Question

Williams Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 8 percent, payable annually. The one-year interest rate is 8 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. Assume a par value of $1,000.

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.) Market value $

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.) Coupon rate %

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.) Value of the call provision $

Answer 1

Solution;

a. The price of the bond today is the present value of the expected price in one year. So, theprice of the bond in one year if interest rates increase will be:

P1= $80 + $80 / .09P1 = $968.89

If interest rates fall, the price if the bond in one year will be:

P1= $80 + $80 / .06P1= $1,413.33

Now we can find the price of the bond today, which will be:

P0= [.35($968.89) + .65($1,413.33)] / 1.08

P0= [.35($968.89) + .65($1,413.33)] / 1.08

P0= $1,164.61

b. So, if interest rates rise, the price of thebonds in one year will be:

P1= C + C / .09

The call premium is notfixed, 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.To find the coupon rate, we can set the desired issue price equal to present value of the expectedvalue of end of year payoffs, and solve for C. Doing so, we find:

P0= $1,000 = [.35(C + C / .09) + .65($1,000 + 2C)] / 1.08

C = $77.63

So the coupon rate necessary to sell the bonds at par value will be:

Coupon rate = $77.633 / $1,000

Coupon rate = .0776 or 7.76%

c. the value of anoncallable bond with the same coupon rate would be:

Non-callable bond value = $77.63 / 0.06 = $1,293.88

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

Value = .65($1,293.88 – 1,077.63) / 1.08

Value = $130.15