Modigliani-Miller theorem Totally Explained

Everything about The Modigliani-miller Theorem totally explained

The Modigliani-Miller theorem (of Franco Modigliani, 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 doesn't matter if the firm's capital is raised by issuing stock or selling debt. It doesn't matter what the firm's dividend policy is. Therefore, the Modigliani-Miller theorem is also often called the capital structure irrelevance principle. Modigliani was awarded the 1985 Nobel Prize in Economics for this and other contributions.
Miller was awarded the 1990 Nobel Prize in Economics, along with Harry Markowitz and William Sharpe, for their "work in the theory of financial economics," with Miller specifically cited for "fundamental contributions to the theory of corporate finance."

Historical background

Miller and Modigliani derived the theorem and wrote their pathbreaking article when they were both professors at the Graduate School of Industrial Administration (GSIA) of Carnegie Mellon University. In contrast to most other business schools, GSIA put an emphasis on an academic approach to business questions. The story goes that Miller and Modigliani were set to teach corporate finance for business students despite the fact that they'd no prior experience in corporate finance. When they read the material that existed they found it inconsistent so they sat down together to try to figure it out. The result of this was the article in the American Economic Review and what has later been known as the M&M theorem.

Propositions

The theorem was originally proven under the assumption of no taxes. It is made up of two propositions which can also be extended to a situation with taxes.
Consider two firms which are identical except for their financial structures. The first (Firm U) is unlevered: that is, it's financed by equity only. The other (Firm L) is levered: it's financed partly by equity, and partly by debt. The Modigliani-Miller theorem states that the value of the two firms is the same.

Without taxes

Proposition I:

V_U = V_L ,

where

V_U

is the value of an unlevered firm = price of buying a firm composed only of equity, and

V_L

is the value of a levered firm = price of buying a firm that's composed of some mix of debt and equity.
To see why this should be true, suppose an investor is considering buying one of the two firms U or L. Instead of purchasing the shares of the levered firm L, he could purchase the shares of firm U and borrow the same amount of money B that firm L does. The eventual returns to either of these investments would be the same. Therefore the price of L must be the same as the price of U minus the money borrowed B, which is the value of L's debt.
This discussion also clarifies the role of some of the theorem's assumptions. We have implicitly assumed that the investor's cost of borrowing money is the same as that of the firm, which need not be true in the presence of asymmetric information or in the absence of efficient markets. Proposition II:

k_e =k_0+ frac

is the debt-to-equity ratio.

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. Their second attempt on capital structure included taxes and identified that as the level of gearing increases by replacing equity with cheap debt the level of the WACC drops and an optimal capital structure does indeed exist at a point where debt is 100%
The following assumptions are made in the propositions with taxes:

corporations are taxed at the rate

T_C

on earnings after interest,

no transaction costs exist, and

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 was first proposed by F. Modigliani and M. Miller in 1958.

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