Question

Firm A has a value of $500 million and Firm B has a value of $300 million. Firm A has 1000 shares outstanding, and Firm B has 1000 shares outstanding. Suppose that the merger would increase cash flows of the combined firm by $5 million in perpetuity. Assuming the cost of capital for the new firm is 10%.

Suppose that instead of paying cash, Firm A acquires B by offering two (new) shares of A for every three shares of B. The net gain to Firm A's shareholders is closest to:

A. $0

B. $10 million

C. $20 million

D. $87 million

E. None of the above

Answer 1

Firm A has a value: $500 million

Firm B has a value: $300 million

Firm A has 1000 shares outstandingand Firm B has 1000 shares outstanding. Firm A acquires B by offering two (new) shares of A for every three shares of B.

Hence, total shares issued to shareholders of B: 10002/3 = 667shares and total shares after merger are 1000 + 667 = 1667 shares.

Merger would increase cash flows of the combined firm by $5 million in perpetuity and the cost of capital for the new firm is 10%.
Hence, value of synergy gain from merger is $5 million/0.10 = $50 millions.

The net gain to Firm A's shareholders is: value of shares after merger - value of shares before merger

The net gain to Firm A's shareholders is:[(500+300+50)*1000/1667]  - 500

The net gain to Firm A's shareholders is: $509.89 million - $500 million = 9.89 million or 10 million approximately.

Correct option is : B 10 million