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 value of ﬁrm B to ﬁrm A?
A) $12,500
B) $57,500
C) $75,000
D) $87,500
E) $125,000

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 value of ﬁrm B to ﬁrm A?
A) $12,500 
B) $57,500 
C) $75,000 
D) $87,500 
E) $125,000

Quizplus · Accepted Answer

To calculate the value of firm B to firm A, we can use the formula:

Value of B to A = Value of B standalone + Synergy - Value of A standalone

We know that the synergy value is $12,500 and both firms are 100% equity-financed, so the value of each firm is equal to its equity. Let's assume the value of firm A is X and the value of firm B is Y.

If firm A uses cash to acquire firm B, its total value (X) will decrease by $82,500 and it will gain the value of firm B (Y). So,

X - 82,500 + Y = X + Y + 12,500

Simplifying the equation, we get:

X = 95,000

If firm A uses stock to acquire firm B, the equation will be:

1.5X + Y = 2X + 12,500

Solving for X, we get:

X = 87,500

Therefore, the value of firm B to firm A is $87,500, assuming that both firms are 100% equity-financed. The answer is D.

Both ﬁRms Are 100% Equity-ﬁNanced