Business•Chapter 4•4 min read

Capital Structure Theory — MM Theorem and Optimal Capital Structure

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1. What Is Capital Structure?

Capital Structure: The way a firm finances its long-term assets — the mix of debt and equity.

Total Capital=Debt(borrowed funds)+EquityDebt Ratio=Total DebtTotal EquityLeverage Ratio=Total DebtTotal Assets\begin{aligned} \text{Total Capital} &= \text{Debt} (\text{borrowed funds}) + \text{Equity} \\ \text{Debt Ratio} &= \frac{\text{Total Debt}}{\text{Total Equity}} \\ \text{Leverage Ratio} &= \frac{\text{Total Debt}}{\text{Total Assets}} \end{aligned}

2. MM Theorem (Modigliani-Miller)

(1) MM Proposition I (Perfect Market, No Taxes)

1958: In a perfect capital market, capital structure does not affect firm value.

V_L = V_U (Value of levered firm = Value of unlevered firm)

Assumptions

  • No taxes
  • No transaction costs
  • Perfect information
  • Risk-free debt

(2) MM Proposition II (Perfect Market, No Taxes)

Shareholders’ required return increases with leverage:

RE=R0+(R0−RD)×(DE)R_E = R_0 + (R_0 - R_D) \times (\frac{D}{E})
  • R_E: Required return on equity
  • R_0: Cost of capital for an unlevered firm
  • R_D: Cost of debt
  • D/E: Debt-to-equity ratio

3. MM Theorem (With Taxes)

(1) MM Proposition I (With Corporate Taxes)

1963: With taxes, debt increases firm value because interest is tax-deductible.

VL=VU+Tc×DV_L = V_U + T_c \times D
  • T_c: Corporate tax rate
  • D: Total debt
  • T_c × D: PV of the Interest Tax Shield

Interest Tax Shield:

Annual tax saving=Interest×Tax rate=(D×RD)×TcExample:Debt$1,000,000∣Interest rate5%∣Tax rate25%Annual saving=$1,000,000×5%×25%=$12,500PV(Tax Shield)=$50,000(assuming perpetual debt)\begin{aligned} \text{Annual tax saving} &= \text{Interest} \times \text{Tax rate} = (D \times R_D) \times T_c \\ &\text{Example}: \text{Debt} \$1,000,000 | \text{Interest rate} 5\% | \text{Tax rate} 25\% \\ \text{Annual saving} &= \$1,000,000 \times 5\% \times 25\% = \$12,500 \\ PV(\text{Tax Shield}) &= \$50,000 \quad \text{(assuming perpetual debt)} \end{aligned}

4. WACC (Weighted Average Cost of Capital)

WACC: The firm’s blended cost of capital, weighting equity and after-tax debt.

WACC=RE×(EV)+RD×(1−Tc)×(DV)WACC = R_E \times (\frac{E}{V}) + R_D \times (1 - T_c) \times (\frac{D}{V})

  • E: Market value of equity

  • D: Market value of debt

  • V = E + D: Total capital value

  • R_E: Cost of equity

  • R_D: Pre-tax cost of debt

  • T_c: Corporate tax rate

  • (1 - T_c): Reflects the tax deductibility of interest

Example:

Equity$6,000,000∣RE=12%Debt$4,000,000∣RD=6%∣Tc=25%WACC=12%×(6/10)+6%×(1−0.25)×(4/10)=7.2%+4.5%×0.4=7.2%+1.8%=9.0%\begin{aligned} Equity \$6,000,000 | R_E &= 12\% \\ Debt \$4,000,000 | R_D &= 6\% | T_c = 25\% \\ WACC &= 12\% \times (6/10) + 6\% \times (1 − 0.25) \times (4/10) \\ &= 7.2\% + 4.5\% \times 0.4 \\ &= 7.2\% + 1.8\% = 9.0\% \end{aligned}

5. Financial Leverage Effects

Operating Leverage: The sensitivity of EBIT to changes in sales revenue.

DOL=ContributionMargin/EBIT=(Sales−VariableCosts)/(Sales−VariableCosts−FixedCosts)\begin{aligned} DOL &= Contribution Margin / EBIT \\ &= (Sales − Variable Costs) / (Sales − Variable Costs − Fixed Costs) \end{aligned}

Financial Leverage: The sensitivity of EPS to changes in EBIT.

DFL=EBITEBIT−Interest→More debt→More interest→Greater EPS volatility\begin{aligned} DFL &= \frac{EBIT}{EBIT − \text{Interest}} \\ &\to \text{More debt} \to \text{More interest} \to \text{Greater EPS volatility} \end{aligned}

Combined Leverage (DTL): DOL × DFL

6. Optimal Capital Structure

MM perfect market + bankruptcy costs:

Optimal Capital Structure

  • Firm Value = V_U + PV(Tax Shield) − PV(Financial Distress Costs)

↑ Debt: ↑ Interest tax shield, ↑ Bankruptcy risk → An optimal point exists (Trade-Off Theory)

7. Key Concept Cards

WACC Formula ★★★★★ : R_E × (E/V) + R_D × (1 − T_c) × (D/V). After-tax cost of debt is included. Memory tip: WACC = cost of equity × E/V + after-tax cost of debt × D/V

MM Tax Effect ★★★★★ : V_L = V_U + T_c × D. With corporate taxes, debt usage raises firm value. Memory tip: More debt → tax shield → higher firm value

Financial Leverage DFL ★★★★☆ : DFL = EBIT / (EBIT − Interest). Higher debt → higher DFL → wider EPS swings. Memory tip: DFL = EBIT ÷ (EBIT − Interest)

8. Practice Quiz

Q. A firm has equity of $4M (cost 15%), debt of $6M (rate 8%), and a tax rate of 30%. What is WACC?

WACC = 15% × (4/10) + 8% × (1 − 0.3) × (6/10) = 6% + 5.6% × 0.6 = 6% + 3.36% = 9.36%

Q. Corporate tax rate is 25% and the firm carries $20M in permanent debt. What is the PV of the interest tax shield?

PV = T_c × D = 0.25 × $20M = $5M

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