# 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. 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.

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).

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.

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).

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