# Project A Case study

Project A: Using Probabilities to Make Decisions (Unit 2)

♥ Heart Scenario: Good economy

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Data

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A financial planning firm has a decision to make.  The company can buy more stocks (B) now, not buy and not sell stock (N) now, or it can sell its stock (S) now.

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The following is from the Google Dictionary:

Bear Market:  a market in which prices are falling, encouraging selling.

Bull Market: a market in which share prices are rising, encouraging buying.

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The future market will be either Bear (E) or Bull (U).

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The following is a payoff table, in thousands of dollars, of profit or loss for this firm based on the decision the firm makes now and the future market.

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 E U B 44 -29 N 24 -11 S 18 4

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The statisticians of the company, using their standard budget, predict the following probabilities:

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P(E) = 0.5                                             P(U) = Complement

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The statisticians report that if the company is charged and additional \$5,000 above the standard fee, they can do more accurate research to obtain sample information that will either be Favorable (F) or Unfavorable (X) with the following probabilities:

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P(F) = 0.5                                             P(X) = Complement

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If the research is favorable, the revised probabilities are:

P(E) = 0.85                                           P(U) =  Complement

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If the research is unfavorable, the revised probabilities are:

P(E) = 0.22                                P(U) = Complement

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Assignment

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Do all calculations, including making the decision tree and any algebra, in Excel; organize it and highlight important boxes in colors so that it can be read and understood very easily.  Put question numbers next to the answers. You may want to use multiple sheets, but please use only one file. Write out all answers, including #15 and #21 in Excel. For all algebra, show work [the written steps you went through to find the answer] and type that into Excel.  Do not submit the paper you may have used to solve the algebra, just copy it and put it all in Excel.

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Very Important:  Input the data only once.  After that, link all calculations from new cells to previous cells, as illustrated in of the videos.  Answers to questions that have the right number but are not linked will be marked incorrect.  Projects that do not link cells will receive a very low grade.

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Find the following:          [The number in the brackets is how many points each question is worth.]

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• The decision using the optimistic approach. [2]
• The decision using the conservative approach. [2]
• The decision using the minimax regret approach. [2]
• The decision using the Expected Opportunity Loss (EOL) [2]
• EV(B) [1]
• EV(N) [1]
• EV(S) [1]
• Best EMV = The decision using EV [1]
• EVwPI [1]
• EVPI [1]

For #11 and #12: make three comparisons, EV(B) to EV(N), EV(B) to EV(S), EV(N) to EV(S).  You will have three cutoff points and four test points.

• The value of probability (p) of E that is the cut off for changing the best decision. [4]
• Draw a number line for #11. [4] (sensitivity analysis)
• The value for which the payoff of E of the best decision must be greater than to keep the best decision the same. [4] (sensitivity analysis)
• The value for which the payoff of U of the best decision must be greater than to keep the best decision the same. [4] (sensitivity analysis)
• Rank p, payoff of E, and payoff of U from least to most sensitive and explain why. Make sure to rank them and explain why you have chosen your order. [2]
• The decision tree [6]
• EVwSI [1]
• EVSI [1]
• Efficiency of the Sample Information [2]
• The Risk Profile [4]
• Based on the cost of obtaining the sample information and its efficiency, is it worth obtaining it? Why? Please include ALL the relevant information for this decision and use specific numbers.   Your answer must discuss EVSI, net EVSI (The EVSI minus the cost of the SI), the Efficiency of the Sample Information (abbreviated “E”) and the Risk Profile. This is the most important question in the project, as you are making the decision to purchase the SI using all you have learned.  Answers that do not include all this will not get credit. [4]P(5.u)

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