lecture2-Capital_Structure

# lecture2-Capital_Structure - Capital Structure September...

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Capital Structure September 12, 2005

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Corporate Finance Outline No tax case Corporate taxes case Other costs and benefits of debt: Bankruptcy costs FCF Hypothesis Empirical evidence
Corporate Finance The capital structure problem Finding the “optimal mix” of securities: Debt, Equity, Preferred Stock etc. that maximises the value of the firm We focus on two polar securities: equity and debt

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Corporate Finance Proposition I Assuming: Total cash flows to security holders are independent of how the firm is financed; There are no transaction costs, No arbitrage opportunities exist, Then the total market value of the firm (the sum of the values all sources of capital) is independent of how the firm is financed
Corporate Finance Proof Suppose firms U and L are identical, except for their capital structures U (unlevered) is 100% equity financed, and is worth 800 L (levered) is (partially) financed with debt. It has a zero coupon bond with a face value of 600 Consider two time periods only: t = 0 (now) and t = 1 CF at t = 1 is random: x {0, 600, 1000, 2000}, all equally likely

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Corporate Finance Proof For the levered firm, payoffs to equity and debt are:
Corporate Finance Proof Claim: V U = V L , where V L = V EL + V DL Suppose not. Then: Strategy A: Buy 50% of firm U Strategy B: buy 50% of the debt of L and 50% of its equity

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Corporate Finance Proof The two strategies provide exactly the same payoffs No-arbitrage implies that the prices of both strategies be the same Cash Flow Strategy A Strategy B 0 0 0 600 300 300 1000 500 300+200 2000 1000 300+700
Corporate Finance Proof Cost of strategy A = 0.5V U = 0.5 x 800 = 400 Cost of strategy B = 0.5 V EL + 0.5 V DL = 0.5 V L They must be equal (why?): 0.5 V L = 400 V L = 800 Therefore, V L = V U To avoid arbitrage , the two firms must have the same value.

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Corporate Finance Proposition II Under the same assumptions: 1) A firm’s cost of capital does not depend on its capital structure 2) The expected rate of return on a firm’s stock (cost of equity) increases in proportion to its debt-equity ratio
Corporate Finance Meaning Intuition: More debt decreases the cost of capital (debt is cheaper) But, it also increases the cost of capital, because it increases the risk of the equity The two effects must cancel each other (this is MM)

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Proof Given expected cash flows {E(X 1 ),E(X 2 ),…,E(X T )}, the firm’s value is: (1) By proposition I, the value (V) is independent of the capital structure, and therefore of D By assumption, {E(X 1 ),E(X 2 ),…,E(X T )} do not change with D either T T 2 2 1 ) WACC 1 ( ) X ( E ... ) WACC
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## This note was uploaded on 11/22/2010 for the course FINANCE 100104 taught by Professor Pfofessorking during the Spring '10 term at Erusmus University Rotterdam .

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lecture2-Capital_Structure - Capital Structure September...

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