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

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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#### Solution Preview

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

Solution:

Let the coupon amount be C.

If the interest rates increase to 15% in one year from now, then the following occurs.

The cash flow to the customer after one year=CF1=Coupon amount+Expected price at the end of year 1=(C+C/15%)=7.666667 ...

#### Solution Summary

This solution describes the steps to estimate the coupon rate at which given bond can sell at par in the probabilistic scenario.