chapter 3 - debt security

8/8/2019 CHAPTER 3 - Debt Security

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Financial Theory 1

CHAPTER 3

DEBT SECURITIES -

BOND VALUATION


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Financial Theory 2

Bonds are issued by borrowers/institutions having a need for money

(Companies or government)

Examples:

Debt securities issued by Government

- Treasury bill- Treasury note

- Treasury bond


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Financial Theory 3

Debt securities issued by Companies(Corporate bonds)

- Secured bonds

- Debentures

- Subordinated bonds

- Convertible bonds

- Zero-coupon bonds


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Financial Theory 4

Bonds are bought by investors/ parties

who possess money

Examples

Institutional investors- Banks

- Insurance companies

- Pension fundsIndividual investors

Need fixed cash flows at regular intervals


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Financial Theory 5

Coupon payment = coupon rate *nominal value

E.g. coupon rate = 5%; nominalvalue = Rs1000

Coupon = 5%*1000 = Rs50


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Financial Theory 6

50 50 50 50 50

1000

40 60 80 70 50

1000

Fixed coupon bond

Variable coupon bond


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Financial Theory 7

Intrinsic value > Market price

Underpriced/ Buys

Intrinsic value < Market price

Overpriced/ Does not buy

Bond value = Market price

Fairly priced/ Normally buys


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Financial Theory 8

Example

The market price of a zero coupon bond is

equal to Rs857.34; it has a maturity of 2

years and pays a nominal of Rs1000.

Determine the annual interest rate on the

bond.

Assume annual interest rate = r

857.34 (1 + r) 2 = 1000

r = (1000/ 857.34) 1 = 7.99 = 8%


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Financial Theory 9

50 50 50

1000

Example

Market price= 986.51

Assume annual interest rate/ discount rate = k

Market price= 986.51= 50/ (1 + k) + 50/ (1 + k) 2 + 1050/ (1 + k) 3

k = 5.5%

(equation solved through linear interpolation)


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Financial Theory 10

Example

Choose a bond:

- Company Bond selling at Rs900; offers acoupon rate of 10%, a nominal of Rs1000

and has maturity of 5 years- Government Bond selling at Rs900; offers

a coupon rate of 10%, a nominal ofRs1000 and has maturity of 5 years


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Financial Theory 11

Intrinsic value of bond (estimated

by investors/financial analysts) =

C/ (1 + k) + C/ (1 + k) 2 +

C/(1 + k) 3+ + C/ (1 + k) T

+ N/ (1 + k) T

C = coupon payment; N = nominalvalue; k = required rate of return;

T = maturity date


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Financial Theory 14

Bond Value = 50/ 1.06 + 50/

1.06 2 + 50/ 1.06 3 + 50/ 1.06

4 + 1050/ 1.06 5 = Rs957.88


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Financial Theory 15

Example:

Verify

1018.8609 (1.04) 2 = 50 (1.04) + 1050

1102 = 1102 (two equivalent ways oflooking at the return on the investment)

t = 0 t = 2t = 1

Rs1018.8609Rs50

Rs1000Rs50


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Financial Theory 16

France Telecom 6,625% 10/11/10

Date

26/11/2004

Price/

115.10

Market Interest

rate/ %

3.743

03/12/2004 115.31 3.699

10/12/2004 115.74 3.616

21/12/2004 115.90 3.577

23/12/2004 115.91 3.571


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Financial Theory 17

Yield to maturity > required rateof return

Buys

Yield to maturity < required rate

of returnDoes not buy

Yield to maturity = required rateof return

Normally Buys


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Financial Theory 18

Current market price of bond

(available from bond market)= C/ (1 + YTM) + C/ (1 +

YTM) 2 + C/ (1 + YTM) 3 + +

C/ (1 + YTM) T + N/ (1 + YTM) T

YTM : Yield to maturity


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Financial Theory 19

Example:

A bond has the followingcharacteristics:

Coupon rate 5%, nominal value

Rs1000 and maturity 2 years.

If the market price of the bond is

equal to Rs960, calculate theyield to maturity of the bond.


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Financial Theory 20

960 = 50/ (1 + YTM) + 50/ (1 +

YTM) 2 + 1000/ (1 + YTM) 2

Multiply both sides by (1 + YTM) 2and simplify:

960 (1 + YTM) 2 - 50 (1 + YTM) 1050 = 0


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Financial Theory 21

Assume (1 + YTM) = A

960 A 2 50 A 1050 = 0

Use quadratic equation formula tosolve

YTM = 7.2191%


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Financial Theory 22

Last

coupon01/05/08

Next

coupon01/05/09

Purchasedate

01/09/08

Maturity:01/05/11


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Financial Theory 23

Assume fixed coupon payments = C

Nominal value = N

Bond price at purchase date = PV of

future cash flows (discounted at

YTM)


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Financial Theory 24

Fractional period =

Number of(days/months)

between purchase date and nextcoupon payment date divided by

total number of(days/ months)over coupon period

E.g. 01/ 09/ 08 to 01/ 05/ 09 = 8months

Fractional period = 8/ 12


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Financial Theory 25

Last

couponE.g.01/05/08

Next

couponE.g.01/05/09

Purchase date

E.g. 01/09/ 08

Fractionalperiod= 8/ 12


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Financial Theory 26

PV coupon at 01/ 05/ 09 = C/ (1

+ YTM) 8/12

PV coupon at 01/ 05/ 10 = C/ (1

+ YTM) 1 + 8/12

PV coupon and nominal at 01/05/11

= [C + N]/ (1 + YTM) 2 + 8/12


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Financial Theory 27

Bond Price (Dirty Price)=

C/ (1 + YTM) 8/12 + C/ (1

+ YTM)1 + 8/12

+ [C + N]/ (1 +

YTM) 2 + 8/12

Dirty price: price at which buyer

purchases bond.


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Financial Theory 28

Last coupon

E.g.01/05/08

Next coupon

E.g.01/05/09

Purchasedate

E.g. 01/09/ 08

Interestearnedby Seller

Interestearnedby Buyer


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Financial Theory 29

Interest earned by seller = accrued

interest

Accrued interest = Coupon paid

from 01/ 05/ 08 to 01/ 09/ 08

= 4/ 12*C


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Financial Theory 30

Dirty Price = Clean Price +

Accrued Interest

Clean price = Dirty price Accruedinterest

Clean price: price at which bond isselling in bond market at purchase

date (01/ 09/ 08)

chapter 3 - debt security

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