Dynamic Strategic Planning - Problem Sets

3. Decision Analysis

 

 

Problem 3.1

(continuation of 2.1)

Your staff in the marketing department estimates that new environmental regulation has a 60% chance of being enacted this year. If the legislation is not enacted at this time, you can assume it will not apply to your power plant.

  1. Draw the decision tree.
  2. Basing your recommendation on expected value, what is the preferred choice?
  3. What is the EVPI concerning the passage of this legislation?
  4. It seems that you could pay a consulting firm specialized in government affairs to get information on whether the new legislation will be enacted. From the evidence of their previous performance, you estimate that the firm is right in its predictions 80% of the time. Draw the decision tree showing this new possibility.
  5. Show all payoffs.
  6. Show all probabilities.
  7. Is the sample information worth 5 million $? Show calculations.
  8. Perfect information about whether the legislation is passed this year could be obtained simply by deferring the project - and its benefits - by a year. What is the true cost of this strategy, in terms of deferred benefits?
  9. How much would you be willing to pay the Government for the right to defer the project by a year?

 

Problem 3.2

(continuation of 2.2)

Your staff in the marketing department estimates that the market will have a positive reaction to the hybrid car with a 60% chance. Assume that the market reacts immediately after the introduction of the hybrid car. Assume further that the reaction (positive or negative) will remain constant during the life of your project.

  1. Draw the decision tree.
  2. Basing your recommendation on expected value, what is the preferred choice?
  3. What is the EVPI concerning the reaction of the market?
  4. It seems that you could pay a consulting firm to get information on how the market will react to the hybrid car. From the evidence of their previous performance, you estimate that the firm is right in its predictions 80% of the time. Draw the decision tree showing this new possibility.
  5. Show all payoffs.
  6. Show all probabilities.
  7. Is the sample information worth 20 million $? Show calculations.
  8. You know for sure that your main competitor is introducing a hybrid into the market this year. Perfect information about market's reaction could be obtained simply by deferring your project - and its benefits - by one year. What is the true cost of this strategy, in terms of deferred benefits?
  9. Given the possibilities of waiting a year or paying the consulting firm $20M for the information, what is your best strategy?

 

Problem 3.3

Imagine yourself the president of the leading producer of document copiers. Most of these machines now use light lenses. You are trying to decide whether to introduce digital technology that could take documents directly off of computers, faxes, etc., in the form of machines known as multi-functional devices (MFD).

The difficulty is that it is not known whether MFD can be made competitively. Your engineering staff says the probability of making a competitive product is 40%, whereas your marketing staff believes that this probability is 80%, based on what they see competitors producing. You now judge either opinion to be equally likely to be correct.

Your sales force estimates that annual operating profits will increase by $100 million if the product is made competitively, but that otherwise it will lose $100 million/year.

  1. Draw your decision tree based on the above information, including all relevant data about outcomes and probabilities. Should you produce MFDs?
  2. What is the expected present value of these annual profits, if they continue indefinitely? Your company s weighted average cost of capital is 20%.
  3. What level of capital investment do these profits justify?
  4. Draw the decision tree that includes a "test", of whether MFDs can be made competitively, before you decide to produce MFDs.
  5. What is the upper bound on the maximum possible increase in value that could be obtained from this test?
  6. Suppose you decide, as a test, to go ahead with MFDs on an experimental basis for a year, using the results to refine your estimates of the probability of making a competitive product. You recognize at this point that the Probability of making a competitive product in any year, as seen by either the engineers or the marketing staff, is independent of what happened in previous years, due to the constant competitive struggle between manufacturers. What is the expected value of this "test" on the long-term decision to make MFDs?
  7. The total initial capital cost of starting MFD production is estimated to be $80 million. What is your recommended strategy?

 

Problem 3.4

Designers of oil pipeline must decide whether to build a parallel gas line at a cost of $100 million. At the present price for gas, the net present value of the gas sales to a proposed power plant would be $120 million. This new plant has a 90% chance of being approved by the regional legislature and constructed. If it is not, the investment in the gas line could not be recovered. They could also change the design to meet perceived environmental concerns, which would increase the cost by $10 million, but increase the probability that the plant will go ahead to 95%.

  1. Draw the decision tree.
  2. What should the company do, if it decides only according to expected value of profit?
  3. What is the Expected Value of Perfect Information concerning the approval and construction of the gas-fired power plant?
  4. The company hires political consultants who have, in the past, correctly anticipated decisions by the regional legislature 60% of the time [probability that they have correctly predicted approval when approval has been given, or disapproval when approval has been denied]. Calculate the probability that the plant will be built, if the consultants indicate that they think the project will be approved.
  5. Estimate the maximum the company might reasonably justify to hire the consultant.

 

Problem 3.5

As a junior consultant, you are advising a major oil company on how to develop a newly discovered oil field. According to geological experts, the capacity of this oil field is either 10M barrels or 5M barrels. These two possibilities (high reserves and low reserves) appear equally likely.

The investment costs required to develop this field and bring the oil to the market would normally be 90M$, which enable you to extract a constant flow of 1M barrel per year, (up to the capacity of the field), starting at the end of the first period.

Alternatively, a smaller investment of 70M$could be made, but then it would only be possible to extract 0.5M barrel per year.

Assuming that the price of oil will be 20M$ per barrel, that the variable costs of extraction are negligible and that the discount rate is equal to 10%, answer the following questions:

  1. Evaluate the NPV of the 90M$ investment assuming high reserves. Give the details of the computation. You can use the following information:
  2. Number of periods

    Series present value at

    5%

    10%

    15%

    3

    2.72

    2.49

    2.28

    5

    4.33

    3.79

    3.35

    8

    6.46

    5.33

    4.49

    10

    7.72

    6.14

    5.02

    15

    10.4

    7.61

    5.85

    20

    12.5

    8.51

    6.26

  3. Do the same for the three other possible situations and summarize your results in the following table. (It is not necessary to give the details this time)
  4.  

    High reserves: 10M barrels

    Low reserves: 5M barrel

    NPV Big investment

       

    NPV Small investment

       

  5. Draw the decision tree, indicating all data
  6. What investment decision would you advise?
  7. An exploration firm proposes you to collect additional information. What in practice is the most you be ready to pay for exploring the field?
  8. During the course of your investigations, you learn that it is possible to estimate the size of the reserves by analyzing oil samples at no cost. This estimation has proven in the past to be 70% reliable. What is the probability of exploiting important reserves if the samples indicate that it is an important reserve? What if they indicate the contrary?
  9. What is the expected value of the test described in question f?
  10. If the true cost if conducting the test described in question f were to be to delay the extraction of oil by 4 months (so that it were to occur at the end of 16 months instead of 12 months), is it worthwhile conduct the test? Show calculations.

 

Problem 3.6

January 2000. As the manager of International Chocolate Inc., you are reflecting over the exceptional sales level of your latest product, Millennium Crunch, during the Christmas - New Year season. You believe that you could certainly build on that success and develop a new line of production.

The initial investment cost for that new line is $2 million, but you are uncertain whether the demand you have observed will be sustained in the future:

Assuming that annual profits are received at the end of the year and that the discount rate is 15%, answer the following questions.

  1. Evaluate the NPV of your investment in all three possible situations, and summarize it in the table below. Give the details of the computation. You can use the following information:
  2. Number of periods

    Approximate series
    present value at

    5 %

    10 %

    15 %

    3

    2.72

    2.49

    2.28

    5

    4.33

    3.79

    3.33

    8

    6.46

    5.33

    4.50

    10

    7.72

    6.14

    5.02

    15

    10.4

    7.61

    5.85

    20

    12.5

    8.51

    6.26

    Summary

    Hit

    Fad

    Strong Product

    NPV

         

  3. You have consulted your marketing department, and they have told you that Millenium Crunch has an equal probability of 30% of being a hit or a just a fad.
  4. Draw the decision tree, indicating all data.

  5. If your goal is to maximize expected monetary value, would you invest the $2 million in the new line? Show calculations.
  6. You know that you could probably wait until next Thanksgiving and get a perfect vision of the market. Assuming that all possible outcomes are unchanged if you wait, draw the revised decision tree corresponding to the test of waiting until Thanksgiving for the certain information.
  7. If you choose to wait until next Thanksgiving, you will not be ready to market for the Christmas season either, and might very well lose one year of sales. You evaluate hence the overall true cost (including both the delay and the lost sales) of conducting the test described in d) to be approximately $200,000.
  8. Do you think it might be worthwhile to wait? Show calculations and explain your choice.

  9. Unsatisfied with this analysis and the risks of losing an opportunity, you wonder if a thorough marketing study could help you make a better decision.
  10. Draw the decision tree corresponding to a marketing test, omitting probabilities for the moment.

  11. By experience, you know that the results of such marketing studies are only 60% reliable: when the product is a hit, the study actually concludes it is a hit only 60% of the time; in 20% of the cases, it would conclude it is a fad, and in another 20%, it would conclude it is a strong product.

Assuming that this reliability is independent of the actual event (the same would happen if it were a fad or a strong product), please compute all the revised probabilities that would result from a marketing study.

Hints:

  1. Add the probabilities calculated in g) to the decision tree drawn in f).
  2. How much would you be ready to pay for the marketing study? Show calculations.

 

Problem 3.7

Sunny Farm ships oranges and grapefruits from Florida to Washington every evening, either by air cargo, which is usually faster (except when the Washington airports are closed by bad weather), or by truck, which is slower but consistently dependable.

Air cargo either arrives at the wholesale market at 5 am or 10 hours later when there is bad weather (which occurs 15% of the time). Trucks arrive reliably at 7 am.

  1. Construct the Sunny Farm decision tree, labeling outcomes and probabilities, and indicate which option better delivers the earlier arrivals on average.
  2. By delaying their choice of shipment (and therefore their arrival) by an hour, Sunny Farm managers can get the latest reports from the air cargo shippers. Their experience is that when the reports forecast delays, 20% of the time the situation clears up by the time the planes take-off (i.e., the forecast of a delay is right 80% of the time). Also, in 10% of the cases, when no delays were anticipated, they still occur (i.e., a forecast of no delay is right 90% of the time). Please draw Sunny Farm's decision tree considering the forecast, labeling all relevant probabilities and outcomes.
  3. Should Sunny Farm wait for the forecast? What should they do?
  4. How long could they wait for a perfect forecast?

 

Problem 3.8

Donna and Jerry form a car pool for traveling to work. After limiting the travel routes to two alternatives, they could not agree on the best way to travel, Donna preferred the expressway, as it was usually the fastest; however, Jerry pointed out that traffic jams on the expressway sometimes led to long delays. Jerry preferred the somewhat longer but more consistent Queen City Avenue. In any case, not knowing the state of the expressway ahead of time, both agreed that they should use whichever route was faster on average. Traveling to work takes 25 minutes on the expressway when traffic is fluid, but 45 minutes when jammed; whereas Queen City Avenue reliably takes 33 minutes. After using the expressway for 1 month (20 days), they found it jammed four times.

  1. Construct a decision tree for choosing the appropriate route, labeling outcomes and probabilities, assuming that these days are representative of future days.
  2. Should they continue to use the expressway?
  3. Last year, Donna has observed that when the radio announced delays, 30% of the time the situation had cleared up by the time she reached the trouble area (i.e., a radio announcement of a delay is correct 70% of the time). Also, in 10% of the cases when normal traffic was reported, she would still end up experiencing delay (i.e., a radio announcement of no delay is correct 90% of the time). Furthermore, Donna noticed that the radio announced traffic delays during 1/6th of their commutes, on average (i.e., the probability of a delay announcement is 1/6). The traffic report is usually broadcast about 2 minutes after they pass the intersection where they must choose between the two routes. In other words, deciding on the basis of the traffic update will require that they delay for 2 minutes at the intersection, just waiting for the radio report. Please draw Donna and Jerry's decision tree. Label all relevant probabilities and outcomes.
  4. Should they wait for the radio report? What should they do?