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The Modigliani-Miller theorem (of Franco Modigliani and Merton Miller) forms the basis for modern thinking on capital structure. The basic theorem states that, in the absence of taxes, bankruptcy costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed. It does not matter if the firm's capital is raised by issuing stock or selling debt. It does not matter what the firm's dividend policy is. The theorem is made up of two propositions which also exist in a situation with taxes.

Propositions Modigliani-Miller theorem (without taxes):

Proposition I: ${\displaystyle V_{L}=V_{U}}$

${\displaystyle V_{L}}$ is the value of a levered firm.

${\displaystyle V_{U}}$ is the value of an unlevered firm.

The value of an unlevered firm (firm financed by equity only) equals value of a levered firm (firm financed by equity and debt). A person investing in a levered firm would not benefit from it in the way that he could invest in the same firm without leverage (assuming this is possible) and borrow money in the same composition the leveraged firm would and at the same rates. In other words the investor is not receiving anything from a levered firm which he could not receive on its own.

Proposition II: ${\displaystyle r_{S}=r_{0}+{\frac {B}{S}}\left({r_{0}-r_{B}}\right)}$

${\displaystyle r_{S}}$ is the cost of equity.

${\displaystyle r_{0}}$ is the cost of capital for an all equity firm.

${\displaystyle r_{B}}$ is the cost of debt.

${\displaystyle {B}/{S}}$ is the debt-to-equity ratio.

This propostion implies that the cost of equity is a linear function of the firm´s debt to equity ratio. A higher debt-to-equity ratio leads to a higher required return on equity, because of the higher risk involved for equity-holders in a companies with debt. The formula is derived from the theory of weighted average cost of capital.

These propositions are true assuming:

-no taxes exist.

-no transaction costs exist.

-individuals and corporations borrow at the same rates.

These seemingly irrelevant results (after all, none of the conditions are met in the real world) is still taught and studied because it tells us something very important. That is, if capital structure matters, it is precisely because one or more of the assumptions is violated. It tells us where to look for determinants of optimal capital structure and how those things might affect optimal capital structure.

Propositions Modigliani-Miller theorem (with taxes):

Proposition I: ${\displaystyle V_{L}=V_{U}+T_{C}B}$

${\displaystyle V_{L}}$ is the value of a levered firm.

${\displaystyle V_{U}}$ is the value of an unlevered firm.

${\displaystyle T_{C}B}$ is the tax rate(T_C) x the value of debt (B)

This means that there are advantages for firms to be levered, since corporations can deduct interest payments. Therefor leverage lowers tax payments. Dividend payments are non-deductible.

Proposition II: ${\displaystyle r_{S}=r_{0}+{\frac {B}{S}}\left({r_{0}-r_{B}}\right)(1-T_{C})}$

${\displaystyle r_{S}}$ is the cost of equity.

${\displaystyle r_{0}}$ is the cost of capital for an all equity firm.

${\displaystyle r_{B}}$ is the cost of debt.

${\displaystyle {B}/{S}}$ is the debt-to-equity ratio.

${\displaystyle T_{c}}$ is the tax rate.

The same relationship as earlier described stating that the cost of equity rises with leverage, because the risk to equity rises, still holds. The formula however has implications for the difference with the WACC.

File:MM2.jpg

Assumptions made in the propositions with taxes are:

-Corporations are taxed at the rate T_C, on earnings after interest.

-No transaction cost exist

-Individuals and corporations borrow at the same rate

Miller and Modigliani published a number of follow-up papers discussing some of these issues.

The theorem first appeared in: F. Modigilani and M. Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment," American Economic Review (June 1958).

See also

Weighted average cost of capital

Debt to equity ratio

Arbitrage pricing theory

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• Finance theories