Consider two? firms, Blue and Berry. Both companies will either make? $30 millio

Question

Consider two? firms, Blue and Berry. Both companies will either make? $30 million or lose? $5 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? 30% and no tax loss carryback or? carryforward?

A. ?$9 million

B. ?$0

C. ?$1.5 million

D. ?$9.5 million

E. ?$3 million

Explanation / Answer

Either 1 company will make $ 20 million profit and then the other one will make $10 million loss. In this case the as two separate entities the after tax profit will be:

Profit of $ 20 million: 20 * (1-30%) = $ 14 million

Loss of $ 10 million : loss of $ 10 million

Thus the sum total of after tax profit will be (14-10) = $ 4 million and since there is perfect negative correlation, this will remain same each year.

However if the two entities are merge as two divisions under one company balancesheet then the combined profit each year will be (20 -10) = $ 10 million on which the tax will be $ 3 million and after tax profit will be $ 7 million

Hence the change in the after tax profit for the combined entity will be (10-7) million = $ 3 million which is option E

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