sesi 5 valuasi obligasi

8/19/2019 Sesi 5 Valuasi Obligasi

1/17

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.


2/17

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


3/17

•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.


4/17

• 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.


5/17

– 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


6/17

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)

==


7/17

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.


8/17

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


9/17

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?


10/17

Mathemat i cal Solut ion:


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 = 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


11/17

Note:

If the coupon rate < discount rate,the bond will sell for a discount.

Supposecou ons aresemi-annual

Bond Example



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


12/17

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:


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


13/17

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

•


14/17

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?


15/17

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


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 %


16/17

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


17/17

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.

sesi 5 valuasi obligasi

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