Basic and Diluted Earnings Per Share

Earnings per share is tested in FAR because it connects income statement presentation with the entity’s capital structure. A candidate must be able to compute basic EPS, identify potential common shares, decide whether each instrument is dilutive, and understand where EPS appears in public-company financial statements.

The exam focus is not whether EPS is useful to investors in general. The exam focus is whether the numerator, denominator, and presentation are correct when the fact pattern includes preferred dividends, midyear share changes, stock dividends, stock splits, options, warrants, convertible debt, convertible preferred stock, losses, or discontinued operations.

Basic EPS

Basic EPS measures income available to common shareholders per weighted-average common share actually outstanding. It does not assume conversion or exercise of potentially dilutive securities.

[ \text{Basic EPS} = \frac{\text{Net income} - \text{Preferred dividends}}{\text{Weighted-average common shares outstanding}} ]

The numerator is income available to common shareholders. Preferred dividends reduce that amount because preferred shareholders have a claim before common shareholders. For cumulative preferred stock, subtract the current-period preferred dividend whether declared or not. For noncumulative preferred stock, subtract the dividend only if declared.

The denominator is weighted-average common shares outstanding. Shares issued during the year are weighted for the portion of the year they were outstanding. Shares repurchased during the year stop being included after the repurchase date. Stock dividends and stock splits are treated retroactively because they change the unit of measure rather than raising new capital.

Weighted-Average Shares Example

Assume a company begins the year with 500,000 common shares outstanding, issues 120,000 shares on April 1, and repurchases 60,000 shares on October 1.

If net income is $1,250,000 and cumulative preferred dividends for the year are $100,000, basic EPS is:

[ \frac{1{,}250{,}000 - 100{,}000}{575{,}000} = $2.00 ]

Diluted EPS

Diluted EPS shows the lowest EPS that would result if dilutive potential common shares were converted or exercised. The calculation starts with basic EPS and then adjusts for instruments that would reduce EPS or increase loss per share.

[ \text{Diluted EPS} = \frac{\text{Adjusted income available to common shareholders}}{\text{Weighted-average common shares} + \text{Dilutive incremental shares}} ]

Potential common shares are included only if they are dilutive. An instrument is antidilutive if including it would increase EPS or reduce loss per share. Antidilutive instruments are excluded from diluted EPS, even if the securities are outstanding.

    flowchart TB
	    A["Start with basic EPS"] --> B["Identify potential common shares"]
	    B --> C["Options and warrants"]
	    B --> D["Convertible debt"]
	    B --> E["Convertible preferred stock"]
	    C --> F["Treasury stock method"]
	    D --> G["If-converted method"]
	    E --> G
	    F --> H["Include only incremental shares if dilutive"]
	    G --> I["Adjust numerator and denominator if dilutive"]
	    H --> J["Report diluted EPS"]
	    I --> J

Treasury Stock Method

Options, warrants, and similar instruments usually use the treasury stock method. The method assumes the instruments are exercised at the beginning of the period, or at issuance date if later. The assumed proceeds are then used to repurchase shares at the average market price for the period.

[ \text{Incremental shares} = \text{Shares issued on assumed exercise} - \frac{\text{Assumed proceeds}}{\text{Average market price}} ]

If the exercise price is higher than the average market price, the instrument is out of the money and antidilutive. If the exercise price is lower than the average market price, only the net incremental shares are added to the denominator. There is normally no numerator adjustment for options or warrants.

Example: 10,000 options are outstanding with an exercise price of $20. The average market price is $25.

If-Converted Method

Convertible debt and convertible preferred stock use the if-converted method. The method assumes conversion at the beginning of the period, or at issuance date if later, but only if the assumed conversion is dilutive.

For convertible debt, the interest addback is net of tax because avoiding interest would also remove the related tax benefit:

[ \text{After-tax interest addback} = \text{Interest expense} \times (1 - \text{tax rate}) ]

For convertible preferred stock, the addback is the preferred dividend because the assumed conversion means the preferred shares would no longer be outstanding as preferred shares.

Comprehensive EPS Example

Assume a company has net income of $2,000,000, cumulative preferred dividends of $100,000, weighted-average common shares of 1,000,000, 20,000 stock options with an exercise price of $30, an average market price of $50, and convertible bonds with $60,000 of annual interest, a 25 percent tax rate, and 50,000 shares issuable on conversion.

Basic EPS:

[ \frac{2{,}000{,}000 - 100{,}000}{1{,}000{,}000} = $1.90 ]

Options under the treasury stock method:

[ 20{,}000 - \frac{20{,}000 \times 30}{50} = 8{,}000 \text{ incremental shares} ]

Convertible bonds under the if-converted method:

[ 60{,}000 \times (1 - 0.25) = 45{,}000 \text{ after-tax interest addback} ]

Diluted EPS, assuming both instruments are dilutive:

[ \frac{1{,}900{,}000 + 45{,}000}{1{,}000{,}000 + 8{,}000 + 50{,}000} = $1.84 ]

The diluted amount is lower than basic EPS, so the potential common shares are dilutive. If adding a security raised EPS above the amount before adding it, that security would be excluded.

Presentation And Disclosure

Public companies with common stock or potential common stock generally present EPS on the face of the income statement. The presentation distinguishes basic EPS from diluted EPS and focuses first on continuing operations.

The notes generally reconcile the numerators and denominators used in basic and diluted EPS. They also identify securities excluded from diluted EPS because they were antidilutive. On the exam, an excluded security is not ignored because it is unimportant; it is ignored because including it would make diluted EPS less conservative.

Common Pitfalls

Key Takeaways

• Basic EPS uses actual weighted-average common shares and income available to common shareholders.
• Diluted EPS includes potential common shares only when they reduce EPS or increase loss per share.
• Options and warrants use the treasury stock method.
• Convertible debt and convertible preferred stock use the if-converted method.
• EPS presentation is tied to continuing operations, discontinued operations when applicable, and net income.

Earnings Per Share Knowledge Check