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Chapter 4Fundamentals of Corporate Finance

Third Edition

Valuing Bonds

Brealey Myers Marcus

slides by Matthew Will

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Topics Covered

Bond Characteristicsreading the financial pages

Bond Prices and Yields

Bond prices and interest rates

YTM vs. current yield

Rate of Return

Interest Rate Risk

The Yield Curve

Nominal and Real Rates of Interest

Default Risk

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Bonds

TerminologyBond - Security that obligates the issuer to

make specified payments to the bondholder.

Coupon - The interest payments made to thebondholder.

Face Value (Par Value or Maturity Value) - Payment

at the maturity of the bond.Coupon Rate - Annual interest payment, as a

percentage of face value.

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Bonds

WARNING

The coupon rate IS NOT the discount rate

used in the Present Value calculations.

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Bonds

WARNING

The coupon rate IS NOT the discount rate

used in the Present Value calculations.

The coupon rate merely tells us what cash flow the

bond will produce.

Since the coupon rate is listed as a %, this

misconception is quite common.

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Bond Pricing

The price of a bond is the Present Value of

all cash flows generated by the bond (i.e.

coupons and face value) discounted at the

required rate of return.

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Bond Pricing

The price of a bond is the Present Value of

all cash flows generated by the bond (i.e.

coupons and face value) discounted at the

required rate of return.

PV

cpn

r

cpn

r

cpn par

r t

( ) ( ) ....

( )

( )1 1 11 2

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Bond Pricing

Example

What is the price of a 6 % annual coupon bond,

with a $1,000 face value, which matures in 3

years? Assume a required return of 5.6%.

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Bond Pricing

Example

What is the price of a 6 % annual coupon bond,

with a $1,000 face value, which matures in 3

years? Assume a required return of 5.6%.

77.010,1$

)056.1(

060,1

)056.1(

60

)056.1(

60321

PV

PV

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Bond Pricing

Example (continued)

What is the price of the bond if the required rate

of return is 6 %?

000,1$

)06.1(

060,1

)06.1(

60

)06.1(

60321

PV

PV

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Bond Pricing

Example (continued)

What is the price of the bond if the required rate

of return is 15 %?

51.794$

)15.1(

060,1

)15.1(

60

)15.1(

60321

PV

PV

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Bond Pricing

Example (continued)

What is the price of the bond if the required rate

of return is 5.6% AND the coupons are paid semi-

annually?

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Bond Pricing

Example (continued)

What is the price of the bond if the required rate

of return is 5.6% AND the coupons are paid semi-

annually?

91.010,1$

)028.1(

030,1

)028.1(

30...

)028.1(

30

)028.1(

306521

PV

PV

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Bond Pricing

Example (continued)

Q: How did the calculation change, given semi-

annual coupons versus annual coupon payments?

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Bond Pricing

Example (continued)

Q: How did the calculation change, given semi-

annual coupons versus annual coupon payments?

Time Periods

Paying coupons twice a

year, instead of oncedoubles the total number of

cash flows to be discounted

in the PV formula.

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Bond Pricing

Example (continued)

Q: How did the calculation change, given semi-

annual coupons versus annual coupon payments?

Time Periods

Paying coupons twice a

year, instead of oncedoubles the total number of

cash flows to be discounted

in the PV formula.

Discount Rate

Since the time periods are

now half years, thediscount rate is also

changed from the annual

rate to the half year rate.

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Bond Yields

Current Yield - Annual coupon payments

divided by bond price.

Yield To Maturity - Interest rate for which

the present value of the bonds payments

equal the price.

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Bond Yields

Calculating Yield to Maturity (YTM=r)

If you are given the price of a bond (PV)

and the coupon rate, the yield to maturity

can be found by solving for r.

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Bond Yields

Calculating Yield to Maturity (YTM=r)

If you are given the price of a bond (PV)

and the coupon rate, the yield to maturity

can be found by solving for r.

PV

cpn

r

cpn

r

cpn par

r t

( ) ( ) ....

( )

( )1 1 11 2

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Bond Yields

Example

What is the YTM of a 6 % annual coupon bond,

with a $1,000 face value, which matures in 3

years? The market price of the bond is $1,010.77

77.010,1$)1(

060,1

)1(

60

)1(

60321

PVrrr

PV

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Bond Yields

WARNING

Calculating YTM by hand can be very

tedious.

It is highly recommended that you learn to

use the IRR or YTM or i functions on

a financial calculator.

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Bond Yields

Rate of Return - Earnings per period per

dollar invested.

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Bond Yields

Rate of Return - Earnings per period per

dollar invested.

Rate of return = total incomeinvestment

Rate of return =Coupon income + price change

investment

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Interest Rate Risk

880

900

920

940

960

980

1,000

1,020

1,040

1,060

1,080

0 5 10 15 20 25 30

Time to Maturity

Bond

Pric

e

Premium Bond

Discount Bond

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Interest Rate Risk

-

500

1,000

1,500

2,000

2,500

3,000

0 2 4 6 8 10

YTM

$Bond

Price

30 yr bond

3 yr bond

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Nominal and Real rates

0

2

4

6

8

10

12

14

16

82

85

88

91

94

97

Year

Percent

Yield on UK

nominal bonds

Yield on UK

indexed bonds

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Default Risk

Credit risk

Default premium

Investment grade

Junk bonds

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Default Risk

Standard

Moody' s & Poor's Safety

Aaa AAA The strongest rating; ability to repay interest and principal

is very strong.

Aa AA Very strong likelihood that interest and principal will be

repaidA A Strong ability to repay, but some vulnerability to changes in

circumstances

Baa BBB Adequate capacity to repay; more vulnerability to changes

in economic circumstances

Ba BB Considerable uncertainty about ability to repay.

B B Likelihood of interest and principal payments over sustained periods is questionable.

Caa CCC Bonds in the Caa/CCC and Ca/CC classes may already be

Ca CC in default or in danger of imminent default

C C C-rated bonds offer little prospect for interest or principal

on the debt ever to be repaid.

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The Yield Curve

Term Structure of Interest Rates - A listing of

bond maturity dates and the interest rates

that correspond with each date.

Yield Curve - Graph of the term structure.

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Web Resources

www.finpipe.com

www.investinginbonds.com

www.bloomberg.com/markets/C13.html

www.bondmarkets.com/publications/IGCORP/what.htm

www.moodys.com

www.standardandpoors.com/ratings

Click to access web sites

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