Modigliani-Miller (M&M) Theorem: The Irrelevance of Capital Structure

The Modigliani-Miller (M&M) theorem is a cornerstone of modern corporate finance theory, developed by economists Franco Modigliani and Merton Miller in the 1950s.

Core Concept (Without Taxes)

The original M&M theorem posits that, under a set of ideal market assumptions, the value of a firm is independent of its capital structure (the mix of debt and equity used to finance its assets).

In simple terms, whether a company finances its operations entirely with equity or with a mix of debt and equity does not affect its overall market value. This is often referred to as the capital structure irrelevance principle.

The value of the firm is instead determined by its expected future earnings and the risk of its underlying assets.

💡 Key Propositions (Without Taxes)

The M&M theorem is articulated through two main propositions:

Proposition I (Value Irrelevance): The total market value of a levered firm ( $V_L$ ) is equal to the total market value of an unlevered firm ( $V_U$ ).
$V_L = V_U$
Proposition II (Cost of Equity): The cost of equity for a levered firm ( $r_E$ ) is a linear function of its debt-to-equity ratio ( $D/E$ ). As the firm increases its use of debt (financial leverage), the cost of equity rises to compensate equity holders for the increased financial risk, resulting in a constant Weighted Average Cost of Capital (WACC).
$r_E = r_0 + (r_0 - r_D) \frac{D}{E}$
Where $r_0$ is the cost of equity for an all-equity (unlevered) firm, and $r_D$ is the cost of debt.

🛠️ Key Assumptions (Without Taxes)

The “irrelevance” conclusion holds only in an idealized world with perfect capital markets and the following assumptions:

No Taxes: There are no corporate or personal taxes.
No Transaction Costs: Buying and selling securities involves no costs (e.g., brokerage fees).
No Bankruptcy Costs: The cost of financial distress or bankruptcy is zero.
Symmetry of Information: All investors have the same information and agree on the future cash flows of the firm.
Equal Borrowing Rates: Firms and investors can borrow and lend at the same rate.

📝 M&M Theorem With Taxes (1963 Revision)

Modigliani and Miller later revised the theorem to acknowledge the real-world impact of corporate taxes.

In a world with corporate taxes, interest payments on debt are typically tax-deductible (creating a tax shield), while dividends on equity are not.

Proposition I (Value With Taxes): The value of a levered firm is greater than the value of an unlevered firm by the present value of the interest tax shield.
$V_L = V_U + T_C \times D$
Where $T_C$ is the corporate tax rate and $D$ is the market value of debt.

This revision suggests that, due to the tax benefit, firms should use as much debt as possible to maximize value. This is the basis for the trade-off theory of capital structure, which balances the benefit of the debt tax shield against the cost of financial distress (which is not zero in the real world).