Named after Italian-born American economist Franco Modigliani (1918-2003) and American economist MERTON MILLER (1923-2000), Modigliani-Miller theory of the cost of capital states that the overall cost of capital remains constant as the financial gearing of a firm increases.

Critics have suggested that the theory ignores the risk of bankruptcy as a firm’s debt increases.

Source:

M H Miller and F Modigliani, ‘Dividend Policy, Growth, and the Valuation of Shares’, Journal of Business, vol. XXXIV (October, 1961), 235-64

## Historical background

Miller and Modigliani derived and published their theorem when they were both professors at the Graduate School of Industrial Administration (GSIA) of Carnegie Mellon University. Despite limited prior experience in corporate finance, Miller and Modigliani were assigned to teach the subject to current business students. Finding the published material on the topic lacking, the professors created the theorem based on their own research^{[citation needed]}. The result of this was the article in the *American Economic Review* and what has later been known as the M&M theorem.

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.

## The theorem

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

{\displaystyle V_{U}=V_{L}\,}

where

{\displaystyle V_{U}} *is the value of an unlevered firm* = price of buying a firm composed only of equity, and {\displaystyle V_{L}} *is the value of a levered firm* = price of buying a firm that is composed of some mix of debt and equity. Another word for levered is *geared*, which has the same meaning.^{[4]}

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, in the absence of efficient markets, or if the investor has a different risk profile than the firm.

### Proposition II

- {\displaystyle r_{E}({\text{Levered}})=r_{E}({\text{Unlevered}})+{\frac {D}{E}}(r_{E}({\text{Unlevered}})-r_{D})}

here

- {\displaystyle r_{E}}
*is the expected rate of return on equity, or cost of equity.* - {\displaystyle r_{D}}
*is the expected rate of return on borrowings, or cost of debt.* - {\displaystyle {\frac {D}{E}}}
*is the 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 company with debt. The formula is derived from the theory of weighted average cost of capital (WACC).

These propositions are true under the following assumptions:

- no transaction costs exist, and
- 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 something very important. That is, capital structure matters precisely because one or more of these assumptions is violated. It tells where to look for determinants of optimal capital structure and how those factors might affect optimal capital structure.

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