VIEWS: 0 PAGES: 37 CATEGORY: Other POSTED ON: 9/6/2010
Finance Analyse de projets d’investissement Professeur André Farber Investment decisions • Objectives for this session : • Review investment rules • NPV, IRR, Payback • BOF Project • Free Cash Flow calculation • Inflation • A project is not a black box: Sensitivity analysis, break even point • Timing: • How long to invest? • When to invest? • Project with different lifes: Equivalent Annual Cost September 8, 2010 Capital budgeting (1) |2 Investment rules • Net Present Value (NPV) NPV – Discounted incremental free cash flows – Rule: invest if NPV>0 IRR • Internal Rate of Return (IRR) r – IRR: discount rate such that NPV=0 – Rule: invest if IRR > Cost of capital • Payback period – Numbers of year to recoup initial investment – No precise rule • Profitability Index (PI) – PI = NPV / Investment – Useful to rank projects if capital spending is limited September 8, 2010 Capital budgeting (1) |3 Internal Rate of Return IRR • Can be viewed as the “yield to maturity” of the project • Remember: the yield to maturity on a bond is the rate that set the present value of the expected cash flows equal to its price • Consider the net investment as the price of the project • The IRR is the rate that sets the present value of the expected cash flows equal to the net investment • The IRR is the rate that sets the net present value equal to zero September 8, 2010 Capital budgeting (1) |4 What do CFOs Use? • % Always or Almost Always • Internal Rate of Return 75.6% • Net Present Value 74.9% • Payback period 56.7% • Discounted payback period 29.5% • Accounting rate of return 30.3% • Profitability index 11.9% • Based on a survey of 392 CFOs Source: Graham, John R. and Harvey R. Campbell, “The Theory and Practice of Corporate Finance: Evidence from the Field”, Journal of Financial Economics 2001 September 8, 2010 Capital budgeting (1) |5 IRR Pitfall 1: Lending or borrowing? • Consider following projects: IRR: borrowing or lending? • 0 1 IRR NPV(10%) 30.00 • A -100 +120 20% 9.09 20.00 Net Present Value • B +100 -120 20% -9.09 10.00 0.00 • A: lending Rule IRR>r 0% 3% 6% 9% % % % % % % % -10.00 • 12 15 18 21 24 27 30 B: borrowing Rule IRR<r -20.00 -30.00 Discount rate Project A Project B September 8, 2010 Capital budgeting (1) |6 IRR Pitfall 2 Multiple Rates of Return • Consider the following project • Year 0 1 2 Multiple Rates of Return • CF -1,600 10,000 -10,000 1500.00 1000.00 • 2 “IRRs” : +25% & +400% Net Present Value 500.00 0.00 • This happens if more than one change 135% 180% 225% 270% 315% 360% 405% 450% 495% 45% 90% 0% -500.00 in sign of cash flows -1000.00 -1500.00 • To overcome problem, use modified -2000.00 IRR method Discount Rate – Reinvest all intermediate cash flows at the cost of capital till end of project – Calculate IRR using the initial investment and the future value of intermediate cash flows September 8, 2010 Capital budgeting (1) |7 IRR Pitfall 3 - Mutually Exclusive Projects Scale Problem (r = 10%) Timing Problem (r = 10%) C0 C1 C2 NPV IRR A -100 +20 +120 17.4 20.0% C0 C1 NPV IRR B -100 +80 +52 15.7 22.5% Small -10 +20 8.2 100% Large -50 +80 22.7 60% A-B 0 -60 +68 1.7 13.3% To choose, look at incremental cash flows C0 C1 NPV IRR L-S -40 +60 14.5 50% September 8, 2010 Capital budgeting (1) |8 Payback • The payback period is the number of years it takes before the cumulative forcasted cash flows equals the initial investment. • Example: Year 0 1 2 3 Payback NPV r=10% A -1,000 500 500 1,000 2 619 B -1,000 0 1,000 0 2 -174 C -1,000 500 500 0 2 -132 • A very flawed method, widely used • Ignores time value of money • Ignores cash flows after cutoff date September 8, 2010 Capital budgeting (1) |9 Profitability Index • Profitability Index = PV(Future Cash Flows) / Initial Investment • A useful tool for selecting among projects when capital budget limited. • The highest weighted average PI September 8, 2010 Capital budgeting (1) |10 NPV - Review • NPV: measure change in market value of company if project accepted • As market value of company V = PV(Future Free Cash Flows) FCFt NPV V t t (1 r ) • V = Vwith project - Vwithout project • Cash flows to consider: – cash flows (not accounting numbers) • do not forget depreciation and changes in WCR – incremental (with project - without project) • forget sunk costs • include opportunity costs • include all incidental effects • beware of allocated overhead costs September 8, 2010 Capital budgeting (1) |11 Inflation • Be consistent in how you handle inflation • Discount nominal cash flows at nominal rate • Discount real cash flows at real rate – Both approaches lead to the same result. • Example: Real cash flow in year 3 = 100 (based on price level at time 0) – Inflation rate = 5% – Real discount rate = 10% Discount real cash flow using real rate Discount nominal cash flow using nominal rate PV = 100 / (1.10)3 = 75.13 Nominal cash flow = 100 (1.05)3 = 115.76 Nominal discount rate = (1.10)(1.05)-1 = 15.5% PV = 115.76 / (1.155)3 = 75.13 September 8, 2010 Capital budgeting (1) |12 Investment Project Analysis: BOF Big Oversea Firm is considering the project Year 0 1 2 3 Initial Investment 60 Resale value 20 Sales 100 100 Cost of sales 50 50 Corporate tax rate = 40% Working Capital Requirement = 25% Sales Discount rate = 10% September 8, 2010 Capital budgeting (1) |13 BOF: Free Cash Flow Calculation Year 0 1 2 3 Sales 100 100 Cost of sales 50 50 EBITDA 50 50 Depreciation 30 30 EBIT 20 20 Taxes 8 8 8 Net income 12 12 -8 Net income 12 12 -8 Depreciation 30 30 0 DWCR 25 0 -25 CFInvestment -60 20 Free Cash Flow -60 17 42 37 September 8, 2010 Capital budgeting (1) |14 BOF: go ahead? • NPV calculation: 17 42 37 NPV 60 17.96 1.10 (1.10) 2 3 (1.10) • Internal Rate of Return = 24% • Payback period = 2 years September 8, 2010 Capital budgeting (1) |15 BOF: checking the numbers • Sensitivity analysis • What if expected sales below expected value? Sales 60 70 80 90 100 NPV -22.11 -12.09 -2.07 7.95 17.96 • Break-even point • What is the level of sales required to break even? • Break even sales = 82 September 8, 2010 Capital budgeting (1) |16 Impact of inflation • Recommendation: • discount nominal cash flow using a nominal discount rate. • Inflation modifies the NPV because: • Depreciation tax shields are lower with inflation • WCR is influenced by inflation September 8, 2010 Capital budgeting (1) |17 BOF Project with inflation rate = 100% Nominal free cash flows Year 0 1 2 3 Sales 200 400 Cost of sales 100 200 EBITDA 100 200 Depreciation 30 30 EBIT 70 170 Taxes 28 68 64 Net income 42 102 -64 Net income 42 102 -64 Depreciation 30 30 0 WCR 50 50 -100 CFInvestment -60 160 Free Cash Flow -60 22 82 196 Nominal discount rate = (1+10%)(1+100%)-1 = 120% NPV = -14.65 IRR = 94% September 8, 2010 Capital budgeting (1) |18 A project is not a black box • Sensitivity analysis: – analysis of the effects of changes in sales, costs,.. on a project. • Scenario analysis: – project analysis given a particular combination of assumptions. • Simulation analysis: – estimations of the probabilities of different outcomes. • Break even analysis – analysis of the level of sales at which the company breaks even. September 8, 2010 Capital budgeting (1) |19 Sensitivity analysis Year 0 Year 1-5 Initial investment 1,500 Revenues 6,000 Variables costs (3,000) Fixed costs (1,791) Depreciation (300) Pretax Profit 909 Tax (TC = 34%) (309) Net Profit 600 Cash flow 900 • NPV calculation (for r = 15%): • NPV = - 1,500 + 900 3.3522 = + 1,517 September 8, 2010 Capital budgeting (1) |20 Sensitivity analysis using Excel • Use Data|Table (Données|Table) =C12 Result to calculate 10 Excel recalculates 20 using these Values to use values (in cell B3 for instance) 30 September 8, 2010 Capital budgeting (1) |21 Sensitivity analysis • 1. Identify key variables • Revenues = Nb engines sold Price per engine • 6,000 3,000 2 • Nb engines sold = Market share Size of market • 3,000 0.30 10,000 • V.Cost =V.cost per unit Number of engines • 3,000 1 3,000 • Total cost = Variable cost + Fixed costs • 4,791 3,000 1,791 September 8, 2010 Capital budgeting (1) |22 Sensitivity analysis • 2. Prepare pessimistic, best, optimistic forecasts (bop) • Variable Pessimistic Best Optimistic • Market size 5,000 10,000 20,000 • Market share 20% 30% 50% • Price 1.9 2 2.2 • V.cost / unit 1.2 1 0.8 • Fixed cost 1,891 1,791 1,741 • Investment 1,900 1,500 1,000 September 8, 2010 Capital budgeting (1) |23 Sensitivity analysis • 3. Recalculate NPV changing one variable at a time • Variable Pessimistic Best Optimist • Market size -1,802 1,517 8,154 • Market share -696 1,517 5,942 • Price 853 1,517 2,844 • V.cost / unit 189 1,517 2,844 • Fixed cost 1,295 1,517 1,628 • Investment 1,208 1,517 1,903 September 8, 2010 Capital budgeting (1) |24 Scenario analysis • Consider plausible combinations of variables • Ex: If recession - market share low - variable cost high - price low September 8, 2010 Capital budgeting (1) |25 Monte Carlo simulation • Tool for considering all combinations • model the project • specify probabilities for forecast errors • select numbers for forecast errors and calculate cash flows • Outcome: simulated distribution of cash flows September 8, 2010 Capital budgeting (1) |26 Monte Carlo Simulation - Example Model Notations Qt quantity Qt = Qt-1 + ut mt unit margin FC fixed costs mt = m + vt Dep depreciation TC corporate tax rate CFt = (Qtmt - FC - Dep)(1-TC)+Dep ut,,vt random variables Procedure Random number generation 1. Generate large number of evolutions Random number Ri : uniform distribution on 2. Calculate average annual cash flows [0,1] 3. Discount using risk-adjusted rate Use RAND() in Excel To simulate ~ N(0,1): NORMSINV(Rand()) September 8, 2010 Capital budgeting (1) |27 Standard normal random variable generation 1.00 0.90 0.80 RAND() 0.70 ALEA() 0.60 0.50 0.40 0.30 0.20 LOI.NORMALE.STANDARD.INVERSE(ALEA()) 0.10 NORMSINV(RAND()) 0.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 -3.00 -2.80 -2.60 -2.40 -2.20 -2.00 -1.80 -1.60 -1.40 -1.20 -1.00 -0.80 -0.60 -0.40 -0.20 September 8, 2010 Capital budgeting (1) |28 Simulated cash flows Cash flow simulation 120,000 100,000 80,000 60,000 40,000 20,000 0 1 2 3 4 5 6 7 8 9 10 September 8, 2010 Capital budgeting (1) |29 Break even analysis • Sales level to break-even? 2 views • Account Profit Break-Even Point: » Accounting profit = 0 • Present Value Break-Even Point: » NPV = 0 September 8, 2010 Capital budgeting (1) |30 Break even analysis with Excel • Use Goal Seek (Valeur cible) • Tell Excel to change the value of one variable until NPV = 0 September 8, 2010 Capital budgeting (1) |31 Timing • Even projects with positive NPV may be more valuable if deferred. • Example • You may sell a barrel of wine at anytime over the next 5 years. Given the future cash flows, when should you sell the wine? 0 1 2 3 4 5 Cash flow 100 130 156 180 202 218 % change 30% 20% 15% 12% 8% • Suppose discount rate r = 10% Wait • NPV if sold now = 100 • NPV if sold in year 1 = 130 / 1.10 = 118 September 8, 2010 Capital budgeting (1) |32 Optimal timing for wine sale? • Calculate NPV(t): NPV at time 0 if wine sold in year t: NPV(t) = Ct / (1+r)t 0 1 2 3 4 5 Cash flow 100 130 156 180 202 218 NPV(t) 100 118.2 129 135 138 135 September 8, 2010 Capital budgeting (1) |33 When to invest • Traditional NPV rule: invest if NPV>0. Is it always valid? • Suppose that you have the following project: – Cost I = 100 – Present value of future cash flows V = 150 – Possibility to mothball the project • Should you start the project? • If you choose to invest, the value of the project is: • Traditional NPV = 150 - 100 = 50 >0 • What if you wait? September 8, 2010 Capital budgeting (1) |34 To mothball or not to mothball? • Suppose that the project might be delayed for one year. • One year later: • Cost is unchanged (I = 100) • Present value of future cash flow = 160 • NPV1 = 160 - 100 = 60 in year 1 • To decide: compare present values at time 0. • Invest now : NPV = 50 • Invest one year later: NPV0 = PV(NPV1) = 60/1.10 = 54.5 • Conclusion: you should delay the investment + Benefit from increase in present value of future cash flows (+10) + Save cost of financing of investment (=10% * 100 = 10) - Lose return on real asset (=10% * 150 = 15) September 8, 2010 Capital budgeting (1) |35 Equivalent Annual Cost • The cost per period with the same present value as the cost of buying and operating a machine. • Equivalent Annual Cost = PV of costs / Annuity factor • Example: cheap & dirty vs good but expensive • Given a 10% cost of capital, which of the following machines would you buy? C0 C1 C2 C3 PV EAC A 15 4 4 4 24.95 10.03 B 10 6 6 20.41 11.76 EAC calculation: A: EAC = PV(Costs) / 3-year annuity factor = 24.95 / 2.487 = 10.03 B: EAC = PV(Costs) / 2-year annuity factor = 20.41 / 1.735 = 11.76 September 8, 2010 Capital budgeting (1) |36 The Decision to Replace • When to replace an existing machine with a new one? • Calculate the equivalent annual cost of the new equipment • Calculate the yearly cost of the old equipment (likely to rise over time as equipment becomes older) • Replace just before the cost of the old equipment exceeds the EAC on new equipment • Example • Annual operating cost of old machine = 8 • Cost of new machine : C0 C1 C2 C3 15 5 5 5 • PV of cost (r = 10%) = 27.4 • EAC = 27.4 / 3-year annuity factor = 11 • Do not replace until operating cost of old machine exceeds 11 September 8, 2010 Capital budgeting (1) |37