Question

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8. Valuing Callable Bonds Canton Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 7 percent, payable annually. The one-year interest rate is 7 percent. Next year, there is a 35 percent probability that interest rates will increase to 9 percent, and there is a 65 percent probability that they will fall to 6 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 cou- pon 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?

Answer 1

Calculate the market value of the bond if interest rate increased as follows: Interest rate P = Coupon + Coupon =S70 + 570 9% = $70+$777.777777777778 = $847.777777777778 or $847.78 Calculate the market value of the bond if interest rate decreased as follows: P1 = Coupon+ Coupon Interest rate =S70 +370 = $70+$1,166.66666666667 = $1,236.66666666667 or $1,236.67 Calculate the present value as follows: 0.35x5847.78 +0.65 x $1,236.67 1+ 7% $296.72 +5803.83 1.07 = $1,028.56

b. Calculate the coupon rate as follows: 00 If the interest rate increased the price of the bond is P =C+ de If the interest rate falls, the price of the bond is P2 =($1,000+C)+C =$1,000 + 20 0.35*{c+C+0.65X($1,000 +2C) Po=— 0.35x{C+ +0.65*($1,000 + 2C) 1+7% 1.07 $1.000 = C = $80.94 $80.94 Coupon rate= $1,000 = 0.08094 or 8.09%

Calculate the call provision as follows: Call provision = 0.65% Call provision =0.65*( -($1,000+c)) = 0.65% (S$0.94-(S1.00+80.94) =0.65X($1.349-51.080.94) = $174.24