1. FINANCE 7. Capital Budgeting (2) Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2007

2. MBA 2007 - Capital Budgeting (2) |2|2 Investment decisions (2) Objectives for this session : A project is not a black box Timing: –How long to invest? –When to invest? Project with different lifes: Equivalent Annual Cost

3. MBA 2007 - Capital Budgeting (2) |3|3 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.

4. MBA 2007 - Capital Budgeting (2) |4|4 Sensitivity analysis Year 0Year 1-5 Initial investment 1,500 Revenues6,000 Variables costs(3,000) Fixed costs(1,791) Depreciation(300) Pretax Profit909 Tax (T C = 34%)(309) Net Profit600 Cash flow900 NPV calculation (for r = 15%): NPV = - 1,500 + 900  3.3522 = + 1,517

5. MBA 2007 - Capital Budgeting (2) |5|5 Sensitivity analysis 1. Identify key variables Revenues = Nb engines sold  Price per engine 6,0003,0002 Nb engines sold = Market share  Size of market 3,0000.3010,000 V.Cost =V.cost per unit  Number of engines 3,00013,000 Total cost = Variable cost +Fixed costs 4,7913,0001,791

6. MBA 2007 - Capital Budgeting (2) |6|6 Sensitivity analysis 2. Prepare pessimistic, best, optimistic forecasts (bop) VariablePessimisticBestOptimistic Market size5,00010,00020,000 Market share20%30%50% Price1.922.2 V.cost / unit1.210.8 Fixed cost1,8911,7911,741 Investment1,9001,5001,000

7. MBA 2007 - Capital Budgeting (2) |7|7 Sensitivity analysis 3. Recalculate NPV changing one variable at a time VariablePessimisticBestOptimist Market size-1,8021,5178,154 Market share-6961,5175,942 Price8531,5172,844 V.cost / unit1891,5172,844 Fixed cost1,2951,5171,628 Investment1,2081,5171,903

8. MBA 2007 - Capital Budgeting (2) |8|8 Scenario analysis Consider plausible combinations of variables Ex: If recession -market share low -variable cost high -price low

9. MBA 2007 - Capital Budgeting (2) |9|9 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

10. MBA 2007 - Capital Budgeting (2) | 10 Monte Carlo Simulation - Example Model Q t = Q t-1 + u t m t = m + v t CF t = (Q t m t - FC - Dep)(1-T C )+Dep Procedure 1. Generate large number of evolutions 2. Calculate average annual cash flows 3. Discount using risk-adjusted rate Notations Q t quantity m t unit margin FCfixed costs Depdepreciation T C corporate tax rate u t,,v t random variables Random number generation Random number R i : uniform distribution on [0,1] Use RAND in Excel To simulate  ~ N(0,1):

11. MBA 2007 - Capital Budgeting (2) | 11 Simulated cash flows

12. MBA 2007 - Capital Budgeting (2) | 12 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

13. MBA 2007 - Capital Budgeting (2) | 13 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? Suppose discount rate r = 10% NPV if sold now = 100 NPV if sold in year 1 = 130 / 1.10 = 118 Wait

14. MBA 2007 - Capital Budgeting (2) | 14 Optimal timing for wine sale? Calculate NPV(t): NPV at time 0 if wine sold in year t: NPV(t) = C t / (1+r) t

15. MBA 2007 - Capital Budgeting (2) | 15 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?

16. MBA 2007 - Capital Budgeting (2) | 16 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 NPV 1 = 160 - 100 = 60 in year 1 To decide: compare present values at time 0. Invest now : NPV = 50 Invest one year later: NPV 0 = PV(NPV 1 ) = 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)

17. MBA 2007 - Capital Budgeting (2) | 17 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? 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

18. MBA 2007 - Capital Budgeting (2) | 18 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 : 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 C 0 C 1 C 2 C 3 15555