Question

KIC, Inc., plans to issue $7 million of bonds with a coupon rate of 7 percent and 20 years to maturity. The current market interest rates on these bonds are 9 percent. In one year, the interest rate on the bonds will be either 8 percent or 4 percent with equal probability. Assume investors are risk-neutral. a. If the bonds are noncallable, what is the price of the bonds today? Assume a par value of $1,000 and semiannual payments. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Price of the bonds $

THE ANSWER IS NOT 815.98! THANKS

Answer 1

The value of bond can be calculated using PV function

With 8% interest rate in one year,

N = 19 x 2 = 38, PMT = 7% x 1000 / 2 = 35, FV = 1000, I/Y = 8% / 2 = 4% => Compute PV = $903.16

Its value today, P0 = 35 / (1 + 9%/2) + (35 + 903.16) / (1 + 9%/2)^2 = $892.59

With 4% interest rate in one year,

N = 19 x 2 = 38, PMT = 7% x 1000 / 2 = 35, FV = 1000, I/Y = 4% / 2 = 2% => Compute PV = $1,396.61

Its value today, P0 = 35 / (1 + 9%/2) + (35 + 1,396.61) / (1 + 9%/2)^2 = $1,344.46

As both probabilities are equally likely,

Price of the bond today = 50% x 892.59 + 50% x 1,344.46 = $1,118.53