Illinois Industries has decided to borrow money by issuing perpetual bonds with
ID: 2729680 • Letter: I
Question
Illinois Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 8.0 percent, payable annually. The one-year interest rate is 8.0 percent. Next year, there is a 35 percent probability that interest rates will increase to 10 percent, and there is a 65 percent probability that they will fall to 6 percent.
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))
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))
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))
Illinois Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 8.0 percent, payable annually. The one-year interest rate is 8.0 percent. Next year, there is a 35 percent probability that interest rates will increase to 10 percent, and there is a 65 percent probability that they will fall to 6 percent.
Explanation / Answer
Part A
Price of a bond is the present value of all future coupon payments.
Annual coupon = 1000 x8%
= 80
If interest rate rises to 10%
Value of the bond next year = annual coupon / interest rate + coupon
= 80/ 0.10 + 80
= 880
If interest rate reduces to 6%
Value of the bond next year = annual coupon / interest rate + coupon
= 80/ 0.06 + 80
= 1413.33
Current value of the bond would be the present value of coupon received next year plus pv of price next year:
Current market value = (0.35 x 880 + 0.65 x 1413.33)/( (1+0.08)
= 1226.6645 / 1.08
= 1135.80
Part B
If there is a fall in interest rate, the bondholder will get the bond redeemed and will receive the call price along with a coupon payment. Therefore In the next year, total amount received would be:
P1 =1000+ C + C
Where C is the coupon amount
As per the question, the current value of this bond should be 1000 (at par).
Po = [0.35 x (C + C/0.10) + 0.65 (1000+C + C)/ (1 +0.08)
1080 = 0.35C + 3.5 C + 650 + 1.3 C
430 = 5.15 C
C= 83.50
Therefore, coupon amount would be 83.50.
Coupon rate = coupon amount/ par value
= 83.50/ 1000
= 8.35%
Part C
Value of non-callable bond on interest rate fall = coupon/ interest rate
= 83.49514563 / 0.06
= 1391.59
Value of call provision = probability of rate fall ( price after rate fall – FV – coupon)
= 0.65 x (1391.59 – 1000- 83.50)
= 0.65 x 308.0858
= 200.26