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Which coupon rate should the bonds have in order to sell at par value?

Author:
January 26th, 2023

Please help with the following problem. Provide step by step calculations.

Bowdeen Manufacturing intends to issue callable, perpetual bonds with annual coupon payments. The bonds are callable at $1,250. One-year interest rates are 10 percent. There is a 50 percent probability that long-term interest rates one year from today will be 15 percent, and a 50 percent probability that they will be 7 percent. Please assume that, if interest rates fall, the bonds will be called.

Which coupon rate should the bonds have in order to sell at par value?

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