Fundamentals of Corporate

Finance

Chapter 6

Valuing Bonds

Topics CoveredThe Bond MarketInterest Rates and Bond PricesCurrent Yield and Yield to MaturityBond Rates and ReturnsThe Yield CurveCorporate Bonds and the Risk of Default

BondsTerminology Bond - Security that obligates the issuer to make specified

payments to the bondholder. Coupon - The interest payments made to the bondholder. Face Value (Par Value or Principal Value) - Payment at the maturity

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

face value.

WARNINGWARNINGThe 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.

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.

PVcpn

r

cpn

r

cpn par

r t

( ) ( )

....( )

( )1 1 11 2

Bond Cash Flows

Bond Pricing

Example

What is the price of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.

Bond Pricing

Example

What is the price of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.

95.081,1$

)0215.1(

050,1

)0215.1(

50

)0215.1(

50321

PV

PV

Bond Pricing

Example (continued)

Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?

Bond Pricing

Example (continued)

What is the price of the bond if the required rate of return is 2.15% AND the coupons are paid semi-annually?

37.082,1$

)01075.1(

025,1

)01075.1(

25...

)01075.1(

25

)01075.1(

256521

PV

PV

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 once

doubles the total number of cash flows to be discounted

in the PV formula.

Discount Rate

Since the time periods are now half years, the discount rate is also

changed from the annual rate to the half year rate.

Bond Pricing

Example (continued)

What is the price of the bond if the required rate of return is 5.0 %?

000,1$

)050.1(

050,1

)050.1(

50

)050.1(

50321

PV

PV

Bond Pricing

Example (continued)

What is the price of the bond if the required rate of return is 8 %?

69.922$

)08.1(

050,1

)08.1(

50

)08.1(

50321

PV

PV

Interest Rate Risk

The value of the 5% bond falls as interest rates rise

700

800

900

1,000

1,100

1,200

0 2 4 6 8 10 12 14 16

Interest rate (%)

Bo

nd

pri

ce (

$)

Interest Rate Risk

-

500

1,000

1,500

2,000

2,500

3,000

0 2 4 6 8 10

YTM

$ B

on

d P

ric

e

30 yr bond

3 yr bond

When the interest rate equals the 5.0% coupon rate, both

bonds sell at face value

Bond Yields

Current Yield - Annual coupon payments divided by bond price.

Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price.

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.

PVcpn

r

cpn

r

cpn par

r t

( ) ( )

....( )

( )1 1 11 2

Bond Yields

Example

What is the YTM of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,081.95.

95.081,1$

)1(

050,1

)1(

50

)1(

50321

PV

rrrPV

YTM = 2.15%

Bond Yields

Rate of Return - Earnings per period per dollar invested.

Rate of return =total income

investment

Rate of return =Coupon income + price change

investment

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.

The Yield Curve

0

1

2

3

4

5

61 3 5 7 9

11

13

15

17

19

21

23

25

27

29

Maturity (years)

Yie

ld %

Treasury strips are bonds that make a single payment. The yields on Treasury strips in February 2008 show that investors received a higher yield on longer term bonds.

Default Risk

Credit (default) risk: the risk that a bond issuer may default on its bonds

Default premium: The additional yield on a bond that investors require for bearing credit risk

Investment grade: Bonds rated Baa or above by Moody’s or BBB or above by S&P

Junk bonds: Bond with a rating below Baa or BBB

Default Risk

StandardMoody' s & Poor's Safety

Aaa AAA The strongest rating; ability to repay interest and principalis very strong.

Aa AA Very strong likelihood that interest and principal will berepaid

A A Strong ability to repay, but some vulnerability to changes incircumstances

Baa BBB Adequate capacity to repay; more vulnerability to changesin 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 beCa CC in default or in danger of imminent defaultC C C-rated bonds offer little prospect for interest or principal

on the debt ever to be repaid.

Default Risk

0

2

4

6

8

10

12Y

ield

sp

read

%

Junk bonds

Baa-rated bonds

Aaa-rated bonds

Yield spreads between corporate and 10-year Treasury bonds