- Economic Climate Country Decline Stable Improve South Korea Philippines Mexico

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1 1) Micro-comp is a Toronto based manufacturer of personal computers. It is planning to build a new manufacturing and distribution facility in South Korea, Philippines, or Mexico. The profit (in $ millions) depends on the financial, labour and political climate, including monetary exchange rates. - Economic Climate Country Decline Stable Improve South Korea Philippines Mexico a. What is the maximax decision? b. What is the maximin decision? c. What is the equally likelihood decision? d. What is the criterion of realism decision. Use alpha of 0.25 e. Develop an opportunity loss table f. What is the minimax regret decision? g. A global economist hired by Micro-comp estimates that the probability that the economic climate overseas and in Mexico will decline is.40, the probability that it will remain approximately the same is 0.50, and the probability that it will improve is Determine Micro-comp s optimal decision using expected value. h. Determine the EOL and the best strategy. i. What is the expected value of perfect information? 2) Susan has been thinking about starting her own independent gasoline station. Susan s problem is to decide how large her station should be. The annual returns will depend both on the size of her station and on a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table Size of Station Good Market Fair Market Poor Market Small Medium Large Very Large a. What is the maximax decision? b. What is the maximin decision? c. What is the equally likelihood decision? d. What is the criterion of realism decision. Use alpha of 0.8 1

2 e. Develop an opportunity loss table f. What is the minimax regret decision? g. After reading about economic predictions, Susan has assigned the probability that the market will be good, fair, and poor at 0.2, 0.35 and 0.45 respectively. Calculate Susan s best decision using EMV. h. What is Susan s choice using the minimum EOL? i. Compute the EVPI and show that it is the same as minimum EOL 3) A machine shop owner is attempting to decide whether to purchase a new drill press or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. Investment Contract (0.7) No Contract (0.3) Drill Press $ $ Grinder $ $ a. Construct a decision tree for this problem. What is the recommended decision using expected value criterion? b. What is the maximum amount of money the investor should pay for additional information regarding the outcomes? c. The machine shop owner is considering hiring a consultant to analyze the situation. The results of the analysis will indicate that either favourable (contract awarded) or unfavourable conditions (not awarded) will occur. There is 0.8 probability that a positive report will result given that favourable conditions actually occur. There is 0.90 probability that a negative report will result given that unfavourable conditions actually occur. Revise the decision tree, and determine best decision using EMV. d. Determine the maximum fee the investor should pay the analyst 4) An investor must decide whether to purchase an apartment building at a cost of $800,000 or purchase land at a cost of $200,000. If the apartment is purchased two states of nature are possible: population growth ($2 M payoff) or no population growth ($225,000 payoff). The probability of growth is 0.6 and the probability of no growth is 0.4. If the investor decides to buy the land he or she can wait three years to see if there is population growth before making a decision about land use. Consequently, there is no payoff for the first three years, as the land is not developed. If the investor decides to buy the land and there is population growth in the three year period (P = 0.6) the investor will then need to decide whether to build apartments at a cost of $800,000 or sell the land for $450,000. If the population continues to grow (P = 0.8) the payoff on the apartment at the end of a ten-year period will be $3 M. If the population does not continue to grow (P = 0.2) the apartment payoff will be only $700,000. 2

3 If there is no population growth in the first three years (P = 0.4) then the investor will either decide to build commercially at a cost of $600,000 or sell the land for only $210,000. If the land is developed commercially and the population grows (P = 0.3) a payoff of $2.3 M is expected and if there is no population growth (P = 0.7) the expected payoff is only $1 M. What is the recommended decision and expected value of the decision? 5) Oscar Weng is planning to raise funds to pay for a scouting trip by running a concession stand during high school soccer game. Oscar needs to decide whether to rent a large insulate thermos from the local rent store for $20 and sell cocoa at the game, or to rent a large refrigerated container for $30 and sell lemonade. Unfortunately, Oscar does not have to the resources to rent both items. Sales depend on whether it is sunny or rainy during the game. The Table below Summarizes, the type of weather and expected profit from each product. Product Sunny Rainy Lemonade $60 $0 Cocoa $20 $80 Based on the local newspaper s prediction, Oscar thinks there is a 60% chance the weather being sunny. a. Draw a decision tree for Oscar s Problem. b. What is the recommended decision using expected value? Oscar s Friend, Susan is budding meteorologist who claims she can predict the weather more accurately than the newspaper. For only $4, she offers to study the weather and tell him is there is a "good chance" or a "bad chance" of it being sunny. The following data are available about the accuracy of Susana s information: The probability that she will say "good chance" is 0.7 If it is sunny, then there is a 0.83 probability that she will say it s a "good chance" If it is rainy, then there is a 0.75 probability that she will say it s a "bad chance" c. Assuming Oscar hires Susana, reconstruct the decision tree and recommend the decision strategy Oscar should follow. d. How much is Susana s information actually worth? 3

4 Answers/Solutions 1) a. Philippines (9.4) b. Mexico (-1.7) c. Mexico (2.57) d. Mexico (0.23) e. Economic Climate Country Decline Stable Improve South Korea Philippines Mexico f. Mexico (3.4) g. Mexico (EMV=1.62) h. Mexico (EOL=0.34) i ) a. Very Large ($ ) b. Small ($ ) c. Very Large ($55 000) d. Very Large ($20 800) e. Size of Station Good Market Fair Market Poor Market Small Medium Large Very Large f. Very Large ($ ) g. Medium (EMV=17 500) h. Medium (EOL=48 500) i. EVPI= ) a. Grinder (EMV=$25 300) 4

5 b. $8 400 c. Hire the analyst. Given positive report purchase a drill press. Given negative report purchase a grinder. d. $5784 4) Buy Land. If growth, Build Apartment. If no growth Build Commercially. EMV=$ ) a. b. Decision: Rent the Large insulated Thermos and Sell Cocoa Posterior Probabilities Table Good Chance Report Prior (P) Conditional (P) Joint (P) Posterior (P) Sunny Rainy

6 Bad Chance Report Prior (P) Conditional (P) Joint (P) Posterior (P) Sunny Rainy c. Decision: Hire Susan. Given a Good Chance report, Rent large Refrigerated Container and Sell Lemonade, EMV Hire Susan. Given a Bad Chance Report, Rent a Large insulated thermos and Sell Cocoa, EMV d. EV with Information-EV without information