Parla International (PI) is in heavy equipment industry. The debt rating for PI is AA and the yield spread on AA rated bonds for five year maturity is 3% per year. The yield on a five year treasury is 4% per year. The company recently announced that it would issue convertible and callable bonds. The bonds will have no coupons and will have a maturity of five years. The price of the bond is $1000 and the bond will pay $1000 at the end of five years. The bond can be converted to 20 shares of PI stock at the end of two years and the issuer has the right to call the bond and pay $1100. The price of PI stock is $35. A call option on PI stock with an exercise price of $50 and maturity of five years is priced at $18. What is the value of the callable option? Use simple compounding and ignore any dilution effects.

Hint:

Callable-convertible bond price = (bond Price without options) + (Convertible Option) (Callable option)