14.3 Earnings Per Share (EPS)

Earnings Per Share (EPS)

Introduction and Presentation Requirements

Earnings Per Share (EPS) is one of the most widely used metrics in financial analysis. Under ASC 260, public companies (and companies that have filed or are in the process of filing registration statements with the SEC) are required to present EPS on the face of the Income Statement.

• Dual Presentation: Entities with a complex capital structure (defined as having potential common shares outstanding, such as options, warrants, convertible bonds, or convertible preferred stock) must present both Basic EPS and Diluted EPS for income from continuing operations and net income.
• Simple Capital Structure: Entities with only common stock, or common stock with no potentially dilutive securities, present only Basic EPS.

Basic Earnings Per Share

Basic EPS measures the earnings performance of the entity based on the actual common shares outstanding during the period.

The Basic EPS Formula

$\text{Basic EPS} = \frac{\text{Net Income} - \text{Preferred Dividends}}{\text{Weighted-Average Common Shares Outstanding (WACSO)}}$

1. Numerator Adjustment: Preferred Dividends

Preferred dividends are deducted from Net Income to arrive at income available to common stockholders. The deduction depends on the type of preferred stock:

• Cumulative Preferred Stock: Deduct the full annual contract dividend (dividend rate * par value * preferred shares outstanding) regardless of whether the dividend was declared or paid during the period.
• Non-Cumulative Preferred Stock: Deduct only the dividend declared during the current period.
• Net Loss Scenario: If the company reports a net loss, preferred dividends are still deducted, which increases the net loss available to common shareholders.

2. Denominator Adjustment: Weighted-Average Common Shares Outstanding (WACSO)

Common shares outstanding must be weighted based on the fraction of the period they were outstanding.

• Shares Issued or Repurchased: Shares issued for cash or retired/repurchased as treasury stock are weighted from the date of the transaction.
• Stock Dividends and Stock Splits: Unlike cash share issuances, stock dividends and stock splits do not add resources to the company. Therefore, they must be applied retroactively to the beginning of the period, as well as to all prior periods presented. If a stock split occurs after the fiscal year-end but before the financial statements are issued, the EPS calculation for the entire period must be adjusted retroactively.
• WACSO Example:
  • Jan 1: 100,000 shares outstanding
  • Apr 1: Issued 20,000 shares for cash (outstanding for 9/12 months)
  • Jul 1: Declared a 2-for-1 stock split (retroactive factor of 2)
  • Oct 1: Repurchased 10,000 shares (outstanding for 3/12 months)
  • Calculation:
    • Jan 1 to Apr 1: $100,000 \times \frac{3}{12} \times 2 = 50,000$ shares
    • Apr 1 to Oct 1: $(100,000 + 20,000) \times \frac{6}{12} \times 2 = 120,000$ shares
    • Oct 1 to Dec 31: $(120,000 - 10,000) \times \frac{3}{12} = 27,500$ shares
    • WACSO = $50,000 + 120,000 + 27,500 = 197,500$ shares.

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Diluted Earnings Per Share

Diluted EPS shows the potential dilution of EPS if all dilutive securities were exercised or converted into common stock.

Diluted EPS Formula

$\text{Diluted EPS} = \frac{\text{Net Income} - \text{Preferred Dividends} + \text{Dilutive Adjustments}}{\text{WACSO} + \text{Dilutive Share Adjustments}}$

The Concept of Anti-Dilution

A security is considered anti-dilutive if its inclusion in the EPS calculation increases EPS or decreases the loss per share. Under GAAP, anti-dilutive securities are excluded from the calculation of Diluted EPS. Each potential common share is tested individually, and they are added to the calculation sequentially from the most dilutive to the least dilutive.

1. The Treasury Stock Method (Options, Warrants, and Stock Rights)

Options and warrants are assumed to be exercised at the beginning of the period (or grant date, if later). Under the treasury stock method:

• The proceeds from the assumed exercise of options (options outstanding * exercise price) are assumed to be used to repurchase treasury shares at the average market price during the period.
• If the exercise price is higher than the average market price, the options are out-of-the-money and anti-dilutive (so they are excluded).
• The net incremental shares (assumed shares issued minus assumed shares repurchased) are added to the denominator of Diluted EPS.
• Formula: $\text{Incremental Denominator Shares} = \text{Options Outstanding} \times \frac{\text{Average Market Price} - \text{Exercise Price}}{\text{Average Market Price}}$
• No adjustment is made to the numerator.

2. The If-Converted Method (Convertible Securities)

Convertible securities are assumed to have been converted at the beginning of the period (or date of issuance, if later).

Convertible Bonds

If bonds are converted:

• Denominator: Add the number of common shares that would be issued upon conversion to the denominator.
• Numerator: Add back the interest expense associated with the convertible bonds, net of tax, because if the bonds were converted, the company would not have incurred interest expense.
• Numerator Adjustment: $\text{Interest Expense Saved} \times (1 - \text{Tax Rate})$

Convertible Preferred Stock

If preferred stock is converted:

• Denominator: Add the number of common shares that would be issued upon conversion to the denominator.
• Numerator: Do not deduct the preferred dividends from Net Income, because if the preferred stock had been converted, no preferred dividends would have been paid.

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Comprehensive EPS Example

Assume Zenith Corporation reports Net Income of $500,000 for the year ended December 31, 2026. The tax rate is 21%. Zenith's capital structure consists of:

• Common Stock: 100,000 weighted-average shares outstanding throughout the year.
• Preferred Stock: 10,000 shares of 6%, $50 par cumulative preferred stock outstanding.
• Options: Options to purchase 20,000 shares of common stock at $15 per share. The average market price of Zenith common stock was $20 during the year.
• Convertible Bonds: $200,000 of 8% bonds, convertible into 10,000 shares of common stock. The bonds were outstanding the entire year.

Step 1: Calculate Basic EPS

• Preferred Dividend = $10,000 \times \$50 \times 6\% = \$30,000$
• Numerator = $\$500,000 - \$30,000 = \$470,000$
• Denominator (WACSO) = $100,000$
• $\text{Basic EPS} = \frac{\$470,000}{100,000} = \$4.70$ per share.

Step 2: Test Stock Options (Treasury Stock Method)

• Average Market Price ($20) is greater than Exercise Price ($15), so options are dilutive.
• Assumed proceeds = $20,000 \times \$15 = \$300,000$
• Assumed shares repurchased = $\frac{\$300,000}{\$20} = 15,000$ shares
• Incremental shares = $20,000 - 15,000 = 5,000$ shares
• Test EPS with options: $\text{EPS} = \frac{\$470,000}{100,000 + 5,000} = \$4.48 \quad (\text{Dilutive compared to } \$4.70)$

Step 3: Test Convertible Bonds (If-Converted Method)

• Denominator Adjustment: Add $10,000$ shares.
• Numerator Adjustment: Add back interest expense net of tax: $\text{Interest Expense} = \$200,000 \times 8\% = \$16,000$ $\text{Interest Saved (Net of Tax)} = \$16,000 \times (1 - 0.21) = \$12,640$
• Test individual effect: $\frac{\$12,640}{10,000} = \$1.264$ per share. Since $1.264 is less than the running EPS of $4.48, the convertible bonds are dilutive.
• Let's compute final Diluted EPS including both: $\text{Numerator} = \$470,000 + \$12,640 = \$482,640$ $\text{Denominator} = 100,000 + 5,000 + 10,000 = 115,000$ $\text{Diluted EPS} = \frac{\$482,640}{115,000} = \$4.20 \text{ per share.}$