# After the recapitalization r wacc 35 7 25 2 5 r wacc

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After the recapitalization, r WACC = (3/5) × 7% + (2/5) × 2% = 5% r WACC did not change as a result of the recapitalization! Since A = E U = D + E L the return on the firm’s assets is equal to the return on the unlevered equity, and both are equal to the return on a value-weighted portfolio of the firm’s debt and equity. Thus: Changes in capital structure do not affect a firm’s r WACC and since V L = C / r WACC , they do not affect a firm’s value either . E L L D L U A WACC r E D E r E D D r r r + + + = = = Lecture 5: MM Propositions

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MM Propositions and WACC What does that imply for the cost of equity? Solve for R E : r E = r A + (r A – r D )(D/E) o r A = WACC= r U is the “cost” of the firm’s business risk and is constant, no matter what is the capital structure o (r A – r D )(D/E) is the “cost” of the firm’s financial risk , i.e., the additional return required by stockholders to compensate for the risk of leverage o Increased leverage increases the cost of equity! o Why? Because more debt makes equity riskier and so increases its cost (equity beta increases). Lecture 5: MM Propositions 21
MM Propositions and WACC Lecture 5: MM Propositions 22

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} Remember than betas are additive, so β A = w D β D + w E β E } We know that, if the debt is risk-free, its beta is zero ( β D =0), so: β A = w E β E } Therefore, we have that β E = (1/w E ) β A = β A (1+D/E) Firms with same business risk can differ in the market risk of their equity if they differ in financial leverage! } If you plug in this beta in the CAPM, you will get exactly the same result as before: r E = r A + (r A – r D )(D/E) Therefore, the MM irrelevance proposition is consistent with CAPM. An Alternative Approach: CAPM Lecture 5: MM Propositions 23
An Alternative Approach: CAPM β E = β A (1 + D/E) } β A is the unlevered beta , i.e. the beta of the firm without any leverage (i.e. the beta of assets) } β E is the levered beta (equity beta) } Therefore, the systematic risk of the stock depends on: Systematic risk of the assets, β A ( Business risk ) Level of leverage, D/E ( Financial risk ) Think about it: leverage increases the volatility of the CF to shareholders, increasing shareholder CF in good times and decreasing them in bad times; therefore, if the CF already comove with the market (positive beta), then leverage will make them comove even more (higher beta) Lecture 5: MM Propositions 24

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MM Irrelevance Proposition is a benchmark Ø If financing decisions are unrelated to investment decisions, then capital structure is irrelevant. Financial policy simply divides the “pie” between different claimholders. Ø If operating cash flows are given (independent of capital structure), the division of the pie is irrelevant. Ø MM should be thought of as a benchmark: if we can identify the conditions under which capital structure is irrelevant, we may be able to infer what makes it relevant!

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