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A government agency suspects that one of the firms it has hired under a cost-plus contract is padding its bills to the government. If padding is going on and if the agency can prove its case in court, it estimates it could save $2 million in disallowed costs. However, the cost of bringing a large-scale legal action against the firm is considerable, about $500,000. The agency's auditors believe that there is a 20 percent chance that padding is going on. Its lawyers reckon that there is a 75 percent chance of proving and winning the legal case (if padding is indeed taking place).
a. If the agency is risk neutral, use a decision tree to determine its best course of action.
b. Suppose the agency can conduct a preliminary investigation (conduct audits and interview dozens of employees) before deciding whether to bring a case. From the investigation, the agency can expect one of two results: a "clean" outcome (C) or a "questionable bill of health" (Q). If cost padding really is going on, there is a 75 percent chance that the investigation will signal Q. If there really is no cost padding, then the chance of C is 80 percent. (There is a 20 percent chance that would-be whistle-blowers, such as disgruntled employees, will allege questionable practices even when no padding is going on.) If an investigation results in outcome Q, what is the chance that cost padding is going on?
c. Use a decision tree to determine the expected value to the agency of conducting an investigation.
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