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 30 percent probability that interest rates will increase to 10 percent, and there is a 70 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

a) If rate = 10%

Value of the bond after a year = C + C / r = 80 + 80 / 10% = $880.00

Value of the bond today = 880 / (1 + 8%) = $814.81

If rate = 6%, value of the bond after a year = 80 + 80 / 6% = $1,413.33

Value of the bond today = 1,413.33 / (1 + 8%) = $1,308.64

Market Value = 814.81 x 30% + 1308.64 x 70% = $1,160.49

b) Bonds will be called in case the interest rates fall to 6%,

then Bond Value in one year = 80 + 1000 + 80 = $1160 and value today = 1160 / 1.08 = $1,074.07

Market Value today = 30% x 814.81 + 70% x 1074.07 = $996.30

Coupon Rate = 80 / 996.30 = 8.03%

c) Value of call provision = 1,160.49 - 996.30 = 164.20