Transcript Economic Evaluation - Massachusetts Institute of Technology
Economic Evaluation
Objective of Analysis
Criteria
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Nature
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Peculiarities
Comparison of Criteria
Recommended Approach Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 1 of 22
Objectives of Economic Evaluation Analysis
Is individual project worthwhile? Above minimum standards?
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This is a “choice”, is it better or not?
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This is easier
Is it best? Is it at top of ranking list?
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This is a “judgment” about details
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This is more difficult
Note difference between “choice” and “judgement” -- a key consideration in selection of method to be used in real options analysis Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 2 of 22
Principal Evaluation Criteria
Net Present Value
Benefit - Cost Ratio
Internal Rate of Return
Cost-Effectiveness Ratio
Pay-Back Period Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 3 of 22
Net Present Value
NPV = B - C (stated in present values)
Objective: To Maximize
Advantage: Focus on Result
Disadvantages
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Interpretation of NPV
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No account for scale, thus difficult to use for ranking Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 4 of 22
Activity: Years:
Present Value and Net Present Value: Example Calculations
Initial 0 1 2 3 4 5 6 7 8 Rehab 9 10 11 12 Cash Flow -100 5 10 20 40 50 40 30 20 -40 35
Use NPV function in Excel. Note carefully that it assumes you mean that all cash flows occur at the end of the relevant period, not at beginning.
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Present Value of cash flows at end of year 1, 2,etc, at rate = NPV (rate,c9:n9) Discount rate expressed either in percent or decimal: 10% or 0.1
$143.58
Net Present Value is above plus cash flow at time zero= NPV(0.1,c9:n9) +b9
$43.58
Note: c9:n9 => range of years 1 to 12; b9 => year 0 Thus formula = NPV of cash flows to start of year 1 + cost investment Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 5 of 22
Difficulty in Interpreting Meaning of NPV
Suppose for example that a project
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costs 1000
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sells 4 years later for 1500
The obvious profit is 500 = 1500 - 1000
From an NPV perspective, however, we get
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NPV = 1500 / (1+r) exp 4 - 1000 This amount depends on discount rate, r
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If r = 10%, NPV ~ 1500 / 1.47 - 1000 ~ 20 Try telling that to tax authorities -- or others!
Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 6 of 22
Evaluation of Projects S and T
Project S T Benefit $ Cost $ Net Value $ 2,002,000 2,000,000 2,000 1,000 Which project has the highest Net Present Value?
Which would you choose?
When might NPV be a good method?
NPV as % of Cost 0.1
100 Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 7 of 22
Benefit - Cost
Ratio =
B /
C (Present Values)
Objective:
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To Maximize
Advantage:
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Common Scale, Useful in Ranking
Disadvantages:
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Treatment of Recurring Costs
B /
C or Net Benefits/Investment = > Bias against operating projects
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Ranking sensitive to r low r = > higher rank for long-term projects Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 8 of 22
A Comparison of a Capital Intensive and Operations Project
(Benefits in Present Values) Project Investment, C Annual Cost, C k r Annual Benefits Annual Return Useful Life T otal Benefits T otal Cost, C k + C r Benefit/Cost Ratio Annual Return Net Value Present K $1,000,000 $50,000 $200,000 $150,000 10 Years $2,000,000 $1,500,000 1.34 better than 15% worse than $500,000 worse than R $1,000,000 $500,000 $700,000 $200,000 10 Years $7,000,000 $6,000,000 1.17
20% $1,000,000 Note: Because B/C counts recurring costs as part of total costs, It disadvantages projects with operating costs (ex: factories), And favors capital intensive projects (hydropower dams) Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 9 of 22
The Ranking of Projects by Benefit-Cost Criterion Can Depend on DR
Project A Investment C k ,$ 1000 Annual Benefits R, $ 200 B 1000 125 Project Life N Years Benefit - cost at discount rate of 3% 10% 10 20 1.73 1.23
(best) 1.86 1.05
(best) Note: Varying the DR changes the Relative value of projects Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 10 of 22
Internal Rate of Return
IRR = r such that NPV = 0
Objective:
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Maximize IRR
Advantages:
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No need to choose r Manipulation by r impossible
Disadvantages:
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Calculations complex -- but easy in spreadsheet
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Ambiguous
Note: ranking by IRR and B/C ratio may differ Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 11 of 22
Data for calculation of IRR
Repeat of Example in Present Value/DCF lecture Example:
Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Investment Net Income Cash Flow 15 -15 2 2 3 3 3 4 1 5 5 5 5 5 3 -2 4 4 5 5 NPV at 12% $0.79
Formula: NPV(12%, B9:K9)
Note: b9:k9 => range of years from 2001 to 2010 This NPV calculation assumes cash flows all at end of year Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 12 of 22
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Spreadsheet Determination of IRR
Year Investment Net Income 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 15 2 3 3 4 5 5 5 3 4 5 6 Cash Flow IRR -15 13.33% 2 3 1 5 5 Formula: IRR(b9:k9) -2 4 5 6
Note: b9:k9 => range of years from 2001 to 2010 This NPV calculation assumes cash flows all at end of year Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 13 of 22
Graphical Determination of IRR
Determination of IRR
15.0
10.0
5.0
0.0
-5.0
1 4 7 10 13 16
Discount rate Engineering Systems Analysis Massachusetts Institute of Technology
Series1
Richard de Neufville © Economic Evaluation Slide 14 of 22
Projects can Lead to Ambiguous Solutions for the Internal Rate of Return
Project P Q Investment, $ C k 200 Annual Benefits $ R 100 Project Life Years N 5
Cash flow 500 200 t NPV 310
Closure cost at Year N-1 $ C c > RN - C k 310
5 % DR
Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 15 of 22
Ranking of Projects by Internal Rate of Return and Benefit-Cost Ratio Can Differ
Project A B Investment, C k , $ 1000 1000 Annual Benefits R, $ 200 125 Project Life N Years 10 20 Benefit - Internal Rate Cost of Return, 0% r = 3% 1.71 15.10
(best) 1.86 10.93
(best) Why is this? Because Relative value of project in B/C depends on DR Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 16 of 22
Pay-Back Period
PBP = Cost/Annual Benefits
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Note: undiscounted
Objective:
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To minimize
Advantages:
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Really simple
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No choice of r
Disadvantages
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Difficult to rank correctly projects with different useful lives or uneven cash flows Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 17 of 22
Evaluation of Projects V and W
Project Investment, C k , $ V W 2000 2000 1 2 3 4 5 6 1000 800 1000 1000 800 800 800 800 800 Payback Period Years NPV at 10% IRR 2 2.5
487 1484 23.4% 32.7% Note: Although Pay-back period gives "wrong" results, many Managers prefer it, because they do not trust forecasts!
Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 18 of 22
Cost- Effectiveness Ratio
Ratio = (Units of Benefit) / Cost
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example: “lives saved/million dollars”
Objective: To Maximize
Advantage: Avoids problem of trying to assign $ values to “intangibles” such as a “life”, “ton of pollution”, etc.
Disadvantage: No sense for minimum standard or limits Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 19 of 22
Data for of Cost-Effectiveness Analysis
Screening X-Rays Lab Tests MRIs Operations Lives Saved Project Cost, Millions Cost-Effectiveness Cumulative Project Cumulative Project Cumulative 20 40 60 75 100 20 60 100 135 175 0.5
2 7 12 25 0.5
2.5
9 19 37 40.0
20.0
8.6
6.3
4.0
40.0
13.3
4.0
3.0
1.9
Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 20 of 22
120 100 80 60 40 20 0 0
Cost-Effectiveness Analysis
Lives Saved by Projects
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Currency, Millions
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Cumulative Lives Saved for Budget
200 180 160 140 120 100 80 60 40 20 0 0 10 20
Currency, Millions
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What is value of life? How much budget should we spend on this?
Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 21 of 22
Recommended Procedure (if you have discretion to choose)
Examine Nature of projects
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Easy to put into $ terms? Steady cash flows? or with closure costs? Or various project lifetimes?
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An operating or a straight capital investment?
Choose Method Accordingly
No method is perfect -- ultimately a judgment
Current “best practice” uses several criteria; uses judgment to decide on project Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 22 of 22
A Note for Optimal Plant Exercise Part 1 Average Costs of Production vary
Total Cost Average Cost 1 5.2
5.2
2 3 5.4
5.6
2.7 1.867
4 5.8
1.45
5 6 1.2
6 7 8 9 6.2
6.4
6.6
6.8
1.03 0.914 0.825 0.756
10 7 0.7
Capital cost =5 Labor and Materials =0.2/part Maximum Capacity= 10
Total Cost vs Average Cost
8 2 0 6 4 1 2 3 4 5 6 7 8 9 10
Number of Parts
Total Cost Average Cost
Engineering Systems Analysis Massachusetts Institute of Technology Richard de Neufville © Economic Evaluation Slide 23 of 22