CP

When the going (nominal) rate of interest is 5 percent with semiannual com-

pounding, the value of this 15-year bond is found as follows:

Inputs: 30 2.5 50 1000

Output: 
1,523.26

Enter N 
30, r 
I 
2.5, PMT 
50, FV 
1000, and then press the PV key to ob-

tain the bond’s value, $1,523.26. The value with semiannual interest payments is

slightly larger than $1,518.98, the value when interest is paid annually. This higher

value occurs because interest payments are received somewhat faster under semian-

nual compounding.

Describe how the annual bond valuation formula is changed to evaluate semian-

nual coupon bonds. Then, write out the revised formula.

Assessing the Risk of a Bond

Interest Rate Risk

As we saw in Chapter 1, interest rates go up and down over time, and an increase in

interest rates leads to a decline in the value of outstanding bonds. This risk of a de-

cline in bond values due to rising interest rates is called interest rate risk.To illus-

trate, suppose you bought some 10 percent MicroDrive bonds at a price of $1,000,

and interest rates in the following year rose to 15 percent. As we saw earlier, the price

of the bonds would fall to $713.78, so you would have a loss of $286.22 per bond.^10

Interest rates can and do rise, and rising rates cause a loss of value for bondholders.

Thus, people or firms who invest in bonds are exposed to risk from changing inter-

est rates.

One’s exposure to interest rate risk is higher on bonds with long maturities than

on those maturing in the near future.^11 This point can be demonstrated by showing

how the value of a 1-year bond with a 10 percent annual coupon fluctuates with

changes in rd, and then comparing these changes with those on a 14-year bond as

calculated previously. The 1-year bond’s values at different interest rates are shown

below:

166 CHAPTER 4 Bonds and Their Valuation

(^10) You would have anaccounting(and tax) loss only if you sold the bond; if you held it to maturity, you would
not have such a loss. However, even if you did not sell, you would still have suffered areal economic loss in an
opportunity cost sensebecause you would have lost the opportunity to invest at 15 percent and would be stuck
with a 10 percent bond in a 15 percent market. In an economic sense, “paper losses” are just as bad as real-
ized accounting losses.
(^11) Actually, a bond’s maturity and coupon rate both affect interest rate risk. Low coupons mean that most of
the bond’s return will come from repayment of principal, whereas on a high coupon bond with the same ma-
turity, more of the cash flows will come in during the early years due to the relatively large coupon pay-
ments. A measurement called “duration,” which finds the average number of years the bond’s PV of cash
flows remain outstanding, has been developed to combine maturity and coupons. A zero coupon bond,
which has no interest payments and whose payments all come at maturity, has a duration equal to the bond’s
maturity. Coupon bonds all have durations that are shorter than maturity, and the higher the coupon rate,
the shorter the duration. Bonds with longer duration are exposed to more interest rate risk.

162 Bonds and Their Valuation