1. FINANCE 11. Capital Structure and Cost of Capital Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2006

2. MBA 2006 Cost of capital |2 Risk and return and capital budgeting Objectives for this session: – Beta of a portfolio – Beta and leverage – Weighted average cost of capital – Modigliani Miller 1958

3. MBA 2006 Cost of capital |3 Beta of a portfolio Consider the following portfolio StockValueBeta An A  P A  A Bn B  P B  B The value of the portfolio is: V = n A  P A + n A  P B The fractions invested in each stock are: X i = ( n i P i ) / V for i = A,B The beta of the portfolio is the weighted average of the betas of the individual stocks  P = X A  A + X B  B

4. MBA 2006 Cost of capital |4 Example Stock$  X ATT3,0000.760.60 Genetech2,0001.400.40 V5,000  P = 0.60 * 0.76 + 0.40 * 1.40 = 1.02

5. MBA 2006 Cost of capital |5 Application 1: cost of capital for a division Firm = collection of assets Example: A company has two divisions Value($ mio)  Electrical1000.50 Chemical5000.90 V600  firm = (100/600) * (0.50) + (500/600) * 0.90 = 0.83 Assume: r f = 5%r M - r f = 6% Expected return on stocks: r = 5% + 6%  0.83 = 9.98 % An adequate hurdle rate for capital budgeting decisions ? No The firm should use required rate of returns based on project risks: Electricity : 5 + 6  0.50 = 8% Chemical : 5 + 6  0.90 = 10.4%

6. MBA 2006 Cost of capital |6 Application 2: leverage and beta Consider an investor who borrows at the risk free rate to invest in the market portfolio Assets$  X Market portfolio2,00012 Risk-free rate-1,0000-1 V1,000  P = 2  1 + (-1)  0 = 2

7. MBA 2006 Cost of capital |7 8% 14% 1 2 Beta M P 8% 14% 20% Sigma Expected Return M P

8. MBA 2006 Cost of capital |8 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 ?

9. MBA 2006 Cost of capital |9 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 10 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)?

10. MBA 2006 Cost of capital |10 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

11. MBA 2006 Cost of capital |11 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

12. MBA 2006 Cost of capital |12 Using MM 58 Value of company: V = 100 InitialFinal Equity100 80 Debt 0 20 Total100100 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%

13. MBA 2006 Cost of capital |13 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

14. MBA 2006 Cost of capital |14 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

15. MBA 2006 Cost of capital |15 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

16. MBA 2006 Cost of capital |16 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% 0.25 12.5% r wacc Additional cost due to leverage

17. MBA 2006 Cost of capital |17 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

18. MBA 2006 Cost of capital |18 Back to example Assume debt is riskless:

19. MBA 2006 Cost of capital |19 Review: MM 58 Debt policy doesn’t matter in perfect capital market MM I: market value of company independent of capital structure V = E + D MM II: WACC independent of capital structure Underlying assumptions: No taxes! Symetric information

20. MBA 2006 Cost of capital |20 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

21. MBA 2006 Cost of capital |21 Example A B Balance Sheet Total Assets 1,000 1,000 Book Equity 1,000 500 Debt (8%) 0 500 Income Statement EBIT 240 240 Interest 0 40 Taxable Income 240 200 Taxes (40%) 96 80 Net Income144 120 Dividend 144 120 Interest 0 40 Total 144 160 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 = 1,440 + 200 = 1,640 (5) Market value of equity: E L = V L - D = 1,640 - 500 = 1,140

22. MBA 2006 Cost of capital |22 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%

23. MBA 2006 Cost of capital |23 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 0.69 + 8% x 0.60 x 0.31 = 8.78%