Illinois Industries has decided to borrow money by issuing perpetual bonds with
ID: 2730519 • Letter: I
Question
Illinois Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 7.5 percent, payable annually. The one year interest rate is 7.5 percent. Next year, there is a 30 percent probability that interest rates will increase to 9 percent and there is a 70 percent probability that they will fall to 6 percent. Question: If the company decides instead to make the bonds callable in one year, what coupon rate ill be demanded by the bondholders for the bonds to sell at par? Assume that the bonds will be called if interest rates fall and the call premium is equal to the annual coupon. Please show steps.
Explanation / Answer
Answer: If interest rates fall, the bonds will be called. In this case, the bondholders will receive the call price, plus the coupon payment, C. The call premium is not fixed, but it is the same as the coupon rate, so the price of the bonds if interest rates fall will be:
P1= ($1,000 + C) + C
P1= $1,000 + 2C
If interest rates rise, the price of the bonds will fall. If the price of the bonds is low, the company will not call them. The firm would be foolish to pay the call price for something worth less than the call price. In this case, the bondholders will receive the coupon payment, C, plus the present value of the remaining payments. So, if interest rates rise, the price of thebonds in one year will be:
P1= C + C / .09
The selling price today of the bonds is the PV of the expected payoffs to the bondholders.To find the coupon rate, we can set the desired issue price equal to present value of the expected value of end of year payoffs, and solve for C. Doing so, we find:
P0= $1,000 = [.30(C + C / .09) + .70($1,000 + 2C)] / 1.075
C = $74.50
So the coupon rate necessary to sell the bonds at par value will be:
Coupon rate = $74.50 / $1,000
Coupon rate = .07450 or 7.45%