Question: Suppose the tax rate is 30% if taxable income is positive and 0% if taxable income is negative. Calculate the expected tax payable for the following four projects. Note that for each project the expected taxable income is $50,000. For each project, also calculate the expected average tax rate (expected total taxes divided by expected taxable income). Explain and discuss your results.
a. Certain payoff $50,000
b. 50% chance of $100,000 and a 50% chance of $0
c. 50% chance of $200,000 and a 50% chance of a loss of $100,000
d. 50% chance of $500,000 and a 50% chance of loss of $400,000
This problem can be solved by preparing a graph similar to Figure 6.1.
1. Draw in the tax-rate schedule for taxable income in the range -$500,000 to +$500,000 with taxable income on the horizontal axis and tax payable on the vertical axis.
2. Mark the two endpoints on the tax schedule for each project. (For project 2 the two endpoints are $0 and $50,000.) Draw a straight line between the two outcomes.
3. Draw a vertical line upward from the horizontal axis at taxable income equal to $50,000.
4. Finally, read off the expected tax payable for each project where the expected tax payable is the intersection point of the lines in (2) and (3).