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# Diluted Earnings per Share Formula

The Diluted Earnings per Share Formula

Diluted earnings per share is the profit for a reporting period per share of common stock outstanding during that period. The measurement includes the number of shares that would have been outstanding during the period if the company had issued common shares for all potential dilutive common stock outstanding during the period.

The reason for stating diluted earnings per share is so that investors can determine how the earnings per share attributable to them could be reduced if a variety of convertible instruments were to be converted to stock. Thus, this measurement presents the worst case for earnings per share. Earnings per share information only needs to be reported by publicly-held businesses.

If a company has more types of stock than common stock in its capital structure, it must present both basic earnings per share and diluted earnings per share information; this presentation must be for both income from continuing operations and net income. This information is reported on the company’s income statement.

To calculate diluted earnings per share, include the effects of all dilutive potential common shares. This means that you increase the number of shares outstanding by the weighted average number of additional common shares that would have been outstanding if the company had converted all dilutive potential common stock to common stock. This dilution may affect the profit or loss in the numerator of the dilutive earnings per share calculation. The formula is:

(Profit or loss attributable to common equity holders of parent company
+ After-tax interest on convertible debt + Convertible preferred dividends)
(Weighted average number of common shares outstanding during the period
+ All dilutive potential common stock)

You may need to make two adjustments to the numerator of this calculation. They are:

• Interest expense. Eliminate any interest expense associated with dilutive potential common stock, since you assume that these shares are converted to common stock. The conversion would eliminate the company’s liability for the interest expense.
• Dividends. Adjust for the after-tax impact of dividends or other types of dilutive potential common shares.

You may need to make additional adjustments to the denominator of this calculation. They are:

• Anti-dilutive shares. If there are any contingent stock issuances that would have an anti-dilutive impact on earnings per share, do not include them in the calculation. This situation arises when a business experiences a loss, because including the dilutive shares in the calculation would reduce the loss per share.
• Dilutive shares. If there is potential dilutive common stock, add all of it to the denominator of the diluted earnings per share calculation. Unless there is more specific information available, assume that these shares are issued at the beginning of the reporting period.
• Dilutive securities termination. If a conversion option lapses during the reporting period for dilutive convertible securities, or if the related debt is extinguished during the reporting period, the effect of these securities should still be included in the denominator of the diluted earnings per share calculation for the period during which they were outstanding.

In addition to the issues just noted, here are a number of additional situations that could impact the calculation of diluted earnings per share:

• Most advantageous exercise price. When you calculate the number of potential shares that could be issued, do so using the most advantageous conversion rate from the perspective of the person or entity holding the security to be converted.
• Settlement assumption. If there is an open contract that could be settled in common stock or cash, assume that it will be settled in common stock, but only if the effect is dilutive. The presumption of settlement in stock can be overcome if there is a reasonable basis for expecting that settlement will be partially or entirely in cash.
• Effects of convertible instruments. If there are convertible instruments outstanding, include their dilutive effect if they dilute earnings per share. You should consider convertible preferred stock to be anti-dilutive when the dividend on any converted shares is greater than basic earnings per share. Similarly, convertible debt is considered anti-dilutive when the interest expense on any converted shares exceeds basic earnings per share.
• Option exercise. If there are any dilutive options and warrants, assume that they are exercised at their exercise price. Then, convert the proceeds into the total number of shares that the holders would have purchased, using the average market price during the reporting period. Then use in the diluted earnings per share calculation the difference between the number of shares assumed to have been issued and the number of shares assumed to have been purchased.
• Put options. If there are purchased put options, only include them in the diluted earnings per share calculation if the exercise price is higher than the average market price during the reporting period.
• Written put options. If there is a written put option that requires a business to repurchase its own stock, include it in the computation of diluted earnings per share, but only if the effect is dilutive.
• Call options. If there are purchased call options, only include them in the diluted earnings per share calculation if the exercise price is lower than the market price.
• Compensation in shares. If employees are awarded shares that have not vested or stock options as forms of compensation, treat these grants as options when calculating diluted earnings per share. Consider these grants to be outstanding on the grant date, rather than any later vesting date.

Example of Diluted Earnings per Share

Lowry Locomotion earns a net profit of \$200,000, and it has 5,000,000 common shares outstanding that sell on the open market for an average of \$12 per share. In addition, there are 300,000 options outstanding that can be converted to Lowry’s common stock at \$10 each.

Lowry’s basic earnings per share is \$200,000 ÷ 5,000,000 common shares, or \$0.04 per share. Lowry’s controller wants to calculate the amount of diluted earnings per share. To do so, he follows these steps:

1. Calculate the number of shares that would have been issued at the market price. Thus, he multiplies the 300,000 options by the average exercise price of \$10 to arrive at a total of \$3,000,000 paid to exercise the options by their holders.
2. Divide the amount paid to exercise the options by the market price to determine the number of shares that could be purchased. Thus, he divides the \$3,000,000 paid to exercise the options by the \$12 average market price to arrive at 250,000 shares that could have been purchased with the proceeds from the options.
3. Subtract the number of shares that could have been purchased from the number of options exercised. Thus, he subtracts the 250,000 shares potentially purchased from the 300,000 options to arrive at a difference of 50,000 shares.
4. Add the incremental number of shares to the shares already outstanding. Thus, he adds the 50,000 incremental shares to the existing 5,000,000 to arrive at 5,050,000 diluted shares.

Based on this information, the controller arrives at diluted earnings per share of \$0.0396, for which the calculation is:

\$200,000 Net profit ÷ 5,050,000 Common shares

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