Both ﬁrms are 100% equity-ﬁnanced. Firm A can acquire ﬁrm B for $82,500 in the form of either cash or stock. The synergy value of the deal is $12,500. What is the price per share of the post-merger ﬁrm following a cash acquisition?

Question

Both ﬁrms are 100% equity-ﬁnanced. Firm A can acquire ﬁrm B for $82,500 in the form of either cash or stock. The synergy value of the deal is $12,500.  What is the price per share of the post-merger ﬁrm following a cash acquisition?

Quizplus · Accepted Answer

To solve this question, we need to first calculate the post-merger value of the firm.

Post-merger value = Value of firm A + Value of firm B + Synergy value 
Post-merger value = $75,000 + $75,000 + $12,500 
Post-merger value = $162,500

Now, we need to calculate the price per share of the post-merger firm following a cash acquisition.

If firm A acquires firm B for cash, then the total cash outflow will be $82,500. This will reduce the value of firm A to $75,000 - $82,500 = -$7,500. Firm A will have a negative value, which means that the post-merger firm will have no value if the acquisition is made for cash.

Therefore, we need to consider the option of acquiring firm B for stock. If firm A acquires firm B for stock, then the number of shares issued will depend on the price per share of the post-merger firm. Let's assume that the price per share is x.

Number of shares issued = $82,500 / x

Post-merger value = Value of firm A + Value of firm B + Synergy value 
Post-merger value = $75,000 + ($75,000 / x) + $12,500

Equating the above equation with the post-merger value calculated earlier, we get:

$162,500 = $75,000 + ($75,000 / x) + $12,500

Solving for x, we get:

x = $25.50

Therefore, the price per share of the post-merger firm following a stock acquisition is $25.50.

Hence, the correct answer is B.

Both ﬁRms Are 100% Equity-ﬁNanced