Fifteen years ago, Roop Industries sold $400 million of convertible bonds. The bonds had a 40-year maturity, a 53⁄4 percent coupon rate, and were sold at their $1,000 par value. The conversion price was set at $62.75; the common stock price was $55 per share. The bonds were subordinated debentures, and they were given an A rating; straight nonconvertible debentures of the same quality yielded about 83⁄4 percent at the time Roopâ€™s bonds were issued.
a. Calculate the premium on the bonds, that is, the percentage excess of the conversion price over the stock price at the time of issue.
b. What is Roopâ€™s annual interest savings on the convertible issue versus a straight-debt issue?
c. Suppose the price of Roopâ€™s common stock fell from $55 on the day the bonds were issued to $32.75 now, 15 years after the issue date. Assume interest rates remained constant. Do you think it is likely that the bonds would have been converted? (Calculate the value of the stock you would receive by converting the bond.)
d. The bonds originally sold for $1,000. If interest rates on A-rated bonds had remained constant at 83⁄4 percent and the stock price had fallen to $32.75, what do you think would have happened to the price of the convertible bonds?
e. Now suppose the price of Roopâ€™s common stock had fallen from $55 on the day the bonds were issued to $32.75 at present, 15 years after the issue. Suppose also that the rate of interest had fallen from 83⁄4 to 53⁄4 percent. Under these conditions, what do you think would have happened to the price of the bonds?