December 2, 2008 Chapter 10: Risk & Capital Budgeting WACC No tax WACC Tax WACC Financial Leverage Operating Leverage Decision Tree Application of Risk Analysis Financial Leverage Financial Leverage: higher financial leverage = higher debt higher debt-to-equity ratio Implications: Example: Firm A & firm B both have assets of $100 million. Both firms must pay 7% interest rate. Calculate ROE for both firms if ROA = 2%; 5%; 10% Firm A: D/E ratio = ¼ Firm B: D/E ratio = 1 ROA = EBIT / Assets ROA = 2% Firm A: D/E = ¼ Firm B: D/E = 1 EBIT = 2,000,000 EBIT = 2,000,000 - Interest = 1,400,000 - Interest = 3,500,000 Pretax Income = 600,000 Pretax Income = - 1,500,000 ROE = 600,000 / 80,000,000 ROE = -1,500,000 / 50,000,000 = .75% = -3% D/E = ¼ Debt = 20 20,000,000 x 7% = 1,400,000 Equity = 80 D/E = 1 Debt = 50 3,500,000 Debt = 50 ROA = 5% Firm A: D/E = ¼ Firm B: D/E = 1 EBIT = 5,000,000 EBIT = 5,000,000 Interest = 1,400,000 Interest = 3,500,000 Pretax Income = 3,600,000 Pretax Income = 1,500,000 ROE = 3,600,000 / 80,000,000 ROE = 1,500,000 / 50,000,000 = 4.5% = 3% ROA = 10% Firm A: D/E = ¼ Firm B: D/E = 1 EBIT = 10,000,000 EBIT = 10,000,000 Interest = 1,400,000 Interest = 3,500,000 Pretax Income = 8,600,000 Pretax Income = 6,500,000 ROE =8,600,000 / 80,000,000 ROE = 6,500,000 / 50,000,000 = 10.75% = 13% ROE B 13 10.75 A 4.5 3 .75 2 5 7.5 10 ROA -3 A has higher ROE w/ lower level of ROA Firm B has higher ROE w/ higher level of ROA ROEB is more sensitive to changes in ROA Profitability B is more volatile B has higher risk Financial Leverage measures how ROE is sensitive to ROA Operating Leverage ( EBIT / EBIT) / ( in Sales / Sales) (EBIT2 ? EBIT1) / (EBIT1) (Sales2 ? Sales1) / Sales1 Example: Firm1: EBIT1 = 10,000,000 EBIT2 = 12,000,000 Sales1 = 100,000,000 Sales2 = 150,000,000 Firm 2: EBIT1 = 9,000,000 EBIT2 = 10,000,000 Sales1 = 100,000,000 Sales2 = 150,000,000 Operating LeverageA = [(12 ? 10) / 10] / [(150 ? 100) / 100] .2 / .5 = .4 or 40% Operating LeverageB = [(10-9) / 9] / [(150 ? 100) / 100] .111 / .5 = .22 or 22% The OL for A is higher than OL for B Given the same % change in Sales, there will be a higher increase in EBITA Financial Leverage measure sensitivity of ROE (profitability) to ROA Operating Leverage measure sensitivity of EBIT to Sales An Approach of Risk Analysis Decision Tree Decision Tree: how our decision (capital budgeting) depends on different probabilities & outcomes of each scenario Example: P10-13 Initial Investment of the project = 20,000,000 to be paid at the end of Yr 2 Initial Study = 2,000,000 to be paid today If the Firm implements the Initial Study, it has 2 yrs to decide whether to invest in the project or not. If the Firm implements the Initial Study, its preliminary results show that: 50% chance of strong mkt The profit will generate 5.2/yr for 8 years 20% chance of moderate mkt The profit will generate 4.5/yr for 8 years 30% chance of weak mkt The profit will generate 4.0/yr for 8 years Cost of Capital = 12% $20 mill investment 50% 5.2/yr for 8 years 25.83 2 yrs from today 20% 4.5/yr for 8 years 22.35 Initial Study ($2,000,000 ? Today) 30% 4.0/yr for 8 years 19.87 Expected NPV = 3.38 No Initial Study ($0) If the market is strong, the PV of 5.2 mill/yr for 8 years is? (PMT / r) x [1 ? (1 / (1+r)n)] = PV of an annuity 5.2 / .12 x [1 ? (1 / (1.12)8] = 25.83 NPV = 25.83 ? 20 = 5.83 If the market is moderate, the PV of 4.5 mill/yr for 8 years is? (PMT / r) x [1 ? (1 / (1+r)n)] = PV of an annuity 4.5 / .12 x [1 ? (1 / (1.12)8} = 22.35 NPV = 22.35 ? 20 = 2.35 If the market is weak, the PV of 4.0 mill/yr for 8 years is? (PMT / r) x [1 ? (1 / (1+r)n)] = PV of an annuity 4.0 / .12 x [1 ? (1 / 1.12)8} = 19.87 NPV = 19.87 ? 20 = -.13 50% 5.83 20% 2.35 30% -.13 Expected NPV: (50% x 5.83) + (20% x 2.35) + (30% x 0) = 3.38 If NPV < 0, NOT INVEST (drop project) Do not use -.13 but substitute 0 Expected NPV (Today): 3.38 / (1.12)2 = 2.70 n = 2 because calculating 2 yrs from today PV[Expected NPV] = 2.70 NPV[Initial Study & Project] = (2.7 ? 2.0) = (.7 > 0) Implement Initial Study ROEA ROEB ROA = 2% .75% -3% ROA = 5% 4.5% 3% ROA = 10% 10.75% 13%