Question

4. 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

If Exchange ratio is 1.2 million for 2 million shares

So value of share of YQB after acquisition we calculate by using total number of shares and value of firm

Total No. of shares = 5 Million + New issue 1.2 Million = 6.2 Million

Value of Firm after merger is $185 Million as given

Value of Share = Combine Value of Firm / Total No. of shares = $185 Million / 6.2 Million = $29.8387 or say $29.84

Value per share of YQB is $29.84 after acquisition.

Exchange ratio so value of stock equivalent to a cash offer of $50 Million.

We assume that 'a' no of shares issued.

Total no of shares after acquisition = 5 Million + a

Combine Value of Firm = $185 Million

Vale per share after acquisition = $185 Million / ( 5 Million + a)

Calculate the value of 'a'

Share issue to HKG x Value per share after acquisition = $50 Million

a x {$1,85,000,000 / 5,000,000 + a } = $50,000,000

185000000a = 250000000000000 +50000000a

135000000a = 250000000000000

a = 1851851.85 or say 1851852 shares should be issue by YQR to HKG so it will be equivalent to $50 Million Cash.

(Calculation for understanding not part of answer

Total no. of shares = 5,000,000 + 1,851,852 = 6,851,852

Combined value of firm = $185 Million

Value per share = $185 Million / 6,851,852 = $26.999999 or say $27

Value of share issue = 1,851,852 x $27 = $50 Million.)