How are basic and diluted earnings per share (EPS) calculated?

EPS Calculation

How are basic and diluted earnings per share (EPS) calculated?
Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares. Diluted EPS includes potential dilutive securities like options, convertible bonds, and convertible preferred stock.

Basic vs Diluted Earnings Per Share (EPS)

EPS measures profit allocated to each ordinary share. It has two forms: basic (actual shares) and diluted (includes potential shares).

Basic EPS:

Measures earnings per actual ordinary shares outstanding.

Diluted EPS:

Measures earnings per share including all potential ordinary shares that could dilute EPS.

Why Both Are Important:

  • Basic EPS shows current profitability per share
  • Diluted EPS shows "worst-case" scenario if all dilutive securities convert
  • Required by IAS 33 for public companies
  • Helps investors compare companies with different capital structures

Basic EPS Calculation

Formula:

Basic EPS = (Net Income - Preferred Dividends) ÷ Weighted Average Ordinary Shares

Components:

  1. Numerator: Net income attributable to ordinary shareholders
    • Net income minus preferred dividends
    • If loss: use net loss
    • Preferred dividends: annual amount, even if not declared
  2. Denominator: Weighted average shares outstanding
    • Shares outstanding × Time outstanding ÷ Total period
    • Excludes treasury shares
    • Includes shares issued during period (time-weighted)

Example Calculation:

  • Net income: $1,000,000
  • Preferred dividends: $100,000
  • Shares outstanding:
    Jan 1: 800,000 shares
    Jul 1: Issued 200,000 new shares
  • Weighted average shares:
    800,000 × 6/12 = 400,000
    1,000,000 × 6/12 = 500,000
    Total = 900,000
  • Basic EPS = ($1,000,000 - $100,000) ÷ 900,000 = $1.00

Diluted EPS Calculation

Formula:

Diluted EPS = (Net Income - Preferred Dividends + Adjustments) ÷ (Weighted Average Shares + Potential Shares)

Common Dilutive Securities:

  1. Stock Options & Warrants: Use treasury stock method
  2. Convertible Bonds: Add back after-tax interest expense
  3. Convertible Preferred Stock: Add back preferred dividends
  4. Contingently Issuable Shares: If conditions met

Treasury Stock Method (for options):

  1. Assume options exercised at beginning of period
  2. Company receives cash (exercise price × shares)
  3. Use cash to buy back shares at average market price
  4. Net increase in shares = Shares issued - Shares repurchased
  5. Only dilutive if exercise price < market price

Example - Options Dilution:

  • Options: 100,000 options at $10 exercise price
  • Average market price: $15
  • Proceeds if exercised: 100,000 × $10 = $1,000,000
  • Shares repurchasable: $1,000,000 ÷ $15 = 66,667 shares
  • Net new shares: 100,000 - 66,667 = 33,333 shares
  • Add to denominator for diluted EPS

Example - Convertible Bonds:

  • Convertible bonds: $1,000,000 at 5% interest
  • Convertible to 50,000 shares
  • Tax rate: 30%
  • Interest expense: $1,000,000 × 5% = $50,000
  • After-tax interest: $50,000 × (1-30%) = $35,000
  • Add $35,000 to numerator
  • Add 50,000 shares to denominator

Anti-dilutive Securities:

  • If security increases EPS, it's anti-dilutive
  • Exclude from diluted EPS calculation
  • Example: Options with exercise price > market price
  • Must test each security separately

Important Notes:

  1. Calculate diluted EPS only if company has dilutive securities
  2. Use most dilutive combination (lowest possible EPS)
  3. Present both basic and diluted EPS on income statement
  4. Restate prior periods for stock splits/dividends
  5. Disclose calculations in notes to financial statements
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