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Problem

Maple Aircraft has issued a 4  convertible subordinated debenture due 2014. The conversion price is $47.00 and the debenture is callable at 102.75% of face value. The market price of the convertible is 91% of face value, and the price of the common is S41.50. Assume that the value of the bond in the absence of a conversion feature is about 65% of face value.

a. What is the conversion ratio of the debenture?

b. If the conversion ratio were 50, what would be the conversion price?

c. What is the conversion value?

d. At what stock price is the conversion value equal to the bond value?

e. Can the market price be less than the conversion value?

f. How much is the convertible holder paying for the option to buy one share of common stock?

g. By how much does the common have to rise by 2014 to justify conversion?

h. When should Maple call the debenture?

Step-by-step solution

The given details can be summarized as under:

Rate of interest = 4.75%

Maturity = 2014

Conversion price = $47.00

Callable value = 102.75% of face value

Market price = 91% of face value

Price of common stock = $41.50

Value of bond in case of no conversion = 65% of face value.

Comment

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Based on the above data, the answers to the questions can be given as below:

(a)

Computation of conversion ratio of the debenture:

The conversion ratio is the number of shares that each debenture is convertible into, usually stated per $100 par value of the bond. This ratio is known from the date of issuance and does not change over the lifetime of the bond.

Conversion price = $47.00

Callable value = 102.75%

Conversion value = $47 × 102.75%

= $48.29

Value per common stock share = $41.50

Conversion ratio =

= 1.16 shares.

Comment

Therefore, the conversion ratio is 1.16 shares.

Comment

(b)

Computation of conversion price, if the conversion ratio is 50 shares:

We have

Conversion ratio = 50 shares

Value of common stock per share = $41.50

Value of conversion = $41.50 × 50 shares

= $2,075

Since, the shares are converted at 102.75%, the conversion price has to be computed at 100%.

Conversion price =

= $2,019.

Comment

Therefore, the conversion price is $2,019.

Comment

(c)

Computation of conversion value:

The conversion value is the amount of conversion at market value. The market value of shares issued is 91% of face value. Hence, the conversion value is:

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Conversion value = 50 shares × $41.50 × 91%

= $1,888.25

Comment

Therefore, the conversion value is $1,888.25.

Comment

(d)

Computation of stock price at which bond price is equal to conversion value:

We have

Conversion value = Stock price × Call value of bond

$1,888.25 = Stock price × ($47.00 × 102.75%)

Stock price =

Stock price = $39.10

Comment

Therefore, the stock price is $39.10.

Comment

(e)

No, the conversion value is computed at the market price of the conversion price. Hence, it cannot be less than the market value.

Comment

(f)

Computation of amount to be payable for one share of common stock:

Total conversion value = $1,888.25

Conversion ratio = 50 shares

Amount to be paid per share =

= $37.77

Hence, the convertible debenture holder is paying $37.77 per share.

Comment

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(g)

Computation of value of common share at 2014:

If the common stock is to be valued at 2014, the conversion feature will be disabled and the value of the bond goes by 65%.

Actual conversion value = $1,888.25

Conversion value in 2014 = $1,888.25 × 165%

= $3,115.6125

Conversion ratio = 50 shares

Value per common share =

= $62.31

Price per common share = $41.50

Required price increase = $62.31 - $41.50

= $20.81 per share

Comment

(h)

If Maple calls the option immediately, then the company will get 46 shares ($1,885.25÷$41.50). If the company waits till 2014, the maturity, then the company will get 30 shares ($1,885.25 ÷ $62.31).

Hence, the company should call the debentures immediately.

Comment

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