Kennedy Gas Works has bonds which mature in 10 years, and have a face value of $1,000. The bonds have a 10 percent quarterly coupon (i.e., the nominal coupon rate is 10 percent). The bonds may be called in five years. The bonds have a nominal yield to maturity of 8 percent and a yield to call of 7.5 percent. What is the call price on the bonds?

Question

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The call price is the present value of the remaining coupon payments and the face value, discounted at the yield to call. The remaining coupon payments are $100 per quarter for 5 years, or 20 payments. The present value of these payments is:PV = $100 * (1 - (1 + 0.075/4)^-20) / (0.075/4) = $1,597.20The present value of the face value is:PV = $1,000 * (1 + 0.075/4)^-20 = $448.34The call price is the sum of these two present values:Call price = $1,597.20 + $448.34 = $1,048.34

Kennedy Gas Works Has Bonds Which Mature in 10 Years