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 firm's equity holders
Begin to receive a payout?

Question

Quizplus · Accepted Answer

To find the level of firm value at which the equity holders will receive a payout, we need to calculate the conversion price per share, which is the ratio of the face value of the bond ($30,000) to the number of shares into which it can be converted (250), or $120 per share. 
Since there are 1,000 zero-coupon convertible bonds outstanding, the total number of shares that could be issued upon conversion is 250,000 (250 x 1,000). 
To calculate the level of firm value at which the equity holders will receive a payout, we need to find the total value of the stockholders' equity, assuming all the bonds are converted. 
The total value of the stockholders' equity will be equal to the number of outstanding shares (500,000) plus the number of shares that could be issued upon conversion of the bonds (250,000), multiplied by the market price per share (P). 
Therefore, the formula for the total value of the stockholders' equity is:
Total value of stockholders' equity = (500,000 + 250,000)P
This will be equal to the total value of the firm when the equity holders break even with the debt holders. 
We know that the total face value of the bonds is $30,000 x 1,000 = $30,000,000. 
The firm value at which the equity holders will begin to receive a payout is when the total value of the stockholders' equity is greater than or equal to the total face value of the bonds. 
Therefore, we can set the equation equal to $30,000,000 and solve for P:
(500,000 + 250,000)P = $30,000,000
P = $30,000,000 / 750,000
P = $40
So the level of firm value at which the equity holders will begin to receive a payout is $40 per share x 750,000 shares = $30,000,000. 
Therefore, the correct answer is option B, when the firm value exceeds $30,000,000. Each bond can be converted into 250 shares, and there are 1000 bonds outstanding, which means there are 250,000 potential shares that can be created through conversion. To find the level of firm value where the equity holders begin to receive a payout, we need to calculate the total value of the bonds and compare it to the total firm value. The total value of the bonds is $30,000 x 1000 = $30,000,000. To reach a firm value where the equity holders begin to receive a payout, the firm would need to be worth at least $30,000,000 + the value of existing shares ($30,000,000 + $500,000,000 = $530,000,000). Therefore, the correct answer is B) when firm value exceeds $30,000,000.

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