Consider two firms, Thither and Yon. Both companies will either make $30 million or lose $10 million every year with equal probability. The companies' profits are perfectly negatively correlated. What are the expected after-tax profits of Thither in any year, assuming a corporate tax rate of 30% and no tax loss carryforward?

Question

Quizplus · Accepted Answer

If Thither's profit is $30 million, its after-tax profit would be $21 million (30 million - 0.3*(30 million)). If Thither's profit is -$10 million, its after-tax profit would be -$10 million after taxes (since tax loss carryforward is not allowed). Since the profits of Thither and Yon are perfectly negatively correlated, the probability that Thither makes $30 million and Yon makes -$10 million is the same as the probability that Thither makes -$10 million and Yon makes $30 million. Thus, Thither's expected after-tax profit would be the average of the after-tax profits in both scenarios:
(1/2)($21 million) + (1/2)(-$10 million) = $5.5 million

Consider Two Firms, Thither and Yon