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Capital Budgeting for Levered firm MMII

# Capital Budgeting for Levered firm MMII - HAAS SCHOOL OF...

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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 II: C APITAL B UDGETING FOR THE L EVERED F IRM This teaching note assumes familiarity with the material in the text dealing with the debt policy [Chapters 18-20]. In keeping with the text, we shall be denoting cost of capital by r . 1. While Modigliani-Miller Proposition I [MM I] deals with the relationship between the value of the unlevered and that of the levered firm, Modigliani-Miller Proposition II [MM II] deals with the relationship among the cost of equity capital, cost of debt capital, and cost of capital for the firm as a whole, which is related to the expected return on the assets. As with MM I, there is a tax-corrected version of MM II. 2. We saw in the previous note that, according to MM I, under “ideal” circumstances: V V U L = . [1] where U V denotes value of the assets of an unlevered firm, and L V denotes the value of the assets of an otherwise identical levered firm. By balance sheet identity: L V D E U + . [2] where D denotes value of the debt, and E value of the equity, of the levered firm. 1 Now, we can estimate the cost of capital for the unlevered firm on the basis of what we learnt in the lecture note called “CAPM and Capital Budgeting.” When the levered firm issues debt, the cost of debt capital will be determined by the market. We want to determine the cost of equity capital for the levered firm in terms of these two known quantities, the cost of capital for the unlevered firm, and the cost of debt capital. In order to do that we need U V , E and D in the same equation. We can get these three in the same equation by putting equations [1] and [2] together: E D V U + = , or D V E U - = This enables us to conclude that the equity of the levered firm [Firm L ] can be thought of as a portfolio of V U and D with a fraction [ ] E V U invested in the assets of the unlevered firm, and a fraction [ ] E D - in the debt of the levered firm. Therefore, the cost of equity capital, which is the expected (or required ) return on the equity, will be a weighted average of the expected returns on the components of the portfolio. Or, algebraically: 1 Since the levered firm is the only firm here with debt, we need not continue to distinguish the debt and equity of the levered firm by subscript L . Modigliani-Miller Propositions II 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 D UA U E r E D r E V r * * - = [3] where E r and D r denote the expected return on the equity and on the debt of the levered firm respectively, and UA r denotes the expected return on the assets 2 of the unlevered firm. Substituting E D V U + = in the numerator of the first term on the right, and gathering coefficients of the debt-equity ratio, [ ] E D , we get: ( 29 D UA UA E r r E D r r - + = * .
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