The common stock of BioTech Industries pays a dividend of $1 per share and has a current market price of $27 per share. The convertible bond is selling for $1100. The payback or breakeven time for the bond is
A) 1.75 years.
B) 2.89 years.
C) 3.20 years.
D) 3.60 years.
E) 4.32 years.

Question

Quizplus · Accepted Answer

To calculate the payback or breakeven time for the convertible bond, we need to consider the conversion ratio, which is the number of shares that each bond can be converted into. Let's assume that the conversion ratio for this bond is 40, which means that each bond can be converted into 40 shares of BioTech Industries common stock.

The conversion value of the bond is the market value of the shares that can be obtained by converting the bond, and it is calculated as follows:

Conversion value = Conversion ratio × Market price per share
Conversion value = 40 × $27
Conversion value = $1,080

The premium of the bond is the difference between its market price and its conversion value, and it is calculated as follows:

Premium = Market price of bond - Conversion value
Premium = $1,100 - $1,080
Premium = $20

The breakeven time is the number of years required for the total value of the dividends received from owning the stock to exceed the premium paid for the bond. In this case, the annual dividend is $1 per share, so the total dividend yield is:

Dividend yield = Annual dividend / Market price per share
Dividend yield = $1 / $27
Dividend yield = 3.7%

To calculate the breakeven time, we can use the following formula:

Breakeven time = Premium / (Dividend yield × Conversion value)
Breakeven time = $20 / (3.7% × $1,080 × 40)
Breakeven time ≈ 2.89 years

Therefore, the best choice is B, with a breakeven time of 2.89 years.

The Common Stock of BioTech Industries Pays a Dividend of $1