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 $64.15, and the common stock price was $58 per share. The bonds were subordinated debentures and were given an A rating; straight nonconvertible debentures of the same quality yielded about 8.85% 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 $58 on the day the bonds were issued to $37.00 now, 15 years after the issue date (also assume the stock price never exceeded $64.15). 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?

   -Select-YesNoItem 6

5. The bonds originally sold for $1,000. If interest rates on A-rated bonds had remained constant at 8.85% and if the stock price had fallen to $37.00, 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 -Select-decreasedincreasedItem 7 from $   at the time of issue to $   fifteen years later.

6. Now suppose that the price of Roop's common stock had fallen from $58 on the day the bonds were issued to $37.00 at present, 15 years after the issue. Suppose also that the interest rate on similar straight debt had fallen from 8.85% 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

   What do you think would have happened to the price of the bonds?

   -Select-The price of the bonds will be slightly more than $1,000.The price of the bonds will be slightly less than $1,000.The price of the bonds will not change.Item 12

Answer 1

a.

Premium on bonds(percentage excess of the conversion price over the stock price =

=[(value of convertibile bonds- common stock price)/ stock price]*100 = ($64.15-$58)/$58*100 = 10.60%

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b.

Annual before tax interest savings =

= [interest on straight non convertible debentures- interest on convertible debentures]* value of the debentures

=[8.85%-5.75%]* $400 Million = $12.40 Million per year.

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c.

Intrinsic Value of the convertible bond = Present value of the future cash flows discounted at normal interest rate

Face value = $1000

N or tenure = 40 years

R or annual normal interest rate = 8.85%

Annual interest per debenture= $1000*5.75% = $57.5

Intrinsic value of the convertible bond = ($57.5 * PVAF @8.85% for 40 Years)+ ($1000 * PVF @8.85% for 40th year)

=>($57.5*10.91931619) + ($1000*0.03364051726) = $661.50

Value per bond of the conversion futures = Face value- Intrinsic value of the convertible bond = $1000-$661.50 = $338.50

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d.

value of the straight bond calculation-

Face value = $1000

N = 40 years-15 years =25 years

Annual interest = $1000*5.75% = $57.5

rate = 8.85%

Current price of the straight bond = PV of the future cash flows

=> ($57.5 * PVAF @8.85% for 25 years ) +($1000*PVF @8.85% at 25th year)

=>($57.5*9.943165842) + ($1000*0.120029823) = $691.76.

Current value if the bond is converted :-

Converion ratio = par value per bond / converion price = $1000/$64.15 = 15.59shares

current value = number of share * price per share = 15.59* $37 =$576.83

As the bond price is more than the converted or conversion price , hence the bond will not be converted.

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e.

The value of the straight bond would have increased from $661.50 at the time of issue to $691.76, 15years later.

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f.

value of the straight bond calculation-

Face value = $1000

N = 40 years-15 years =25 years

Annual interest = $1000*5.75% = $57.5

rate = 5.75%

Current price of the straight bond = PV of the future cash flows

=> ($57.5 * PVAF @5.75% for 25 years ) +($1000*PVF @5.75% at 25th year)

=>($57.5*13.09274671) + ($1000*0.247167064) = $1000.

Current value if the bond is converted :-

Converion ratio = par value per bond / converion price = $1000/$64.15 = 15.59shares

current value = number of share * price per share = 15.59* $37 =$576.83

The price of the bonds will be slightly less than $1,000 as the price of the share price is decreasing.

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