Can someone clearly explain both Modigliani-Miller propositions — with and without taxes — and when each applies?

Modigliani-Miller (MM) is the foundation of capital structure theory. Start with the idealized version, then add real-world frictions.

MM Without Taxes (Perfect Markets):

Proposition I: The value of a firm is independent of its capital structure.

V_Levered = V_Unlevered

Intuition: In perfect markets (no taxes, no bankruptcy costs, no information asymmetry), how you slice the pizza doesn't change its total size. Whether you finance with 100% equity or 50/50 debt-equity, firm value is the same.

Proposition II: The cost of equity increases linearly with leverage.

r_e = r_0 + (r_0 - r_d) x (D/E)

Where r_0 is the cost of capital for an all-equity firm. As you add debt, equity becomes riskier (residual claimants bear more risk), so shareholders demand a higher return. But the WACC stays constant because cheaper debt is exactly offset by more expensive equity.

MM With Taxes:

Proposition I: Firm value increases with leverage due to the tax shield.

V_Levered = V_Unlevered + (Tax Rate x Debt)

Proposition II: Cost of equity still rises with leverage, but WACC declines.

r_e = r_0 + (r_0 - r_d) x (D/E) x (1 - Tax Rate)

The (1 - Tax Rate) dampener means equity's cost rises more slowly than in the no-tax case, so WACC falls as you add debt.

Numerical Example:

Pinecrest Corp has r_0 = 10%, r_d = 5%, Tax Rate = 30%, D/E = 0.8.

Without taxes: r_e = 10% + (10% - 5%) x 0.8 = 10% + 4% = 14%

WACC = (1/1.8) x 14% + (0.8/1.8) x 5% = 7.78% + 2.22% = 10% (unchanged!)

With taxes: r_e = 10% + (10% - 5%) x 0.8 x (1 - 0.30) = 10% + 2.8% = 12.8%

WACC = (1/1.8) x 12.8% + (0.8/1.8) x 5% x (1-0.30) = 7.11% + 1.56% = 8.67% (lower!)

The Practical Takeaway:

MM with taxes implies firms should use 100% debt — obviously unrealistic. This is why the trade-off theory (adding distress costs) and pecking order theory (information asymmetry) were developed. Think of MM as the baseline that explains WHY leverage matters, with real-world modifications explaining HOW MUCH leverage is optimal.

Test your understanding with our CFA Level II Corporate Issuers practice questions.