Three years into the project, Corin and Lance have decided to get married. Because this union creates some difficult tax decisions, the couple is carefully considering their options. In particular, they are considering a risky tax strategy that often results in a tax audit. If their taxes are audited, it is certain that some shortcuts that Lance previously took will be noticed by the auditor, resulting in a substantial fine ($250,000). However, if there is no audit, then this tax strategy has the benefit of delaying the required reporting date of some income streams. The tax value of this benefit is $20,000. Note, if they use this strategy and are audited, then they will not realize the $20,000 benefit. If Corin and Lance choose not to use this strategy, the associated tax value is $0. Their accountant, Ms. Weiss, has been provided some valuable information. Out of 100 known cases where an audit took place, 25 of them involved the risky tax strategy that is being considered. In 500 known cases where no audit took place, 100 of them involved the risky tax strategy. Ms. Weiss also knows that, barring any additional information, tax audits have a probability of 0.01.

i) Find the probability of being audited given that the risky tax strategy is used and the probability of not being audited given that the risky tax strategy is used (Hint, use Bayes Theorem).

ii) Using the probabilities from i), find the expected value of using the tax strategy. Based on this, should the strategy be used?

iii) Suppose the Corin and Lance have adopted an exponential utility function: U(x) = 1 e -x/100 .

Using the probabilities from i), find the expected utility of using the tax strategy. Also, find the expected utility of not using the tax strategy. Based on this, should the strategy be used? Note: you should use units of thousands here, so instead of the loss of -250,000 and the benefit of 20,000, you should use -250 and 20, respectively