# Bonds with Semiannual Coupons

Although some bonds pay interest annually, the vast majority actually pay interest semiannually. To evaluate semiannual payment bonds, we must modify the valuation model (Equation 4-1) as follows:

1. Divide the annual coupon interest payment by 2 to determine the dollars of interest paid each six months.

2. Multiply the years to maturity, N, by 2 to determine the number of semiannual periods.

3. Divide the nominal (quoted) interest rate, rd, by 2 to determine the periodic (semiannual) interest rate.

By making these changes, we obtain the following equation for finding the value of a bond that pays interest semiannually:

To illustrate, assume now that MicroDrive's bonds pay \$50 interest each six months rather than \$100 at the end of each year. Thus, each interest payment is only half as large, but there are twice as many of them. The coupon rate is thus "10 percent, semiannual payments." This is the nominal, or quoted, rate.9

9In this situation, the nominal coupon rate of "10 percent, semiannually," is the rate that bond dealers, corporate treasurers, and investors generally would discuss. Of course, the effective annual rate would be higher than 10 percent at the time the bond was issued:

EAR = EFF% = (1 + ) -1 = (l + -y- b -1 = (1.05)2 -1 = 10.25%.

Note also that 10 percent with annual payments is different than 10 percent with semiannual payments. Thus, we have assumed a change in effective rates in this section from the situation in the preceding section, where we assumed 10 percent with annual payments.

When the going (nominal) rate of interest is 5 percent with semiannual compounding, the value of this 15-year bond is found as follows:

Inputs:

Output:

pmt|

1000 fv i

1,523.26

Enter N = 30, r = I = 2.5, PMT = 50, FV = 1000, and then press the PV key to obtain 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 semiannual compounding.

Setf-Test Question

Describe how the annual bond valuation formula is changed to evaluate semiannual coupon bonds. Then, write out the revised formula.