Problem $21-5$ Mergers and P$/$E Ratios $($LO$1)$

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 $$80.$ Firm Foundation has a P$/$E multiple of $16,$ has $1$ million shares outstanding, and sells at a price per share of $$40.$

a$.$ 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.

b$.$ What will be the price per share for Castle?

Note: Do not round intermediate calculations.

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

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

d$.$ 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.

e$.$ 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.

f$.$ 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.