A firm needs $1.5 million of new long-term financing. The firm is considering the sale of common stock or a convertible bond. The current market price of the common stock is $16 per share. To sell this new issue, the stock would have to be underpriced by $1 and sold for $15 per share. The firm currently has 600,000 shares of common stock outstanding. The alternative is to issue 30-year, 8 percent, and $1,000 par-value convertible bonds. The conversion price would be set at $20 per share, and the bond could be sold at par. The earnings for the firm are expected to be $700,000 in the coming year. Which plan results in less dilution of the earnings per share?

Question

Quizplus · Accepted Answer

To calculate the dilution of earnings per share (EPS), we need to calculate the new EPS after the issuance of either common stock or convertible bonds.

For the common stock option, the firm needs to sell 100,000 shares ($1.5 million / $15 per share) to raise the required funds. This will result in a total of 700,000 shares outstanding (600,000 existing shares + 100,000 new shares). The earnings for the firm are expected to be $700,000, so the EPS would be:

EPS (common stock) = Earnings / Total Shares Outstanding
EPS (common stock) = $700,000 / 700,000 shares
EPS (common stock) = $1.00

This means that the issuance of common stock will dilute the EPS to $1.00.

For the convertible bond option, we need to calculate the number of shares the bondholders can convert their bonds into. The conversion price is $20 per share, and each bond has a face value of $1,000, so the number of shares per bond is:

Number of shares per bond = Face Value / Conversion Price
Number of shares per bond = $1,000 / $20 per share
Number of shares per bond = 50 shares

The firm needs to issue $1.5 million in convertible bonds, so the number of bonds to issue is:

Number of bonds = Total Amount / Face Value
Number of bonds = $1.5 million / $1,000 per bond
Number of bonds = 1,500 bonds

This means that the total number of shares after the conversion of all bonds will be:

Total shares after conversion = Number of bonds x Number of shares per bond
Total shares after conversion = 1,500 bonds x 50 shares per bond
Total shares after conversion = 75,000 shares

Adding the existing shares, the total number of shares outstanding will be:

Total Shares Outstanding = Existing Shares + Shares from Conversion
Total Shares Outstanding = 600,000 shares + 75,000 shares
Total Shares Outstanding = 675,000 shares

The EPS for the convertible bond option would be:

EPS (convertible bond) = Earnings / Total Shares Outstanding
EPS (convertible bond) = $700,000 / 675,000 shares
EPS (convertible bond) = $1.04

This means that the issuance of convertible bonds will result in less dilution of EPS than the issuance of common stock, as the EPS will only be diluted to $1.04 compared to $1.00. Therefore, issuing convertible bonds is the better choice.

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