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 an estimated cost of $2 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 test market option, 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 the expected value of perfect information.

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

d. Find the expected value of sample information.

How large can the cost of trying out the product in a test market be and still be worthwhile to do? 

e. Assume now that the estimate of $2 million for the cost of trying out the product in a test market is correct. 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. For each of these two financial figures, perform sensitivity analysis to check how the results in part c would change if the value of the financial figure were at either end of this range of variability (without any change in the value of the other financial figure). Then do the same for the four cases where both financial figures are at one end or the other of their ranges of variability.