt service

If there is too little principal (or if there are too few proceeds) increase target debt service

To solve for a target par or proceeds amount

Make an initial guess for target debt service

Rescale accordingly

0

01

P

PDSDS

TTT

ldquoDST1rdquo = New target debt service

ldquoDSTT0rdquo = Initial target debt service

ldquoPTrdquo = Target par amount

ldquoP0rdquo = Par amount from initial target debt service

Iterate if necessary

1

1

n

TnTnT

P

PDSDS

It may be necessary to adjust by taking the average when within one denomination

22

2

1

1

T

n

nT

n

nTnT

P

P

DS

P

DSDS

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 40: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

40

Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5000000 $3250000 300 $1747400 $4997400 $2600

2016 $5000000 $3345000 300 $1649900 $4994900 $5100

2017 $5000000 $3450000 350 $1549550 $4999550 $450

2018 $5000000 $3570000 500 $1428800 $4998800 $1200

2019 $5000000 $3745000 500 $1250300 $4995300 $4700

2020 $5000000 $3935000 500 $1063050 $4998050 $1950

2021 $5000000 $4130000 500 $866300 $4996300 $3700

2022 $5000000 $4335000 475 $659800 $4994800 $5200

2023 $5000000 $4545000 475 $453888 $4998888 $1113

2024 $5000000 $4760000 500 $238000 $4998000 $2000

Total $50000000 $39065000 $10906988 $49971988 $28013

346721195$

00006539$

00000040$0000005$

1

1

T

T

DS

DS

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 41: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Year

Target Debt

Service Principal Coupon Interest Debt Service

Difference

between

Target and

Actual DS

2015 $5119672 $3330000 300 $1789375 $5119375 $297

2016 $5119672 $3430000 300 $1689475 $5119475 $197

2017 $5119672 $3530000 350 $1586575 $5116575 $3097

2018 $5119672 $3655000 500 $1463025 $5118025 $1647

2019 $5119672 $3835000 500 $1280275 $5115275 $4397

2020 $5119672 $4030000 500 $1088525 $5118525 $1147

2021 $5119672 $4230000 500 $887025 $5117025 $2647

2022 $5119672 $4440000 475 $675525 $5115525 $4147

2023 $5119672 $4650000 475 $464625 $5114625 $5047

2024 $5119672 $4875000 500 $243750 $5118750 $922

Total $51196723 $40005000 $11168175 $51173175 $23548

Debt Amortization

Adjusting for Target Proceeds (Contrsquod) presented by

41

Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234

Attempt Target Debt Service Resultant Principal Solution Method

1 $500000000 $3906500000 Rescale

2 511967234 4000500000 Rescale

3 511903246 3999500000 Rescale

4 511935240 4000000000 Average

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 42: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonus Excel Functions

Bond cash flows literacy intermediate bond math (Part 1)

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 43: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonus Excel Functions

Using PRICE() presented by

43

Needs to be supplemented for

Par bonds

Rounding and

Call provisions for premium bonds

Effective form for bonds callable at

par is as follows

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 100

=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))

Check for par bond

Round down to 3 decimal

places Check for premium coupon using

call date as maturity if needed

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 44: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonus Excel Functions

Using PRICE() presented by

44

For bonds with multiple call prices must evaluate result for

each case

=IF(B3=B4100TRUNC(MIN(

PRICE(B1 B2B3B41002) PRICE(B1

B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)

)3))

A B

1 Delivery 5142014

2 Maturity 512028

3 Coupon 500

4 Yield 365

5 Call Date1 512024

6 Call Price1 102

7 Call Date2 512025

8 Call Price2 101

9 Call Date3 512026

10 Call Price3 100

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 45: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

3

7

Bonus Excel Functions

Using EDATE() and EOMONTH() presented by

45

Used to create regularly aligned dates for principal

amortization or debt service schedules

=EOMONTH(A25)+1

=EDATE(A66)

A B C D

1 Date Principal Coupon Interest

2 5142014

1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

1112016 2210000

8 512017 1105000 400 2210000

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 46: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonus Excel Functions

Using SUMPRODUCT() presented by

46

Used to calculate interest for entire bond series (with multiple

coupons and principal amounts)

Tip Values

in last cells

must not be

blank

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B6B$8C6C$8)2

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 47: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Bonus Excel Functions

Using YEARFRAC() presented by

47

Used to calculate interest for irregular periods and for

ACTACT day count basis

Tip Allows

for the same

formula to

be used the

cash flow

schedule

A B C D

1 Date Principal Coupon Interest

2 5142014

3 1112014 $4439417

4 512015 $1000000 200 4785000

5 1112015 3785000

6 512016 1050000 300 3785000

7 1112016 2210000

8 512017 1105000 400 2210000

=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions
Page 48: Bond Cash Flows Literacy - State Treasurer's Office · 7/8/2014 · BOND CASH FLOWS LITERACY ... Understanding Cash Flow Schedules ... “PV” = Present Value “FV” = Future Cash

Questions presented by

48

Thank you for your participation

A Certificate of Attendance will be emailed to you within a week

For MCLE credit please email cdiac_educationtreasurercagov

The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted

  • Bonds and Loans
  • Calculating Bond Prices
  • Cash Flow Schedules
  • Debt Amortization
  • Bonus Excel Functions