Figuring info related to bonds 215

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; 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 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 that the stock price never exceeded $62.75). Assume interest rates remained constant. What is the current price of the straight bonds 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 the stock price had fallen to $32.75, 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 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 rate of interest 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?