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

stock prices are: $$8$ per share for A and $$5$ per share for B$.$ There are $12$

million shares of A and $10$ million shares of B outstanding. The boards expect

the deal to generate synergies equal to $$20$ million in net present value.

Assume that the current market valuations of A and B are a good estimate of

their true values as standalone entities.

$($a$)$ Initially, A offered to B: $$4$ per share in cash and $0\mathrm{.}2$

shares of newly$-$issued shares of A for each share of B$.$ Should the

board of B endorse the offer $($assuming they want at least a $20\%$

premium over their current stock price$)?$

$($b$)$ The board of B demanded to raise the offer to $$8$ per

share in cash $($and no shares$).$ Is this deal in the interest of the

shareholders of A $($assuming that they are happy if they break

even$)?$

solve B