Lecture Note on Modigliani-Miller Propositions I

Lecture Note on Modigliani-Miller Propositions I - HAAS...

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H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY UGBA 103 A VINASH V ERMA M ODIGLIANI -M ILLER P ROPOSITIONS I [MM I AND MMT I] This teaching note assumes familiarity with the material in the text dealing with Modigliani-Miller Propositions [Chapters 18-20 BMA]. 1. A firm that has financed its assets in part by issuing debt rather than entirely by issuing equity is said to have financial leverage , or in short just leverage , in its capital structure . We want to study how the value of a firm as a whole is affected by changes in its capital structure, which is to say, by changes in the mix of debt and equity as sources of finance. Given the focus of this note on leverage, we shall be keeping everything other than leverage fixed when we compare two firms. Let us therefore assume that there are two firms with identical assets that produce identical future cash flows with identical time and risk characteristics. Further, let us assume that the identical assets of each firm produce identical random cash flows of I ~ $ every period in perpetuity. 1 Now, suppose one of these firms is financed entirely by equity. In other words, it has no financial leverage in its capital structure, or is unlevered . We shall be calling it Firm U . Further, let us suppose that the other firm has chosen to finance a part of its assets by debt. It is therefore levered . We shall call it Firm L . We shall denote by V U the value of the assets of the unlevered firm, and by V L the value of the assets of the [otherwise identical] levered firm. In order to study whether, under what circumstances, and by how much, financial leverage changes the value of a firm, we shall compare U V and L V . Now, by balance sheet identity: L L L E D V + [1] where L D denotes the value of the debt, and L E the value of the equity, of the levered firm. 2. In this and the following paragraphs, a no-arbitrage argument is presented that shows that, under certain circumstances, leverage has no impact on value, i.e., U L V V = . Consider Investor X , who owns 1% of the equity of the unlevered firm. Since the unlevered firm has no debt, U U E V = . Therefore, the current value of the investment of Investor X is ( 29 U V * 01 . 0 $ . Let us assume that there are no corporate taxes, and therefore the cash flows 1 That the income occurs in perpetuity has been assumed for computational ease. Modigliani-Miller Propositions I 1
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H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY UGBA 103 A VINASH V ERMA generated every period are available for distribution to the stakeholders in the firm in their entirety. Since equityholders of the unlevered firm are the only stakeholders, they are entitled to all of the cash flows that the assets generate every period. In other words, equityholders of the unlevered firm are entitled to I ~ $ , and as somebody who owns 1% of the equity, Investor X is entitled to ) ~ * 01 . 0 $( I 3. Now consider Investor Y , who owns 1% of the equity and 1% of the
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This note was uploaded on 04/30/2010 for the course L&S 101 taught by Professor Chow during the Spring '10 term at University of California, Berkeley.

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Lecture Note on Modigliani-Miller Propositions I - HAAS...

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