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.) a. Market value b. Coupon rate c. Value of the call provision

Answer 1

a.  The price of the bond in one year if interest rates increase -

P1= (Coupon rate*Par value) + [(Coupon rate*Par value)/35% probability that interest rate will increase to 8%)

P1=(6.5%*1000) +[(6.5%*1000)/0.08]

P1=65+65/0.08=$877.5  (with a probability of 0.35)

Similarly, if the interest rate fall, the price if the bond in one year -

P1=65+65/0.05=$1365   (with a probability of 0.65)

The price of the bond today,

P0= $877.5 *(probability of 0.35) + $1365 *(probability of 0.65)= ($877.5 * 0.35)+ ($1365 *0.65) = 307.125+887.25=$1194.375 OR

P0= $1194.38

B. If interest rates rise, the price of the bonds in one year =

P1= C + C / .08

where C is coupon payment.

The price of the bonds if interest rates fall =

P1= ($1,000 + C) + C

P1= $1,000 + 2C

The desired issue price equal to present value of the expected value of end of year payoffs, and solve for C. Thus,

P0= $1,000 = [.35(C + C / .08) + .65($1,000 + 2C)] / 1.065

C=$68.88

ie, the coupon rate = 68.88%

C. The value of the call provision is given by the difference between the value of an outstanding, non-callable bond and the call provision.

the value of a non callable bond = (C=$68.88)/0.05= $1377.6

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

= .65($1377.6 - (1000+68.88)) / 1.065

= .65($1377.6 - 1068.88) / 1.065

=$188.42

The value of the call provision to the company is $188.42