FINANCE 7. Capital Budgeting (2)

1. FINANCE7. Capital Budgeting (2) Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2007

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 MBA 2007 - Capital Budgeting (2)

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. MBA 2007 - Capital Budgeting (2)

4. 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 MBA 2007 - Capital Budgeting (2)

5. 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 MBA 2007 - Capital Budgeting (2)

6. Sensitivity analysis • 2. Prepare pessimistic, best, optimistic forecasts (bop) • VariablePessimistic 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 MBA 2007 - Capital Budgeting (2)

7. 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 MBA 2007 - Capital Budgeting (2)

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

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 MBA 2007 - Capital Budgeting (2)

10. Model Qt = Qt-1 + ut mt = m + vt CFt = (Qtmt - FC - Dep)(1-TC)+Dep Procedure 1. Generate large number of evolutions 2. Calculate average annual cash flows 3. Discount using risk-adjusted rate Notations Qt quantity mt unit margin FC fixed costs Dep depreciation TC corporate tax rate ut,,vt random variables Random number generation Random number Ri: uniform distribution on [0,1] Use RAND in Excel To simulate  ~ N(0,1): Monte Carlo Simulation - Example MBA 2007 - Capital Budgeting (2)

11. Simulated cash flows 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 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 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) = Ct / (1+r)t 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? 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 • 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) 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 = 10.03B: EAC = PV(Costs) / 2-year annuity factor = 20.41 / 1.735 = 11.76 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 C0C1C2 C315 5 5 5 MBA 2007 - Capital Budgeting (2)