1. ARUNABHA SAHA Final Exam: Large Instrument Manufacturer, Inc.

2. 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.

3. 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

4. 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

5. Decision Diagram Num of Αlpha Failures Value Train UDC engineers OR Outsource Continue with Existing Arrangement Total Beta Failure Cost Num of Beta Failures Cost of Alpha Failures Cost of Beta Failures Units Sold Total Revenue Total Alpha Failure Cost Sell ROE-II to UDC Training Cost Initial Cost (Training + Installation)

6. NPV of Each Strategy at Base Case 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

7. Comparison of Alternatives (100% range) 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

8. Assessing Important Uncertainties (95%) 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

9. Probabilistic Assessment Discretizing (Equal Areas – Shortcut) Low(0-25%)Mid(25-75%)High(75-100) Avg Repair Cost(alpha) 8.919.9512.5 Avg Repair Cost (Beta) 6.9289.5 Num Alpha failures (per yr) 11.90%15.00%19.00% Num Beta failures (per yr) 64.50%70.00%75.50% Units Sold 24.53049.5 Training Cost 3.55812.44 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.

10. Decision Tree (Condensed) 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

11. Probabilistic Dominance Profit in $1000s This graph shows the CDF of the Certain Equivalent of 4 alternatives

12. Dominance Contd.. TypeDominance ExistsComments/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 1 st Order Yes “Train UDC” Dominates “Existing Option” 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) 2 nd Order Yes “Train UDC” Dominates “Contract with IPX” and “Do not Sell” “Contract IPX” Dominates “Do not Sell”

13. Value of Information 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

14. Value of Control (1 degree) 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 151.09 148.28

15. Sensitivity Analysis: Unit Cost

16. Sensitivity Analysis (Training Cost)

17. Sensitivity Analysis— Num of Alpha Failures

18. Sensitivity Analysis— Risk Aversion The decision does not change with change in risk aversion and Train UDC is the best option

19. 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.

20. FULL DECISION TREE Appendix

21. Decision Tree (Train WDC Part 1)

22. Decision Tree: Train WDC Part 2

23. Decision Tree: Train WDC Part 3

24. Decision Tree: Contract IPX