###### Accounting Equations

Financial statement elements (assets, liabilities, owners’ equity, revenue and expenses) are used as... **Read More**

Both IFRS and US GAAP mandate the presentation of earnings per share (EPS) on the income statement, specifically for net profit or loss (net income) and profit or loss (income) from continuing operations. The method of calculating EPS varies, contingent on whether the company possesses a simple or complex capital structure.

A company is said to have a complex capital structure if it has issued any financial instrument potentially convertible into common stock (or ordinary shares). Examples of these financial instruments include convertible bonds, convertible preferred stock, and employee stock options. The company is said to have a simple capital structure if its capital structure does not include such potentially convertible financial instruments.

Financial instruments that are potentially convertible into common stock could dilute or decrease EPS due to an increase in ordinary shares after conversion. The EPS that results from the conversion of all dilutive financial instruments is called diluted EPS.

Basic EPS describes EPS that does not involve the conversion of dilutive financial instruments. It is calculated using the reported earnings available to common shareholders of a company and the weighted average number of outstanding shares.

Companies are required to report both basic and diluted EPS.

Basic EPS is computed as follows:

$$ \text{Basic EPS}=\frac{\text{Net income}-\text{Preferred dividends}}{\text{Weighted average number of shares outstanding}} $$

Where ‘net income – preferred dividends’ is the amount of income available to common shareholders, and ‘weighted average number of outstanding shares is a time weighting of outstanding common shares.

Basic EPS will equal diluted EPS whenever a company has a simple capital structure. However, if a company has a complex capital structure, then diluted EPS will be less than or equal to basic EPS.

**Calculation of Diluted EPS for Three Types of Potentially Dilutive Financial Instruments**:** Convertible Preferred**,** Convertible Debt**,** and Employee Stock Options**

- Calculation of diluted EPS, whenever a company has outstanding convertible preferred stock, is done using the if-converted method. The if-converted method looks at the effect of converting the convertible preferred shares at the beginning of the period. This results in a higher weighted average number of outstanding shares and a higher net income available to common shareholders than in the basic EPS calculation.$$ \text{Dilutes EPS}=\frac{\text{Net Income}}{(\text{Weighted average number of outstanding shares} \\ + { \text{New common shares that would have been issued} \\ \text{at conversion)}}} $$
- Calculation of diluted EPS, whenever a company has a convertible outstanding debt, is also done using the if-converted method.$$ \text{Diluted EPS}= \frac{ \left(\text{Net Income} \\ + \text{After-tax Interest on Convertible Debt} \\ – \text{Preferred Dividends} \right)}{(\text{Weighted Average Number of Outstanding shares} \\ + {\text{Additional Common Shares that would have been} \\ \text{Issued at Conversion)}}} $$
- Calculation of diluted EPS whenever a company has outstanding stock options, warrants, or their equivalents, is done as if the financial instruments had been exercised and the company used the proceeds to repurchase as many shares of common stock as possible at the average market price of common stock during the period. The methodology is called the treasury stock method under US GAAP.$$ \text{Diluted EPS}=\frac{(\text{Net Income} – \text{Preferred Dividends})}{ \text{Weighted Average Number of Outstanding Shares} \\ + (\text{New Shares that would have been purchased with Cash Received upon Exercise} \\ – \text{Shares that could have been purchased with cash received upon exercise} \\ \times \text{Proportion of year during which the Financial Instruments were Outstanding})} $$

Dilutive and anti-dilutive securities can impact the calculation of earnings per share (EPS) in opposite ways. It is, therefore, essential to ascertain whether including a financial instrument in the EPS calculation has dilutive or anti-dilutive properties.

Dilutive versus Anti-dilutive Securities and Implications for EPS Calculation

Dilutive securities are those financial instruments that are potentially convertible into common stock and could potentially dilute or decrease EPS due to the increase in the number of ordinary shares after conversion.

In contrast, some potentially convertible securities are anti-dilutive. This means their inclusion in the EPS calculation would result in higher EPS than the company’s basic EPS. Under both IFRS and US GAAP, however, these anti-dilutive securities are excluded from the calculation of diluted EPS.

As a rule, diluted EPS should always be less than or equal to basic EPS. Besides, it should reflect the maximum potential dilution from the conversion of potentially dilutive financial instruments.

Example of Basic and Diluted EPS

A company has a net income of $2,000,000, an average of 250,000 shares of common outstanding stock, and 10,000 shares of convertible preferred stock. Each preferred share pays a dividend of $13 per share and is convertible into one share of the company’s stock. What is the company’s basic and diluted EPS?

**Solution**

$$ \text{Basic EPS}=\frac{\text{Net income}-\text{Preferred dividends}}{\text{Weighted average number of shares outstanding}} $$

$$ \begin{align*} \text{Net income}–\text{Preferred dividend} & =\$2,000,000 – 10,000 \times \$13 \\

\text{Net income} – \text{Preferred dividend} &=\$2,000,000-\$130,000=\$1,870,000 \end{align*} $$

Therefore,

$$ \text{Basic EPS}=\frac{\$1,870,000}{250,000}=\$7.48 $$

Diluted EPS calculation using the equation:

$$ \text{Diluted EPS}=\frac{(\text{Net Income} – \text{Preferred Dividends})}{\text{Weighted Average Number of Outstanding Shares} \\ + (\text{New Shares that would have been purchased with Cash Received upon Exercise} \\ – \text{Shares that could have been purchased with cash received upon exercise} \\ \times \text{Proportion of year during which the Financial Instruments were Outstanding})} $$

If each convertible preferred stock is converted into one share, then, under the if-converted method, the company has an additional \(10,000 \times 1 = 10,000\) common outstanding stock, and no preferred dividend would be paid.

Therefore,

$$ \text{Diluted EPS}=\frac{\$2,000,000}{(250,000+10,000)}=\$7.69 $$

Given that this value is greater than the basic EPS of $7.48, the convertible preferred shares are said to be anti-dilutive. As such, the effect of their conversion would be excluded from the diluted EPS calculation. As a result, Diluted EPS = Basic EPS = $7.48.

## Question

If, at the end of its financial year, a company has a net income of $10 million, 2,000,000 shares of common outstanding stock, and no preferred stock or convertible financial instruments, which of the following is accurate?

- The company has a simple capital structure with a basic EPS of $5.00.
- The company has a complex capital structure with a diluted EPS of $5.00.
- The company has a complex capital structure with a diluted EPS of less than $5.00.

Solution

The correct answer is A.The company has a simple capital structure given that it does not have any potentially convertible financial instrument and has a basic EPS of $10,000,000/2,000,000 shares = $5.00.