Ch4. Capital Structure Theory — MM Theorem and Optimal Capital Structure

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) + Equity

Debt Ratio     = Total Debt / Total Equity
Leverage Ratio = Total Debt / Total Assets

MM Theorem (Modigliani-Miller)

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

MM Proposition II (Perfect Market, No Taxes)

Shareholders’ required return increases with leverage:

R_E = R_0 + (R_0 - R_D) × (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

MM Theorem (With Taxes)

MM Proposition I (With Corporate Taxes)

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

V_L = V_U + T_c × 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 × R_D) × T_c

Example: Debt $1,000,000 | Interest rate 5% | Tax rate 25%
Annual saving = $1,000,000 × 5% × 25% = $12,500
PV(Tax Shield) = $50,000  (assuming perpetual debt)

WACC (Weighted Average Cost of Capital)

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

WACC = R_E × (E/V) + R_D × (1 - T_c) × (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  |  R_E = 12%
Debt   $4,000,000  |  R_D = 6%  |  T_c = 25%

WACC = 12% × (6/10) + 6% × (1 − 0.25) × (4/10)
     = 7.2% + 4.5% × 0.4
     = 7.2% + 1.8% = 9.0%

Financial Leverage Effects

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

DOL = Contribution Margin / EBIT
    = (Sales − Variable Costs) / (Sales − Variable Costs − Fixed Costs)

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

DFL = EBIT / (EBIT − Interest)

→ More debt → More interest → Greater EPS volatility

Combined Leverage (DTL): DOL × DFL

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)

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)

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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