Bowdeen Manufacturing intends to use callable perpetual bonds. The bonds are callable at $1,250. One-year interest rates are 12%. There is a 60$ probability that long-term interest rates one year from today will be 15%. With a 40% probability, long term interest rates will be 8%. To simplify the firm's accounting, Bowdeen would like to issue the bonds at par ($1,000). What must the coupon on the bonds be for Bowdeen to be able to sell them at par?
If interest rates rise to 15%, the price of the Bowdeen bonds will fall, which means the bonds would not be
called since the price would be less than the call price. In that case, the bond would be worth C/.15 where C is the coupon payment since bonds are perpetual the present value would be the coupon payment/interest rate. The total bond holding would be ...
The solution explains how to calculate the coupon interest on callable bonds so that they can be sold at par. It includes about 200 words of explanation along with calculations of the coupon payment.