BACKGROUND: After several years of supplying its famous Wood Varnish Double IPA to several upscale boutique corner grocers, the Beckett family decided that it was time to diversify their product line in light of increasing competition from other craft brewers. Salinger Beckett, a recent biochemistry graduate, suggested that they exploit the growing market for undrinkable beer by introducing a triple IPA. "I've perfected it in the lab," he said. "The fumes make your eyes water and it tastes like Pine-Sol!" He then provided his estimates of costs for the project. Based on Salingers figures, Matilda Beckett, the family accountant, estimated that if sales are high, the total contribution margin from the product will be $350,000. If sales are medium, the total contribution margin from the product will be $200,000. If sales are low, the total contribution margin from the product will be $70,000. Fixed costs for the project will be $200,000. If they do not undertake the project, the family will simply put the $200,000 in a money market fund currently earning 4 percent. Matilda is uncertain as to what the probability distribution of sales will be, but she estimates a prior probability of .3 for high sales, .3 for medium sales, and .4 for low sales. The Beckett family can obtain additional information from a survey of various craft beer grocers and publicans to determine the true demand for the new product. The accuracy of the survey is such that it will predict high sales 80 percent of the time when actual sales will be high. When sales will be high, the test predicts low sales 10 percent of the time and medium sales 10 percent of the time. Accuracy is similar for the other two potential sales levels. That is, when sales will be medium, the test predicts medium sales 80 percent of the time, and predicts each of the other two categories 10 percent of the time. When sales will be low, the test predicts low sales 80 percent of the time, and predicts each of the other two categories 10 percent of the time. The cost of the survey is estimated to be $20,000.

Using a one-year time horizon, please use the provided Excel spreadsheet to (1) use Bayes Rule to calculate revised (posterior) probabilities from prior probabilities and (2) prepare a decision tree (use Precision Tree) to cell reference the probability calculations to capture the problem facing the Beckett family.

Answer the following questions: 1. Without the above survey, what action should they take? 2. Should the Beckett family conduct the survey? If so, what is the optimal decision for each survey prediction? 3. What is the maximum amount they should be willing to pay for this particular (imperfect) survey, which is commonly called EVSI? 4. What is the value of perfect information (EVPI) in this case?