Basic and Diluted EPS

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.

Simple vs. Complex Capital Structures

A company’s capital consists of equity and debt. Certain equity types have priority over others, and some debt, along with other instruments, can be converted into equity.

According to IFRS, the equity type for which earnings per share (EPS) is calculated is known as ordinary equity. Ordinary shares rank below all other equity types. Essentially, ordinary shareholders are the company’s owners—the equity holders who are last in line to be paid in company liquidation and who stand to gain the most when the company performs well.

Under US GAAP, this ordinary equity is called common stock or common shares, reflecting the terminology used in the US.  We will use the terms “ordinary shares,” “common stock,” and “common shares” interchangeably, at least for this matter.

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 a company’s common shareholders and the weighted average number of outstanding shares.

Companies are required to report both basic and diluted EPS.

Basic EPS

Basic EPS is the amount of income available to common shareholders divided by the weighted average number of common shares outstanding over a period. In this case, income that is accessible to ordinary shareholders is the net income left over after any preferred dividends have been distributed.

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’- amount of income available to common shareholders,

‘weighted average number of outstanding shares‘ – time weighting of outstanding common shares.

Example: Calculating Basic EPS

For the fiscal year ending on December 31, 2020, Fisher Enterprises reported a net income of USD 3,400,000. The company declared and paid USD 300,000 in dividends on preferred stock. The company’s common stock share information is presented in the following table:

$$\begin{array}{l|c}
\text{Shares outstanding on January 1, 2020} & 1,200,000 \\ \hline
\text{Shares issued on March 1, 2020} & 300,000 \\ \hline
\text{Shares repurchased (treasury shares) on September 1, 2020} & (150,000) \\ \hline
\text{Shares outstanding on December 31, 2020} & 1,350,000 \\
\end{array}$$
The company’s basic earnings per share (EPS) for the year is closest to:
Solution

The first step is to calculate the weighted average number of shares outstanding based on the duration each share quantity was outstanding:
1,200,000 shares × (2 months/12 months) = 200,000
1,500,000 shares × (6 months/12 months) = 750,000
1,350,000 shares × (4 months/12 months) = 450,000
Weighted average number of shares outstanding = 1,400,000
As such, Fisher Enterprise’s Basic EPS is:
$$\begin{align}\text{Basic EPS} &=\frac{\text{ (Net income – Preferred dividends)}}{\text{Weighted average number of shares}}\\& =\frac{\text{(USD 3,400,000 – USD 300,000)}}{\text{1,400,000}}\\& = \text{USD}\  2.21\end{align}$$

Diluted EPS

Note that when a company has a simple capital structure (lacks any financial instruments that could potentially dilute earnings), its basic earnings per share (EPS) will be the same as its diluted EPS. On the other hand, if the company possesses financial instruments that could dilute earnings, its diluted EPS might vary from its basic EPS. By definition, diluted EPS is always equal to or less than basic EPS.

We shall consider three potential categories of dilutive financial instruments diluted EPS:

1. Convertible preferred stock.
2. Convertible debt.
3. Employee stock options.

Diluted EPS: If-Converted Method (Convertible Preferred Stock)

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.

Note that conversion of convertible shares 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 because, due to conversion, the company will no longer pay preferred dividends.

Therefore, the formula for calculating diluted EPS using the if-converted method for preferred stock is given as follows:

$$ \text{Dilutes EPS}=\frac{\text{Net Income}}{(\text{Weighted average number of outstanding shares} \\ + { \text{New common shares that would have been issued} \\ \text{at conversion)}}} $$

Example: Calculating Diluted EPS using the If-Converted Method (Convertible Preferred Stock)

As of December 31, 2022, a hypothetical company, Vista Utilities, reported a net income of USD 2,250,000. Over the year, the company had an average of 600,000 shares of common stock outstanding, 25,000 shares of convertible preferred stock, and no other potentially dilutive financial instruments. Each share of preferred stock pays an annual dividend of USD 12 and is convertible into 6 shares of Vista Utilities’ common stock.

Vista Utilities’ basic and diluted earnings per share (EPS) are closest to:

Solution

Should the 25,000 shares of convertible preferred stock be converted, Vista Utilities would issue an additional 150,000 shares of common stock (6 shares of common for each of the 25,000 shares of preferred).

Without the conversion, the company would not need to disburse preferred dividends totaling USD 300,000 (25,000 shares of preferred at USD 12 per share). Therefore, the company’s basic EPS would be USD 3.25, and its diluted EPS would be USD 2.81, as illustrated in the modified table:

$$\begin{array}{l|c|c}
& \text{Basic EPS} & \text{Diluted EPS Using}\\
&&\text{If-Converted Method} \\ \hline
\text{Net income} & \text{USD2,250,000} & \text{USD2,250,000} \\ \hline
\text{Preferred dividend} & -300,000 & 0 \\ \hline
\text{Numerator} & \text{USD1,950,000} & \text{USD2,250,000} \\ \hline
\text{Weighted average number}&&\\
\text{of shares outstanding} & 600,000 & 600,000 \\ \hline
\text{Additional shares}&&\\
\text{issued if preferred converted} & 0 & 150,000 \\ \hline
\text{Denominator} & 600,000 & 750,000 \\ \hline
\text{EPS} & \text{USD3.25} & \text{USD3.00}
\end{array}$$

Diluted EPS: If-Converted Method (Convertible Debt Oustanding)

Calculation of diluted EPS, whenever a company has a convertible outstanding debt, is also done using the if-converted method. In other words, Diluted EPS is determined under the assumption that convertible debt was converted into equity at the start of the period. If the conversion of debt to equity had occurred, there would no longer be any outstanding debt securities but rather a greater number of common stock shares. Moreover, had this conversion happened, the company would not have incurred interest expenses on the convertible debt, thereby boosting the net income available to common shareholders by the interest expense amount after taxes.

As such, the formula for calculating diluted EPS using the if-converted method for convertible debt is given by:

$$ \text{Diluted EPS}= \frac{ \left(\text{Net Income} \\ + \text{After-tax Interest on Convertible Debt} \\ – \text{Preferred Dividends} \right)}{(\text{Weighted Average Number of Outstanding shares} \\ + {\text{Additional Common Shares that would have been} \\ \text{Issued at Conversion)}}} $$

Example: Calculating Diluted EPS using the If-Converted Method (Convertible Debt Oustanding)

For the fiscal year concluding on December 31, 2022, a hypothetical company, TechGenix Limited, reported a net income of USD 825,000. The firm had a weighted average of 780,000 shares of common stock outstanding. The company’s potential dilutive securities include USD 60,000 of 5 percent convertible bonds, which are convertible into a total of 15,000 shares of common stock. With a tax rate of 25 percent, compute the basic and diluted earnings per share (EPS) for TechGenix Limited.

Solution

Consider the following table:

$$
\begin{array}{l|c|c}
& \text{Basic EPS} & \text{Diluted EPS Using}\\
&&\text{If-Converted Method} \\ \hline
\text{Net income} & \text{USD 825,000} & \text{USD 825,000} \\ \hline
\text{After-tax cost of interest} & & \text{USD 2,250} \\ \hline
\text{Numerator} & \text{USD 825,000} & \text{USD 827,250} \\ \hline
\text{Weighted average number of}&&\\
\text{shares outstanding} & 780,000 & 780,000 \\ \hline
\text{If converted} & 0 & 15,000 \\ \hline
\text{Denominator} & 780,000 & 795,000 \\ \hline
\text{EPS} & \text{USD 1.06} & \text{USD 1.04} \\
\end{array}
$$

The diluted EPS in the above table is calculated as:

$$\begin{align}\text{Diluted EPS}&= \frac{ \left(\text{Net Income} \\ + \text{After-tax Interest on Convertible Debt} \\ – \text{Preferred Dividends} \right)}{(\text{Weighted Average Number of Outstanding shares} \\ + {\text{Additional Common Shares that would have been} \\ \text{Issued at Conversion)}}}\\ &=\frac{825,000+((1-0.25) \times 0.05\times 60,000)-0}{780,000+15,000}\\ &=\frac{825,000 + (0.75 \times 0.05 \times 60,000)}{795,000}\\ &=\frac{825,000 + 2,250}{795,000}\\ &=\frac{827,250}{795,000}\\ &=1.04\end{align}$$

Note that If the convertible bonds were converted, the bond liability would cease to exist, and instead, TechGenix Limited would have an additional 15,000 shares of common stock outstanding. Also, if the bonds were converted, the company would save on interest payments of USD 3,000 (5 percent of USD 60,000), increasing the net income for common shareholders by USD 2,250 after taxes [= USD 3,000 × (1 – 0.25)].

Diluted EPS: The Treasury Stock Method

When a company possesses financial instruments like stock options or warrants, the computation of diluted earnings per share (EPS) assumes these instruments are exercised. The company utilizes the proceeds from this exercise to buy back as many shares of its common stock as it can at the period’s average market price.

Consequently, the diluted EPS calculation adjusts the weighted average number of shares outstanding, increasing it by the net amount of shares issued upon the exercise of the instruments minus the shares that could be bought back with the exercise proceeds. Under US GAAP, this approach is referred to as the treasury stock method, as it often leads to companies holding the repurchased shares as treasury stock. Although not explicitly named, IFRS employs the same technique for such calculations.

Generally speaking, in determining diluted EPS with this technique, the hypothetical exercise of these financial instruments is presumed to result in:

• The company receiving cash in return for issuing new shares upon the exercise.
• The company utilizing the cash gained to buy back shares at the period’s weighted average market price.

As such, the formula to calculate diluted EPS using the treasury stock method for options is given as:

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

Example: Calculating Diluted EPS using the If-Converted Method (Treasury Stock Method)

Advanced Robotics Inc., a hypothetical company, disclosed a net profit of USD 1.5 million for the fiscal year ending December 31, 2023, with an average of 950,000 ordinary shares outstanding throughout the year. At the start of the fiscal year, Advanced Robotics had issued 25,000 warrants with a strike price of USD40 each. No other convertible financial instruments were present. During the year, the average market value of the firm’s stock was USD60 per share.

The basic and diluted earnings per share (EPS) for the company are closest to:

Solution

Applying the treasury stock method, we compute that the exercise of all warrants would have generated USD1 million (USD40 for each of the 25,000 warrants). These warrants would not be open; the company would have an additional 25,000 shares in circulation. The treasury stock method assumes that the company would use the proceeds from the warrant exercises to buy back shares at the average market price. With the USD1 million from the warrant exercises, Advanced Robotics could repurchase 16,667 (=1,000,000/60) shares at USD60 each. Thus, the incremental share count is 8,333 (25,000 original warrants less 16,667 shares repurchased). The diluted EPS calculation does not adjust the numerator. The new figures reveal that the basic EPS for Advanced Robotics was USD1.58, while the diluted EPS was USD1.55.

To represent this numerically, you could use a similar table format:

$$
\begin{array}{l|c|c}
& \textbf{Basic EPS} & \textbf{Diluted EPS Using}\\
&&\textbf{Treasury Stock Method} \\ \hline
\text{Net Income} & \text{USD 1,500,000} & \text{USD 1,500,000} \\ \hline
\text{Numerator} & \text{USD 1,500,000} & \text{USD 1,500,000} \\ \hline
\text{Weighted average number}&&\\
\text{of shares outstanding} & 950,000 & 950,000 \\ \hline
\text{If converted} & 0 & 8,333 \\ \hline
\text{Denominator} & 950,000 & 958,333 \\ \hline
\text{EPS} & \text{USD 1.58} & \text{USD 1.57} \\
\end{array}
$$

Note that the diluted EPS above is calculated as:

$$\begin{align} \text{Diluted EPS}&=\frac{(\text{Net Income} – \text{Preferred Dividends})}{ \text{Weighted Average Number of Outstanding Shares} \\ + (\text{New Shares that would have been purchased with Cash Received upon Exercise} \\ – \text{Shares that could have been purchased with cash received upon exercise} \\ \times \text{Proportion of year during which the Financial Instruments were Outstanding})} \\&=\frac{\text{USD}\ 1,500,000-0)}{950,000 +[(25,000-16,667)\times 1]}=1.57\end{align}$$

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 diluted 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: Showing the Antidilutive Effect

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:

$$ \text{Dilutes EPS}=\frac{\text{Net Income}}{(\text{Weighted average number of outstanding shares} \\ + { \text{New common shares that would have been issued} \\ \text{at conversion)}}} $$

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?

1. The company has a simple capital structure with a basic EPS of $5.00.
2. The company has a complex capital structure with a diluted EPS of $5.00.
3. 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.