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FB2201 Management Sciences IITopic 3: Decision Analysis (Part 3) (Solutions)Q3.19Shir Khan is considering investing some money that he inherited. The following payoff table gives the profits that would be realized during the next year for each of three investment alternatives Shir is considering:State of NatureDecision AlternativeGood EconomyPoor EconomyStock market80,000-20,000Bond30,00020,000CDs23,00023,000Probability0.50.5(a).What decision would maximize expected profits?SolutionState of NatureDecision AlternativeGood Economy, (0.5)Poor Economy, (0.5)EMVStock market80,000-20,00030,000Bond30,00020,00025,000CDs23,00023,00023,000EMV (Stock market) = 80,000×0.5 + (-20,000) ×0.5 = 30,000EMV (Bond) = 30,000×0.5 + 20,000×0.5 = 25,000EMV (CDs) = 23,000×0.5 + 23,000×0.5 = 23,000The best decision is to invest in stock market with EMV = $30,000.(b).What is the maximum amount that should be paid for a perfect forecast of the economy?SolutionEVPI = EV (with prefect information) - (Maximum EV without prefect information) = (0.5×80,000) + (0.5×23,000) - 30,000 = 51,500 - 30,000 = $21,5001
Q3.22In Problem 3-21, you helped Ziang Zameen determine the best investment strategy. Now, Zameen is thinking about paying for a stock market newsletter. A friend of Zameen said that these types of letter s could predict very accurately whether the market would be good, fair, or poor. Then, based on these predictions, Ziang could make better investment decisions.(a).What is the most that Ziang would be willing to pay for a newsletter?SolutionEV with Perfect Information=1,400×0.4 + 900×0.4 + 900×0.2 = $1,100EMV (CD) without information = $900Therefore, the most Ziang would be willing to pay for a newsletter =1,100 – 900 = $200.(b).Ziang now believes that a good market will give a return of only 11% instead of 14%. Will this information change the amount that Ziang would be willing to pay for a newsletter? If your answer is yes, determine the most that Ziang would be willing to pay, given this new information.