Modigliani-Miller theorem
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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.
This seemingly irrelevant result (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.
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)