Question

PKC Ltd is considering raising $120 million from the markets. In its recent management meeting, Winnie Poon, the CFO, suggested PKC to issue perpetual bonds with a face value of $1,000 each and a coupon rate of 8.1% paid annually. The current market interest rate is 8%. Winnie estimates a 0.3 probability that next year’s interest rate will increase to 10%, and a 0.7 probability that it will fall to 6%.

(a) Calculate the current market value of the perpetual bond If PKC issues perpetual bond based on Winnie’s suggestion . (Show your calculations).

(b) The CEO, John Lung, decides to include a call provision in the bond contract such that the bonds are callable in one year. Calculate the coupon rate of the callable bonds such that the bonds will be sold at par. Assume the bonds will be called if the interest rates fall and the call premium is $150. (Show your calculations).

(c) Suppose after evaluating market conditions, PKC finally issued callable bonds with a coupon rate of 8.2% paid annually, and the call premium is equal to 16% of the principal amount of bonds. The total principal amount of the bonds issued is $100 million. The firm is subject to a tax rate of 35%.

Assume it is now 1 year after the callable bonds were issued and the current market interest rate is 7.35%. PKC is considering calling back the callable bonds. If the transaction cost of refunding equals $1,000,000, should KPC call back the callable bonds? (Show your calculations).

Answer 1

(a) PV (perpetual bond) = Coupon payment/discount rate = $810/8% = $1012.50

(b) Price of callable bond = Price of straight bond - Price of call option

Price of callable bond = Par Value of bonds = $1000

Price of call option = $150

Price of straight bond = Coupon payment/discount rate = (Coupon rate*Par value) / 8%

Substituting, we get

Coupon rate = 9.20%

(c) Price of callable bond = Price of straight bond - Price of call option

Price of straight perpetual bond = Coupon payment/discount rate = $820/8% = $1025

Price of call option = Call premium = 0.16*$1000 = $160

Therefore, Price of callable bond = $1025 + $160 = $1185

The firm issued 100,000 of these bonds.