Suppose that there is a 25% chance that an investment of $1,000 will rise in value to $1,400,a 25% chance that the investment will remain at $1,000,and a 50% chance that the investment will fall in value to $500.The government introduces a 50% tax on returns to investment and allows a deduction against taxable income for any losses (assume that the tax rate is 50%).What is the expected return on the investment?

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The expected return on the investment, considering the tax implications, can be calculated as follows:1. If the investment rises to $1,400, the gain is $400. With a 50% tax, the net gain is $200 (50% of $400). The probability of this happening is 25%, so the expected return from this outcome is 0.25 * $200 = $50.2. If the investment remains at $1,000, there is no gain or loss, so the expected return from this outcome is $0.3. If the investment falls to $500, the loss is $500. With a 50% deduction allowed against taxable income for losses, the investor can deduct $250 (50% of $500). However, since this is a deduction against taxable income rather than a tax credit, the actual monetary return to the investor is $0 because the deduction only offsets potential tax liabilities on other income, not providing a direct benefit from the investment itself. Thus, the expected return from this outcome is 0.50 * -$500 = -$250.Adding these expected returns together: $50 + $0 - $250 = -$200.However, the calculation for the loss scenario was incorrectly interpreted regarding the tax benefit. The correct approach should consider the tax deduction as a direct reduction in the loss amount, effectively halving the loss due to the 50% tax rate. Therefore, the correct calculation for the loss scenario should be:3. Corrected: If the investment falls to $500, the loss is $500. With the ability to deduct this loss, the effective loss is halved to $250 due to the 50% tax rate. The probability of this happening is 50%, so the expected return from this outcome is 0.50 * -$250 = -$125.Correcting the calculation with the proper understanding of the tax deduction on losses, the expected returns should be recalculated, leading to a different conclusion than initially presented. The correct expected return calculation would account for the tax benefits correctly, potentially altering the final answer.

Suppose That There Is a 25% Chance That an Investment