Question

Convertible Bond Analysis

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 $61.20, and the common stock price was $54 per share. The bonds were subordinated debentures and were given an A rating; straight nonconvertible debentures of the same quality yielded about 8.30% at the time Roop's bonds were issued.

1. 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.

%

2. 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.

$   million per year

3. 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.

$   per bond

4. Suppose the price of Roop's common stock fell from $54 on the day the bonds were issued to $32.50 now, 15 years after the issue date (also assume the stock price never exceeded $61.20). 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.

$   per share

Do you think it is likely that the bonds will be converted?

· · The bonds originally sold for $1,000. If interest rates on A-rated bonds had remained constant at 8.30% and if the stock price had fallen to $32.50, 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.

· Now suppose that the price of Roop's common stock had fallen from $54 on the day the bonds were issued to $32.50 at present, 15 years after the issue. Suppose also that the interest rate on similar straight debt had fallen from 8.30% 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.

$   per bond

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

$   per share    

Answer 1

a). Bond premium = (conversion price/share price) -1 = (61.20/54)-1 = 13.33%

b). Annual before-tax earnings = (coupon rate on straight bond - coupon rate on convertible bond)*Debt amount

= (8.30%-5.75%)*400 = 10.20 million per year

c). Price of convertible bond: FV = 1,000; N = 40; PMT (annual coupon) = 5.75%*1,000 = 57.5; rate = 8.30%, solve for PV.

Price = 705.43

Value per bond of the conversion feature = par value - price = 1,000 - 705.43 = 294.57

d). Value as a straight bond: FV = 1,000; N = 40-15 = 25; PMT = 57.5; rate = 8.90%, solve for PV. Price = 734.63

Current value if bond is converted:

Conversion ratio = par value of bond/conversion price = 1,000/61.20 = 16.34 shares

Current value = number of shares*current share price = 16.34*32.5 = 531.05

The bond is worth more than the converted price so the bond will not be converted.

e). The value of the straight bonds would have increased from $705.43 at the time of issue to $734.63, fifteen years later.