Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totalling $200 million.

Firms Involved in the Takeover

Acquirer Target

Assets ($m) 6000 800

Debt ($m) 2000 300

Share price ($) 50 25

Number of shares (m) 80 20

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Assume a cash offer will be made that Acquirer pays $X for each share of the Target. The cash will be paid out of the firm's cash holding, so no new debt or equity will be raised. The manager of Acquirer expects the share price of the merged firm will increase to $51 when the deal is completed. Calculate the value of X.