Firm A has a value of $200 million and Firm B has a value of $120 million. Merging the two would enable cost savings with a present value of $30 million. Firm A purchases Firm B for $130 million. How much do Firm A's shareholders gain from this merger?
A)$30 million
B)$20 million
C)$15 million
D)$10 million

Question

Quizplus · Accepted Answer

The value of Firm A before the merger is $200 million. After the merger, the value of the combined firm (A + B) is $200 million + $120 million = $320 million. However, Firm A purchases Firm B for $130 million, so the net value gain for the shareholders is $320 million - $130 million = $190 million.

But we also need to consider the present value of the cost savings, which is $30 million. Since this is a benefit for both Firm A and Firm B shareholders, we need to split it based on their ownership percentages. Let's assume that Firm A shareholders own 60% of the combined firm and Firm B shareholders own 40%.

Then, the present value of the cost savings for Firm A shareholders is:

PV(A) = 0.6 x $30 million = $18 million

And the present value of the cost savings for Firm B shareholders is:

PV(B) = 0.4 x $30 million = $12 million

Adding these values to the net value gain, we get:

Total value gain = $190 million + $18 million = $208 million

And finally, the gain for Firm A's shareholders is:

Gain = Total value gain - Purchase price of Firm B = $208 million - $130 million = $78 million

Therefore, the correct answer is B) $20 million.

Firm a Has a Value of $200 Million and Firm