Question

Williams Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 6.5 percent, payable annually, and a par value of $1,000. The one-year interest rate is 6.5 percent. Next year, there is a 35 percent probability that interest rates will increase to 8 percent and a 65 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 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 enter your answer as a percent rounded 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 answer to 2 decimal places, e.g., 32.16.) Market value Coupon rate c. Value of the call provision

Answer 1

A.

Today's bond price is the present value of the expected price in one year. So, the price of the bond in one year if interest rates increase will be:

P1 = value of bond at end of year one = $60 + $60/0.08 = $810 (with a probability of 0.45)

Similarly, if the interest rate fall, the price if the bond in one year will be:

P1 = value of bond at end of year one = $60 + $60/0.05 = $1,260 (with a probability of 0.55)

From the above data, we can find the price of the bond today, which will be:

P0 = ($810*0.45 + $1,260*0.55)/1.06

P0 = $997.64

B.

The price of the bonds will fall if the interest rate rises. If the price of the bonds is low, the company will not call them. Then the only payment the bondholders receive is the coupon payment, C plus the present value of the remaining payments. So, if interest rates rise, the price of the bonds in one year will be:

P1= C + C / .08

If interest rates fall, the assumption is that 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

The selling price today of the bonds is the PV of the expected payoffs to the bondholders.

We can use the desired issue price, which will be equal to present value of the expected value of end of year payoffs, and solve for C. Thus,

P0= $1,000 = [.45(C + C / .08) + .55($1,000 + 2C)] / 1.06

C = $71.08

ie, the coupon rate = 71.08%

C.

Value of call provision

From the point of view of company, the value of the call provision is given by the difference between the value of an outstanding, non-callable bond and the call provision.

So, the value of a noncallable bond with the same coupon rate would be:

Non-callable bond value = $71.08 / 0.05 = $1,421.6

So, the value of the call provision to the company is:

Value = .55($1,421.6 - 1,071.08) / 1.06

Value = $181.87