A convertible bond has the following features (rounding allowed in answers): Fac

Question

A convertible bond has the following features (rounding allowed in answers):

Face Value: $1,000
Maturity: 10 years
Annual coupon: $80
Call Price: $1,100
Conversion Price: $50

I. The bond may be converted into how many shares?
II. What is the current value of the convertible as a bond if prevailing interest rates are 9%?
III. What is the current value of the convertible as a stock if the current stock price is $45 per share?
IV. Based on (II) and (III) and assuming a market premium of $50, what should the current price of the bond be?
V. Above, in question IV, if the prevailing interest declines to 7% and all else stays the same, should you sell the bond or hold it? Justify your answer.

Explanation / Answer

1) Convertible bonds:

To know the number of shares, divide the face value by the conversion price.

Number of shares = $1,000 / $50 = 20

2) Conversion value of bond = 20 shares X ($1000 X 9%) = $1,800

3) Conversion value of stock = 20 shares X $45 = $900

4) Conversion premium = $1800 - Current price of the bond

               $50                 = $1800 - Current price of bond

Current price of bond    = $1,750

5) Conversion value of bond = 20 shares X ($1000 X 7%) = $1,700

Conversion premium = $1700 - Current price of the bond

$50 = $1700 - Current price of bond

Current price of bond = $1,650

The bond cannot be sold for less price. Hence, it should be hold.

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