1. Professeur André Farber
Théorie Financière Analyse de projets d’investissement (2)
Professeur André Farber

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
Tfin 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.
Tfin 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
Tax (TC = 34%) (309)
Net Profit
Cash flow
NPV calculation (for r = 15%):
NPV = - 1,  = + 1,517
Tfin Capital budgeting (2)

5. Sensitivity analysis 1. Identify key variables
Revenues = Nb engines sold  Price per engine
6,000 3,
Nb engines sold = Market share  Size of market
3, ,000
V.Cost =V.cost per unit  Number of engines
3, ,000
Total cost = Variable cost + Fixed costs
4,791 3,000 1,791
Tfin Capital budgeting (2)

6. Sensitivity analysis
2. Prepare pessimistic, best, optimistic forecasts (bop)
Variable Pessimistic Best Optimistic
Market size 5, , ,000
Market share 20% 30% 50%
Price
V.cost / unit
Fixed cost 1,891 1,791 1,741
Investment 1,900 1,500 1,000
Tfin 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 ,517 5,942
Price ,517 2,844
V.cost / unit ,517 2,844
Fixed cost 1,295 1,517 1,628
Investment 1,208 1,517 1,903
Tfin Capital budgeting (2)

8. Scenario analysis Consider plausible combinations of variables
Ex: If recession
market share low
variable cost high
price low
Tfin 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
Tfin 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): NORMSINV(Rand())
Tfin Capital budgeting (2)

11. Simulated cash flows
Tfin 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
Tfin 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
Tfin 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
Tfin Capital budgeting (2)

15. When to invest
Traditional NPV rule: invest if NPV> 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 = = 50 >0
What if you wait?
Tfin 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 = = 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)
The analyzis of when to invest in a determist setting is based on A. Dixit and R. Pindyck Investment under Uncertainty, Princeton University Press 1994 (Chapter 5)
The net present value at time 0 of an investment at time t is:
NPV(t) = [V(t) - I] e-rt
where
V(t) = present value of future cash flows at time t
I = cost of investment
e-rt = discount factor (r is the continuously compounded interest rate)
Taking the first derivative with respect to t gives:
NPV’(t) = [V’(t) - rV(t) + rI] e-rt
The terms between brackets represent the costs and benefits of delaying the investment:
V’(t): variation in the value of future cash flows (>0)
- rV(t): opportunity cost of waiting to invest (<0)
rI: opportunity cost of investment (>0)
Tfin 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 = / = B: EAC = PV(Costs) / 2-year annuity factor = / = 11.76
Tfin 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 C
Tfin Capital budgeting (2)