Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionIII. Valuation of Future
Cash Flows- Interest Rates and Bond
Valuation
(^238) © The McGraw−Hill
Companies, 2002
longer-term bonds have greater interest rate risk. For the two issues maturing in 2033,
notice that the one with the lower coupon rate had larger gains and losses, which is what
we would expect based on our second point regarding coupon rates and interest rate risk.
Finding the Yield to Maturity: More Trial and Error
Frequently, we will know a bond’s price, coupon rate, and maturity date, but not its yield
to maturity. For example, suppose we are interested in a six-year, 8 percent coupon
bond. A broker quotes a price of $955.14. What is the yield on this bond?
We’ve seen that the price of a bond can be written as the sum of its annuity and lump-
sum components. Knowing that there is an $80 coupon for six years and a $1,000 face
value, we can say that the price is:
$955.14 $80 [1 1/(1 r)^6 ]/r1,000/(1 r)^6
where ris the unknown discount rate, or yield to maturity. We have one equation here
and one unknown, but we cannot solve it for rexplicitly. The only way to find the an-
swer is to use trial and error.
This problem is essentially identical to the one we examined in the last chapter when
we tried to find the unknown interest rate on an annuity. However, finding the rate (or
yield) on a bond is even more complicated because of the $1,000 face amount.
We can speed up the trial-and-error process by using what we know about bond prices
and yields. In this case, the bond has an $80 coupon and is selling at a discount. We thus
know that the yield is greater than 8 percent. If we compute the price at 10 percent:
Bond value $80 (1 1/1.10^6 )/.10 1,000/1.10^6
$80 4.3553 1,000/1.7716
$912.89
At 10 percent, the value we calculate is lower than the actual price, so 10 percent is too
high. The true yield must be somewhere between 8 and 10 percent. At this point, it’s
“plug and chug” to find the answer. You would probably want to try 9 percent next. If
you did, you would see that this is in fact the bond’s yield to maturity.
Our discussion of bond valuation is summarized in Table 7.1.
208 PART THREE Valuation of Future Cash Flows
TABLE 7.1
Summary of Bond
ValuationI. Finding the value of a bond
Bond value C[1 1/(1 r)t]/rF/(1 r)t
where
CCoupon paid each period
rRate per period
tNumber of periods
FBond’s face value
II. Finding the yield on a bond
Given a bond value, coupon, time to maturity, and face value, it is possible to find
the implicit discount rate, or yield to maturity, by trial and error only. To do this, try
different discount rates until the calculated bond value equals the given value (or
let a financial calculator do it for you). Remember that increasing the rate
decreasesthe bond value.Current market rates are
available at
http://www.bankrate.com.