Leverage. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Overview

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1 Leverage FINANCE 35 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University Overview Capital Structure does not matter! Modigliani & Miller propositions Implications for corporate debt policy Capital structure and required returns The weighted average cost of capital (WACC) Un-levering betas Optimal debt policy 2

2 Does Leverage Matter? Example:Buy a house, sell after 1 year Cost: \$1, Interest rate: 1% House price Return to you with mortgage of change % % 5% 9% The Impact of Leverage Leverage increases shareholders expected return Leverage also increases the riskiness of returns The way an individual house is financed has no effect on: the value of the house the volatility of the house price Asset cash flows and risks are independent of financing Limited liability does not affect this conclusion, but returns for borrower and lender are different The firm is only a collection of assets 4

3 Capital Structure Does not Matter! The Modigliani-Miller Propositions Under the assumption that: There are no taxes. There are no costs of financial distress. There are no asymmetries of information. The investment and operating policies of the firm are given. the value of a firm is independent of its capital structure (MM Proposition I). 5 How Do Returns Depend on Risk? How do the returns on debt and equity depend on the returns of the firm? Define: r D D1 D = D We always have: V = E + D It is easy to show that: V = E + r E E1 E = E V 1,V do not depend on leverage (MM Proposition I), hence: V1 V E D ra = = re + rd V V V 1 1 D1 V1 V = V In a perfect capital market, the firm s weighted average cost of capital is independent of its capital structure.(modigliani-miller Proposition II). r A 6

4 The Weighted Average Cost of Capital (WACC) The main consequence of MM Proposition II is that we can calculate the cost of capital as a weighted average of the cost of debt and the cost of equity: r E = WACC = re V A + We know all the variables on the right-hand side of the equation Determine r E, r D using asset pricing model D, E are given as market values sometimes approximated by book values Use WACC formula to compute cost of capital for capital budgeting r D D V 7 What Determines the Cost of Capital? MM Proposition II says that WACC does not depend on leverage Returns on debt and equity change as leverage changes! D re = ra + ( ra rd ) E Return on equity compensates for two sources of risk: business risk - reflected in r A. financial risk - reflected in r A -r D, increases in leverage. Expected return on debt may also increase if debt becomes risky. As leverage increases two things happen: Equity-holders demand higher returns, but: Finance more projects by (relatively cheaper) debt. MM implies that these two effects cancel exactly! 8

5 Leverage and the Cost of Capital A Graphical Illustration Required Return r e r* r F r d D/E 9 Capital Structure and Returns - Example MacBeth Spot Removers is 1% equity financed and considers a debt/equity-swap (also called a leveraged recapitalization): Currently: \$12m equity \$2m operating income (perpetuity) Plan: Retire equity worth \$6m Expected return on debt: 1% What is the required return on equity after the recapitalization? What is the debt placed in the recapitalization worth? What is the perpetual stream of dividends and interest? 1

6 MacBeth Spot Removers Issue \$6m debt, retire \$6m equity Cash flows to firm remain unaffected Uses of funds (in perpetuity): Interest =.1*\$6m=\$6, Dividends = Operating Income - Interest = \$1.4m Return on equity = \$1.4m/\$6m=23.3% Then cost of capital calculations give us: WACC =.5*23.3%+.5*1%=16.7% Cost of capital=\$2m/\$12m=16.7% 11 Perfect Capital Markets: Leverage and the CAPM The CAPM can be used to compute all of these discount rates: Use the equity beta to compute the return on equity: E[r E ] = r f + b E (E[r M ]- r f ). Use the debt beta to compute the return on debt: E[r D ] = r f + b D (E[r M ]- r f ). Use the asset beta to compute a return commensurate with the business risk of the assets: E[r A ] = r f + b A (E[r M ]- r f ). The beta of the assets (b A ) is also known as the beta of equity in an unlevered firm (b U ). The equity in an unlevered firm has no financial risk, only business risk. The only source of risk in the unlevered firm is the inherent business risk of the assets themselves. 12

7 Perfect Capital Markets: Leverage and the Cost of Capital The firm s asset beta is a weighted average of the debt and equity betas: D E A = D + V E V This implies the following relationship between the firm s equity beta and its leverage: E = A + A D ( ) D E Note: the same relations that hold for required rates of return hold also for betas! 13 Leverage and Beta Reconsider the leveraged recapitalization of MacBeth Spot Removers. Assume a risk-free interest rate of r f = 1.% and a market risk premium of [E(r M )-r f ] = 8.%. Debt beta = Asset beta =.833 After the recapitalization we have: Equity beta = Debt beta = Asset beta =.5*+.5*1.667=.833 How does shareholder wealth change? 14

8 Accounting for Leverage in Capital Budgeting Each investment project has its own cost of capital that depends upon the risk of the investment. NPV must be computed using a discount rate appropriate for the project, not the firm. The risk of the investment project depends upon its unlevered (asset) beta. The unlevered cost of capital can be estimated using the CAPM. How do we find this? Step 1: Compute the beta of the assets by unlevering another firm s equity beta. Step 2: Use the CAPM to determine a required return to compensate investors for bearing this inherent business risk. Step 3: Use this required return to find the NPV. 15 Capital Budgeting Example Your firm is currently in the computer software business, but is considering investing in the development of a new airline. Information on your firm and the airline industry are given below: Your Firm Airline Industry Equity Be t a Debt-Equity Ratio 67% Estimate of debt beta

9 Capital Budgeting Example Your airline project: expected to cost \$2 million per year for the next 5 years. expected to generate after-tax cash flows of \$1 million per year indefinitely thereafter. the risk-free interest rate is 9%. and the market risk premium is 8%. 17 Capital Budgeting Example Step 1: Unlever Equity Beta for Airlines Hence: E D Asset Airlines = Equity + V Debt V A =1.95* *.4 =1.22 Step 2: Calculate the Cost of Capital: r A = (.8)=.1876 Step 3: Calculate the NPV of the Project NPV = t= 6 \$1 (1.1876) t 5 t=1 \$2 = 38.92million (1.1876) t 18

10 Two ways of Dealing with Leverage 1) Unlever betas 2) Weighted Average Cost of Capital Security betas Capital structure Cost of Equity Cost of Debt Asset beta Capital structure Cost of capital Cost of capital 19 Summary Capital structure is irrelevant unless there are market imperfections to exploit Leverage changes the required rates of return on debt and equity, but not the required rate of return on a company unless taxes are important Two ways to calculate cost of capital of the leveraged firm: Weighted average cost of capital suitable if you know costs of debt and equity Unlevering betas suitable for new projects or companies. More on these issues in FINANCE 351!!! 2

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