Bowdeen Manufacturing intends to issue callable, perpetual bonds with annual cou

Question

Bowdeen Manufacturing intends to issue callable, perpetual bonds with annual coupon payments. The bonds are callable at $1,270. One-year interest rates are 11 percent. There is a 60 percent probability that long-term interest rates one year from today will be 12 percent, and a 40 percent probability that they will be 10 percent. Assume that if interest rates fall the bonds will be called. What coupon rate should the bonds have in order to sell at par value? Assume a par value of $1,000. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation / Answer

Solution

Step 1: determine end-of-yr payoff if rates drop to 10%

            = call price plus coupon

            = 1270 + C

Step 2: determine end-of-yr payoff if rates rise to 12%

            = bondholders' position at year end

            = C/0.12 + C

Step 3: Set desired issue price equal to PV of Expected Value of end of year payoffs, and solve for C:

Expected Value of end of year payoffs = E(payoffs)

= (Prob of rate drop)(payoff if rate drops) + (Prob of rate rise)(payoff if rate rises)

Issue Price = E(payoffs)/(1+discount rate)

1000 = ((0.4)*(1270+100.34)+(0.6)*(100.34/0.12+100.34))/1.11

C = 100.34

Therefore, the required coupon rate is

100.34/1000 = 0.10034

=10.03%    …..Answer

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