Show me the steps to solve The boards of company A and B are negotiating an M&A deal. The current stock$$prices are: pA$=$$$10$ per share for A and pB$=$$$11$ per share for B$.$ There are $100$ million$$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$$s shareholder: $$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$?$