fin13 - Taxes, Capital Structure and the Modigliani- Miller...

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1 Taxes, Capital Structure and the Modigliani- Miller theorem To understand how taxes affect a firm’s financing choices, one must first understand what financing choices would be like without taxes. Hence the spring-board for discussion of this topic is the no- tax capital structure irrelevance theorem offered by Franco Modigliani and Merton Miller (1958). ± Are the production and investment decisions of the firms influenced by their financial structure? ± The market value of a firm is given by : Equity + Debt = E + D = V . The objective of the managers is the maximization of the firm’s value i.e. of its share price ( no agency problems) . Debt finance is cheaper than equity finance ( r d < r e ), because equity is more risky than debt, so that the risk premium for debt is lower than the risk premium for equity. Traditional theory: If a firm substitutes debt for equity, it will reduce its cost of capital, so increasing the firm’s value: () E D D r r r E D E r E D D r r d e e e d a + = + + + = . But , when the D/E ratio is considered too high, both equity-holders and debt-holders will start demanding higher returns so that the cost of capital of the firm will rise. Hence, there exists an optimal cost minimizing value of the D/E ratio. average cost of capital debt/equity ratio M-M
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2 ± Modigliani- Miller (M-M) proposition 1: The value of a firm is the same regardless of whether it finances itself with debt or equity. The weighted average cost of capital: r a is constant. Assumptions of M-M: 1. Perfect and frictionless markets 2. no transaction costs 3. no default risk 4. no taxation 5. both firms and investors can borrow at the same r d interest rate, i.e. no arbitrage opportunity (also 1) M-M proved the irrelevance theorem by showing that if two firms are identical except for their capital structures, an opportunity to earn arbitrage profits exists if the total values of the two firms are not the same. Numerical example: Consider two firms: one has no debt while the other is leveraged ( i.e . has debts). They are identical in every other respect. In particular, they have the same level of operating profits: X . Let A have 1000 shares issued at $1 and B have issued 500 shares (at $1) and $500 of debt. Firm A Firm B Equity E 1000 500 Debt D 0 500 ± 100 shares of B (1/5 E B ) give right to receive a return: RX r D d =− 1 5 1 5 ± 200 shares of A (1/5 E A ) bought using $100 of borrowed money (100=1/5 D B ) give the same return: r D d 1 5 1 5 ± The two investments yield the same return (and have the same financial risk). Hence 1/5 of A must have the same value of 1/5 of B : both shares should be equally priced. If not, arbitrageurs will have profitable operations at their disposal.
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3 ± M-M proposition 2: The rate of return on equity grows linearly with the debt ratio . In class, before using the Mariott Restaurant example to illustrate how to compute beta when there are comparison firms, we showed that: (when introducing the “investing in risky projects” section, i.e. note 11, p 11, last line) ( ) rr D E ea a d =+ This ends the proof.
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This note was uploaded on 05/21/2008 for the course ECON 3330 taught by Professor Mbiekop during the Spring '08 term at Cornell University (Engineering School).

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fin13 - Taxes, Capital Structure and the Modigliani- Miller...

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