Problem: Valuing Callable Bonds
Illinois Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 6.0 percent, payable annually. The one-year interest rate is 6.0 percent. Next year, there is a 45 percent probability that interest rates will increase to 8 percent, and there is a 55 percent probability that they will fall to 5 percent.
a. What will the market value of these bonds be if they are noncallable? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
b. If the company decides instead to make the bonds callable in one year, what coupon rate will be demanded by the bondholders for the bonds to sell at par? Assume that the bonds will be called if interest rates fall and that the call premium is equal to the annual coupon. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
c. What will be the value of the call provision to the company? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))