Question

Valuing Callable Bonds
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 1-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?
b. If the company decides instead to make the bonds callable in one year, what coupon 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.
c. What will be the value of the call provision to the company?

(Do not round your intermediate calculations.)

Answer 1

Answer 1) In case of perpetual payment , terminal value = Cash flow / Interest rate.

Coupon of bond = 1000*6.5% = $ 65

The price of the bond today is the present value of the expected price in one year.

Vale the bond in one year (interest rates increase 8%) P1= 65 + 65/0.08 = 877.5

Vale the bond in one year (interest rates decrease 5%) P1= 65 + 65/0.05 = 1365

the price of the bond today with concept of probability = 0.35*877.5+0.65*1365 = $ 1194.65

Answer 2) with the increase of interest rate , the value of the bonds will fall. so, company will not call them.

P1 =C + C/0.08

as premium is not fixed , the price of the bonds if interest rates fall will be P1= ($1,000 + C) + C => P1= 1000+2C

Using the both equation together

=> C = 1000/(11.5)=$ 86.95

C= 8.695% coupon rate.

Answer 3) the value of the call provision = Difference between non-callable bond and non-callable bond.

=[0.65 ×($1,365 – 877.5)] / 1.09 = $ 290.711