Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 1 Corporate Finance Modigliani Miller Professor André Farber Université Libre de Bruxelles Solvay Business School

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 2 Practice of corporate finance: evidence from the field Graham & Harvey (2001) : survey of 392 CFOs about cost of capital, capital budgeting, capital structure. «..executives use the mainline techniques that business schools have taught for years, NPV and CAPM to value projects and to estimate the cost of equity. Interestingly, financial executives are much less likely to follows the academically proscribed factor and theories when determining capital structure » Are theories valid? Are CFOs ignorant? Are business schools better at teaching capital budgeting and the cost of capital than at teaching capital structure? Graham and Harvey Journal of Financial Economics 60 (2001)

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 3 The message from CFOs: Capital budgeting

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 4 The message from CFOs : cost of equity

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 5 Cost of capital with debt Up to now, the analysis has proceeded based on the assumption that investment decisions are independent of financing decisions. Does the value of a company change the cost of capital change if leverage changes ?

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 6 An example CAPM holds – Risk-free rate = 5%, Market risk premium = 6% Consider an all-equity firm: Market value V100 Beta1 Cost of capital11% (=5% + 6% * 1) Now consider borrowing 20 to buy back shares. Why such a move? Debt is cheaper than equity Replacing equity with debt should reduce the average cost of financing What will be the final impact On the value of the company? (Equity + Debt)? On the weighted average cost of capital (WACC)?

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 7 Weighted Average Cost of Capital An average of: The cost of equity r equity The cost of debt r debt Weighted by their relative market values (E/V and D/V) Note: V = E + D

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 8 Modigliani Miller (1958) Assume perfect capital markets: not taxes, no transaction costs Proposition I: The market value of any firm is independent of its capital structure: V = E+D = V U Proposition II: The weighted average cost of capital is independent of its capital structure r wacc = r A r A is the cost of capital of an all equity firm

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 9 MM 58: Proof 1 period C = expected future cash flow If company unlevered:

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 10 MM 58: Proof (II) If levered (assuming riskless debt): But: Div = C - (1+r f ) D So: =VU=VU

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 11 Using MM 58 Value of company: V = 100 InitialFinal Equity Debt 0 20 Total MM I WACC = r A 11%11% MM II Cost of debt-5% (assuming risk-free debt) D/V00.20 Cost of equity11%12.50% (to obtain r wacc = 11%) E/V100%80%

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 12 Why is r wacc unchanged? Consider someone owning a portfolio of all firm’s securities (debt and equity) with X equity = E/V (80% in example ) and X debt = D/V (20%) Expected return on portfolio = r equity * X equity + r debt * X debt This is equal to the WACC (see definition): r portoflio = r wacc But she/he would, in fact, own a fraction of the company. The expected return would be equal to the expected return of the unlevered (all equity) firm r portoflio = r A The weighted average cost of capital is thus equal to the cost of capital of an all equity firm r wacc = r A

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 13 What are MM I and MM II related? Assumption: perpetuities (to simplify the presentation) For a levered companies, earnings before interest and taxes will be split between interest payments and dividends payments EBIT = Int + Div Market value of equity: present value of future dividends discounted at the cost of equity E = Div / r equity Market value of debt: present value of future interest discounted at the cost of debt D = Int / r debt

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 14 Relationship between the value of company and WACC From the definition of the WACC: r wacc * V = r equity * E + r debt * D As r equity * E = Div and r debt * D = Int r wacc * V = EBIT V = EBIT / r wacc Market value of levered firm EBIT is independent of leverage If value of company varies with leverage, so does WACC in opposite direction

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 15 MM II: another presentation The equality r wacc = r A can be written as: Expected return on equity is an increasing function of leverage: rArA D/E r equity 11% r debt 5% % r wacc Additional cost due to leverage

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 16 Why does r equity increases with leverage? Because leverage increases the risk of equity. To see this, back to the portfolio with both debt and equity. Beta of portfolio:  portfolio =  equity * X equity +  debt * X debt But also:  portfolio =  Asset So: or

Solvay Business School – Université Libre de Bruxelles 22/06/2015ExMaFin Modgliani Miller 17 Back to example Assume debt is riskless: Beta asset = 1 Beta equity = 1(1+20/80) = 1.25 Cost of equity = 5% + 6%  1.25 = 12.50