# A Complete Breakdown of the Diluted EPS Formula

The Diluted EPS formula is a metric that describes a company’s earnings power versus its shares outstanding in the stock market.

Diluted EPS varies from basic EPS because it assumes all convertible securities of the company are converted into common stock. Convertible securities refers to the company’s preferred shares, employee stock options, warrants, and debentures, if any.

Editor’s Note: This is a guest contribution by Christina Pomoni.

## Diluted EPS or Basic EPS?

The income statement of a company gives you an idea of how profitable a firm is as a whole. However, as an investor, you want to know how much of that value accrues to each share you own.

Basic EPS helps with this, but without taking into account any potential dilution. The Basic Earnings Per Share formula is:

Net income divided by the number of shares outstanding during the same period.

Therefore, if the net income is \$1,250,000 and the number of shares outstanding is 800,000, the basic EPS is \$1,250,000 / 800,000 = \$1.56. If the number of shares outstanding changes during the accounting period, you need to use the average number of shares:

Number of shares outstanding at the beginning of period = 800,000
Number of shares outstanding at the end of period = 300,000

Basic EPS = \$1,250,000 / [(800,000 + 300,000)/2]
= \$1,250,000 / 550,000
= \$2.27

Notice that the basic EPS increases as the number of shares decreases. Nevertheless, the calculation of the basic EPS is straightforward.

On the other hand, the diluted EPS adjusts the number of shares by considering all the potential dilution that a company can be subject to. Dilution lowers the reported EPS because it increases the weighted number of shares outstanding.

Consider this: in the previous example, the company issues 300,000 more common stocks following a conversion of employee stock options. In this case:

Diluted EPS = \$1,250,000 / [(800,000 + 300,000)/ 2 + 300,000]
= \$1,250,000 / 850,000
= \$1.47

Here is the entire picture of the basic EPS and the diluted EPS calculations.

## Where to Find and How to Calculate the Diluted EPS

Diluted EPS is normally provided in the firm’s income statement. The reason for stating diluted EPS is so that you know, as an investor, how the company attributes its earnings per share and how these earnings can be reduced, should the company use its convertible securities.

Here is where you can find diluted EPS in an income statement:

Notice that the diluted number of shares is higher than the basic weighted average shares, and therefore, the diluted EPS is lower than the basic EPS.

Another way to get the diluted EPS is using the diluted EPS formula:

Diluted EPS= (Net Income – Preferred Dividends) / Weighted Average Number of Dilutive Common Shares

The diluted EPS formula seems straightforward; yet, things get complicated when it comes to calculating diluted shares with stock options involved. In fact, when a company issues stock options, you need to consider how many shares could be bought if the stock options were converted into common stocks.

For example, a company exercises 200,000 stock options at a strike price of \$15, thereby paying \$3,000,000. If the stock currently trades at \$85.54, the value of options in shares is \$3,000,000 / \$85.54 = 35,071. Therefore, the diluted shares are the difference between the options issues and the value of options in shares, so 200,000 – 35,071 = 164,929 shares.

Also, the company has preferred dividends of \$1,850,000, and 5,000 bonds at an interest rate of 10%, which are convertible into 15 shares each.

Therefore:

Now, you can apply the diluted EPS formula as follows:

Diluted EPS = (Net Income – Preferred Dividends + Bond Interest) / Diluted Shares + Stock Options + Convertible bonds
= [(\$10,000,000 – \$1,850,000) + (\$75,000 x 10%)] / (164,929 + \$3,000,000 + \$75,000)
= (\$8,150,000 + \$7,500) / \$3,239,929 = \$8,157,500 / \$3,239,929
= \$2.52

Note that in the numerator we are adding the bond interest expense because the diluted EPS assumes that the bond conversion takes place at the beginning of the accounting period. Similarly, in the denominator we are taking into account the diluted shares as calculated above, the conversion of the bond and the exercise of the stock options.

A very common way that companies employ to lower the number of shares outstanding, thereby increasing EPS, is the share repurchase or share buyback. The share buyback is a good way to increase the EPS, yet it doesn’t actually change the firm’s operating cash flows.

Consider this:

A company has a net income of \$1,250,000 and 800,000 shares outstanding, so the EPS is \$1.56. The current stock price is \$65.25, so the equity is \$52,200,000 (\$65.25 x 800,000). The company uses its free cash flows for investment opportunities and debt repayment and has a payout ratio of 58%, which is set for distribution to the shareholders. Earnings growth is 5%, and ROE is 11%.

Here are the inputs:

The company’s management decides a share buyback of 58%. Based on the earnings growth of 5%, the net income becomes \$1,250,000 x (1+5%) = \$1,312,500. So, the repurchase cash is \$1,312,500 x 58% = \$761,250.

The share buyback can signal to investors that the company considers the stock undervalued. This can lead to investors buying more shares, causing the price to rise.

Say the stock price rises to \$65.25 x (1+11%) = \$72.43. Now, the company’s equity is (\$72.43 x 800,000) – \$761,250 = \$57,180,750.

So, the new number of shares outstanding is \$57,180,750 / \$72.43 = 789,489. The new EPS is \$1.66.

Here is the situation before and after the repurchase:

Following the share buyback, the company has lowered its number of shares and has increased its EPS. Investors have taken the move as a positive signal, expecting that cash will be returned to them when free cash flows are available in excess of the company’s financing needs.

Moreover, share buyback serves as an incentive for stock options to offset their potential dilutive effect. All these expectations are beneficial to the shareholder because the company uses its free cash flows to reinvest in itself.

On the other hand, the firm’s operating cash flows have not changed. The EPS is higher because the number of shares is lower and the net income has grown. So, the share buyback tends to push the price up, but technically it could go up or down.

Nevertheless, the diluted EPS is a valuable metric for investors and financial analysts to evaluate the earnings of a company on the basis of its shares outstanding as well as a potential dilution of its convertible securities.

Updated: 8/04/22

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