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# Basic and diluted EPS

Both IFRS and US GAAP require presentation of earnings per share (EPS) on the face of the income statement. EPS is used in many important ratios such as price to earnings (P/E) ratio, etc.

EPS is presented for ordinary shares (also called common stock or common share), shares which are subordinate to all other types of equity, and which represent the ultimate ownership of a company.

If a company has no securities which can be converted to ordinary shares, it is said to have a simple capital structure, otherwise, it is said to have a complex capital structure.

Companies are required to present both basic EPS and diluted EPS, both for total net income and for income from continuing operations.

## Basic EPS

Basic EPS is calculated by dividing earnings available to ordinary shares by the weighted average number of ordinary shares.

$Basic\ EPS=\frac{NI\ -P}{W}$

Where NI is net income, P is preferred dividends and W is the weighted average number of ordinary shares.

Preferred dividends are subtracted because they have a preferred claim over common stock.

The weighted average number of shares is calculated by time-weighting the number of shares. If the total number of shares changes due to stock dividend or split, it is adjusted retrospectively.

## Diluted EPS

Diluted EPS is the EPS calculated under the assumption that all dilutive financial instruments are converted. If a company has no convertible securities, basic EPS is equal to diluted EPS, otherwise diluted EPS is always less than the basic EPS. The important point to note is that not all convertible securities are dilutive.

If a company has convertible preferred stock, diluted EPS is calculated by assuming what would happen if those securities are converted. First, such a conversion would increase the numerator because there would no longer be any preferred dividend. Second, it would increase the number of shares outstanding. Diluted EPS of a company whose only convertible securities are preferred stock is calculated as follows:

$Diluted\ EPS=\frac{NI}{W\ +N}$

Where N refers to the new shares issued. The inherent assumption is that the conversion would occur at the start of the year.

If a company only has convertible debt, its conversion would increase numerator because no interest expense would be deducted, but this would also increase taxes. Hence, we need to add after-tax interest to net income minus preferred dividends. We also add the new number of shares to the denominator:

$Basic\ EPS=\frac{NI\ -P+I}{W+N}$

Where I is the after-tax interest on convertible debt.

$Basic\ EPS=\frac{NI\ -P}{W+(N-T)\times Y}$