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

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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?

#### 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.

\$2.19