McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Valuing Bonds

A bond is a debt instrument issued by governments or corporations to raise money

The successful investor must be able to:• Understand bond structure

• Calculate bond rates of return

• Understand interest rate risk

• Differentiate between real and nominal returns

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Bond BasicsWhen governments or companies issue bonds, they promise to make a

series of interest payments and then repay the debt.

Bond• Security that obligates the issuer to make specified payments to the bondholder.

Face Value• Payment at the maturity of the bond.

Coupon• The interest payments paid to the bondholder.

Coupon Rate• Annual interest payment as a percentage of face value.

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Bond Pricing: ExampleTreasury bond prices are quoted in 32nds

rather than in decimals.

For a $1000 face value bond with a bid price of 103:05 and an asked price of 103:06, how much would an investor pay

for the bond?

6103% 103.1875%

32

1.031875 $1,000 $1,031.875

of face value

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Bond Pricing

1 2

( )....

(1 ) (1 ) (1 )t

coupon coupon coupon parPV

r r r

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Bond Pricing: Example

What is the price of a 9% annual coupon bond with a par value of $1,000 that matures in 3 years? Assume a required

rate of return of 4%.

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Bond PricingA bond is a package of two investments: an annuity

and a final repayment.

( ) ( )

1 (1 )where

1and

(1 )

Bond Coupons ParValue

Bond

t

t

PV PV PV

PV coupon Annuity Factor par value Discount Factor

rAnnuity Factor

r

Discount Factorr

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Bond Pricing: ExampleWhat is the value of a 3-year annuity that pays $90 each year and an additional $1,000 at the date of the final repayment? Assume a discount rate of 4%.

3

3

1 (1 .04) 1$90 $1,000

.04 (1 .04)

$1,138.75

BondPV

bondPV coupon annuity factor par value discount factor

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Bond Prices & Interest RatesAs interest rates change, so do bond prices.

What is the present value of a 4% coupon bond with face value $1,000 that matures in 3 years? Assume a discount rate of 5%.

What is the present value of this same bond at a discount rate of 2%?

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Bond YieldsTo calculate how much we earn on a bond investment,

we can calculate two types of bond yields:

Current Yield

Yield to Maturity

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Current Yield: ExampleSuppose you spend $1,150 for a $1,000 face value bond that pays a $60 annual coupon payment for 3

years.

What is the bond’s current yield?

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Yield to Maturity

Yield to Maturity:

tr

parcoupon

r

coupon

r

couponPV

)1(

)(....

)1()1( 21

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Yield to Maturity: ExampleSuppose you spend $1,150 for a $1,000 face value bond

that pays a $60 annual coupon payment for 3 years.

What is the bond’s yield to maturity?

321 )1(

)000,1$60($

)1(

60$

)1(

60$150,1$

rrr

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Rate of Return

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Rate of Return: ExampleSuppose you purchase a 5% coupon bond, par value $1,000,

with 5 years until maturity, for $975.00 today. After one year you sell the bond for $965.00.

What was the rate of return during the period?

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The Yield Curve

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Interest Rates & InflationIn the presence of inflation, an investor’s real interest

rate is always less than the nominal interest rate.

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Interest Rates & InflationIf you invest in a security that pays 10% interest annually and inflation is 6%, what is your real

interest rate?

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Interest Rates & Inflation: Example

Treasury Inflation Protected Securities (TIPS)

Example:

If you invest in 5% coupon, 3 year TIPS and inflation is 3% each year, what are your real annual cash flows?

Year 1 2 3

Real cash flows $50 $50 $1,050

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The Risk of DefaultWhen investing in bonds, there is always the

risk that the issuer may default.

Default risk

Default premium

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The Risk of DefaultBonds come in many categories, with returns

commensurate with risk.Credit agency

Investment-grade bonds

Junk bonds

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Types of Corporate Bonds

Zero-Coupon Bonds

Floating-Rate Bonds

Convertible Bonds

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Appendix A: Treasury Bond Rates

10-year U.S. Treasury bond interest rates, 1900-2010

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Appendix B: Real vs. Nominal Yields

Red line – Real yield on long-term UK indexed bondsBlue line – Nominal yield on long-term UK bonds

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Appendix C: Credit Ratings