Question $1.[$Answer all parts showing all work, refrence formulas and solutions in

The boards of company A and $B$ are negotiating an M&A deal. The current stock

prices are: $p_A=$$$10$ per share for A and $p_B=$$$11$ per share for $B.$ There are $100$ million shares of A and $90$ million shares of $B$ outstanding. The boards expect the deal to generate synergies equal to $$100$ million in present value. Assume that the current market valuations of A and $B$ are a good estimate of their true values as standalone entities.

$($a$)[10$ points$]$ Initially, A offered $1$ newly$-$issued share of A for each share of

B$.$ What is the value of this offer for target shareholders? Should they

accept the offer?

$($b$)[10$ points$]$ The negotiation then progressed to an offer worth $$12$ per

share for B$\text{'}$s shareholder: $$6$ in cash and $$6$ in stocks. What is the new

exchange ratio $x$ associated with this offer? Is this deal in the interest of

the shareholders of $A?$

$($c$)[10$ points$]$ The board of $B$ then demanded the deal to be a merger of

equals in which shareholders of $B$ receive no cash but enough newly

issued shares in A to own exactly $50\%$ of the equity of A $($after the

merger$).$ What is the exchange ratio $x$ associated with this offer? Is this

deal in the interest of the shareholders of $A?$