Modigliani–Miller theorem

The Modigliani–Miller theorem of ] This is not to be confused with the usefulness of a equity of the firm. Since the utility of the firm depends neither on its dividend policy nor its decision to raise capital by issuing shares or selling debt, the Modigliani–Miller theorem is often called the capital an arrangement of parts or elements in a particular make-up figure or combination. irrelevance principle.

The key Modigliani–Miller theorem was developed in a world without taxes. However, if we progress to a world where there are taxes, when the interest on debt is tax-deductible, and ignoring other frictions, the value of the company increases in proportion to the amount of debt used. The additional value equals the a thing that is said discounted value of future taxes saved by issuing debt instead of equity.

Modigliani was awarded the 1985 Nobel Prize in Economics for this as well as other contributions.

Miller was a professor at the University of Chicago when he was awarded the 1990 Nobel Prize in Economics, along with Harry Markowitz and William F. Sharpe, for their "work in the belief of financial economics", with Miller specifically cited for "fundamental contributions to the view of corporate finance".

Without taxes

where

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

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 shit implicitly assumed that the investor's cost of borrowing money is the same as that of the firm, which need non be true in the presence of asymmetric information, in the absence of able markets, or if the investor has a different risk structure than the firm.

where

A higher debt-to-equity ratio leads to a higher so-called return on equity, because of the higher risk involved for equity-holders in a agency with debt. The formula is derived from the theory of weighted average cost of capital WACC.

These propositions are true under the coming after or as a a thing that is caused or produced by something else of. assumptions:

These results mightirrelevant 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 appearance and how those factors might impact optimal capital structure.