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^239

Companies, 2002

CHAPTER 7 Interest Rates and Bond Valuation 209

Bond Yields

You’re looking at two bonds identical in every way except for their coupons and, of course,

their prices. Both have 12 years to maturity. The first bond has a 10 percent coupon rate and

sells for $935.08. The second has a 12 percent coupon rate. What do you think it would sell

for?

Because the two bonds are very similar, they will be priced to yield about the same rate.

We first need to calculate the yield on the 10 percent coupon bond. Proceeding as before, we

know that the yield must be greater than 10 percent because the bond is selling at a discount.

The bond has a fairly long maturity of 12 years. We’ve seen that long-term bond prices are rel-

atively sensitive to interest rate changes, so the yield is probably close to 10 percent. A little

trial and error reveals that the yield is actually 11 percent:

Bond value $100 (1 
1/1.11^12 )/.11 1,000/1.11^12

$100 6.4924 1,000/3.4985

$649.24 285.84

$935.08

With an 11 percent yield, the second bond will sell at a premium because of its $120

coupon. Its value is:

Bond value $120 (1 
1/1.11^12 )/.11 1,000/1.11^12

$120 6.4924 1,000/3.4985

$779.08 285.84

$1,064.92

EXAMPLE 7.2

CALCULATOR HINTS

How to Calculate Bond Prices and Yields Using

a Financial Calculator

Many financial calculators have fairly sophisticated built-in bond valuation routines.

However, these vary quite a lot in implementation, and not all financial calculators have

them. As a result, we will illustrate a simple way to handle bond problems that will work

on just about any financial calculator.

To begin, of course, we first remember to clear out the calculator! Next, for Example

7.2, we have two bonds to consider, both with 12 years to maturity. The first one sells for

$935.08 and has a 10 percent coupon rate. To find its yield, we can do the following:

Notice that here we have entered both a future value of $1,000, representing the bond’s

face value, and a payment of 10 percent of $1,000, or $100, per year, representing the

bond’s annual coupon. Also notice that we have a negative sign on the bond’s price, which

we have entered as the present value.

N %i PMT PV FV

Enter 12 100 
935.08 1,000

Solve for 11