Peabody Energy plans to issue a convertible bond in the near future. The bond will pay a $1,000 maturity value in exactly 30 years. The coupon rate will be 1 percent (with a semiannual coupon, of course). The holder of the bond will have the right, but not the obligation, to exchange the bond for 40 shares of Peabody Energy common stock at any time following the issue date.
Required: Estimate the market value of the Peabody Energy convertible bond. You should assume that the standard deviation of the return on Peabody common stock will be 40 percent. The TRACE reporting system is a reliable source of information on the value of Peabody’s outstanding debt. You may use the Black-Scholes option pricing model to value the embedded conversion option