sesi 5 valuasi obligasi
TRANSCRIPT
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Drs. Embun Prowanta, MM, CFP, ERMCP, CSA
• Fixed-income securities have a specifiedpayment schedule– Dates and amount of interest and principal payments
FIXED INCOME SECURITIES
known in advance
BondsBonds
– Bondholders are lending the corporationmoney for some stated period of time.
– Bonds can be traded in the secondarymarket.
– Price at which a given bond trades isdetermined by market conditions andterms of the bond.
Definition of a Bond
• A bond is a legally binding agreement betweena borrower and a lender that specifies the:– Par (face) value
– Coupon rate
– Yield to Maturity
– Maturity Date
• The yield to maturity is the required marketinterest rate on the bond.
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How to Value Bonds
• Primary Principle:– Value of financial securities = PV of expected future
cash flows
• Bond value is, therefore, determined by the
value.
• Interest rates are inversely related to present(i.e., bond) values.
Characteristic of Bonds
• Bonds pay coupon (interest) paymentsat fixed intervals and pay the par valueat maturity.
00 11 2 . . .2 . . . nn
C C C+ FVC C C+ FV
Bond TerminologyBond Terminology
Par Value or Face Value
Coupon Interest Rate– Borrowers (firms) typically make periodic interest
payments to the bondholders.
– Coupon & zero coupon
Maturity– Time at which the original principal (Par Value) is repaid
to the bondholder.
Indenture
– Document which details the legal obligation of thecorporation to the bondholders.
• Based On Issuer– Federal government securities - T-bonds
– Federal agency securities
– Municipal securities - General obligation bonds, Revenue bonds
• Tax implications for investors
BOND TYPES
– Corporate bonds
• Convertible bonds may be exchanged for another asset
• Risk that issuer may default on payments
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•Based on Coupon Payment• Zero Coupon Bonds• Fixed Rate Coupon Bonds• Floating Coupon Bonds• Reverse Floater• Inflation Index Bond
BOND TYPES
•Based On Collateral :• secured bonds
• Mortgage Bonds
• Equipment Trust Bonds
• Unsecured bonds :• Debenture Bonds
• Subordinate Bonds
• Rating companies– Moody’s Investor Service
– Standard & Poor’s
Default Risk and Ratings
• Rating Categories– Investment grade
– Speculative grade
Bond RatingsBond Ratings
Moody’s and Standard & Poors regularly monitorcorporate financial statements and assign a ratingto the corporation’s debt– similar to a personal credit report
AA
A
BBB
BB
B
CCC
CC Low Quality
C No interest being paid
D Currently in Default
GradeGrade
JunkJunk
RATING SYMBOLS AND DEFINITIONS by PEFINDO
Long – Term Debt Short – Term Debt Capaci ty and abil i ty of a company
to meet its financial commitments
id AAA id A1 Super ior
id AA id A2 Very Str ong
id A id A3 Stro ng
id BBB id A4 Adequate
id BB id B Somewhat Weak
id B Weak Non-investment
id CCC id C Vulnerable
id D id D Default
The ratings from id AA t o id B may be modified by the addition of a plus (+) orminus (-) sign to show relative strength within th e rating category.
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• Sinking funds
• Subordination of future debt
• Dividend restrictions
•
Protection Against Default International Bonds
• Represent a rapidly growing category– Reflects willingness of borrowers to borrow across
borders
• International bond investors face two types ofpolitical risk– Repatriation-of-funds risk
• A government may block payments of principal or interest
– Sovereign risk• A government may refuse to honor its debts
Foreign Bonds
• Categories of foreign bonds– Yankee bonds
• Issued by non-U.S. borrowers within the U.S.
– Samurai bonds• Yen-denominated bonds issued in Ja an b non-Ja anese
borrowers
– Shogun bonds• Non-yen-denominated bonds issued in Japan by non-
Japanese borrowers
– Bulldog bonds
• Issued by non-British borrowers in the U.K.—denominated inpounds
The Bond Indenture
• The bond contract between the firmand the trustee representing thebondholders.
• Lists all of the bond’s features:
coupon, par value, maturity, etc.
• Lists restrictive provisions which aredesigned to protect bondholders.
• Describes repayment provisions.
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– Macroeconomic condition
– Issuer’s Industry
– Issuer Performance/creditworthy
Bond Price Determinants
Bond Valuation
– nstrument tructure• Rating
• Pricing
• Covenant
– Market Liquidity
Value
• Book Value: value of an asset as shown on afirm’s balance sheet; historical cost.
• Liquidation value: amount that could bereceived if an asset were sold individually.
• Market value: observed value of an asset inthe marketplace; determined by supply anddemand.
• Intrinsic value: economic or fair value of anasset; the present value of the asset’sexpected future cash flows.
Security Valuation
• In general, the intrinsic value of anasset = the present value of thestream of expected cash flowsdiscounted at an a ro riate re uiredrate of return.
• Can the intrinsic value of an asset
differ from its market value?
Valuation
V =V =
nn
Ct1 + k)t
• Ct = cash flow to be received at time t .
• k = the investor’s required rate of return.• V = the intrinsic value of the asset.
t = 1t = 1
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Bond Concepts
Bond prices and market interest rates move inopposite directions.
When coupon rate = YTM, price = par value When coupon rate > YTM, price > par value
prem um on When coupon rate < YTM, price < par value
(discount bond)
M
Bond Value ($)
1,372
1,211
1,000
Ytm = 7%.
Ytm = 10%.
Years remaining to Maturity
837
775
30 25 20 15 10 5 0
Ytm = 13%.
Bond Valuation
Sebuah obligasi memiliki karakteristik : Nilai pari= Rp 1 miliar, akan jatuh tempo dalam 5 tahun,Tingkat kupon = 15 % per tahun (annually) danyield to maturity adalah sebesar 17 %. Hargawajar dari obligasi tersebut adalah :
a. Lebih kecil dari Rp 1 M
b. Rp 1 miliar
c. Rp 1,17 miliar
d. Rp 1,68 miliar
Bond Valuation
RpCt RpFV
(1 + Yb)t (1 + Yb)
nBP = +BP = +
nn
BP = Rp Ct (PVIFA Yb, n) + Rp FV(PVIF Yb, n)
==
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YTM and Bond Value
1200
1300
d V a l u e
When the YTM < coupon, the bond
trades at a premium.
=
800
1000
1100
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Discount Rate
B o n
6 3/8
,
bond trades at par.
When the YTM > coupon, the bond trades at a discount.
Bond Example Revisited
• Using our previous example, now assume thatthe required yield is 11%.
• How does this change the bond’s price?
L
06/1/1
875.31$
06/30/6
875.31$
06/31/12
875.31$
10/30/6
875.031,1$
10/31/12
69.825$)055.1(
000,1$
)055.1(
11
211.
875.31$1010
=+⎥⎦
⎤⎢⎣
⎡−=PV
Pure Discount Bonds
• Make no periodic interest payments (coupon rate = 0%)
• The entire yield to maturity comes from the differencebetween the purchase price and the par value.
• Cannot sell for more than par value
• omet mes ca e zeroes, eep scount on s, ororiginal issue discount bonds (OIDs)
• Treasury Bills and principal-only Treasury strips aregood examples of zeroes.
Pure Discount Bonds
• Make no periodic interest payments (coupon rate = 0%)
• The entire yield to maturity comes from the differencebetween the purchase price and the par value.
• Cannot sell for more than par value
• omet mes ca e zeroes, eep scount on s, ororiginal issue discount bonds (OIDs)
• Treasury Bills and principal-only Treasury strips aregood examples of zeroes.
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Pure Discount Bonds
Information needed for valuing pure discount bonds:– Time to maturity (T ) = Maturity date - today’s date– Face value (F )– Discount rate (r )
T R
FV PV
)1( +
=
Present value of a pure discount bond at time 0:
L
0
0$
1
0$
2
0$
1−T
F $
T
Pure Discount Bond: Example
Find the value of a 30-year zero-coupon bondwith a $1,000 par value and a YTM of 6%.
11.174$)06.1(
000,1$
)1( 30 ==
+=
T R
FV PV
L
L
0 1 2 29
,
30
Bond Example
• Suppose our firm decides to issue 20-yearbonds with a par value of Rp 1 Bio andannual coupon payments. The return on
currently 12%, so we decide to offer a 12%coupon interest rate.
• What would be a fair price for these bonds?
1000120 120 120 . . . 120
Bond Example
0 1 2 3 . . . 20
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Mathemat i cal Solut i on:
BP = PMT (PVIFA k, n ) + FV (PVIF k, n )
BP = 120 (PVIFA .12, 20 ) + 1000 (PVIF .12, 20 )
Bond Example
1
BP = PMT 1 - (1 + i)n + FV / (1 + i)n
i
Mathemat ical Solut ion:
1
BP = PMT 1 - (1 + i)n + FV / (1 + i)n
Bond Example
i
1
BP = 120 1 - (1.12 )20 + 1000/ (1.12) 20
.12
= Rp 1 Bio
Note Note::
If theIf the cou on ratecou on rate == discount ratediscount ratethe bond will sell forthe bond will sell for par valuepar value..
• Suppose interest rates fallimmediately after we issue thebonds. The required return on
Bond Example
.
• What would happen to the bond’sintrinsic value?
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Mathemat i cal Solut ion:
BP = PMT (PVIFA k, n ) + FV (PVIF k, n )
BP = 120 (PVIFA .10, 20 ) + 1000 (PVIF .10, 20 )
1
Bond Example
BP = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.10 )20 + 1000/ (1.10) 20 =
.10
PV = Rp 1,170 Bio
Note:
If the coupon rate > discount rate,e on w se or a prem um.
• Suppose interest rates riseimmediately after we issue thebonds. The required return onbonds of similar risk rises to 14%.
Bond Example
• What would happen to the bond’sintrinsic value?
Bond Example
Mathemat i cal Solut ion:
BP = PMT (PVIFA k, n ) + FV (PVIF k, n )
BP = 120 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 )
1
BP = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
BP = 120 1 - (1.14 )20 + 1000/ (1.14) 20 = 867,54 M
.14
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Note:
If the coupon rate < discount rate,the bond will sell for a discount.
Supposecou ons aresemi-annual
Bond Example
Mathemat i cal Solut i on:
BP = PMT (PVIFA k, n ) + FV (PVIF k, n )
BP = 60 (PVIFA .07, 40 ) + 1000 (PVIF .07, 40 )
1
BP = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
BP = 60 1 - (1.07 )40 + 1000 / (1.07) 40 =
.07
BP = Rp 866,68 M
Sebuah obligasi dengan dengan nilai nominal$1,000, waktu jatuh tempo 5 tahun,membayar kupon 10% per tahun danmemiliki y i e l d to matu r i t y sebesar 8%. Jikayield to maturity tidak berubah, 1 tahun darise arang arga o gas erse u a an :a. Lebih mahalb. Lebih murahc. Tidak berubahd. Tidak bisa ditentukan
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Conditions Required to Earn aBond’s Expected YTM
• A bond’s computed YTM will only actually beearned if:– The bond is held to maturity
– The bond issuer does not default in the timing oramount of scheduled payments
– All the cash flows are immediately reinvested toearn the bond’s YTM
Yield To Maturity
• The expected rate of return on abond.
• The rate of return investors earn on a.
$Ct $M
(1 + kb)t (1 + kb)
nPP00 = += +
nn
t = 1t = 1
YTM Example
• Suppose we paid $898.90 for a$1,000 par 10% coupon bondwith 8 years to maturity and
- .
• What is our yield to maturity?
YTM Example
Mathemat ical Solut ion:
BP = PMT (PVIFA k, n ) + FV (PVIF k, n )
898.90 = 50 (PVIFA k, 16 ) + 1000 (PVIF k, 16 )
1
BP = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1898.90 = 50 1 - (1 + i )16 + 1000 / (1 + i) 16
i
solve using tr ial and error
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YTM Approximation Formula
YTM =
C + FV - BP
n
2
Prices and Yields (required rates of return) havean inverse relationship
• When yields get very high the value of the bondwill be very low
Bond Prices and Yields
• When yields approach zero, the value of thebond approaches the sum of the cash flows
Price
Prices and Yield
Yield
Bond’s Risk
• Credi t Risk / defaul t r isk
• Inter est Rat e Risk
• Liquidi t y Risk
•
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Accrued Interest
♦Bonds pay coupon payments periodically− Annually, semi-annually, quarterly, etc.
♦When a bond is purchased on a daybetween its scheduled interest payment,buyer must pay seller for accrued interest
− Interest that has been earned but not yet paidby issuer
Accrued Interest
• Accrued interest calculation:
( )
Accrued # of days since last coupon payment
Coupon PaymentInterest# of days between scheduled coupon payment dates
Calculation
⎛ ⎞= ⎜ ⎟
⎝ ⎠
us, t e actua prce or a on s t e on s c ean
price plus the accrued interest
− Known as the bond’s invoice price, full price or dirty price♦ U.S. newspapers quote clean prices
− But buyers must pay the dirty price, which is always higherif bond is between coupon payment dates
• However, difference is not substantial
Zero Coupon Bonds
• No coupon interest payments.
• The bond holder’s return isdetermined entirely by the pricediscount.
Zero Example
• Suppose you pay $508 for a zerocoupon bond that has 10 yearsleft to maturity.
• What is your yield to maturity?
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Zero Example
• Suppose you pay $508 for a zerocoupon bond that has 10 yearsleft to maturity.
• What is your yield to maturity?
0 100 10
--$508 $1000$508 $1000
Mathemat i cal Solut i on:
PV = FV (PVIF i, n )
508 = 1000 (PVIF i, 10 )
Zero Example
0 10
PV = -508 FV = 1000
. = i, 10 use ta e
PV = FV /(1 + i) 10
508 = 1000 /(1 + i)10
1.9685 = (1 + i)10
i = 7%
Yield to Maturity Example
1
100035950
20
1 r T
t
t ++= ∑
=
10 yr Maturity Coupon Rate = 7%
Price = $950
Solve for r = semiannual rate
r = 3.8635%
Yield Measures
Bond Equivalent Yield
7.72% = 3.86% x 2
Effective Annual Yield2 - =. - .
Current Yield
Annual Interest / Market Price
$70 / $950 = 7.37 %
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Realized Yield versus YTM
• Reinvestment Assumptions
• Holding Period Return– Changes in rates affects returns
– Reinvestment of coupon payments
– Change in price of the bond
Other Measures of Bonds’ Yields
• Yield-to-call (YTC)
– A bond issuer may call a bond beforeits original maturity date
•Need to calculate the bond’s YTC– Similar to YTM, except replace T as the time-
to-call rather than time-to-maturity
Other Measures of Bond’s Yields
• Current yield—every non-zero bond has a positivecurrent yield
Annual coupon $ interestCurrent Yield
Current price of bond =
− Investors desiring high investment cash flows areinterested in a bond’s current yield
Holding-Period Return:Single Period
HPR = [ I + ( P0 - P1 )] / P0where
I = interest payment
P1 = price in one period
P0 = purchase price
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Holding-Period Example
CR = 8% YTM = 8% N=10 years
Semiannual Compounding P0 = $1000
In six months the rate falls to 7%
=1 .
HPR = [40 + ( 1068.55 - 1000)] / 1000
HPR = 10.85% (semiannual)
Suppose the bond was issued 20years ago and now has 10 years
to maturity. What yield tomaturit remained at 10% or at
13%, or at 7%?
• At maturity, the value of any bond mustequal its par value.
• The value of a premium bond woulddecrease to 1 000.
• The value of a discount bond wouldincrease to $1,000.
• A par bond stays at $1,000 if Ytm remainsconstant.