Transcript Finance Analyse de projets d’investissement

Finance
Analyse de projets d’investissement
Professeur André Farber
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
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Investment rules
• Net Present Value (NPV)
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
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IRR
r
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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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What do CFOs Use?
•
•
•
•
•
•
•
% Always or Almost Always
Internal Rate of Return
Net Present Value
Payback period
Discounted payback period
Accounting rate of return
Profitability index
75.6%
74.9%
56.7%
29.5%
30.3%
11.9%
• 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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IRR Pitfall 1: Lending or borrowing?
•
Consider following projects:
IRR: borrowing or lending?
20.00
10.00
0.00
-10.00
6%
9%
12
%
15
%
18
%
21
%
24
%
27
%
30
%
A: lending
Rule IRR>r
B: borrowing Rule IRR<r
30.00
0%
3%
•
•
0 1
IRR NPV(10%)
A -100 +120 20%
9.09
B +100 -120 20%
-9.09
Net Present Value
•
•
•
-20.00
-30.00
Discount rate
Project A
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Project B
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IRR Pitfall 2 Multiple Rates of Return
•
•
•
Consider the following project
Year
0
1
2
CF
-1,600 10,000 -10,000
Multiple Rates of Return
•
To overcome problem, use modified
IRR method
–
–
500.00
-1500.00
-2000.00
Discount Rate
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495%
450%
405%
360%
315%
270%
-1000.00
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
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225%
-500.00
180%
0.00
135%
This happens if more than one change
in sign of cash flows
1000.00
90%
+400%
45%
•
2 “IRRs” : +25% &
0%
•
Net Present Value
1500.00
IRR Pitfall 3 - Mutually Exclusive Projects
Scale Problem (r = 10%)
Small
Large
C0
-10
-50
C1
+20
+80
NPV IRR
8.2 100%
22.7 60%
Timing Problem
(r = 10%)
C0
C1
C2
NPV IRR
A -100 +20 +120
17.4 20.0%
B -100 +80 +52
15.7 22.5%
A-B 0
-60
+68
1.7
13.3%
To choose, look at incremental cash flows
C0
C1 NPV IRR
L-S
-40 +60 14.5 50%
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Payback
• The payback period is the number of years it takes before the cumulative
forcasted cash flows equals the initial investment.
• Example:
Year
0
1
2
3
Payback NPV
•
A
-1,000
500
500
1,000
2
r=10%
619
B
-1,000
0
1,000
0
2
-174
C
-1,000
500
500
0
2
-132
A very flawed method, widely used
• Ignores time value of money
• Ignores cash flows after cutoff date
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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
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NPV - Review
• NPV: measure change in market value of company if project accepted
• As market value of company V = PV(Future Free Cash Flows)
NPV  V  
FCFt
t (1  r )
t
• 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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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
Discount nominal cash flow using nominal rate
PV = 100 / (1.10)3 = 75.13
Nominal cash flow = 100 (1.05)3 = 115.76
Nominal discount rate = (1.10)(1.05)-1 = 15.5%
PV = 115.76 / (1.155)3 = 75.13
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Investment Project Analysis: BOF
Big Oversea Firm is considering the project
Year
0
Initial Investment
60
1
2
Resale value
3
20
Sales
100
100
Cost of sales
50
50
Corporate tax rate = 40%
Working Capital Requirement = 25% Sales
Discount rate = 10%
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BOF: Free Cash Flow Calculation
Year
0
1
2
100
100
Cost of sales
50
50
EBITDA
50
50
Depreciation
30
30
EBIT
20
20
Taxes
8
8
8
Net income
12
12
-8
Net income
12
12
-8
Depreciation
30
30
0
DWCR
25
0
-25
Sales
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CFInvestment
-60
Free Cash Flow
-60
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3
20
17
42
37
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BOF: go ahead?
• NPV calculation:
NPV  60 
17
42
37


 17.96
2
3
1.10 (1.10)
(1.10)
• Internal Rate of Return = 24%
• Payback period = 2 years
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BOF: checking the numbers
• Sensitivity analysis
• What if expected sales below expected value?
Sales
60
70
80
90
NPV
-22.11
-12.09
-2.07
7.95
100
17.96
• Break-even point
• What is the level of sales required to break even?
• Break even sales = 82
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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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BOF Project with inflation rate = 100%
Nominal free cash flows
Year
Sales
Cost of sales
EBITDA
Depreciation
EBIT
Taxes
Net income
0
Net income
Depreciation
WCR
CFInvestment
Free Cash Flow
-60
-60
1
200
100
100
30
70
28
42
2
400
200
200
30
170
68
102
42
30
50
102
30
50
22
82
3
64
-64
-64
0
-100
160
196
Nominal discount rate = (1+10%)(1+100%)-1 = 120%
NPV = -14.65
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IRR = 94%
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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 using Excel
• Use Data|Table (Données|Table)
=C12
10
Values to use
(in cell B3 for
instance)
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Result to calculate
Excel
recalculates
using these
values
20
30
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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
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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
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Pessimistic
5,000
20%
1.9
1.2
1,891
1,900
Best
10,000
30%
2
1
1,791
1,500
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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
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•
•
•
•
•
•
Variable
Market size
Market share
Price
V.cost / unit
Fixed cost
Investment
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Pessimistic
-1,802
-696
853
189
1,295
1,208
Best
1,517
1,517
1,517
1,517
1,517
1,517
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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
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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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Standard normal random variable generation
1.00
0.90
0.80
RAND()
0.70
ALEA()
0.60
0.50
0.40
0.30
0.20
LOI.NORMALE.STANDARD.INVERSE(ALEA())
0.10
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3.00
2.80
2.60
2.40
2.20
2.00
1.80
1.60
1.40
1.00
0.80
0.60
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
-1.20
-1.40
-1.60
-1.80
-2.00
-2.20
-2.40
-2.60
-2.80
-3.00
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1.20
NORMSINV(RAND())
0.00
Simulated cash flows
Cash flow simulation
120,000
100,000
80,000
60,000
40,000
20,000
0
1
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2
3
4
5
6
7
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8
9
10
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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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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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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
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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
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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
• Cost of new machine :
C0
C1
C2
C3
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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