Modigliani-Miller Theorems

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Modigliani-Miller Theorems


The Modigliani-Miller (M&M) theorems, developed by economists Franco Modigliani (19182003) and Merton Miller (19232000) in a series of papers, represent a major milestone in corporate finance theory. Modigliani and Miller won Nobel prizes in economics in 1985 and 1990, respectively, in part for their contributions to what are often referred to as the capital structure irrelevance and dividend irrelevance theorems.

Contrary to financial theory of the time, which focused on institutions, the M&M theorems were among the first efforts by economists to bring rigorous analysis to the understanding of corporate finance issues. Corporate financial capital, the funds invested in a firm, consists of money borrowed from others (bonds and loans) and business owners' own money (stock). Lenders receive a stated rate of interest and have the first claim on corporate assets. Stockholders receive all remaining current and future profits of the company. Leverage represents the proportion of debt (bonds and loans) to stock. Modigliani and Miller (1958) presented the idea that, assuming perfect financial markets and in the absence of taxes, the value of a levered firm is the same as that of an unlevered firm if both firms represent the same investment opportunities. In other words, change in capital structure (the mixture of debt and stock) alone does not affect a firm's value. Their no-arbitrage proof stated that, if these firms have different values, investors will be able to replicate the higher-valued firm with the lower-valued firm plus their own borrowing or lending. Alternatively, management of the firm can change the capital structure of the firm to achieve its highest value. In a later paper, Modigliani and Miller argued that a firm's value is not affected by its dividend policy (payment to stockholders) because increased return in the form of dividends is offset by the reduction in the firm's assets.

The M&M framework and methodology had a major impact in shaping future research. In the decades that followed, the corporate finance literature was significantly enriched by attempts to relax various original M&M assumptions, such as no taxation and no bankruptcy costs. The no-arbitrage proof has also become part of financial economists' standard toolkit and was applied in many prominent works, such as the development of the put-call parity in option pricing theory.

Introducing corporate income tax into the model leads to the naive result that the firm should depend on debt financing alone to maximize the benefit of the tax shield. The reason that this is not observed in the business world is because the tax benefit for debt financing at the firm level is counterbalanced by unfavorable tax treatment at the household level. Dividends and bond returns are taxed annually, while taxes on unrealized equity returns can be indefinitely deferred. In most jurisdictions, corporations and households are subject to different tax rates. The risk of bankruptcy also limits the amount of debt a firm should use, since the cost of equity increases with leverage. Consequently, different tax situations and risk preferences demand firms with different kinds of capital structures. The fact that firms choose different tax structures attests to the validity of the capital structure irrelevance theorem, rather than discrediting it.

Relaxing the assumption that managers and shareholders have the same information about a firm's cash flow, researchers developed the signaling theory of dividends. Because managers tend to have information not yet available to shareholders, their action to increase or decrease dividends often reflects information not yet embedded in the stock price. This extension of the M&M theorems explains why stock prices often react to changes in dividends.

SEE ALSO Capital; Expectations; Expectations, Rational; Finance; Leverage; Market Fundamentals; Modigliani, Franco; Wealth


Miller, Merton. 1988. The Modigliani-Miller Propositions after Thirty Years. Journal of Economic Perspectives 2 (4): 99120.

Miller, Merton, and Franco Modigliani. 1961. Dividend Policy, Growth, and the Valuation of Shares. Journal of Business 34: 411433.

Modigliani, Franco, and Merton Miller. 1958. The Cost of Capital, Corporation Finance, and the Theory of Investment. American Economic Review 48: 261297.

Shi Larry Cao