FINANCE
7. Capital Budgeting (2)
Professor André Farber
Solvay Business School
Université Libre de Bruxelles
Fall 2007
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
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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.
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Sensitivity analysis
Initial investment
Revenues
Variables costs
Fixed costs
Depreciation
Pretax Profit
Tax (TC = 34%)
Net Profit
Cash flow
Year 0
1,500
Year 1-5
6,000
(3,000)
(1,791)
(300)
909
(309)
600
900
• NPV calculation (for r = 15%):
• NPV = - 1,500 + 900  3.3522 = + 1,517
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Sensitivity analysis
• 1. Identify key variables
•
•
•
•
•
•
•
•
Revenues = Nb engines sold 
6,000
3,000
Nb engines sold = Market share
3,000
0.30
V.Cost =V.cost per unit 
3,000
1
Total cost = Variable cost +
4,791
3,000
Price per engine
2

Size of market
10,000
Number of engines
3,000
Fixed costs
1,791
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Sensitivity analysis
• 2. Prepare pessimistic, best, optimistic forecasts (bop)
•
•
•
•
•
•
•
Variable
Market size
Market share
Price
V.cost / unit
Fixed cost
Investment
Pessimistic
5,000
20%
1.9
1.2
1,891
1,900
Best
10,000
30%
2
1
1,791
1,500
Optimistic
20,000
50%
2.2
0.8
1,741
1,000
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Sensitivity analysis
• 3. Recalculate NPV changing one variable at a time
•
•
•
•
•
•
•
Variable
Market size
Market share
Price
V.cost / unit
Fixed cost
Investment
Pessimistic
-1,802
-696
853
189
1,295
1,208
Best
1,517
1,517
1,517
1,517
1,517
1,517
Optimist
8,154
5,942
2,844
2,844
1,628
1,903
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Scenario analysis
• Consider plausible combinations of variables
• Ex: If recession
- market share low
- variable cost high
- price low
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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
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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  ~ 12
N(0,1):
   Ri  6
i 1
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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
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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
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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?
Cash flow
% change
0
1
2
3
4
5
100
130
156
180
202
218
30%
20%
15%
12%
8%
• Suppose discount rate r = 10%
• NPV if sold now = 100
• NPV if sold in year 1 = 130 / 1.10 = 118
Wait
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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
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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?
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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)
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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
B
10
6
6
4
24.95
10.03
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
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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
C0
C1
C2
C3
• Cost of new machine :
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
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