Final Exam: Large Instrument
Manufacturer, Inc.
ARUNABHA SAHA
Recommendations
 Our intial recommendation to LIM at this point is
to pursue the alternative that involves training
UDC to handle Beta failures.
 We further recommend a subsequent analysis
taking into account much of the information from
the first round and assessing the uncertainties.
Outline
 Decision Tools Used
 Framing
 Decision Hierarchy
 Decision Diagram
 Deterministic Analysis
 NPV of Alternatives
 Deterministic Sensitivity
 Probabilistic Analysis
 Decision Tree
 Probabilistic Dominance
 Appraisal
 Sensitivity Analysis
 Value of Information and
Control
 Recommendations for future
analysis
Decision Hierarchy
• Policy is to be Risk-Neutral in this Range.
• Making a profit is the end goal of this exercise. Selling a
product but not making a profit is not a desirable option.
• ROE-II will be sold only for a period of 5 years hence any
strategy should be optimized for the next 5 year period.
Policy


Strategy
Tactics
To sell ROE-II to UDC or not ?
Eliminate or mitigate the risk associated with
servicing that caused the bad experience with
ROE-II
 Determine the uncertainties early and how they
affect the eventual outcome.
 Concentrate on evaluating the important
uncertainties before making the decision
 Attempt to control the important uncertainties by
means at our disposal
Decision Diagram
Num of
Αlpha
Failures
Total
Alpha
Failure
Cost
Sell ROE-II to
UDC
Cost of
Alpha
Failures
Num of
Beta
Failures
Cost of
Beta
Failures
Total Beta
Failure
Cost
Units Sold
Total
Revenue
Continue with
Existing
Arrangement
Training
Cost
Initial Cost
(Training +
Installation)
Train UDC
engineers OR
Outsource
Value
NPV of Each Strategy at Base Case
200
178
150
150
NPV in $1000s
100
50
0
Existing
Train UDC
Contract IPX
Do not
-8 Sell
-50
-100
-105
-150
We can see that in the base case
• “Training UDC” is the best option
• Contracting with IPX is also an attractive
• Existing option is far worse than either training or contracting
Comparison of Alternatives (100% range)
Range of Profit for the 4 Alternatives
Do not Sell
Mid: 147K
Contract IPX
Mid:178K
Mid:-105K
Train WDC
Existing
-800
-600
-400
-200
0
Profit in $1000s
200
400
600
800
The Key takeaway here is that the “Training UDC” option is the more profitable
option in the base case. However the “Train UDC” option also has a higher
range (-88, 595) than Contract IPX(0, 347). This “can” imply more risk
associated with the “Training WDC” Option
Assessing Important Uncertainties (95%)
Existing Arrangement
Train UDC
Beta Repair Cost
Training Cost
Num of Beta Failures
Units Sold
Num of Alpha Failures
Num of Alpha Failures
Units Sold
Avg Cost
Alpha Repair Cost
-$300.00 -$250.00 -$200.00 -$150.00 -$100.00
-$50.00
$0.00
0.00
50.00
100.00
150.00
From the tornado diagrams above we observe that.
•
•
•
•
4 Uncertainties to be assessed for Alternative 1 (Existing arrangement).
3 Uncertainties for Alternative 2 (Training UDC for servicing)
1 Uncertainty for Alternative 3 (Contract with IPX)
Alternative 4(Do not Sell) has no uncertainties
200.00
250.00
300.00
350.00
Probabilistic Assessment
Discretizing (Equal Areas – Shortcut)
Low(0-25%)
Mid(25-75%)
High(75-100)
8.91
9.95
12.5
6.92
8
9.5
Num Alpha failures (per yr)
11.90%
15.00%
19.00%
Num Beta failures (per yr)
64.50%
70.00%
75.50%
Units Sold
24.5
30
49.5
Training Cost
3.55
8
12.44
Avg Repair Cost(alpha)
Avg Repair Cost (Beta)
We divided the continuous probabilities into the range {0-25%, 25-75%, 75-100%}.
We then arrived at the the values in the table above as the cumulative mean over
the individual ranges.
We will use these values to further refine our model.
Decision Tree (Condensed)
Value Measure U-Value
Existing Alternative
-116.92
-116.92
195.91
195.91
161.75
161.75
-8.00
-8.00
Train UDC
195.9063
Contract IPX
Do not Sell
• Alternative 2 (Train UDC) has the best CE and is the initial recommendation if there is no
room for further analysis
• We do recommend further analysis on uncertainties to assess their impact and devise plans
to control them or mitigate their impact
Probabilistic Dominance
1.2000
1.0000
0.8000
Train UDC
Contract IPX
0.6000
Do not Sell
Existing
0.4000
0.2000
-400
-300
-200
0.0000
-100
0
100
Profit in $1000s
200
300
400
500
600
This graph shows the CDF of the Certain Equivalent of 4 alternatives
Dominance Contd..
Type
Dominance Exists
Comments/Insight
Deterministic
No
There is always a point where any
Alternative X is greater than any other
Alternative Y.
Therefore you are never 100% sure that
the alternative you select is better than
any other for the entire universe of
possibilities
1st Order
Yes
This implies that “Train UDC” is a better
alternative than the “Existing” alternative
over the entire probability space.
We can discard “Existing” option for
further analysis for almost all practical
cases (See note on slide)
“Train UDC” Dominates “Existing Option”
2nd Order
Yes
“Train UDC” Dominates “Contract with IPX”
and “Do not Sell”
“Contract IPX” Dominates “Do not Sell”
Value of Information
Value of Information
35
28.6
30
25
20
15
14.31
10
6.28
5
0
Units Sold
Training Cost
Num of Alpha Failures
• If LIM is able to get information on “Training Cost” in advance then $28.6K is
the highest it should be willing to pay
• Similarly $14.31K for information on “Units Sold” and $6.28K for Alpha failures
Value of Control (1 degree)
VoC
151.5
151
150.5
150
149.5
149
148.5
148
147.5
147
146.5
151.09
148.28
Units Sold = 50
VoC
Training Cost = $12.44K
If LIM can control the value of “Units Sold” to 50 units then $151.09K is the most it
should be willing to pay, likewise $148.28K for pegging Training Cost to $12.44K
Sensitivity Analysis: Unit Cost
Closed/Open Loop Sensitivity Analysis (Units Sold)
400
Contract
IPX
350
347
300
289.75
Train
UDC
250
Train
UDC
Open Loop
200
Closed Loop
175.625
150
142.625
100
50
0
Low
Base
High
Sensitivity Analysis (Training Cost)
Closed/Open Loop Sensitivty on Training Cost
400
350
344.1875
300
250
Train
UDC
Contract
IPX
200
Open
196.063
196.0625
Closed
161.75
150
Train
UDC
100
50
47.3125
0
Low
Base
High
Sensitivity Analysis— Num of Alpha Failures
Sensitivity to Num of Alpha Repairs
300
250
248.375
Contract IPX
200
Train UDC
199.313
161.75
150
Train UDC
136.625
Train
UDC
100
50
0
Low
Base
High
Closed
Open
Sensitivity Analysis— Risk Aversion
Sensitivity To Risk Aversion
1
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
CE
0.1
CE
0.01
0.001
Risk Aversion Coefficient (γ)
The decision does not change with change in risk aversion and Train UDC is the
best option
Conclusions
 Items for a second-round assessment
 Determine Value of Information and VoC for multiple degrees
e.g (Units Sold & Training Cost)
 Identify tools that can effectively provide Control or Information
on the uncertainty parameters and evaluate their
effectiveness.
 Revaluate Risk-Preference
 Study if options be used as a tool to mitigate risk ? Instead
of Contracting with IPX, buy the option to contract with IPX.
 Evaluate an insurance purchase for uncertainties that cannot
be controlled.
Appendix
FULL DECISION TREE
Decision Tree (Train WDC Part 1)
Value Measure U-Value
0.25 Alpha Failures Low
0.25 Units Sold Low
249
291
291
248
248
209
209
356
356
312
312
256
256
587
587
515
515
422
422
0.5 Alpha Failures Mid
249
0.25 Alpha Failures High
0.25 Alpha Failures Low
0.25 Training Low
344.188 344.188
0.5 Units Sold Base
309
0.5 Alpha Failures Mid
309
0.25 Alpha Failures High
0.25 Alpha Failures Low
0.25 Units Sold High
509.75
0.5 Alpha Failures Mid
509.75
0.25 Alpha Failures High
Decision Tree: Train WDC Part 2
0.25 Alpha Failures Low
0.25 Units Sold Low
143.5
182
182
146
146
100
100
222
222
179
179
122
122
367
367
295
295
202
202
0.5 Alpha Failures Mid
143.5
0.25 Alpha Failures High
0.25 Alpha Failures Low
0.5 Training Base
196.063 196.063
0.5 Units Sold Base
175.5
0.5 Alpha Failures Mid
175.5
0.25 Alpha Failures High
0.25 Alpha Failures Low
0.25 Units Sold High
289.75
0.5 Alpha Failures Mid
289.75
0.25 Alpha Failures High
Decision Tree: Train WDC Part 3
0.25 Alpha Failures Low
0.25 Units Sold Low
34.5
73
73
37
37
-9
-9
89
89
46
46
-11
-11
147
147
75
75
-18
-18
0.5 Alpha Failures Mid
34.5
0.25 Alpha Failures High
0.25 Alpha Failures Low
0.25 Training High
47.3125 47.3125
0.5 Units Sold Base
42.5
0.5 Alpha Failures Mid
42.5
0.25 Alpha Failures High
0.25 Alpha Failures Low
0.25 Units Sold High
69.75
0.5 Alpha Failures Mid
69.75
0.25 Alpha Failures High
Decision Tree: Contract IPX
Value Measure
U-Value
0.25 Units Sold Low
-15
-15
150
150
347
347
0.5 Units Sold Medium
161.75
0.25 Units Sold High