Théorie Financière Structure financière et coût du capital Professeur André Farber

June 13, 2015 Structure financière |2 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 ?

June 13, 2015 Structure financière |3 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 WACC = r A r A is the cost of capital of an all equity firm

June 13, 2015 Structure financière |4 Weighted Average Cost of Capital (no taxes) 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

June 13, 2015 Structure financière |5 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)?

June 13, 2015 Structure financière |6 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%

June 13, 2015 Structure financière |7 Cost of equity calculation Value of all-equity firm Value of equity Value of debt V (=V U ) = E + D rErE rDrD rArA

June 13, 2015 Structure financière |8 Why is 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 = 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 WACC = r A

June 13, 2015 Structure financière |9 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

June 13, 2015 Structure financière |10 Relationship between the value of company and WACC From the definition of the WACC: WACC * V = r equity * E + r debt * D As r equity * E = Div and r debt * D = Int r wacc * V = EBIT V = EBIT / WACC Market value of levered firm EBIT is independent of leverage If value of company varies with leverage, so does WACC in opposite direction

June 13, 2015 Structure financière |11 MM II: another presentation The equality 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

June 13, 2015 Structure financière |12 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

June 13, 2015 Structure financière |13 Back to example Assume debt is riskless:

June 13, 2015 Structure financière |14 Corporate Tax Shield Interest are tax deductible => tax shield Tax shield = Interest payment × Corporate Tax Rate = (r D × D) × T C r D : cost of new debt D : market value of debt Value of levered firm = Value if all-equity-financed + PV(Tax Shield) PV(Tax Shield) - Assume permanent borrowing V L =V U + T C D

June 13, 2015 Structure financière |15 Cost of equity calculation Value of all-equity firm Value of tax shield Value of equity Value of debt V U + T = E + D rErE rDrD rArA rDrD

June 13, 2015 Structure financière |16 Cost of equity calculation (2) If r TS = r D & VTS = T C D Similar formulas for beta equity (replace r by β) General formula

June 13, 2015 Structure financière |17 WACC

June 13, 2015 Structure financière |18 Example A B Balance Sheet Total Assets 1,000 1,000 Book Equity 1, Debt (8%) Income Statement EBIT Interest 0 40 Taxable Income Taxes (40%) Net Income Dividend Interest 0 40 Total Assume r A = 10% (1) Value of all-equity-firm: V U = 144 / 0.10 = 1,440 (2) PV(Tax Shield): Tax Shield = 40 x 0.40 = 16 PV(TaxShield) = 16/0.08 = 200 (3) Value of levered company: V L = 1, = 1,640 (5) Market value of equity: E L = V L - D = 1, = 1,140

June 13, 2015 Structure financière |19 What about cost of equity? 1) Cost of equity increases with leverage: 2) Beta of equity increases Proof: But V U = EBIT(1-T C )/r A and E = V U + T C D – D Replace and solve In example: r E = 10% +(10%-8%)(1-0.4)(500/1,140) = 10.53% or r E = DIV/E = 120/1,140 = 10.53%

June 13, 2015 Structure financière |20 What about the weighted average cost of capital? Weighted average cost of capital decreases with leverage Weighted average cost of capital: discount rate used to calculate the market value of firm by discounting net operating profit less adjusted taxes (NOPLAT) NOPLAT = Net Income + Interest + Tax Shield = (EBIT-r D D)(1-T C ) + r D D +T C r D D = Net Income for all-equity-firm = EBIT(1-T C ) VL = NOPLAT / WACC As: In example: NOPLAT = 144 V L = 1,640 WACC = 10.53% x % x 0.60 x 0.31 = 8.78%