Consider two firms,Zoe Corporation and Marley Company.Both corporations will either make $20,000 or lose $5,000 every year with equal probability.The firms' profits are perfectly negatively correlated.If the corporate tax rate is 21%,what are the total expected after-tax profits if the two firms are combined into one corporation,assuming no tax-loss carryforwards or carrybacks?

Question

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First, let's calculate the expected after-tax profits for each firm separately:

For Zoe Corporation:
- If it makes $20,000: its taxable income is $20,000, so it pays $4,200 ($20,000 x 21%) in taxes, and its after-tax profit is $15,800.
- If it loses $5,000: it has a tax loss of $5,000, so it doesn't pay any taxes, and its after-tax profit is -$5,000.

Thus, Zoe Corporation's expected after-tax profit is:
(0.5 x $15,800) + (0.5 x -$5,000) = $5,900

For Marley Company:
- If it makes $20,000: its taxable income is $20,000, so it pays $4,200 ($20,000 x 21%) in taxes, and its after-tax profit is $15,800.
- If it loses $5,000: it has a tax loss of $5,000, so it doesn't pay any taxes, and its after-tax profit is -$5,000.

Thus, Marley Company's expected after-tax profit is:
(0.5 x $15,800) + (0.5 x -$5,000) = $5,900

Now, let's consider the combined corporation. The total profit of the combined corporation is the sum of the profits of Zoe Corporation and Marley Company. However, since their profits are perfectly negatively correlated, their sum can range from -$5,000 to $40,000 with equal probability. Thus, the expected total profit of the combined corporation is:

(0.5 x -$5,000) + (0.5 x $40,000) = $17,500

Applying the 21% tax rate, the expected after-tax profit of the combined corporation is:

$17,500 x (1-21%) = $13,825

Therefore, the answer is:
Choice C: $9,750

Consider Two Firms,Zoe Corporation and Marley Company