# Question

The Morton Ward Company is considering the introduction of a new product that is believed to have a 50-50 chance of being successful. One option is to try out the product in a test market, at a cost of $5 million, before making the introduction decision. Past experience shows that ultimately successful products are approved in the test market 80 percent of the time, whereas ultimately unsuccessful products are approved in the test market only 25 percent of the time. If the product is successful, the net profit to the company will be $40 million; if unsuccessful, the net loss will be $15 million.

(a) Discarding the option of trying out the product in a test market, develop a decision analysis formulation of the problem by identifying the decision alternatives, states of nature, and payoff table. Then apply Bayes’ decision rule to determine the optimal decision alternative.

(b) Find EVPI.

(c) Now include the option of trying out the product in a test market. Use ASPE (and the Excel template for posterior probabilities) to construct and solve the decision tree for this problem.

(d) Perform sensitivity analysis systematically for the option considered in part (c) by generating a data table that shows the optimal policy and the expected payoff when the prior probability that the new product will be successful is 0, 0.1, 0.2,., 1.

(e) Assume now that the prior probability that the new product will be successful is 0.5. However, there is some uncertainty in the stated profit and loss figures ($40 million and $15 million). Either could vary from its base by as much as 25 percent in either direction. Use ASPE calculations to generate a graph for each that plots the expected profit over this range of variability.

(a) Discarding the option of trying out the product in a test market, develop a decision analysis formulation of the problem by identifying the decision alternatives, states of nature, and payoff table. Then apply Bayes’ decision rule to determine the optimal decision alternative.

(b) Find EVPI.

(c) Now include the option of trying out the product in a test market. Use ASPE (and the Excel template for posterior probabilities) to construct and solve the decision tree for this problem.

(d) Perform sensitivity analysis systematically for the option considered in part (c) by generating a data table that shows the optimal policy and the expected payoff when the prior probability that the new product will be successful is 0, 0.1, 0.2,., 1.

(e) Assume now that the prior probability that the new product will be successful is 0.5. However, there is some uncertainty in the stated profit and loss figures ($40 million and $15 million). Either could vary from its base by as much as 25 percent in either direction. Use ASPE calculations to generate a graph for each that plots the expected profit over this range of variability.

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