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FINANCE 11. Capital Structure and Cost of Capital

FINANCE 11. Capital Structure and Cost of Capital. Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2006. Risk and return and capital budgeting. Objectives for this session: Beta of a portfolio Beta and leverage Weighted average cost of capital

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FINANCE 11. Capital Structure and Cost of Capital

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  1. FINANCE11. Capital Structure and Cost of Capital Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2006

  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 MBA 2006 Cost of capital

  3. Beta of a portfolio • Consider the following portfolio Stock Value Beta A nA PAA B nB PBB • The value of the portfolio is: V = nA PA+nA PB • The fractions invested in each stock are: Xi = ( ni Pi) / V for i = A,B • The beta of the portfolio is the weighted average of the betas of the individual stocks P = XA A + XB B MBA 2006 Cost of capital

  4. Example • Stock $  X • ATT 3,000 0.76 0.60 • Genetech 2,000 1.40 0.40 • V 5,000 • P = 0.60 * 0.76 + 0.40 * 1.40 = 1.02 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)  • Electrical 100 0.50 • Chemical 500 0.90 • V 600 • firm = (100/600) * (0.50) + (500/600) * 0.90 = 0.83 • Assume: rf = 5% rM - rf = 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% 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 portfolio 2,000 1 2 • Risk-free rate -1,000 0 -1 • V 1,000 • P = 2  1 + (-1)  0 = 2 MBA 2006 Cost of capital

  7. Expected Return Expected Return P 20% P M 14% 14% M 8% 8% 2 Sigma 1 Beta 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 ? 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 V 100 • Beta 1 • Cost of capital 11% (=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)? MBA 2006 Cost of capital

  10. Weighted Average Cost of Capital • An average of: • The cost of equity requity • The cost of debt rdebt • Weighted by their relative market values (E/V and D/V) • Note: V = E + D 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 = VU • Proposition II: • The weighted average cost of capital is independent of its capital structure rwacc = rA • rA is the cost of capital of an all equity firm MBA 2006 Cost of capital

  12. Using MM 58 • Value of company: V = 100 • Initial Final • Equity 100 80 • Debt 0 20 • Total 100 100 MM I • WACC = rA 11% 11% MM II • Cost of debt - 5% (assuming risk-free debt) • D/V 0 0.20 • Cost of equity 11% 12.50% (to obtain rwacc = 11%) • E/V 100% 80% MBA 2006 Cost of capital

  13. Why is rwacc unchanged? • Consider someone owning a portfolio of all firm’s securities (debt and equity) with Xequity= E/V (80% in example ) and Xdebt= D/V (20%) • Expected return on portfolio = requity * Xequity + rdebt * Xdebt • This is equal to the WACC (see definition): rportoflio= rwacc • 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 rportoflio = rA • The weighted average cost of capital is thus equal to the cost of capital of an all equity firm rwacc = rA 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 / requity • Market value of debt: present value of future interest discounted at the cost of debt D = Int / rdebt MBA 2006 Cost of capital

  15. Relationship between the value of company and WACC • From the definition of the WACC: rwacc* V = requity * E + rdebt * D • As requity * E = Div and rdebt * D = Int rwacc* V = EBIT V = EBIT / rwacc Market value of levered firm EBIT is independent of leverage If value of company varies with leverage, so does WACC in opposite direction MBA 2006 Cost of capital

  16. MM II: another presentation • The equality rwacc = rA can be written as: • Expected return on equity is an increasing function of leverage: requity 12.5% Additional cost due to leverage 11% rwacc rA 5% rdebt D/E 0.25 MBA 2006 Cost of capital

  17. Why does requity 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 * Xequity + debt * Xdebt • But also: portfolio = Asset • So: • or MBA 2006 Cost of capital

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

  20. Corporate Tax Shield • Interest are tax deductible => tax shield • Tax shield = Interest payment × Corporate Tax Rate = (rD× D) × TC • rD: 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 VL=VU + TCD MBA 2006 Cost of capital

  21. 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 Income 144 120 Dividend 144 120 Interest 0 40 Total 144 160 Assume rA= 10% (1) Value of all-equity-firm: VU = 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: VL = 1,440 + 200 = 1,640 (5) Market value of equity: EL = VL - D = 1,640 - 500 = 1,140 Example MBA 2006 Cost of capital

  22. What about cost of equity? Proof: But VU = EBIT(1-TC)/rA and E = VU + TCD – D Replace and solve 1) Cost of equity increases with leverage: 2) Beta of equity increases In example: rE = 10% +(10%-8%)(1-0.4)(500/1,140) = 10.53% or rE= DIV/E = 120/1,140 = 10.53% 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-rDD)(1-TC) + rDD +TCrDD • = Net Income for all-equity-firm = EBIT(1-TC) VL = NOPLAT / WACC • As: In example: NOPLAT = 144 VL= 1,640 WACC = 10.53% x 0.69 + 8% x 0.60 x 0.31 = 8.78% MBA 2006 Cost of capital

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