Variance Investigation (Appendix)

David Smiley is the manager of Photobonics Manufacturing. He notices that the operation in the last four weeks has had an unfavorable materials usage variance of $25,000. He is trying to decide whether to investi- gate this variance. If he investigates and discovers that the process is out of control (i.e., not due to a random occurrence and therefore not likely to correct itself), corrective actions will likely cost the firm $5,000. The cost of investigation is expected to be $2,500. The company would suffer an estimated total loss (in present-value terms) of $55,000 if the out-of-control operation continues. Smiley estimates the probability the operation is out of control is 60 percent.

Required

1. What are the expected costs of investigating and of not investigating? Should the operation be investigated? Why or why not?

2. What is the indifference probability that the operation is out of control?

3. What is the expected value of perfect information (EVPI) in this case? EVPI is defined as the maximum value the manager would pay to have knowledge (i.e., certainty) of whether the process is in control or out of control. In this decision context, the EVPI can be thought of as the difference between the expected cost with perfect information and the expected cost without perfect information. To calculate the former, we need to choose for each possible state of nature the best course of action (decision) and then multiply the associated "cost" for this decision by the probability of that state of nature occurring. We then sum these resulting expected costs to get the expected cost with perfect information.

Thus, EVPI = Expected cost with perfect information - Expected cost without perfect information = Expected cost with perfect information - Expected value of cost-minimizing choice under uncertainty = Maximum amount manager would be willing to pay for perfect information.