Castles in the Sand currently sells at a price$-$earnings multiple of $20.$ The firm has $2$ million shares outstanding and sells at a price per share of $$90.$ Firm Foundation has a P$/$E multiple of $18,$ has $1$ million shares outstanding, and sells at a price per share of $$45.$

If Castles acquires the other firm by exchanging one of its shares for every two of Firm Foundation, what will be the earnings per share of the merged firm?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

What will be the price per share for Castle?

Note: Do not round intermediate calculations.

What would be Firm Foundation's value of stock post merger?

Note: Do not round intermediate calculations. Enter your answer in millions.

What should be the P$/$E of the new firm if the merger has no economic gains?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Calculate Castles$$ price per share if the market does not realize that the P$/$E ratio of the merged firm ought to differ from Castles$$ premerger ratio.

Note: Do not round intermediate calculations.

How are the gains from the merger split between shareholders of the two firms if the market is fooled as in part $($e$)?$

Note: Enter your answers in millions.