Company A considers acquiring company B$.$ Shares of the company A trade at $$30$ and there are $5,000$ of A shares outstanding. Company B has $200$ shares outstanding worth $$100$ each. If A acquires B$,$ then the resulting synergy will amount to $$10,000.$

Suppose A offers to exchange every B$$s share for four shares in the merged company.

$1.$What will be the share price of the merged company?

$2.$ What will be the total benefit for the existing shareholders of A$?$

$3.$ What will be the total benefit for the existing shareholders of B$?$

$4.$ Suppose A offers to exchange every B$$s share for $$130$ in cash. What will be the share price of the merged company?

$5.$ Suppose A offers to exchange every B$$s share for $$130$ in cash. What will be the total benefit for the existing shareholders of A$?$

$6.$ Suppose A offers to exchange every B$$s share for $$130$ in cash. What will be the total benefit for the existing shareholders of B$?$