Introductory Corporate Finance: Leverage - ModiglianiMiller Propositions, MM I and II Without Taxes With Corporate Taxes With Personal Taxes

What This Is

The Modigliani-Miller (MM) Propositions are a set of theories in corporate finance that describe the relationship between a company's capital structure and its value. The propositions were developed by Franco Modigliani and Merton Miller in the 1950s and 1960s. They matter in corporate finance because they help us understand how a company's capital structure affects its value and how investors should think about risk and return. For example, consider a company like Apple, which has a market capitalization of $2 trillion and a debt-to-equity ratio of 0.2. According to MM Proposition I, Apple's value is independent of its capital structure, but with taxes, the value of Apple's debt increases due to the interest tax shield.

Key Formulas & Models

• WACC = wd × rd(1-T) + wps × rps + we × re – weighted average cost of capital; used as discount rate.
  • wd: proportion of debt in capital structure
  • rd: cost of debt
  • T: corporate tax rate
  • wps: proportion of preferred stock in capital structure
  • rps: cost of preferred stock
  • we: proportion of equity in capital structure
  • re: cost of equity
• DOL = Q(P-V) / (Q(P-V)-F) – degree of operating leverage; measures EBIT sensitivity to sales.
  • Q: sales
  • P: price per unit
  • V: variable cost per unit
  • F: fixed cost
• DFL = EBIT / (1 - T) – debt-free leverage; measures EBIT sensitivity to sales after taxes.
  • EBIT: earnings before interest and taxes
  • T: corporate tax rate
• Sustainable Growth Rate = ROE × (1 - Retention Ratio) – measures a company's ability to grow without external financing.
  • ROE: return on equity
  • Retention Ratio: proportion of earnings retained by the company
• WACC = (D / (D + E)) × rD + (E / (D + E)) × rE – weighted average cost of capital; used as discount rate.
  • D: debt
  • E: equity
  • rD: cost of debt
  • rE: cost of equity
• Earnings Per Share (EPS) = Net Income / Number of Outstanding Shares – measures a company's profitability per share.
  • Net Income: company's net income
  • Number of Outstanding Shares: number of shares held by investors
• Dividend Yield = Dividend Per Share / Current Stock Price – measures a company's dividend payout ratio.
  • Dividend Per Share: company's dividend payout per share
  • Current Stock Price: current market price of the company's stock

Step-by-Step Calculation

1. Calculate the weighted average cost of capital (WACC) using the formula WACC = wd × rd(1-T) + wps × rps + we × re.
2. Calculate the degree of operating leverage (DOL) using the formula DOL = Q(P-V) / (Q(P-V)-F).
3. Calculate the debt-free leverage (DFL) using the formula DFL = EBIT / (1 - T).
4. Calculate the sustainable growth rate using the formula Sustainable Growth Rate = ROE × (1 - Retention Ratio).
5. Calculate the earnings per share (EPS) using the formula EPS = Net Income / Number of Outstanding Shares.
6. Calculate the dividend yield using the formula Dividend Yield = Dividend Per Share / Current Stock Price.

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
  • Correction: Use market value for WACC to reflect the current market price of the company's debt and equity.
• Mistake: Ignoring flotation costs when calculating WACC.
  • Correction: Include flotation costs in the calculation of WACC to reflect the cost of issuing new debt or equity.
• Mistake: Confusing sunk cost with opportunity cost.
  • Correction: Use opportunity cost when making investment decisions, not sunk cost.
• Mistake: Assuming that the cost of debt is constant over time.
  • Correction: Use the current market yield on debt to estimate the cost of debt.
• Mistake: Ignoring the impact of taxes on the cost of debt.
  • Correction: Include the impact of taxes on the cost of debt when calculating WACC.

Exam / CFA Tips

• Tip: Be careful when distinguishing between MM Proposition I (no taxes) and MM Proposition II (with taxes).
• Tip: Understand the difference between IRR and NPV ranking.
• Tip: Be aware of the dividend irrelevance theorem and its implications for investment decisions.
• Tip: Use the correct formula for calculating WACC, including the impact of taxes on the cost of debt.

Quick Practice Problem

A company has EBIT of $10M, interest $2M, tax 25% – compute DFL.

Answer: DFL = $10M / (1 - 0.25) = $13.33M

Explanation: The company's debt-free leverage (DFL) is calculated by dividing its earnings before interest and taxes (EBIT) by one minus the corporate tax rate.

Last-Minute Cram Sheet

• WACC = wd × rd(1-T) + wps × rps + we × re – weighted average cost of capital
• DOL = Q(P-V) / (Q(P-V)-F) – degree of operating leverage
• DFL = EBIT / (1 - T) – debt-free leverage
• Sustainable Growth Rate = ROE × (1 - Retention Ratio) – measures a company's ability to grow without external financing
• Earnings Per Share (EPS) = Net Income / Number of Outstanding Shares – measures a company's profitability per share
• Dividend Yield = Dividend Per Share / Current Stock Price – measures a company's dividend payout ratio
• MM Proposition I (no taxes): Firm value is independent of capital structure
• MM Proposition II (with taxes): Firm value increases with debt due to the interest tax shield
• In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield
• WACC is not the same as the cost of equity or the cost of debt