Question

Consider the following premerger information about a bidding firm (Firm B) and a target firm (Firm T). Assume that both firms have no debt outstanding.

    

	Firm B			Firm T
Shares outstanding		6,200			1,400
Price per share	$	48		$	18

  

Firm B has estimated that the value of the synergistic benefits from acquiring Firm T is $9,600. Firm T can be acquired for $20 per share in cash or by exchange of stock wherein B offers one of its share for every two of T's share.

  

a.	Are the shareholders of Firm T better off with the cash offer or the stock offer?
b.	At what exchange ratio of B shares to T shares would the shareholders in T be indifferent between the two offers? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

Answer 1

Solution :

Part A )

Total value of the merged firm = share price of B* number of share of B + share price of T * number of share of T

V = 6200*48 + 1400 *18 = 297,600 + 25,200 = 322,800

Total share of T is 1400 hence they will receive 1400/2 = 700 shares of the combined firm.

Total share of combined firm = 6200+700 = 6900

Share price of combined firm = value / number of share = 322,800/6900 = 46.78

Firm T will get 1 share for every 2 share means effective price per share = 46.78 /2 = 23.39

In cash transaction form T will receive $20 per share and in share transaction they will receive $23.39

So they they are better off in share transaction.

Part B )

In order to find the exchange ratio let's assume exchange ratio is x

Now number of share = 6200 + 1400* X

We know that the market value of the firm is 322800

Share price = P = 322800/(6200+1400X )

Share price P = 20/x ( because $20 will be paid per share and X is the exchange rate and P is the share price of combined firm )

When they are indifference in both the option then

322800/ ( 6200 + 1400X ) = 20 /X

322800X = 20*6200 + 20 *1400 X

322800X - 28000X = 124000

294800X = 124000

X = 0.4206

Exchange ratio = 0.4206