Sue Reynolds is considering investing in a retail store. Sue estimates that the probability of a successful store will be 0.6. A successful store will give a return of $100,000. If Sue invests in the store but it is unsuccessful, she will see a loss of $80,000.
a) Sue has the option of conducting a study (at a cost of $20,000) as input into her investment decision. If she conducts the study, there is a 0.6 probability that the study will predict the store will be successful and a 0.4 probability that the study will predict the store will be unsuccessful (these values are the marginal probabilities). If the study predicts the store will be successful, there is a 0.9 probability that the store will be a success yet if the study predicts the store will be unsuccessful the probability the store is unsuccessful is 0.8 (these values are posterior probabilities). Formulate a two-stage decision tree to capture both the obtain information decision and the build the store decision. Use TreePlan to construct and solve a decision tree for this problem. What are Sue’s optimal decisions with the EMV criteria?
b) What is the expected net gain from sampling?
c) When incorporating the conduct study decision, Sue had difficulty identifying the marginal probability study predicts the store will be successful. Perform a sensitivity analysis on this parameter to identify if changing the value would lead to a different optimal decision.
Please solve using decision tree in excel