A convertible bond has a 7.40 percent, semi-annual coupon and a conversation rat

Question

A convertible bond has a 7.40 percent, semi-annual coupon and a conversation rate of $31.25. The bond has a face value of $1,000 and matures in 11.5 years. The current yield to maturity for bonds of similar risk is 6.2 percent, but due to the bond’s convertible feature, it usually trades at a 5 percent premium over the non-convertible bond. Assume that you buy this bond today and sell or convert it to stock one year from now when the yield to maturity is 6.8 percent and the stock price is $38. What will be your return on this investment, and indicate whether you sold the bond or converted it to stock?

Explanation / Answer

Step 1: Calculation of Non convertible bond Current Price

                Price of Bond = Present value of coupons and redemption value

                Price of Bond = $31 / (1 + 0.031) 1 + …. + $1,031 / (1 + 0.031) 23

                Price of Bond = $1,097.64

Step 2: Calculation of price of Convertible Bond:

                Convertible bond are trading at a premium of 5% over non convertible bonds.

                Convertible bond price = $1097.64 * (1.05) = $1,152.52

When YTM increase, the price of bond decrease, than return on investment is equal to coupon amount / investment or price of bond

Return on investment = $31 / $1097.64 = 0.028 or 2.8%

Buy the bond instead of convert into stock because conversion results into high cash outflow.

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