Post on 15-Jan-2016
FINANCE7. Capital Budgeting (2)
Professor André Farber
Solvay Business SchoolUniversité Libre de BruxellesFall 2007
MBA 2007 - Capital Budgeting (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
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)
• 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
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
Monte Carlo Simulation - Example
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):
12
16
iiR
MBA 2007 - Capital Budgeting (2) |11
Simulated cash flows
Cash flow simulation
0
20,000
40,000
60,000
80,000
100,000
120,000
1 2 3 4 5 6 7 8 9 10
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
0 1 2 3 4 5
Cash flow 100 130 156 180 202 218
% change 30% 20% 15% 12% 8%
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
0 1 2 3 4 5
Cash flow 100 130 156 180 202 218
NPV(t) 100 118.2 129 135 138 135
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?
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 = 10.03B: 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
C0 C1 C2 C3
15 5 5 5