(3 points) In its most simple form, a convertible bond is similar to a fixed-rate bond with a provision that at maturity, the holders can choose to either receive the principal back, or convert the principal repayment into shares of the issuing company at a pre-determined conversion rate.

Suppose your company wants to raise funds by issuing this most simple form of convertible bonds. The bond will have a maturity of 3 years and will be issued at par (i.e., you sell the bond at its face value, $1,000). Coupons will be paid every year. At 3 maturity, each bond allows its holder to convert the principal repayment into 20 shares of your companys stock. The stock is currently traded at $40/share. Its volatility is 25% per annum. The current risk-free rate is 4% for all terms. Your companys credit rating is currently BBB. Typically, BBB-rated firms have to pay 3% p.a. more than the risk-free rate when they borrow. That is, if your company wanted to issue a straight bond (i.e., one with no conversion provision) now, it would have to pay 7% p.a. in coupons in order for the bond to be priced at par.

You were asked to set the coupon rate for the bond. Under a 3-period binomial framework, what coupon rate will you set? Note that according to bond convention, the coupon rate that you set will be in annual compounding because the bond in this case pays coupons every year. For example, if you set a coupon rate of 5% p.a., it means that every year the holder will receive $50.

[Hint: The buyers of your convertible bonds have an option. They pay for this option by having to accept a lower coupon rate on the bond.]