Question

Happily Ever After

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 ($100,000). However, if there is no audit, then this tax strategy has the benefit of delaying the required reporting date of some income streams. The value of this benefit is $5000.

Their accountant, Ms. Weiss, has been provided some valuable information. Out of 100 known cases where an audit took place, 40 of them involved the risky tax strategy that is being considered. In 500 known cases where no audit took place, 50 of them involved the risky tax strategy. Ms. Weiss also knows that, barring any additional information, tax audits have a probability of 0.01. If the couple decides not to use the risky tax strategy, then they expect to see no benefit or penalty. i) Perform the appropriate analysis to help Ms. Weiss determine if the couple should use the tax strategy. ii) Unbeknownst to Ms. Weiss, Corin and Lance have agreed that their interests can be accurately represented by the exponential utility function U(x) = 1 – e^(-x/100). Will this cause Ms. Weiss to give a different recommendation? Why or why not?

Answer 1

Answer:

By using, given data

Tax audits have a probability of 0.01.

(1)

Here as per the case if their taxes are audited,because of some short cuts used by Lance in the past,it may cost them penality of$100000 and if no audit will take place then it may benfit them by $5000.Here there is huge difference in the amount of benefit and penality.Probability shows that in 100 cases every 1/4 is audited through risky tax strategy and among 500 cases,in this only 50 involved risky tax strategy audit.in 0.04 % risk is involved if couple is involved in risky tax strategy and there is no benefit or penality if couple not uses risky tax strategy.As the risk involved is low but if occurs the penality amount is very high and even also penality is far more than higher than the benefits.I would suggest that couple should not go for risky tax strategy.

(2)

In this , the exponential utility function is U(x) = 1 – e^(-x/100)

Answer is No ,why because ,the exponential function will not cause Ms.Weiss to give a different recommendation.She would be saying the same thing that couple should not take such huge risk of $100000.