**Modigliani-Miller theorem**

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 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. 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 professo rs at the Graduate School of Industrial Administration (GSIA) of Carnegie

teach corporate finance for business students despite the fact that they had no prior experience in corpora te 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 MM theorem.

**Propositions**

The theorem was originally proved under the assumption of no taxes. It is made up of two propositions which can also b e 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 is financed by **equity **only. The other (Firm L) is levered: it is

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: **where *VU is the value of an unlevered firm *= price of buying a firm composed only of equity, and *VL is the value of a levered firm *= price of buying a firm that is

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. Inst ead 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 i nvestments 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:**

*y is the required rate of return on equity, or cost of equity.*

*c*0 *is the cost of capital for an all equity firm.*

*b is the required rate of return on borrowings, or cost of debt.*

*D */ *E is the debt-to-equity ratio.*

This proposition states 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 co mpany with debt. The formula is derived from the theory of weighted average cost

of capital.

These propositions are true assuming the following assumptions:

no taxes exist,

no transaction costs exist, and

Proposition II with risky debt. As leverage (D/E) increases,

the WACC stays constant.

individuals and corporations borrow at the same rates.

These results might seem irrelevant (after all, none of the conditions are met in the real world), but the theorem is still taught and studied because it tells us something very important. That

is, capital structure

matters precisely because one or more of these assumptions are violated. It tells us where to look for dete rminants of optimal capital structure and how those factors might affect optimal

capital structure.

**With taxes**

**Proposition I:**

where

*VL is the value of a levered firm.*

*VU is the value of an unlevered firm.*

*TCD is the tax rate (TC) x the value of debt (D)*

This means that there are advantages for firms to be levered, since corporations can deduct interest paymen ts. Therefore leverage lowers tax payments. Dividend payments are

non-deductible.

**Proposition II:**

where

*rE is the required rate of return on equity, or cost of equity.*

*r*0 *is the cost of capital for an all equity firm.*

*rD is the required rate of return on borrowings, or cost of debt.*

*D */ *E is the debt-to-equity ratio.*

*Tc 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 incr eases 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 *TC *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 first appeared in: F. Modigliani and M. Miller, "The Cost of Capital, Corporation Finance and t he Theory of Investment," *American Economic Review*

The Modigliani-Miller theorem, which justifies near limitless financial leverage, has largely boosted economic and financial activities. But it also brought increased complexity, lack of

transparency, higher risk and uncertainty in those activities.

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