Chapter 5 Fundamentals of Corporate Finance Fourth Edition Valuing Bonds Slides by Matthew Will McGraw Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies,

Chapter 5Fundamentals of

Corporate FinanceFourth Edition

Valuing Bonds

Slides by

Matthew Will

McGraw Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved

Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved

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McGraw Hill/Irwin

Topics Covered

Bond Characteristics reading 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 Variations in Corporate Bonds


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McGraw Hill/Irwin

BondsTerminologyBond - 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 Maturity Value) - Payment

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

percentage of face value.


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McGraw Hill/Irwin

Bonds

WARNINGWARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations.


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McGraw Hill/Irwin

Bonds

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.

Since the coupon rate is listed as a %, this misconception is quite common.


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McGraw Hill/Irwin

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


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McGraw Hill/Irwin

Bond Pricing

Example

What is the price of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 3.9%.

29.072,1$

)039.1(

065,1

)039.1(

65

)039.1(

65321

PV

PV


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McGraw Hill/Irwin

Bond Pricing

Example (continued)

What is the price of the bond if the required rate of return is 6.5 %?

000,1$

)065.1(

065,1

)065.1(

65

)065.1(

65321

PV

PV


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McGraw Hill/Irwin

Bond Pricing

Example (continued)

What is the price of the bond if the required rate of return is 15 %?

93.805$

)15.1(

065,1

)15.1(

65

)15.1(

65321

PV

PV


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McGraw Hill/Irwin

Bond Pricing

Example (continued)

What is the price of the bond if the required rate of return is 6.0% AND the coupons are paid semi-annually?

94.072,1$

)0195.1(

50.032,1

)0195.1(

50.32...

)0195.1(

50.32

)0195.1(

50.326521

PV

PV


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McGraw Hill/Irwin

Bond Pricing

Example (continued)

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


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McGraw Hill/Irwin

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.


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McGraw Hill/Irwin

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.


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McGraw Hill/Irwin

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


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McGraw Hill/Irwin

Bond Yields

Example

What is the YTM of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,072.29.

29.072,1$

)1(

065,1

)1(

65

)1(

65321

PV

rrrPV


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McGraw Hill/Irwin

Bond Yields

WARNINGWARNINGCalculating 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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McGraw Hill/Irwin

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


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McGraw Hill/Irwin

Bond Valuation Spreadsheet

Valuing bonds using a spreadsheet

6.5 % coupon 6% couponmaturing May 2005 10-year maturity

Settlement date 5/15/02 1/1/00Maturity date 5/15/05 1/1/10Annual coupon rate 0.065 0.06Yield to maturity 0.039 0.07Redemption value (% of face value) 100 100Coupon payments per year 1 1

Bond price (% of par) 107.229 92.976

=PRICE(B7,B8,B9,B10,B11,B12)

Esc and Double click on spreadsheet to access


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McGraw Hill/Irwin

Bond Yield Spreadsheet

Finding yield to maturity using a spreadsheetMay 2005 maturity bond, coupon rate = 6.5%, maturity = 3 years

Annual coupons Semiannual coupons

Settlement date 5/15/02 5/15/02Maturity date 5/15/05 5/15/05Annual coupon rate 0.065 0.065Bond price 107.229 107.229Redemption value (% of face value) 100 100Coupon payments per year 1 2

Yield to maturity (decimal) 0.04 0.0392

=YIELD(B7,B8,B9,B10,B11,B12)

Esc and Double click on spreadsheet to access


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McGraw Hill/Irwin

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

Bo

nd

Pri

ce

Price path for Premium Bond

Price path for Discount BondToday

Maturity


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McGraw Hill/Irwin

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 6.5% coupon rate, both

bonds sell at face value


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McGraw Hill/Irwin

Nominal and Real rates

0

2

4

6

8

10

12

14

1682 85 88 91 94 97

2000

Year

Pe

rce

nt

Yield on UK nominal bonds

Yield on UK indexed bonds


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McGraw Hill/Irwin

Default Risk

Credit riskDefault premiumInvestment gradeJunk bonds


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McGraw Hill/Irwin

Default RiskStandard

Moody' 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.


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McGraw Hill/Irwin

Corporate Bonds

Zero couponsFloating rate bondsConvertible bonds


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McGraw Hill/Irwin

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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McGraw Hill/Irwin

Web Resources

www.investinginbonds.com

www.moodys.com/cust/default.asp

www.standardandpoor.com

http://gozips.uakron.edu/~drd/ratings.html

www.smartmoney.com/bonds

www.ustreas.gov

www.ustreas.gov/offices/domestic-finance/debt-management/interest-rate/index.html

www.bondmarkets.com

www.publicdebt.treas.gov/sec/sec.htm

www.bondsonline.com/asp/research/glossary.asp

Click to access web sitesClick to access web sites

Internet connection requiredInternet connection required

Chapter 5 Fundamentals of Corporate Finance Fourth Edition Valuing Bonds Slides by Matthew Will McGraw Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies,

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