CHAPTER 6 Interest Rates and Bond Valuation 289is its market value to a given change in the required return. In other words, short
maturities have less interest rate risk than long maturities when all other features
(coupon interest rate, par value, and interest payment frequency) are the same.
This is because of the mathematics of time value; the present values of short-term
cash flows change far less than the present values of longer-term cash flows in
response to a given change in the discount rate (required return).EXAMPLE The effect of changing required returns on bonds of differing maturity can be
illustrated by using Mills Company’s bond and Figure 6.6. If the required return
rises from 10% to 12% (see the dashed line at 8 years), the bond’s value
decreases from $1,000 to $901—a 9.9% decrease. If the same change in required
return had occurred with only 3 years to maturity (see the dashed line at 3 years),
the bond’s value would have dropped to just $952—only a 4.8% decrease. Simi-
lar types of responses can be seen for the change in bond value associated with
decreases in required returns. The shorter the time to maturity, the less the impact
on bond value caused by a given change in the required return.In Practice
Many investors buy bonds to get a
steady stream of interest pay-
ments. So why would anyone buy a
zero-coupon bond, which doesn’t
offer that stream of cash flows?
One reason is the cost of “zeros.”
Because they pay no interest, ze-
ros sell at a deep discount from par
value: A $1,000, 30-year govern-
ment agency zero-coupon bond
might cost about $175. At maturity,
the investor receives the $1,000 par
value. The difference between the
price of the bond and its par value
is the return to the investor. Stated
as an annual yield, the return re-
flects the compounding of interest,
just as though the issuer had paid
interest during bond term. In this
example, the bond yields 6 percent.
Even though a corporate is-
suer of a zero-coupon bond makes
no cash interest payments, for tax
purposes it can take an interest
deduction. To calculate the annual
implicit interest expense, the is-
suer must first determine the
bond’s value at the beginning of
each year by using the formula
M /(1kd)n, where Mthe par
value in dollars, kdthe required
return, and nthe number of
years to maturity. The difference in
the bond’s value from year to year
is the implicit interest.
Assume that a corporation
issues a 5-year zero-coupon bond
with a $1,000 par value and a re-
quired yield of 6.5 percent. Apply-
ing the above formula, we discover
that the initial price of this bond is
$729.88 [$1,000/(10.065)^5
$1,000/1.3700867]. Total implicitinterest over the 5 years is $270.12
($1,000 – $729.88). The following
table uses the formula to calculate
the bond’s value at the end of each
year and the implicit interest ex-
pense that the corporation can
deduct each year.
Sources:Adapted from Hope Hamashige,
“More than Zero,” Los Angeles Times
(September 16, 1997), p. D-6; Donald Jay
Korn, “Getting Something for Nothing,”
Black Enterprise(April 2000), downloaded
from http://www.findarticles.com;“Putting Com-
pound Interest to Work Through Zero
Coupon Bonds,” The Bond Market Associa-
tion, PR Newswire (June 24, 1998), down-
loaded from http://www.ask.elibrary.com.FOCUS ONPRACTICE The Value of a Zero
Beginning Ending Implicit
Year value value Interest Expense
1 $729.88 $ 777.32 $ 47.44
2 777.32 827.84 50.52
3 827.84 881.66 53.82
4 881.66 938.97 57.315 938.97 1,000.00 (^6) (^1) . (^0) (^3)
Total $
2
7
0
.
1
2