Consider two firms,Blue and Berry.Both companies will either make $20 million or lose $10 million every year with equal probability.The companies' profits are perfectly negatively correlated,so that in any year,one company makes $20 million and the other loses $10 million.If the two firms merge but are run as two independent divisions,what is the change in expected after-tax profits of the combined company (BlueBerry)in any year versus the combined expected after-tax profits of the two separate companies in any year,assuming a corporate tax rate of 40% and no tax loss carryback or carryforward?

Question

Quizplus · Accepted Answer

When the two firms are separate, the expected profit for each firm is calculated as the average of making $20 million and losing $10 million, which is $5 million. With a 40% tax rate, the after-tax profit for each firm is $5 million * (1 - 0.4) = $3 million. For both firms combined, this is $6 million.When the firms merge, in any given year, one division makes $20 million and the other loses $10 million, resulting in a net profit of $10 million for the merged company. The after-tax profit is $10 million * (1 - 0.4) = $6 million.The change in expected after-tax profits of the combined company versus the combined expected after-tax profits of the two separate companies is $6 million (merged) - $6 million (separate) = $0. However, the correct calculation involves recognizing that the tax savings from offsetting the $10 million loss against the $20 million profit in the merged company scenario actually results in a higher effective profit due to the way corporate taxes are applied. Specifically, without the ability to offset losses, the separate companies pay taxes on profits without the benefit of reducing taxable income with the losses from the other company. Given the error in the initial explanation, the correct answer should reflect the benefit of merging the companies in terms of tax efficiency, which was not accurately captured. The correct approach would involve calculating the tax savings from being able to offset the $10 million loss against the $20 million profit, which would result in a net taxable income of $10 million for the merged company, leading to a tax of $4 million (40% of $10 million) and an after-tax profit of $6 million. Since each company separately would have an expected after-tax profit of $3 million (as initially calculated), the combined expected after-tax profit would be $6 million without any merger benefits considered. The mistake in the explanation led to an incorrect conclusion, and the correct answer should reflect the advantages of merging in terms of tax efficiency, which was not properly accounted for. Given the mistake in the initial explanation, the correct answer should actually reflect no change ($0) in expected after-tax profits due to the incorrect assumption about tax benefits from merging the profits and losses, as the initial calculation did not properly account for the tax implications of merging.

Consider Two Firms,Blue and Berry