1. Finance Analyse de projets d’investissement
Professeur André Farber

2. Investment decisions Objectives for this session :
Review investment rules
NPV, IRR, Payback
BOF Project
Free Cash Flow calculation
Inflation
A project is not a black box: Sensitivity analysis, break even point
Timing:
How long to invest?
When to invest?
Project with different lifes: Equivalent Annual Cost
Capital budgeting (1)

3. Investment rules Net Present Value (NPV)
Discounted incremental free cash flows
Rule: invest if NPV>0
Internal Rate of Return (IRR)
IRR: discount rate such that NPV=0
Rule: invest if IRR > Cost of capital
Payback period
Numbers of year to recoup initial investment
No precise rule
Profitability Index (PI)
PI = NPV / Investment
Useful to rank projects if capital spending is limited
NPV
IRR r
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4. Internal Rate of Return IRR
Can be viewed as the “yield to maturity” of the project
Remember: the yield to maturity on a bond is the rate that set the present value of the expected cash flows equal to its price
Consider the net investment as the price of the project
The IRR is the rate that sets the present value of the expected cash flows equal to the net investment
The IRR is the rate that sets the net present value equal to zero
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5. What do CFOs Use? % Always or Almost Always
Internal Rate of Return %
Net Present Value %
Payback period %
Discounted payback period 29.5%
Accounting rate of return 30.3%
Profitability index %
Based on a survey of 392 CFOs
Source: Graham, John R. and Harvey R. Campbell, “The Theory and Practice of Corporate Finance: Evidence from the Field”, Journal of Financial Economics 2001
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6. IRR Pitfall 1: Lending or borrowing?
Consider following projects:
IRR NPV(10%)
A %
B %
A: lending Rule IRR>r
B: borrowing Rule IRR<r
Negative investment: example
A famous author is about to meet his editor. The deal that he is considering to accept to write a new finance text is the following.
1. The author will receive an up front payment of $1,000,000
2. During the next 3 year, he will be busy writing the book. It will cost him $500,000 a year in term of consulting foregone (no consulting is allowed while writing).
The current interest rate is 10%.
His financial calculator tells him that the IRR on this deal is 23%
Should he sign the contract?
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7. IRR Pitfall 2 Multiple Rates of Return
Consider the following project
Year
CF , , ,000
2 “IRRs” : +25% & %
This happens if more than one change in sign of cash flows
To overcome problem, use modified IRR method
Reinvest all intermediate cash flows at the cost of capital till end of project
Calculate IRR using the initial investment and the future value of intermediate cash flows
Suppose now the editor (see previous slide) announce that the author will receive $20,000 a year in perpetuity once the book is published.
Is this a better deal?
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8. IRR Pitfall 3 - Mutually Exclusive Projects
Scale Problem (r = 10%)
C C1 NPV IRR
Small %
Large %
To choose, look at incremental cash flows
C C1 NPV IRR
L-S %
Timing Problem (r = 10%)
C C C NPV IRR
A %
B %
A-B %
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9. Payback
The payback period is the number of years it takes before the cumulative forcasted cash flows equals the initial investment.
Example:
A very flawed method, widely used
Ignores time value of money
Ignores cash flows after cutoff date
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10. Profitability Index
Profitability Index = PV(Future Cash Flows) / Initial Investment
A useful tool for selecting among projects when capital budget limited.
The highest weighted average PI
Beyond PI: Linear Programming
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11. NPV - Review
NPV: measure change in market value of company if project accepted
As market value of company V = PV(Future Free Cash Flows)
V = Vwith project - Vwithout project
Cash flows to consider:
cash flows (not accounting numbers)
do not forget depreciation and changes in WCR
incremental (with project - without project)
forget sunk costs
include opportunity costs
include all incidental effects
beware of allocated overhead costs
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12. Inflation Be consistent in how you handle inflation
Discount nominal cash flows at nominal rate
Discount real cash flows at real rate
Both approaches lead to the same result.
Example: Real cash flow in year 3 = 100 (based on price level at time 0)
Inflation rate = 5%
Real discount rate = 10%
Discount real cash flow using real rate
PV = 100 / (1.10)3 = 75.13
Discount nominal cash flow using nominal rate
Nominal cash flow = 100 (1.05)3 = Nominal discount rate = (1.10)(1.05)-1 = 15.5% PV = / (1.155)3 = 75.13
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13. Investment Project Analysis: BOF
Big Oversea Firm is considering the project
Big Oversea Firm (BOF) is considering going into a new project. The capital tool required for the project costs $60m. The marketing department predict that sales will be $100m per year for the next 2 years, after which the market will cease to exist. The initial investment will be depreciated down to zero using the straight-line method. Cost of good sold and operating expenses are predicted to be 50 percent of sales. After 2 years, the tool can be sold for $20m. The tax rate of BOF is 40%. The required rate of return on BOF is 10%. The inflation rate is zero.
Based on RWJ Q&P 7.12
Corporate tax rate = 40% Working Capital Requirement = 25% Sales Discount rate = 10%
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14. BOF: Free Cash Flow Calculation
Year 1 2 3
Sales
100
Cost of sales 50
EBITDA
Depreciation 30
EBIT 20
Taxes 8
Net income 12 -8
DWCR 25
-25
CFInvestment
-60
Free Cash Flow 17 42 37
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15. BOF: go ahead? NPV calculation: Internal Rate of Return = 24%
Payback period = 2 years
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16. BOF: checking the numbers
Sensitivity analysis
What if expected sales below expected value?
Break-even point
What is the level of sales required to break even?
Break even sales = 82
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17. Impact of inflation Recommendation:
discount nominal cash flow using a nominal discount rate.
Inflation modifies the NPV because:
Depreciation tax shields are lower with inflation
WCR is influenced by inflation
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18. BOF Project with inflation rate = 100%
Nominal free cash flows
Nominal discount rate = (1+10%)(1+100%)-1 = 120%
NPV = IRR = 94%
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19. 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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20. 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
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21. Sensitivity analysis using Excel
Use Data|Table (Données|Table)
=C12 10 20 30
Result to calculate
Excel recalculates using these values
Values to use
(in cell B3 for instance)
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22. 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
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23. 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
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24. 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
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25. Scenario analysis Consider plausible combinations of variables
Ex: If recession
market share low
variable cost high
price low
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26. 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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27. 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())
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28. Standard normal random variable generation
ALEA()
LOI.NORMALE.STANDARD.INVERSE(ALEA())
NORMSINV(RAND())
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29. Simulated cash flows
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30. 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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31. Break even analysis with Excel
Use Goal Seek (Valeur cible)
Tell Excel to change the value of one variable until NPV = 0
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32. 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
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33. Optimal timing for wine sale?
Calculate NPV(t): NPV at time 0 if wine sold in year t:
NPV(t) = Ct / (1+r)t
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34. 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?
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35. 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)
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36. 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
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37. 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
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