Question

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 $63.30, and the common stock price was $51 per share. The bonds were subordinated debentures and were given an A rating; straight nonconvertible debentures of the same quality yielded about 8.70% 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. Do not round intermediate calculations. Round your answer to two decimal places.

b. What is Roop's annual before-tax interest savings on the convertible issue versus a straight-debt issue? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $25,500,000 should be entered as 25.5. Round your answer to two decimal places.

c. At the time the bonds were issued, what was the value per bond of the conversion feature? Do not round intermediate calculations. Round your answer to the nearest cent.

d.Suppose the price of Roop's common stock fell from $51 on the day the bonds were issued to $34.00 now, 15 years after the issue date (also assume the stock price never exceeded $63.30). Assume interest rates remained constant. What is the current price of the straight-bond portion of the convertible bond? Do not round intermediate calculations. Round your answer to the nearest cent. Enter all amounts as a positive number.

What is the current value if a bondholder converts a bond? Do not round intermediate calculations. Round your answer to the nearest cent.

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 8.70% and if the stock price had fallen to $34.00, 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.) Round your answers to the nearest cent. Enter all amounts as a positive number.

The value of straight bond would have from $ at the time of issue to $ fifteen years later.

f.Now suppose that the price of Roop's common stock had fallen from $51 on the day the bonds were issued to $34.00 at present, 15 years after the issue. Suppose also that the interest rate on similar straight debt had fallen from 8.70% to 5.75%. Under these conditions, what is the current price of the straight-bond portion of the convertible bond? Do not round intermediate calculations. Round your answer to the nearest dollar. Enter all amounts as a positive number.

What is the current value if a bondholder converts a bond? Do not round intermediate calculations. Round your answer to the nearest cent.

PLEASE SHOW WORK

Answer 1

Answer:

1. The premium on the bonds:

Premium on bond = (Market conversion price – current stock price) / current stock price*100

Premium on bond = (63.30 – 51) / 51 * 100 = 24.12%

1. Roop's annual before-tax interest savings on the convertible issue versus a straight-debt issue:

Annual before-tax interest savings = Payment of straight debt issue – Convertible bond payment

Payment of straight debt issue = 8.70% * 400,000,000 = $34,800,000

Convertible bond payment = 5.75% * 400,000,000 = $23,000,000

Annual before-tax interest savings = 34,800,000 – 23,000,000

                                                                    = $11,800,000

1. The value per bond of conversion feature:

Rate = 8.70%

Years to maturity = 40

Par value = $1000

Coupon rate = 5.75%

Payment = 1000 * 5.75% = $57.5

Future value = 1000

Using excel I have calculated the present value,

PV = $672.97

The bond was sold at par value,

The value per bond of conversion feature = $1000 - $672.97 = $327.03

   d. The current price of the straight-bond portion of the convertible bond:

The current price would be $672.97 (calculated in part c.)