# Coupon rate to sell at par value

Bowdeen Manufacturing intends to issue callable, perpetual bonds with annual coupon payments. The bonds are callable at $1,280. One-year interest rates are 12 percent. There is a 50 percent probability that long-term interest rates one year from today will be 17 percent, and a 50 percent probability that they will be 8 percent. Assume that if interest rates fall the bonds will be called.

Required:

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

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#### Solution Preview

The bonds are perpetual bonds. This implies that the price of the bond will be Annual Coupon / Interest rate. The price of the bond is the present value of interest and interest is a perpetuity here.

Let C be the annual coupon needed for the bonds to sell at par.

If interest rates rise to 17%, ...

#### Solution Summary

The solution explains how to calculate the coupon rate so as to sell the bonds at par value