Question 22.1: Consider two firms, Yin Corporation and Yang Corporation. Bo...
Consider two firms, Yin Corporation and Yang Corporation. Both corporations will either make $50 million or lose $20 million every year with equal probability. The only difference is that the firms’ profits are perfectly negatively correlated. That is, any year Yang Corporation earns $50 million, Yin Corporation loses $20 million, and vice versa. Assume that the corporate tax rate is 34%. What are the total expected after-tax profits of both firms when they are two separate firms? What are the expected after-tax profits if the two firms are combined into one corporation called Yin-Yang Corporation, but are run as two independent divisions? (Assume it is not possible to carry back or carry forward any losses.)
PLAN
We need to calculate the after-tax profits of each firm in both the profitable and unprofitable states by multiplying profits by (1 – tax rate ). We can then compute expected after-tax profits as the weighted average of the after-tax profits in the profitable and unprofitable states. If the firms are combined, their total profits in any year would always be $50 million – $20 million = $30 million, so the after-tax profit will always be $30 × (1 – tax rate ).
EXECUTE
Let’s start with Yin Corporation. In the profitable state, the firm must pay corporate taxes, so after-tax profits are $50 × (1 – 0.34) = $33 million. No taxes are owed when the firm reports losses, so the after-tax profits in the unprofitable state are –$20 million.
Thus, the expected after-tax profits of Ying Corporation are 33(0.5) + (–20) (0.5) = $6.5 million. Because Yang Corporation has identical expected profits, its expected profits are also $6.5 million. Thus, the total expected profit of both companies operated separately is $13 million.
The merged corporation, Ying-Yang Corporation, would have after-tax profits of $30 × (1 – 0.34) = $19.8 million.
EVALUATE
Yin-Yang Corporation has significantly higher after-tax profits than the total stand-alone after-tax profits of Yin Corporation and Yang Corporation. This is because the losses on one division reduce the taxes on the other division’s profits.