Intro to Finance: Capital Structure - ModiglianiMiller Propositions, MM I II with and without Taxes

What This Is

The Modigliani-Miller (M&M) Propositions are a set of theories in corporate finance that describe the relationship between a company's capital structure and its cost of capital. M&M I and II explain how a company's value is affected by its capital structure, with and without taxes. For example, consider Apple Inc. with a market value of $2 trillion and a debt-to-equity ratio of 0.2. If Apple increases its debt-to-equity ratio to 0.5, its cost of capital might decrease, but its value might not change significantly, according to M&M I.

Key Formulas & Symbols

• WACC = (E/V) × Re + (D/V) × Rd × (1 - Tc) where WACC = weighted average cost of capital, E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt, Tc = corporate tax rate.
• Cost of Equity (Ke) = Rf +-× (Rm - Rf) where Ke = cost of equity, Rf = risk-free rate,-= beta, Rm = market return.
• Cost of Debt (Kd) = (1 - Tc) × (1 + Rd) where Kd = cost of debt, Rd = cost of debt, Tc = corporate tax rate.
• Market Value of Equity (E) = Number of Shares × Market Price per Share
• Market Value of Debt (D) = Face Value × (1 + Coupon Rate)^Years
• Debt-to-Equity Ratio (D/E) = D/E
• Capital Structure (D/E) = D/E
• Value of the Firm (V) = E + D

Step-by-Step Calculation

1. Calculate the cost of equity (Ke) using the CAPM formula: Ke = Rf +-× (Rm - Rf).
2. Calculate the cost of debt (Kd) using the formula: Kd = (1 - Tc) × (1 + Rd).
3. Calculate the weighted average cost of capital (WACC) using the formula: WACC = (E/V) × Ke + (D/V) × Kd × (1 - Tc).
4. Calculate the market value of equity (E) and market value of debt (D) using the formulas: E = Number of Shares × Market Price per Share and D = Face Value × (1 + Coupon Rate)^Years.
5. Calculate the debt-to-equity ratio (D/E) using the formula: D/E = D/E.

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value for WACC, as it reflects the current market price of the company's securities.
• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR is the rate at which the NPV of a project is zero, while NPV is the present value of a project's cash flows.
• Mistake: Assuming that a company's value is solely determined by its capital structure.
• Correction: M&M I and II show that a company's value is determined by its cost of capital, which is influenced by its capital structure.

Exam / CFA Tips

• Tip: Be careful with the wording of questions, as they might be trying to trick you into using the wrong formula or assumption.
• Tip: Make sure to read the question carefully and understand what is being asked before starting to calculate.
• Tip: Use the CAPM formula to calculate the cost of equity, as it is a fundamental concept in finance.

Quick Practice Problem

Apple Inc. has a market value of $2 trillion, a debt-to-equity ratio of 0.2, and a corporate tax rate of 20%. If the risk-free rate is 2% and the market return is 8%, what is Apple's weighted average cost of capital (WACC)?

Answer: WACC = 4.5% (using the CAPM formula and the given values).

Last-Minute Cram Sheet

• WACC = (E/V) × Ke + (D/V) × Kd × (1 - Tc)
• Ke = Rf +-× (Rm - Rf)
• Kd = (1 - Tc) × (1 + Rd)
• E = Number of Shares × Market Price per Share
• D = Face Value × (1 + Coupon Rate)^Years
• D/E = D/E
• V = E + D
• M&M I: A company's value is determined by its cost of capital, not its capital structure.
• M&M II: A company's value is determined by its cost of capital, which is influenced by its capital structure.
• The dividend discount model (DDM) requires g < r – otherwise the model explodes.
• The weighted average cost of capital (WACC) is a weighted average of the cost of equity and the cost of debt.