Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

III. Valuation of Future

Cash Flows

7. Interest Rates and Bond
   Valuation

© The McGraw−Hill^233

Companies, 2002

separately and adding the results together. First, at the going rate of 8 percent, the pres-
ent value of the $1,000 paid in 10 years is:

Present value $1,000/1.08^10 $1,000/2.1589 $463.19

Second, the bond offers $80 per year for 10 years; the present value of this annuity
stream is:

Annuity present value $80 (1 
1/1.08^10 )/.08

$80 (1 
1/2.1589)/.08

$80 6.7101

$536.81

We can now add the values for the two parts together to get the bond’s value:

Total bond value $463.19536.81$1,000
This bond sells for exactly its face value. This is not a coincidence. The going inter-
est rate in the market is 8 percent. Considered as an interest-only loan, what interest rate
does this bond have? With an $80 coupon, this bond pays exactly 8 percent interest only
when it sells for $1,000.
To illustrate what happens as interest rates change, suppose that a year has gone by.
The Xanth bond now has nine years to maturity. If the interest rate in the market has
risen to 10 percent, what will the bond be worth? To find out, we repeat the present
value calculations with 9 years instead of 10, and a 10 percent yield instead of an 8 per-
cent yield. First, the present value of the $1,000 paid in nine years at 10 percent is:

Present value $1,000/1.10^9 $1,000/2.3579 $424.10

Second, the bond now offers $80 per year for nine years; the present value of this annu-
ity stream at 10 percent is:

Annuity present value $80 (1 
1/1.10^9 )/.10

$80 (1 
1/2.3579)/.10

$80 5.7590

$460.72

We can now add the values for the two parts together to get the bond’s value:

Total bond value $424.10460.72$884.82

CHAPTER 7 Interest Rates and Bond Valuation 203

FIGURE 7.1

Year

Cash flows

Coupon $ 80

1,000

$1,080

Face value

012345678910

$80 $80 $80 $80 $80 $80 $80 $80 $80

$80 $80 $80 $80 $80 $80 $80 $80 $80

As shown, the Xanth bond has an annual coupon of $80 and a face, or par, value of $1,000 paid at maturity in 10 years.

Cash Flows for Xanth Co. Bond

A good bond site to visit is

bonds.yahoo.com, which

has loads of useful

information.