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# Castles in the Sand: Mergers and Price-Earnings Ratios

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Castles in the Sand currently sells at a price-earnings multiple of 10. The firm has 2 million shares outstanding, and sells at a price per share of \$40. Firm Foundation has a price-earnings ratio (P/E) multiple of 8, has 1 million shares outstanding, and sells at a price per share of \$20.

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

b. What should be the price-earnings ratio of the new firm if the merger has no economic gains? What will happen to Castles' price per share? Show that shareholders of neither Castles nor Firm Foundation realize any change in wealth.

c. What will happen to Castles' price per share if the market does not realize that the price-earnings ratio of the merged firm ought to differ from Castles' pre-merger ratio?

d. How are the gains from the merger split between shareholders of the two firms if the market is fooled as in part c?

#### Solution Preview

a.
Ps = Share Price
PE = Price to Earnings Ratio = Ps / EPS
EPS = Earnings per Share = Earnings / No of Shares
So, EPS = Ps / PE
Earnings = EPS * No of Shares

Before the Merger:
For CIS -
Ps = \$40
PE = 10
No. of Shares = 2,000,000

EPS = Ps / PE = \$40 / 10 = \$4.00
Earnings = EPS x No. of Shares = \$4.00 x 2,000,000 = \$8,000,000

For FF:
Ps = \$20
PE = 8
No. of Shares = 1,000,000

EPS = Ps / PE = \$20 / 8 = \$2.50
Earnings = EPS x No. of Shares = \$2.50 x 1,000,000 = \$2,500,000

After the Merger:
Combined Earnings = \$8,000,000 + \$2,500,000 = ...

#### Solution Summary

This response discusses the price-earning ratio of Castles in the Sand and its relation to a merger.

\$2.19

## Mergers and P/E Ratios.

Mergers and P/E Ratios.

Castles in the Sand currently sells at a price-earnings multiple of 10. The firm has 2 million shares outstanding, and sells at a price per share of \$40. Firm Foundation has a P/E multiple of 8, has 1 million shares outstanding, and sells at a price per share of
\$20.

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

b. What should be the P/E of the new firm if the merger has no economic gains? What will
happen to Castles's price per share? Show that shareholders of neither Castles nor Firm
Foundation realize any change in wealth.

c. What will happen to Castles's price per share if the market does not realize that the P/E ratio of the merged firm ought to differ from Castles's premerger ratio?

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

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