On $1$st October $2018$ City Ltd$.$ is considering whether to buy Exchange Corp.

City currently trades at $3$ per share and has $50$ million shares outstanding; Exchange trades at $6$ per

share and has $20$ million shares outstanding. The merger is expected to generate $30$ million in

synergies $($in present value terms$).$

$($a$)$ Suppose that City offers $2$ and $1$ new share of City for each share of Exchange. What is the

value of this offer for Exchange's shareholders? Will they accept the offer?