A three-year convertible bond with a face value of $100 has been issued by company ABC. It pays a coupon of $5 at the end of each year. It can be converted into ABC’s equity at the end of the first year or at the end of the second year. At the end of the first year, it can be exchanged for 3.6 shares immediately after the coupon date. At the end of the second year it can be exchanged for 3.5 shares immediately after the coupon date. The current stock price is $25 and the stock price volatility is 25%. No dividends are paid on the stock. The risk-free interest rate is 5% with continuous compounding. The yield on bonds issued by ABC is 7% with continuous compounding and the recovery rate is 30%.
(a) Use a three-step tree to calculate the value of the bond
(b) How much is the conversion option worth?
(c) What difference does it make to the value of the bond and the value of the conversion option if the bond is callable any time within the first two years for $115?
(d) Explain how your analysis would change if there were a dividend payment of $1 on the equity at the six month, 18-month, and 30-month points. Detailed calculations are not required.
(Hint: Use equation (24.2) to estimate the average hazard rate.)