FM12 Ch 17 Tool Kit - A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15...

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1/1/2007 Chapter 17. Tool Kit for Capital Structure Decisions: Extensions Modigliani and Miller without Taxes Proposition I. 1. The weighted average cost of capital is independent of the firm's capital structure. 2. The WACC of a firm with debt is equal to the unlevered cost of equity. Proposition II. Example of an arbitrage opportunity in zero-growth firms: Input Data Firm U Firm L No Debt Some Debt EBIT $900,000 $900,000 Debt $0 $4,000,000 NA 7.5% 10% 10% Value of Stock $9,000,000 $6,000,000 Total Market Value of Firm $9,000,000 $10,000,000 Value of Firm = Value of Stock + Value of Debt Borrow amt. Invest $100,000 Portfolio of U, Buy equal to 10% in risk free Debt, and risk Buy 10% of U of L's Debt asset free asset 10% of L Cost $900,000 ($400,000) $100,000 $600,000 $600,000 Income $90,000 ($30,000) $7,500 $67,500 $60,000 CAPITAL STRUCTURE THEORY: ARBITRAGE PROOFS OF THE MODIGLIANI-MILLER MODELS (Section 17.1) Franco Modigliani and Merton Miller developed a model to examine the impact of debt on firm value. In this first version it is assumed that taxes are zero. The cost of equity, r sL = r sU + Risk premium = r sU + (r sU -r d )(D/S) Suppose that r sL = r sU = 10%. We will show that this leads to an arbitrage opportunity. rd rs Value of Stock = (EBIT - r d D)/r S Compare an investment in L with a "synthetic" investment that duplicates L's leverage using an investment in U and borrowing on the investor's own account. Notice that for the same $600,000 investment, you can get $7,500 more in annual income by forming your own portfolio of U and "home made debt" than you get from an investment in L. MM argue that this won't persist--that investors would buy U and purchase the portfolio, driving up the price of U. At the same time, they would sell their shares of L, driving down its price. A
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FM12 Ch 17 Tool Kit - A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15...

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