Question

1. YQR has a market value of $125 million and 5 million shares outstanding. HKG has a market value of $40 million and 2 million shares outstanding. YQR thinks of taking over HKG with a premium of $10 million. The combined firm will be worth $185 million. If YQR offers 1.2 million shares of its stock in exchange for the 2 million shares of HKG, what will the stock price of YQR be after the acquisition? What exchange ratio between the two stocks would make the value of a stock offer equivalent to a cash offer of $50 million?

Answer 1

value of combined firm = 185 million

Stock value after acquisition = Value of combined firm / No of total shares

No of total shares = Shares od YQR + New issue to HKG

= 5,000,000 (given) + 1,200,000 (new issue)

= 6,200,000

Stock Value after acquisition = 185,000,000 / 6,200,000

= 29.84

Now,

Cash offer = Stock offer

Let the exchange ratio be X

Value of firm firm Y after acquisition = (Value per shares after acquisition) * (No of shares)

= (Value of combined firm / Total no of shares) * (2,000,000 * X)

= (185,000,000 / (5,000,000 + 2,000,000 * X)) * (2,000,000*X)

Equating it with Cash Offer

50,000,000 =  (185,000,000 / (5,000,000 + 2,000,000 * X)) * (2,000,000*X)

Solving it X will be 0.9259

Exchange Ratio of 0.9259 will make the cash offer and share offer equivalent.

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