April 21,2025 113 Notes

Earnings Per Share (EPS)

Overview

• Basic Earnings Per Share (EPS): Net income available to common shareholders divided by weighted average common stock outstanding.

• Capital Structure: How a company brings capital into the firm.

  • Debt.

  • Equity (issuing shares or retained earnings).

Simple vs. Complex Capital Structure

Simple Capital Structure

• Common stock and possibly preferred stock.

• No potential diluters.

• Only basic EPS is reported.

Complex Capital Structure

• Potential diluters exist. Examples:

  • Convertible debt (bonds that can be converted into stock).

  • Stock options.

  • Warrants.

  • Restricted shares.

  • Convertible preferred stock.

• Both basic and diluted EPS are reported (if dilutive).

• If potential diluters are anti-dilutive, they are ignored, and only basic EPS is reported.

Basic Earnings Per Share

• Formula: (\text{Net Income} - \text{Preferred Dividends}) / \text{Weighted Average Common Shares Outstanding}

• Components:

  • Net income available to common shareholders.

  • Weighted average common shares outstanding.

Net Income Available

• Includes detail regarding preferred dividends.

Preferred Dividends

• If dividends are actually declared, subtract them.

• Non-cumulative preferred stock: If no declaration, do not subtract.

• Cumulative preferred stock: Subtract the current period dividend, whether or not declared. Ignore dividends in arrears.

Weighted Average Common Shares Outstanding

• Beginning balance of common shares.

• Events that can change the number of shares:

  • Issuance of new common shares.

  • Buybacks (treasury stock).

  • Stock dividends.

  • Stock splits.

• Waiting by time for new issuances or buybacks.

• Stock dividends and splits are treated retroactively to the earliest period reported.

Exercise: Computing Weighted Average Shares

• Scenario:

  • 175,000 shares outstanding at the beginning of the year.

  • 40% stock dividend issued on July 1.

  • 20,000 shares purchased for treasury on October 1.

  • Two-for-one stock split declared on December 31.

• Calculations:

  • January 1: 175,000 shares.

    • Adjust for stock dividend: 175,000 \times 1.40 = 245,000

    • Adjust for stock split: 245,000 \times 2 = 490,000

    • Multiply by time weighting: 490,000 \times (12/12) = 490,000

  • October 1: Treasury stock purchase.

    • Shares repurchased: 20,000.

    • Adjust for stock split: 20,000 \times 2 = 40,000

    • Multiply by time weighting: 40,000 \times (3/12) = 10,000

  • Total weighted average shares outstanding: 490,000 - 10,000 = 480,000

Computing Earnings Per Share: Example

• Simple capital structure (no potential diluters).

• Net income: $1,000,000.

• Preferred stock: 10,000 shares with a par value of $20 and a dividend rate of 5%.

• Weighted average shares outstanding: 480,000.

• Calculations:

  • Preferred dividend: 10,000 \text{ shares} \times $20 \text{ par value} \times 0.05 = $10,000

  • Basic EPS: ($1,000,000 - $10,000) / 480,000 = $2.06

Preferred Dividends: Various Scenarios

Declared and Paid Dividends

• Subtract the actual declared dividend.

Cumulative Preferred Stock

• Subtract only the current period dividend. Ignore any dividends in arrears.

Non-Cumulative Preferred Stock and No Dividends Declared

• Do not subtract any dividend.

Financial Statement Presentation

• Earnings per share is an integral part of the income statement, appearing at the bottom.

• Proper Heading:

  • Name of the company.

  • Income statement.

  • For the period ending [date].

• Presentation format:

  • Net income.

  • Basic earnings per share.

Complex Capital Structures

Potential Diluters

• Convertible bonds.

• Convertible preferred stock.

• Stock options.

If-Converted Method

• Include the effects of potential diluters only if they are dilutive.

• Assume conversion at the beginning of the period (BOP).

• If anti-dilutive, exclude them.

Steps to Compute Diluted EPS

1. Start with basic EPS: (\text{Net Income} - \text{Preferred Dividends}) / \text{Weighted Average Common Shares Outstanding}

2. Determine individual dilution of each potential diluter: \frac{\text{Numerator Effect}}{\text{Denominator Effect}}

   • Convertible Bonds: \frac{\text{Interest Expense} \times (1 - \text{Tax Rate})}{\text{New Common Shares from Conversion}}

   • Convertible Preferred: \frac{\text{Preferred Dividend}}{\text{New Common Shares from Conversion}}

3. Rank the potential diluters from smallest to largest dilution.

4. Include the effects of individual diluters into basic EPS one at a time, testing for continued dilution after each incorporation. Compare to the computation above it.

Example

• Basic EPS: $2.25.

• Convertible Bonds dilution effect: $2.00 (dilutive).

• Convertible Preferred dilution effect: $0.75 (dilutive).

• Ranked from smallest to largest: Convertible Preferred ($0.75), Convertible Bonds ($2.00).

• Incorporate Convertible Preferred into Basic EPS:

  • New EPS = $2.23 (still dilutive, keep it).

• Incorporate Convertible Bonds:

  • New EPS = $2.18 (still dilutive, keep it). This it the final diluted EPS.

Decision Making

• Show all decision-making steps.

• At each step, compare the new EPS to the previous EPS calculation (not always to the basic EPS).

• If a potential diluter increases the EPS (anti-dilutive), throw it out and stop.

Complex Example

• Common stock outstanding: 110,000 shares.

• Convertible preferred: 10,000 shares, $3 per share dividend.

• 8% convertible bonds: $1,000,000.

• Tax rate: 25%.

• Net Income: $850,000.

• Preferred stock convertible into 20,000 shares of common stock.

• Bonds convertible into 30,000 shares of common stock.

Steps

1. Basic Earnings Per Share

   • (\text{Net Income} - \text{Preferred Dividends}) / \text{Common Shares}

   • ($850,000 - (10,000 \times $3)) / 110,000 = $7.45

2. Individual Dilution

   • Convertible Preferred:

     • \frac{$30,000}{20,000} = $1.50

     • Dilutive: $1.50 < $7.45. Keep it.

   • Convertible Bonds:

     • \frac{0.08 \times $1,000,000 \times (1 - 0.25)}{30,000} = $2.00

     • Dilutive: $2.00 < $7.45. Keep it.

3. Rank

   • $1.50 (Preferred), $2.00 (Bonds)

4. Incorporate

   • Preferred:

     • ($850,000 - $30,000 + $30,000) / (110,000 + 20,000) = $6.54

     • Dilutive: $6.54 < $7.45. Keep it.

   • Bonds:

     • ($850,000 + $60,000 ) / (130,000 + 30,000) = $5.69

     • Dilutive: $5.69 < $6.54. Keep it.

• Diluted EPS = $5.69.

Financial Statement Presentation

• Company Income statement for the period ending 12/31.

• Net income: 850,000.

• Report both basic and diluted EPS.

• Basic earnings per share of $7.45.

• Diluted earnings per share, $5.69.

Stock Options and Restricted Stock

Stock Options

• Dilutive: Exercise price < average market price. Use the treasury stock method.

• Anti-dilutive: Exercise price > average market price. Throw it out.

Treasury Stock Method

• Numerator effect: Always zero.

• Denominator effect: Increment in common shares.

• The company uses the cash received from the exercise of the options to buy back treasury shares.

• \text{New Shares Issued} - \text{Treasury Shares Bought Back}

• Treasury Shares Bought Back: Cash / Average Market Price

Restricted Stock

• Use treasury stock method in concept.

• Use the unearned compensation expense in lieu of cash proceeds.

• It only appears in concept.

Financial Statement Presentation for EPS

• Income from continuing operations, discontinued operations, and net income for both basic and diluted EPS.

Exercise: Stock Options

• Net income: $800,000.

• 200,000 common shares outstanding on average.

• Average market price: $50.

• 20,000 stock options outstanding to purchase 20,000 common shares.

• Exercise price: $25.

Steps

1. Basic Earnings Per Share: 800,000 / 200,000 = $4.00.

2. Diluted Earnings Per Share:

   • Dilutive? Yes, $25 < $50.

   • Numerator: 0

   • Number of shares to be purchased: 20,000.
     Cash Proceed = Exercise price * The number of shares being purchased = $25 * 20,000 = $500,000

• Treasury Stock Buyback: $500,000 / $50 = 10,000 shares. Denominator: 20,000-10,000 = 10,000.

  • Income from Continuing Operations.
    Basic = 800,000 + 0 / 200,000 + 10,000 = $3.81

  • Dilutive? Yes, $3.81 < $4.00

Presentation of Earnings Per Share

Income Statement Example

• Income from continuing operations: $1,000,000.

• Discontinued operations: $200,000.

• Report basic earnings per share with proper heading.

  • Basic - Change the numerator.
    If Use Net Income the EPS = 4

• Net Income EPS = $1,000,000/200,000 = $5

• If You use Discontinued Operations the EPS = $200,000/200,000 = $1

• Report diluted earnings per share.

  • Basic will equal: income from continuing operations = 1,000,000/210,000 = $4.76

  • Basic will equal: Discontinued operations: $200,000/210,000 = $.95

  • Net income: $3.81.

Fendelacar Example

• Common stock: Authorized 100,000 shares, 50,000 shares issued and outstanding.

• Preferred stock: $50 par, 7% cumulative, convertible into common stock share per share (2,000 shares).

• No dividends declared during the year.

• Net income: $150,000.

• Stock options outstanding all year for 10,000 shares of common stock at $15 per share.

• Average market price of the common stock: $25 per share.

Potential Diluters

• Preferred stock

• Stock options