Fifteen years ago, Roop Industries sold $400 million of convertible bonds. The bonds had a 40-year maturity, a 5.75% coupon rate, and paid interest
annually. They were sold at their $1,000 par value. The conversion price was set at $62.75, and the common stock price was $55 per share. The bonds were
subordinated debentures and were given an A rating; straight nonconvertible debentures of the same quality yielded about 8.75% at the time Roop"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 Roop"s annual before-tax interest savings on the convertible issue versus a straight-debt issue?
c. At the time the bonds were issued, what was the value per bond of the conversion feature?
d. Suppose the price of Roop"s common stock fell from $55 on the day the bonds were issued to $32.75 now, 15 years after the issue date (also assume the
stock price never exceeded $ XXXXXXXXXXAssume interest rates remained constant. What is the current price of the straight-bond portion of the convertible
bond? What is the current value if a bondholder converts a bond? Do you think it is likely that the bonds will be converted?
e. The bonds originally sold for $1,000. If interest rates on A-rated bonds had remained constant at 8.75% and if the stock price had fallen to $32.75,
then what do you think would have happened to the price of the convertible bonds? (Assume no change in the standard deviation of stock returns.)
f. Now suppose that the price of Roop"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 interest rate on similar straight debt had fallen from 8.75% to 5.75%. Under these conditions, what is the current price of the
straight-bond portion of the convertible bond? What is the current value if a bondholder converts a bond? What do you think would have happened to the
price of the bonds?