Transcript Production Functions - Massachusetts Institute of Technology

Analysis of Outcomes
• What criteria?
• VARG, concept and construction
• Robustness?
• Other dimensions
• Hassan satellite example
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 1 of 19
What Criteria?

“Expected Value” has been the index
of choice for valuation…

Why is this appropriate?

Is this measure sufficient?
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 2 of 19
When do we see expected value?
First
Expected
Decision
Value
Expected Value
based on
recognizing
possibility of
Carbon Tax
= 10.8
Start
When do we
meet this value?
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Build
Big
Build
Medium
7.00
10.80
Chance
Event
9.00
Expand Outcome
Decision
Carbon
Tax
0.40
25.00
N/A
25
No
Tax
0.60
-5.00
N/A
5
Carbon
Tax
0.40
18.00
Go Big
18
Stay
14
Go Big
2
Stay
6
Go Big
15
Go
Medium
10
Stay
0
Go Big
4
Go
Medium
5
Stay
0
No
Tax
No
Build
Proba- Outcome
bility
Carbon
Tax
No
Tax
0.60
0.40
0.60
6.00
15.00
5.00
Richard de Neufville
©
Analysis of Outcomes Slide 3 of 19
Other dimensions to explore

The worst that could happen
People are “risk averse”, sensitive to loss
 With some notion of probability of loss


The best that might occur

Upside also important

Capex (capital expenditure = investment)

Some measure of Benefit-cost
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 4 of 19
VAR


VAR is a standard concept in finance
= “Value at Risk”
Given with a percentage = probability
losses do not exceed a particular level


Example: 10% VAR = - 85
Motivated by lenders, who are mainly
concerned about getting repaid
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 5 of 19
Value at Gain



We have developed this concept as
counterpart of “VAR”
It represents the upside potential of a
project
Motivated by investors, interested in
amount they may gain (not especially
interesting to bankers…)
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 6 of 19
VARG diagram




VARG diagram (or “curve”) combines
VAR and “Value at Gain”
It is the cumulative distribution of
outcomes
Going from worst case at x% probability
To best case with y% probability
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 7 of 19
VARG diagram for Gulf Oil Case
1 .0 0
Cumulative Probability
0 .9 0
0 .8 0
0 .7 0
0 .6 0
0 .5 0
0 .4 0
0 .3 0
0 .2 0
0 .1 0
0 .0 0
1 5 ,0 0 0 1 7 ,0 0 0 1 9 ,0 0 0 2 1 ,0 0 0 2 3 ,0 0 0 2 5 ,0 0 0 2 7 ,0 0 0 2 9 ,0 0 0 3 1 ,0 0 0 3 3 ,0 0 0
NPV ($, million)
I nflexible
E N P V - I nflex.
Bas ic E c on. M odel
12% VAR of only 16k; 4% VAG of ~ 30k
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 8 of 19
How do we construct VARG?
See Decision Analysis example
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 9 of 19
What are elements of VARG?
First
Expected
Decision
Value
What are possible
outcomes?
Answer: 18 and 6
Start
… and associated
probabilities?
Ans: 0.4 and 0.6
So VARG is as on
next slide.
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Build
Big
Build
Medium
7.00
10.80
Chance
Event
9.00
Expand Outcome
Decision
Carbon
Tax
0.40
25.00
N/A
25
No
Tax
0.60
-5.00
N/A
5
Carbon
Tax
0.40
18.00
Go Big
18
Stay
14
Go Big
2
Stay
6
Go Big
15
Go
Medium
10
Stay
0
Go Big
4
Go
Medium
5
Stay
0
No
Tax
No
Build
Proba- Outcome
bility
Carbon
Tax
No
Tax
0.60
0.40
0.60
6.00
15.00
5.00
Richard de Neufville
©
Analysis of Outcomes Slide 10 of 19
Construction of VARG
VARG for Wind Energy Example
x , y coordinates
6
6
18
18
0
0.6
0.6
1
Cumulative Probability
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
Value of Outcome
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 11 of 19
20
VARG Useful to Compare Alternatives
1 .0 0
Cumulative Probability
0 .9 0
0 .8 0
0 .7 0
0 .6 0
0 .5 0
0 .4 0
0 .3 0
0 .2 0
0 .1 0
0 .0 0
1 5 ,0 0 0 1 7 ,0 0 0 1 9 ,0 0 0 2 1 ,0 0 0 2 3 ,0 0 0 2 5 ,0 0 0 2 7 ,0 0 0 2 9 ,0 0 0 3 1 ,0 0 0 3 3 ,0 0 0
NPV ($, million)
I nflexible
E N P V - Flex.
Flexible
Bas ic E c on. M odel
E N P V - I nflex.
VARG diagrams can show relative merit of alternative designs
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 12 of 19
Concept of “Robustness”



Popular Basis for Design (“Taguchi
method”)
Robust design ≡ “a product whose
performance is minimally sensitive to
factors causing variability…”
Robustness measured by standard
deviation of distribution of outcomes
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 13 of 19
Illustration of Robustness
Probability
More Robust
Smaller standard
deviation
Outcome
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 14 of 19
Do we want robustness?


When might robustness be a good
measure of performance?
When we really want a particular result




Tuning into a signal
Fitting parts together, etc
Is this what we want for maximizing value?
No!! We want to limit downside but make
upside as large as possible => higher σ
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 15 of 19
Robustness does not
maximize expected value
Probability
Less Robust
Higher Expected
Value
Outcome
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 16 of 19
Other Dimensions for Evaluation





In addition to
 Expected Value
 Minimum and Maximum Values
Capex = Initial Capital Expenditure =
Investment
“Benefit-Cost” ratio of EV / Capex
Value Added by Flexibility
Others? … depends on users
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 17 of 19
Example: Hassan Satellite Case
Architectural Value
Parameter ($ million)
Rigid Fleet
Flexible Fleet I
Flexible Fleet II
Flexible Fleet III
E(NPV)
49.94
95.81
56.20
19.40
Std(NPV)
3.69
4.63
3.74
1.63
-
45.86
6.26
-30.55
Fixed cost, pay year 1
242
275
341
170
Fixed cost, pay year 6
242
-
-
170
PV(fixed cost) at year 1
392
275
341
276
Maximum possible gain
192
193
142
73
Maximum possible loss
162
68
131
86
Flexibility Value
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 18 of 19
Take-Aways

“Expected Value” not sufficient Measure

VARG diagram powerful visual image



Shows Maximum and Minimum
Compares alternatives
Keep in mind



Capex
Benefit-Cost of “Expected Value / Capex”
Value of Flexibility (more on this later)
Engineering Systems Analysis for Design
Massachusetts Institute of Technology
Richard de Neufville
©
Analysis of Outcomes Slide 19 of 19