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 $1,220. One-year interest rates are 10 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 9 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

Perpetual bonds when interest raise

P1 = C + C/12%

If the interest reduces, bonds will be called

P1 = C + 1220

P0 = 0.6*(C + C/12%) + 0.4*(C + 1220)

P0 = 1000 (Par value)

0.6*(C + C/12%) + 0.4*(C + 1220)  = 1000

0.6*C + 5*C + 0.4*C + 488 = 1000

6*C = 512

C = 512/6 = 85.33

Rate = 85.33 / 1000

   = 0.08533 = 8.53%

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