A zero-coupon, convertible bond promises to pay $30,000 at maturity and can be converted into 250 shares of the firm's stock. There are 1,000 of these bonds outstanding, and the firm has
500,000 shares of stock outstanding. At what level of firm value will the bondholders choose
To convert?

Question

Quizplus · Accepted Answer

The conversion ratio for each bond is 250 shares, and there are 1,000 bonds outstanding, so in total, 250,000 shares could be issued if all bondholders choose to convert.

Setting the value of the convertible bond equal to the conversion value (the value of the shares received from conversion), we get:

$30,000 = 250 x V
V = $120

Therefore, if the firm value exceeds $120 per share, bondholders would choose to convert. With 500,000 shares outstanding, the firm value would need to exceed $60 million for bondholders to choose conversion. Thus, the correct choice is (A). Each bond can be converted into 250 shares, so if all 1,000 bonds are converted, that would result in 250,000 additional shares of stock outstanding (250 shares/bond x 1,000 bonds = 250,000 shares). 
To find the level of firm value at which bondholders would choose to convert, we need to compare the value of the bond at maturity ($30,000) to the value of 250 shares of stock. If the stock is trading at a price greater than $120 per share ($30,000 / 250 shares), it would be more valuable to convert the bond into stock. 
Since there are 500,000 shares outstanding before the conversion and 250,000 additional shares after conversion (assuming all bonds are converted), the new total number of shares outstanding would be 750,000. 
Thus, at a firm value of $90 million ($120 per share x 750,000 shares), the stock price would exceed $120 per share and bondholders would likely choose to convert. Therefore, the correct answer is B.

A Zero-Coupon, Convertible Bond Promises to Pay $30,000 at Maturity