FINA2303 Topic 04 Bond Valuation (1)

8/18/2019 FINA2303 Topic 04 Bond Valuation (1)

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Topic 4: Bond Valuation


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Topic 4 Bond Valuation M K Lai Page 2

Learning Outcomes

discounted cash flows (DCF) approach

bond terminology zero-coupon bonds and coupon bonds

interest rate risk

credit risk and bond ratings (extra)

yield curve


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Valuation Model

in making financial decisions, we have to

estimate the fair value of a financialinstrument/firm in many occasions

mergers and acquisitions, company research

report, expert opinion in court, corporaterestructuring

we can use a valuation model to do so

one of the most commonly used valuation

models is the discounted cash flow (DCF)

approach


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Discounted Cash Flow Approach

steps

estimate the future cash flows generated bythe financial instrument

estimate the required rate of return (or known

as the discount rate) based on time value ofmoney and risk of the financial instrument(use modern financial theories)

calculate the present value of the future cashflows and it is the fair value of the financialinstrument

application: bond valuation and stock valuation


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Example: DCF Model

$24.87.beto

estimatedisinstrumentfinancialtheofvaluefairThe

87.24$ %)121(

32$

%)121(

5.1$

%121

1$PV

32

=

+

+

+

+

+

=



Bond

when a company wishes to borrow money frominvestors on a long-term basis, it does so by

issuing debt securities that are generally knownas bonds

contractual obligation of issuer (borrower) to paya specific amount of money to investors (calledbondholders) as creditors at some time in thefuture

regular interest/coupon payments

principal repayment at maturity



Bond

0

…

N321 N-1

bond

price

CPN CPNCPNCPNCPN

CPN = coupon payment

FV = face value

FV



Bond

total return on bond

1.2.

(sold before maturity)

(held to maturity)


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Bond Certificate

bond certificate: a document states the terms

and conditions of a bond as well as the amounts

and dates of the payments to be made

mostly scripless trading nowadays


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Bond Certificate

Bond trading is

scripless withelectronic book entry

in Hong Kong!


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Bond Indenture/Agreement

interest payment dates: the specified dates formaking interest payments

face/par/nominal value or principal amount:notional amount of bond to compute interestpayments and is due at bond’s maturity

coupon/nominal rate: specified quotedinterest rate (APR) to determine periodicinterest payments at the time of issue

coupon (payment): the promised interestpayment of a bond, paid periodically until thematurity date of a bond


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annual coupon = face value * coupon rate

periodic coupon = annual coupon/numberof payments per year, e.g. annual coupon/2for semi-annual coupon payments

description of property used as security/collateral secured bond (with collateral) vs. unsecured

bond (without collateral)

seniority of claims upon company’sliquidation (which is senior?)

other things being equal, which offers a

higher market interest rate?

less risky(lower market interest rate)


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protective covenant that limits certain actions the

issuing company may otherwise wish to take

during the term of the bond (positive or negative)

credit rating: show credit worthiness of issuer

embedded option: an option-like feature includedin a bond to give a specified right to either the

bond issuer or the bondholder, e.g. a callable

bond allows the bond issuer to redeem the bondat a specified redemption price before maturity

and it will affect the price and yield of the bond


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Case Study on Bond Terms

source: Fantasia


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source: Fantasia

embedded option


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source: Fantasia


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source: Fantasia


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Example: Bond Basics

Consider a 3-year 5% $50,000 par bond at a

prevailing market interest rate of 4%. The coupon

are made on a semi-annual basis.

coupon rate: 5%

par/face/nominal value: $50,000 annual coupon = $50,000*5% = $2,500

semi-annual coupon = $2,500/2 = $1,250 term to maturity or tenor: 3 years

yield (to maturity): 4% (to be discussed later)


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Types of Bonds

government bond: bond issued by government

short-term: Treasury bill long-term: Treasury note and bond

corporate bond: bond issued by a company

coupon bond: receive both regular coupons and

face value at maturity

zero-coupon (pure discount) bond: receive facevalue of bond at maturity only; coupon rate = 0%

(what to earn?)

perpetual bond: bond without a maturity date


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Zero-Coupon Bond

source: HKMA


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Bond Valuation Model

application of discounted cash flow approach

cash flows to bondholders periodic coupon payments CPN

par value at maturity FV

discount rate = market interest rate y (not the

same as coupon rate – what is the difference

between them?) term to maturity = N years


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Bond Valuation Model

N

N

1tNt

y)(1FV pricebond

bondcoupon -zero

)y1(

FV

)y1(

CPN pricebond

bondcoupon

+

=

+

+

+

=∑=


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Example: Coupon Bond

Consider a 5%, 3-year, $50,000 par bond with

annual coupon payments. If the market interest

rate on the bond is 4%, what is its value now?

premium.aattradesbondthe

value,facethethanhigherispricebondtheWhen

.55.387,51$

%)41(

500,52$

%)41(

500,2$

4%)(1

$2,500 pricebond 32

=

++

++

+=


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Example: Zero-Coupon Bond

Consider a 2-year, $50,000 par zero-coupon bond.

If the market interest rate on the bond is 3%,

what is its value now?

discount.aattradetosaidisbondthe

value,facethethanlessispricebondtheWhen

80.129,47$%)31(

000,50$ pricebond 2 =

+=


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Yield to Maturity

yield (to maturity) is a measure of the average

rate of return on a bond under two conditions

1.

2.

calculated average rate of return that makes the

present value of future cash flows generated by abond equal to its bond price

1. reinvest the coupons in the bond2. hold the bond to maturity


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Yield to Maturity

N

N

1tNt

YTM)(1

FV

pricebond

bondcoupon -zero

) YTM1(FV

YTM)(1CPN pricebond

bondcoupon

+=

+

+

+

=∑=


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Yield to Maturity

for a zero-coupon bond with term-to-maturity of N

years, the yield to maturity must be equal to N-

year market interest rate

N

N

y)(1

FV pricebond

) YTM1(

FV

pricebond

+

=

+=


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A bond has a price of $1,030.42. It has a par

value of $1,000, an annual coupon of $30, and a

maturity of two years. What is its yield to

maturity?

%38.4 YTM

) YTM1(

060,1$

YTM)(1

$60 $1,030.42

2

=

+

+

+

=


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The current bond price is $48,000. What is its

yield to maturity?

%37.1TM

) YTM1(000,50$ $48,000 3

=

+

=


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Risk-Free Interest Rates

spot (risk-free) interest rates: default-free, zero-

coupon yields of risk-free bond

yield curve: a graph to show the bond yields (YTM)

(a measure of the market interest rates) as afunction of the bonds’ term to maturity (TTM)

(usually upward-sloping)


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zero-coupon yield curve: a plot of the yield of risk-

free zero-coupon bonds (STRIPS – Separate

Trading of Registered Interest and Principal of

Securities) as a function of the bond’s maturity

date

can also plot coupon-paying yield curve by

using on-the-run coupon bonds


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yield to maturity

term to maturity

zero-coupon yield curve


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Market Practice

many bond professionals use the yield to

maturity to represent the market interest rate,

e.g. they use the yield to determine the bond

price (instead of the other way around)


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semi-annual coupons. If the yield to maturity is

3%, what is the bond price?

$980.731.5%)(1

010,1$

%)5.11(10$

%)5.11(10$

%5.11$10$ pricebond

10$2

2%*$1,000 couponannualsemi

%5.12

3% YTMannual -semi

4

32

=+

+

+

+

+

+

+

=

==−

==


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If the yield to maturity 5%, what is the bond price?

$783.535%)(1

000,1$ pricebond

5 =

+

=

Valuing a Coupon Bond with Zero-


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Valuing a Coupon Bond with Zero

Coupon Prices and Yields consider a 5%, 2-year, $1,000 par bond with

annual coupon payments

0 1 2

$50 $1,050

year

-bond price

equivalent to a1-year $50 par

zero-coupon

bond

equivalent to a2-year $1,050

par zero-

coupon bond

STRIPS*



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Coupon Prices and Yields

in the bond market

1-year zero-coupon bond trades at 96.62 (% of

face value) at a yield of 3.5% (YTM1)

2-year zero-coupon bond trades at 92.45 at a

yield of 4% (YTM2) assume all bonds have the same risk



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%99.3TM

) YTM1(

050,1$

)TM Y (1

$5009.019,1$

error)roundingtoduee(differenc

09.019,1$%)41(

050,1$3.5%)(1

$50 pricebond

04.019,1$92.45%*$1,050%62.96*50$pricebond

2

2

=

+

+

+

=

=

+

+

+

=

=+=



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if the bond price deviates from $1,019.04, itgives rise to an arbitrage opportunity

for example, the bond price is $1,000

buy the bond and sell (issue) $50 par 1-yearzero-coupon bond at 96.62 and sell (issue)$1,050 par 2-year zero-coupon bond at 92.45

P&L = $50*96.62%+$1,050*92.45%-$1,000= $19.04 (arbitrage profit)

You receive $50 from the bond in year 1 andpay off 1-year zero-coupon bond and $1,050 inyear 2 to pay off 2-year zero-coupon bond



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g p


yield to maturity is a weighted average of thezero-coupon yields (remember that they are the

same as the market interest rates) if zero-coupon yield curve is upward-sloping,

yield-to-maturity decreases with coupon rate

(why?) if zero-coupon yield curve is downward-sloping,

yield to maturity increases with coupon rate

(why?)

with a flat zero-coupon yield curve, same yieldto maturity for all coupon rates

Wh B d P i Ch g ?


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Why Bond Prices Change?

most issuers choose to set a coupon rate close to

the market interest rate so that the bonds will

initially issued at par (not for zero-coupon bonds

which must be issued at a discount)

relationship between bond price and market

interest rate/yield (why?)

market interest rate usually increases with risk

and term to maturity of a bond

Wh B d Pri Ch g ?


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Why Bond Prices Change?

subsequently, market interest rate changes andbond price is not necessary equal to the face

valuewhen coupon rate is higher than market

interest rate/yield, bond trades at a and

bond price is than face value (why?)when coupon rate is equal to market interest

rate/yield, bond trades at and bond price

is face valuewhen coupon rate is lower than market

interest rate/yield, bond trades at a and

bond price is than face value


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Example: Premium Par and Discount


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Example: Premium, Par and Discount


annual coupon payments. What is the bond price

if the yield to maturity is (a) 6%; (b) 5% and (c)

4%?

(premium)$1,018.86

4%)(1

$1,050

%)4(1

50$ pricebond(c)

(par)$1,0005%)(1

$1,050

%)5(1

50$

pricebond(b)

(discount)$981.676%)(1

$1,050%)6(1 50$ pricebond(a)

2

2

2

=

+

+

+

=

=+++=

=

+

+

+

=

Time and Bond Prices


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as the next coupon from a bond grows nearer, the

bond price increases to reflect the increasing

present value of the cash flow

it will peak right before the coupon is made and

will drop when coupon is made (buyer cannotreceive the coupon any more)

convergence property: bond price moves

gradually to the face value and it is equal to theface value on the maturity date when the last

coupon is made (why?)



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yield = 5%

Example: Time and Bond Prices


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Example: Time and Bond Prices


If the yield of 5% is constant over time, what is

the bond price in year 0, year 1, year 2 and year 3right after the coupon is made.

$1,0003yearinpricebond

$952.385%)(1

$1,000 2yearinpricebond

$907.03

5%)(1


$863.84%)5(1


2

3

=

=

+

=

=

+

=

=+

=

Interest Rate Risk and Bond Prices


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Interest Rate Risk and Bond Prices

interest rate risk: the risk that arises for

bondholders from fluctuating interest rates

the longer the term to maturity, the higher the

interest rate risk (why?)

the lower coupon rate, the higher the interestrate risk (why?)

Example: Interest Rate Risk and Term to


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Maturity

consider two bonds (5-year and 10-year) with 5%

annual coupons and a par value of $100

$20

$40

$60

$80

$100

$120

$140

$160

0% 5% 10% 15% 20%

bond price

yield

5% 5-year bond

5% 10-year bond

Example: Interest Rate Risk and Term to


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Maturity

5% 10-year bond 5% 5-year bond

0% 150.00 125.00

1% 137.89 119.41

2% 126.95 114.143% 117.06 109.16

4% 108.11 104.45

5% 100.00 100.00

6% 92.64 95.79

7% 85.95 91.80

8% 79.87 88.02

9% 74.33 84.44

10% 69.28 81.05

11% 64.66 77.82

12% 60.45 74.77

13% 56.59 71.8614% 53.05 69.10

15% 49.81 66.48

16% 46.83 63.98

17% 44.10 61.61

18% 41.58 59.35

19% 39.25 57.19

20% 37.11 55.14

bond priceyield

change in bond price for 5%10-year bond = ($92.64-

$100)/$100 = -7.36%


$100)/$100 = -4.21%

Example: Interest Rate Risk and Coupon


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Rate

consider two 5-year bonds with 1% and 10%

annual coupons and a par value of $100

$20

$40

$60

$80

$100

$120

$140

$160

0% 5% 10% 15% 20%

bond price

yield

10% 5-year bond

1% 15-year bond

Example: Interest Rate Risk and Coupon


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Rate

10% 5-year bond 1% 5-year bond

0% 150.00 105.00

1% 148.53 100.00

2% 147.13 95.293% 145.80 90.84

4% 144.52 86.64

5% 143.29 82.68

6% 142.12 78.94

7% 141.00 75.40

8% 139.93 72.059% 138.90 68.88

10% 137.91 65.88

11% 136.96 63.04

12% 136.05 60.35

13% 135.17 57.79

14% 134.33 55.37

15% 133.52 53.07

16% 132.74 50.89

17% 131.99 48.81

18% 131.27 46.84

19% 130.58 44.9620% 129.91 43.18

bond priceyield


$143.29)/$143.29 = -0.82%


$82.68)/$82.68 = -4.53%

Bond Prices and Accrued Interest


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dirty/invoice/settlement price: a bond’s actualcash price

accrued interest: amount of the next couponpayment that has already accrued, i.e. accrued

interest = coupon * (days since last couponpayment up to that day/days in current couponperiod)

calculated based on day count convention, e.g.Actual/360, Actual/365, Actual/Actual,30/360



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clean price: a bond’s cash price less an

adjustment for accrued interest, i.e. clean price =

dirty price – accrued interest, and dealers usuallyquote this price (as a percentage of face value)

from the perspective of an investor, weobserve the clean price and calculate the

accrued interest; hence, dirty price = clean

price + accrued interest


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source: HKEx

face value =

$10,000

clean price =

$10,000*106.3%= $10,630

dirty price =

$10,630 +$105.86 =

$10,735.86

Example: Bond Prices and Accrued

I t t


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Interest

The dirty price of a 5%, 5-year $1,000 par bondwith semi-annual coupon payments is $985. The

number of days from the last coupon payment upto the settlement date of the bond trade is 45days. The number of days between the last

coupon payment to the next coupon payment is182. Calculate the accrued interest and the cleanprice.

accrued interest = ($1,000*5%/2)*45/182 =$6.18

clean price = $985 - $6.18 = $978.82

Credit Risk and Bond Rating


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g

corporate bonds are risky because there is a

chance that the issuer may not be able to settle

the debt obligations

credit risk: the risk of default by the issuer of any

risky bond that the bond’s cash flows are not

known with certainty

investors pay for a bond with higher credit

risk yield to maturity is for a bond with higher

credit risk

lower



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g

yield to maturity (based on promised cash

flows) is than the expected return (based

on expected cash flows) because of the chanceof default (why?)

bond/credit rating: an assessment to show the

possibility of default by the bond issuer

different yield curves for bonds with different

bond ratings credit rating agencies: Standard and Poor’s,

Moody’s and Fitch

higher

for yield to maturity--> we expect no credit risk



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Moody's S&P FitchAaa AAA AAA

Aa1 AA+ AA+

Aa2 AA AA

Aa3 AA- AA-A1 A+ A+

A2 A A

A3 A- A-

Baa1 BBB+ BBB+

Baa2 BBB BBB

Baa3 BBB- BBB-

Ba1 BB+ BB+

Ba2 BB BB

Ba3 BB- BB-

B1 B+ B+

B2 B BB3 B- B-

Caa1 CCC+ CCC+

Caa2 CCC+ CCC+

Caa3 CCC- CCC-

Ca CC CC

C C CD D

investmentgrade bonds

non-investment

grade, speculative,

junk or high yield

bonds

if you buy these, you are subjected a low

credit risk

Challenging Questions


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1. Give two examples of a positive covenant in abond indenture.

A. B.

2. Give two examples of a negative covenant in abond indenture.

A.

B.3. Explain the difference between the coupon rate,

the yield to maturity and the market interest

rate.

put up collateral to back up the bond

make regular interest payments and principal repayment at maturity

cannot issue a new bond with a claim priority than the old one

cannot announce a dividend higher than a specified level before principal repayment

upward sloping yield to maturity(calculated number)



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4. Why is the yield curve upward-sloping more

often than not?

5. What is the implication of an upward-sloping

yield curve?



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6. Other things being equal, which of the following

bonds should have the highest yield?

A. a term to maturity of 10 years and a credit

rating of AA

B. a term to maturity of 10 years and a creditrating of BB

C. a term to maturity of 5 years and a credit

rating of AA

D. a term to maturity of 5 years and a credit

rating of BB



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7. A very important concept in finance is the risk-

free rate, i.e. the rate of return of a risk-free

financial instrument. Which of the following islikely to be used as a proxy for the risk-free rate?

Explain why.

A. Hong Kong Interbank Offered Rate, HIBOR

B. total return on stock of Tracker Fund (an

index fund replicating Hang Seng Index) C. yield on bond issued by HKSAR Government

D. yield on bond issued by AAA-rated company



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8. Other things being equal, which of the following

bonds should have the highest interest rate risk?

A. a term to maturity of 10 years and a

coupon rate of 10%

B. a term to maturity of 10 years and acoupon rate of 5%

C. a term to maturity of 5 years and a coupon

rate of 10%

D. a term to maturity of 5 years and a coupon

rate of 5%

face value will constitute a higher rate



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9. Other things being equal, if the interest rate isexpected to fall and you have to buy a bond, is it

better to buy a bond with a shorter maturity orone with a longer maturity? Explain.

10.Is the price calculated from the bond valuation

model the clean price or the dirty price? Explain.11.If a bond’s yield to maturity does not change,

how does its price change between coupon

payments?12.Explain why the expected return of a corporate

bond does not equal its yield to maturity.

bond price

bond price rise, coupon payments



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13.The market interest rate increases when

the credit standing of the bond issuer is ;

the term to maturity of the bond is ; and

the demand for the bond is in the

market.14.Explain what is meant by credit risk and interest

rate risk.

15.If short-term interest rates are lower than long-

term rates, why might a borrower still choose to

finance with long-term debt?

lower

longer

lower

bond price lower bond price and market interest rate (inverse)

demand and supply for short period of time

short term is more fluctuate

1. stable source of funds



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16.The price-yield relationship of a bond is a convex

curve (as shown). The impact on the size in the

bond price change will not be symmetrical foran increase and a decrease of 1% change in

interest rate. If the bond price effect from a 1%

decrease in the interest rate is usually than

that from a 1% increase in the interest rate. This

is known as positive convexity.

higher



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bond price

yieldi

P positiveconvexity



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17.Nowadays, a bond issuer tends to include anoption-like feature to a bond. For example, it

may include a redemption provision in the bondindenture to allow it to redeem the bonds at aspecified redemption price before maturity of

the bond. The bond is called a callable bond. Ifan investor buys a callable bond, he effectivelybuys a straight bond (without any option-likefeatures) and buys an embedded option. Otherthings being equal, as compared to a straightbond, the callable bond tends to have aprice and a yield. Explain.

sell to the issuer

higher

lower



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18.Most bonds are traded over-the-counter through

a dealer market where large financial

institutions (especially banks) act as the dealers.In the dealer quotation of the bond price, which

price is likely to be higher, the bid price or the

ask price? Which yield is likely to be higher, thebid yield or the ask yield?

dealer: for profit

thus ask price must be higherthe bid yieldif ask price is higherask yield is lower

FINA2303 Topic 04 Bond Valuation (1)

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Transcript of FINA2303 Topic 04 Bond Valuation (1)