Modigliani-Miller Theorem

The Modigliani-Miller theorem (M&M theorem) is a cornerstone of financial economics, developed by Franco Modigliani and Merton Miller in 1958. Their work fundamentally changed the understanding of corporate finance by demonstrating under certain conditions, the value of a firm is unaffected by its capital structure.

Historical Context

The theorem was introduced in a time when the prevailing thought was that a company could increase its value by changing its debt-to-equity ratio. Modigliani and Miller's paper titled "The Cost of Capital, Corporation Finance and the Theory of Investment" challenged this notion by using rigorous mathematical proofs to show that in a perfect market, the choice between debt and equity financing does not affect the firm's market value.

Core Propositions

Proposition I

Proposition I states that in a world with no taxes, bankruptcy costs, agency costs, or asymmetric information, and in an efficient market, the value of a firm is unaffected by how it is financed. This can be summarized as:

VL = VU

Where V_L is the value of a levered firm and V_U is the value of an unlevered firm.

Proposition II

Proposition II extends the first proposition by stating that the cost of equity rises linearly with the firm's debt-to-equity ratio:

rE = rA + (rA - rD) * (D/E)

Here, r_E is the cost of equity, r_A is the cost of capital for an all-equity firm, r_D is the cost of debt, D is the market value of debt, and E is the market value of equity.

Assumptions of the Theorem

• No transaction costs
• No taxes
• No bankruptcy costs
• Investors can borrow at the same rate as corporations
• Perfect capital markets, where all investors have the same information and expectations
• Symmetric information
• No agency costs

Relaxing Assumptions

Subsequent modifications to the theorem include:

• Taxes: When corporate taxes are considered, the theorem suggests that debt financing can increase the firm's value due to the tax shield on interest payments.
• Bankruptcy Costs: The presence of bankruptcy costs introduces an optimal capital structure where the benefits of debt (tax shield) are balanced against the costs of potential financial distress.
• Agency Costs: The conflicts of interest between shareholders and managers or between shareholders and bondholders can affect the capital structure decision.

Impact and Criticisms

The Modigliani-Miller theorem has had a profound impact on corporate finance theory, providing a benchmark for understanding the effects of capital structure. However, it has been critiqued for its unrealistic assumptions:

• The real world has taxes, bankruptcy costs, and asymmetric information.
• Agency problems and transaction costs are significant in practice.
• The theorem's applicability in less than perfect markets is limited.

Sources

• Investopedia - Modigliani-Miller Theorem
• Khan Academy - Modigliani-Miller Theorem
• Original Paper by Modigliani and Miller

Related Topics

• Capital Structure
• Weighted Average Cost of Capital
• Agency Theory
• Trade-off Theory