(a) Orange 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? (8 marks)

(b) E&F 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. (5 marks)

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