# Diluted Earnings per Share

## Definition

The term diluted earnings per share refers to a hypothetical calculation that assumes all dilutive securities were converted to common stock.  The dilutive earnings per share calculation involves adjustments to earnings of the company as well as the number of shares outstanding.  Examples of dilutive securities include convertible bonds and preferred stock, warrants and stock options.

### Calculation

Where:

• Adjusted Earnings = Net Income - Preferred Dividends + Convertible Preferred Dividends + Convertible Bond Interest x (1 - Tax Rate)
• Adjusted Common Shares = Weighted Average Shares + Converted Preferred Shares + Converted Bond Shares + Shares from Issuable Stock Options and Warrants

### Explanation

Also referred to as fully diluted earnings per share, this measure is of interest to holders of common stock since it models what happens if all dilutive securities were converted.  Companies issue dilutive securities for a number of reasons.  Convertible bonds and preferred stock may include this feature to attract investors, while stock warrants may be issued to raise capital.

When calculating fully diluted EPS, securities that have an antidilutive effect should be excluded.  For example, if the exercise price of an option or warrant is greater than the market price, the conversion would be antidilutive.  If the exercise price were less than the market price of stock, the securities would be dilutive.

When the right to convert preferred stock and bonds is exercised, the number of shares of common stock outstanding will increase.  An increase to the denominator in the earnings per share equation will cause the value to decrease.  However, when this occurs, the company is no longer obligated to pay the dividend on the preferred stock or interest on the bonds that were converted.  This causes the numerator of the equation to increase, thereby partially offsetting the increase to the denominator.

### Example

In the current accounting period, Company A's net income was \$10,000,000 and the weighted average number of shares of common stock outstanding was 12,000,000.  The company had 10,000 bonds with a face value of \$1,000 and a coupon rate of 10.0%.  Each bond is convertible to 100 shares of common stock.

Company A also has 500,000 shares of \$10.00 preferred stock, which pay a dividend of 10.0%.  Each share of preferred stock can be converted to two shares of common stock.  Company A also has 1,000 stock options outstanding, allowing the holder to receive 5 shares of common stock.  The exercise price on the options is \$12.00.  Company A's common stock is currently trading at \$11.00 per share and its tax rate is 40%.

Company A's earnings per share would be calculated as follows:

= \$10,000,000 / 12,000,000, or \$0.833 per share

The fully diluted earnings per share would be calculated as follows:

Adjusted Earnings = Net Income - Preferred Dividends + Convertible Preferred Dividends + Convertible Bond Interest x (1 - Tax Rate)

= \$10,000,000 + 500,000 shares preferred x \$10.00 x 10% + 10,000 bonds x \$1,000 x 10.0% x (1 - 40%)
= \$10,000,000 + \$500,000 + \$600,000, or \$11,100,000

Note:  The above equation assumes all preferred stock is convertible to common shares; therefore, there are no remaining preferred dividends after conversion.

Adjusted Common Shares = Weighted Average Shares + Converted Preferred Shares + Converted Bond Shares + Shares from Issuable Stock Options and Warrants

= 12,000,000 + 500,000 preferred shares x 2 + 10,000 bonds x 100
= 12,000,000 + 1,000,000 + 1,000,000, or 14,000,000 shares