# O key intuition leverage amplifies the firms

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o Key intuition: leverage amplifies the firm’s financial risk and thus increases the risk of equity (even with no risk of default). ( ) D U L U E r r E D r r + = Lecture 5: MM Propositions

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15 Proofs of MM1 & MM2 Firm U Firm L Cash Flow C C -Interest 0 – r D D Earnings C C – r D D Payments to debt 0 r D D Payments to equity C C – r D D Payments to all investors C C The intuition of why the value of these two firms is the same is based on the idea of home-made leverage . It means that investors are indifferent between buying L or U because, after buying any of the firms, they can always replicate the capital structure of the other in their own portfolios. Lecture 5: MM Propositions
16 Proofs of MM1 & MM2 Form two portfolios that generate the same perpetual cash flows: One based on the levered firm (Port L) Another based on the unlevered firm (Port U) By no arbitrage, Port L and Port U must have the same cost. Port L: buy α % of L’s equity – Cost: α E L Future cash flow: α (C – r D D) Port U: buy α % of U’s equity and borrow an amount equivalent to α % of L’s debt – Cost: α E U α D Future cash flow: α C – r D α D = α (C – r D D) Lecture 5: MM Propositions

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17 Proofs of MM1 & MM2 Since the two portfolios generate the same future cash flows, they must be worth the same or there would be arbitrage! Thus, α E L = α E U α D or E L = E U – D or E L + D = E U Therefore we get MM1: V L = V U Recall that E L + D = E U = A (market values), and view the firm’s assets (unlevered equity) as a portfolio of debt and equity. Thus, Therefore we get MM2 : A U E L L D L r r r E D E r E D D = = + + + ) ( D U L U E r r E D r r + = Lecture 5: MM Propositions
18 A Leveraged Recapitalization ICC has 50M shares worth \$10 per share and no debt. Its cost of capital is r U = 5%. It has a perpetual random CF with mean \$25M and it pays no taxes. ICC plans a leveraged recapitalization: issue \$200M in perpetual debt at r D = 2% and repurchase shares. Value before: V U = 50M × \$10 = \$500M (= \$25M/.05) Value after: V L = \$500M = \$200M + E L E L = \$300M Note 1: this implies that \$300M = (\$25M – .02 × \$200M) / r E , and thus r E = 7% (also check that r E = .05 + (200M/300M) × (.05 – .02)). Note 2: upon announcement, the share price does not change. Repurchase \$200M / \$10 = 20M shares leaving 50M – 20M = 30M. Bottom line: the recapitalization does not affect firm value or share prices, but it increases the cost of equity. Lecture 5: MM Propositions

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19 The Effect of Leverage on Risk & Return Suppose ICC’s CF can be \$5, \$25, or \$50 Mean=.53 ; Stdev=.45 Mean=.74 ; Stdev=.74 The higher leverage as a result of the recap increases the expected EPS, but it also increases the risk of EPS and thus investors require a higher return on equity. In the end share prices are not affected: Price before = E(EPS) / r U = \$.53 / .05 = \$10.6 Price after = E(EPS) / r E = \$.74 / .07 = \$10.6 ICC With D=\$0 (\$M) ICC With D=\$200M (\$M) CF 5 25 50 CF 5 25 50 - Interest 0 0 0 - Interest -4 -4 -4 Earnings 5 25 50 Earnings 1 21 46 EPS (\$) 0.1 0.5 1 EPS (\$) 0.03 0.7 1.5 Lecture 5: MM Propositions
20 MM Propositions and WACC Before the recapitalization, r WACC = r U = 5%.

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