(a) Apple Bank is planning to issue callable perpetual annual coupon bonds with a par value of $10,000. The bonds are callable at $11,750. Interest rates for one year are 9%. The probabilities of long-term interest rates after one year being 10% and 8% are 0.6 and 0.4 respectively. Assume the bonds will be called if interest rates fall. What is the coupon rate such that the bonds will be sold at par?

(b) C&C Corporation issued an annual coupon convertible bond with a coupon rate of 9% and a face value of $1,000. The bond will mature 3 years from today. The market interest rate is 12%. The conversion ratio is 12 shares. The current stock price is $100 per share.

(i) Calculate the option value of the bond if each convertible bond is trading at $1,320.

(ii) Explain the meaning of your answer in part (i) above