Please assist with the given problem. Provide step by step calculations.
Problem: 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?