Modigliani–Miller theorem

A set of propositions showing that, under specified market assumptions, a firm’s value is independent of its financing mix. Extensions show how corporate taxes can make debt affect value.

Capital structure: The mix of debt and equity a firm uses to finance its operations and investments. The theorem asks whether this financing mix changes firm value.
Perfect capital market: An idealized financial market with frictionless trading, complete information, and no price-taking investor able to affect prices. The original propositions rely on frictionless market conditions.
Tax shield: A reduction in taxable income or taxes produced by a deductible expense or other tax provision. Interest deductibility creates the debt tax advantage in the theorem’s tax extension.
Franco Modigliani: An Italian-American economist who shared the 1985 Nobel Prize in Economic Sciences for work on household saving and financial markets. He co-developed the capital-structure propositions.
Arbitrage: Trading that exploits price differences to obtain a profit without net investment or risk. Investors’ arbitrage eliminates price differences between equivalent leveraged and unleveraged firms.
Corporate tax: A tax imposed on the profits or income of corporations. The tax extension changes the relative cost of debt and equity.
Trade-off theory: A theory of capital structure balancing the tax benefits of debt against expected financial distress costs. It adds a real-world cost that limits debt’s value-enhancing tax benefit.
Merton Miller: An American economist who shared the 1990 Nobel Prize in Economic Sciences for work on financial economics. He co-developed the theorem and later clarified its tax implications.
Homemade leverage: An investor’s use of personal borrowing or lending to alter the leverage of a portfolio. Investors can reproduce corporate leverage themselves, undermining financing-based value differences.
Bankruptcy cost: The direct and indirect costs a firm incurs when financial distress leads to default or reorganization. These costs can offset the tax benefits of borrowing excluded by the basic theorem.

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Fisher separation theoremRelated: Both results use idealized capital markets to isolate corporate decisions from irrelevant financial arrangements.