Question

In the absence of the conversion feature, the current yield is calculated as the annual coupon divided by the market price, which is 4.75%/0.91 = 5.22%. The yield to maturity is the internal rate of return on the bond and is calculated as the annual interest plus any gain or loss on the bond if held to maturity, divided by the current market price. As there is no gain or loss if held to maturity, the yield to maturity is equal to the current yield, which is 5.22%.

The conversion ratio of the debenture is the number of shares that the debenture can be converted into divided by the face value of the debenture. The conversion ratio can be calculated as follows:

Conversion ratio = Face value of debenture / Conversion price Conversion ratio = $1,000 / $47 Conversion ratio = 21.28 shares per debenture

If the conversion ratio were 50, the conversion price would be calculated as follows:

Conversion price = Face value of debenture / Conversion ratio Conversion price = $1,000 / 50 Conversion price = $20

The conversion value is the market price of the common stock multiplied by the conversion ratio. The conversion value can be calculated as follows:

Conversion value = Conversion ratio x Market price of common stock Conversion value = 21.28 x $41.50 Conversion value = $882.80

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

The bond value in the absence of a conversion feature is 65% of the face value, or $650. To find the stock price at which the conversion value equals the bond value, we can set the conversion value equal to $650 and solve for the stock price:

Conversion value = Bond value Conversion ratio x Market price of common stock = 0.65 x Face value of debenture 21.28 x Stock price = 0.65 x $1,000 Stock price = $30.83

To find the stock price at which the conversion value equals the bond value:

Conversion ratio x Stock price = Bond value

21.28 x Stock price = $650 Stock price = $30.53

The market price can be less than the conversion value, but in general, the market price of a convertible bond should not be lower than the conversion value, as this would make it more attractive for investors to buy the bond and convert it to stock, putting upward pressure on the stock price.

Convertible holder pays = Market price – Bond value in the absence of conversion

Bond value = 65% x Face value

Bond value = $650

Market price = 91% x Face value

Market price = $910

Convertible holder pays = $910 – $650

Convertible holder pays = $260

To justify conversion, the common stock price needs to rise enough to compensate for the difference between the bond value and the conversion value. The convertible holder pays $650 for the bond but can convert it to stock worth $882.80 (assuming a conversion ratio of 21.28 shares per debenture and a market price of $41.50 per share). Therefore, the common stock price needs to rise by:

Common stock price increase = Conversion value – Bond value Common stock price increase = $882.80 –

Common stock price increase = $882.80 – $650 = $232.80

This means that the common stock price needs to rise by $232.80 to compensate for the difference between the bond value and the conversion value and justify the conversion.

Since the conversion ratio is 21.28, the common stock price needs to rise by:

$232.80 / 21.28 = $10.94

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