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 will the price per share be of the post-merger ﬁrm if payment is made in stock?

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 will the price per share be of the post-merger ﬁrm if payment is made in stock?

Quizplus · Accepted Answer

If payment is made in stock, Firm A will issue new shares to acquire Firm B.

First, we need to calculate the total value of the post-merger firm:

Total value = value of Firm A + value of Firm B + synergy value

Since both firms are 100% equity-financed, their values are equal to their stock prices multiplied by their number of shares:

Value of Firm A = P(A) x N(A)
Value of Firm B = P(B) x N(B)

Plugging in the given numbers:

Value of Firm A = $17.50 x 10,000 = $175,000
Value of Firm B = P(B) x 5,000

Total value = $175,000 + P(B) x 5,000 + $12,500
Total value = $187,500 + P(B) x 5,000

Since Firm A can acquire Firm B for $82,500, we can set up an equation:

$82,500 = P(B) x 5,000

Solving for P(B):

P(B) = $82,500 / 5,000
P(B) = $16.50 per share

Finally, we can calculate the price per share of the post-merger firm if payment is made in stock. Firm A will issue a total of 5,000 new shares (to acquire Firm B), so the total number of shares outstanding after the merger will be:

Total shares = N(A) + N(B) = 10,000 + 5,000 = 15,000

The new stock price can be calculated as:

New stock price = Total value / Total shares

Plugging in the values:

New stock price = ($175,000 + $82,500 + $12,500) / 15,000
New stock price = $270,000 / 15,000
New stock price = $18.00 per share

Therefore, the answer is B) $25.38.

Both ﬁRms Are 100% Equity-ﬁNanced