chap005 valuaing bonds

8/9/2019 Chap005 Valuaing Bonds

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Chapter 5 Fundamentals of

Corporate Finance

Fifth Edition

Slid es by

Matthew W ill

McGraw-Hill/Irwin Copyright 2007 by The McGraw-Hill Companies, Inc. All rights reserved

V a luing Bo nd s


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Copyright 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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T op ics Covere d

B ond Characteristicsreading the financial pages

Interest Rates and B ond PricesCurrent Yield and Yield to MaturityB ond Rates and ReturnsThe Yield CurveCorporate B onds and the Risk of Default


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Bo nd s

TerminologyB ond - Security that obligates the issuer tomake specified payments to the bondholder.

Coupon - The interest payments made to the bondholder.Face Value (Par Value or Principal Value) - Paymentat the maturity of the bond.Coupon Rate - Annual interest payment, as a

percentage of face value.


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Bo nd s

W ARNINGW ARNINGThe coupon rate IS NOT the discount rateused 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 %, thismisconception is quite common.


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Bo nd Pr icing

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 therequired rate of return.

PV cpn

r cpn

r cpn par

r t ! ( ) ( ) ....( )

( )1 1 11 2


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Bo nd Pr icing

ExampleWh at is t h e price of a 5.5 % annual coupon bond,wit h a $1,000 face value, w h ich matures in 3

years? Assume a required return of 3.5%.

03.056,1$)

035.1(

055,1

)035

.1(

55

)035

.1(

55321

!

!

PV

PV


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Bo nd Cash F lows


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Bo nd Pr icing

Example (continued)What is the price of the bond if the required rateof return is 5.5 %?

000,1$

)055.1(

055,1)055.1(

55

)055.1(

55321

!

!

PV

PV


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Bo nd Pr icing

Example (continued)What is the price of the bond if the required rateof return is 15 %?

09.783$

)15.1(

055,1)15.1(

55

)15.1(

55321

!

!

PV

PV


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Bo nd Pr icing

Example (continued)What is the price of the bond if the required rateof return is 3.5% AND the coupons are paid semi-annually?

49.056,1$)0 175.1(

50.0 27,1)0 175.1(

50.27...

)0 175.1(

50.27)0 175.1(

50.276521

!

!

PV

PV


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Bo nd Pr icing

Example (continued)Q: How did t h e calculation c h ange, given semi-

annual coupons versus annual coupon payments?


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Bo nd Pr icing

Example (continued)Q: How did t h e calculation c h ange, given semi-

annual coupons versus annual coupon payments?

T ime Periods

Paying coupons twice a

year, instead of oncedoubles t h e total number of cas h flows to be discounted

in t h e PV formula.

Discount Rate

Since t h e time periods are

nowh

alf years, t h

ediscount rate is alsoch anged from t h e annual rate to t h e h alf year rate.


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Bo nd Yield s

Current Yield - Annual coupon paymentsdivided by bond price.

Yield To Maturity - Interest rate for whichthe present value of the bonds paymentsequal the price.


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Bo nd Yield s

Calculating Yield to Maturity (YTM=r)If you are given the price of a bond (PV)

and the coupon rate, the yield to maturitycan be found by solving for r.

PV cpn

r cpn

r cpn par

r t ! ( ) ( ) ....( )

( )1 1 11 2


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Bo nd Yield s

ExampleWh at is t h e YTM of a 5.5 % annual coupon bond,wit h a $1,000 face value, w h ich matures in 3

years? T h e market price of t h e bond is $1,056.03.

03.056,1$)1(

055,1

)1(

55

)1(

55321

!

!

PV r r r

PV


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Bo nd Yield s

W ARNINGW ARNINGCalculating YTM by hand can be very

tedious.

It is highly recommended that you learn to

use the IRR or YTM or i functions ona financial calculator.


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Bo nd Yield s

Rate of Return - Earnings per period per dollar invested.

Rate of returntotal incomeinvestment

Rate of returnoupon income + price change

investment


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Bo nd V a lu at ion Sprea dsheet

Valuing bonds using a spreadshee t

5.5 % coupon 5.5% couponma turing Ma y 2005 10-ye ar ma turity

Settlement date 5/15/05 1/1/05Maturity date 5/15/08 1/1/15

Annual coupon rate 0.055 0.055Yield to maturity 0.035 0.035Redemption value (% of face value) 100 100Coupon payments per year 1 1

Bond price (% of par) 105.603 116.633

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

Esc and Double click on spreadsheet to access


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Bo nd Yield Sprea dsheet

Finding yield to ma turity using a spreadsheetMay 2008 maturity bond, coupon rate = 5.5%, ma turity = 3 yea rs

Annual coupons Semiannual coupons

Settlement date 5/15/05 5/15/05Maturity date 5/15/08 5/15/08

Annual coupon rate 0.055 0.055Bond price 105.603 105.603Redemption value (% of face value) 100 100Coupon payments per year 1 2

Yield to maturity (decimal) 0.035 0.0352

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

Esc and Double click on spreadsheet to access


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I n terest Rate R isk

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

B o n

d P r i c e

Price path for Premium B ond

Price path for Discount B ondToday

Maturity


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I n terest Rate R isk

-

500

1,000

1,500

2,000

2,500

3,000

0 2 4 6 8 10

YTM

$ B

P r

30 yr bond

3 yr bond

W hen the interest rate equalsthe 5 .5 % coupon rate, both

bonds sell at face value


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N om in a l and Rea l rates

0

2

4

6

8

10

12

14

8 5 8 6 8 7 8 8 8 9 9 0 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 2 0

0 0 2 0

0 1 2 0

0 2 2 0

0 3 2 0

0 4 2 0

0 5

Yea r

e r e n t

Yield on UK nominal bonds

Yield on UK indexed bonds


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D efa ul t R isk

Credit risk Default premium

Investment gradeJunk bonds


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D efa ul t R isk Standa d

d ' s & 's Safet

Aaa AAA The s es ating; ability to epay intere st and principalis ery strong .

Aa AA Very strong likelihood that intere st and principal ill berepaid

A A Strong ability to repay , but some ulnerability to change s incircum stance s

Baa BBB Adequate capacity to repay; more ulnerability to change sin economic circum stance s

Ba BB onsiderable uncertainty about ability to repay .

B B L ikelihood of intere st and principal payment s over sustained period s is que stionable .

aa 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 bond s offer little pros pect for intere st or principal

on the debt ever to be repaid .


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Corporate Bo nd s

Z ero couponsFloating rate bonds

Convertible bonds


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T he Y ield C urve

Term Structure of Interest Rates - A listing of bond maturity dates and the interest ratesthat correspond with each date.

Yield Curve - Graph of the term structure.

chap005 valuaing bonds

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