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# Mergers and P/E Ratios.

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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)?

https://brainmass.com/economics/principles-of-mathematical-economics/mergers-and-p-e-ratios-123169

#### Solution Preview

A.
Ps = Share Price
PE = Price to Earnings Ratio = Ps / EPS
EPS = Earnings per Share = Earnings / No of Shares

So we have
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 = \$10,500,000

Total ...

\$2.19

## Finance - Merger gains, Mergers and P/E Ratios, Stock versus Cash Offers.

6. Merger Gains. Acquiring Corp. is considering a takeover of Takeover Target Inc. Acquiring has 10 million shares outstanding, which sell for \$40 each. Takeover Target has 5 million shares outstanding, which sell for \$20 each. If the merger gains are estimated at \$25 million, what is the highest price per share that Acquiring should be willing to pay to Takeover Target shareholders?

7. Mergers and P/E Ratios. If Acquiring Corp. from Problem 6 has a price-earnings ratio of 12 and Takeover Target has a P/E ratio of 8, what should be the P/E ratio of the merged firm? Assume in this case that the merger is financed by an issue of new Acquiring Corp. shares. Takeover Target will get one Acquiring share for every two Takeover Target shares held.

Problem #8 is for reference only- to solve problem 9
8. Merger Gains and Costs. Velcro Saddles is contemplating the acquisition of Pogo Ski Sticks, Inc. The values of the two companies as separate entities are \$20 million and \$10 million, respectively. Velcro Saddles estimates that by combining the two companies, it will reduce marketing and administrative costs by \$500,000 per year in perpetuity. Velcro Saddles is willing to pay \$14 million cash for Pogo. The opportunity cost of capital is 8 percent.
1. What is the gain from merger?
2. What is the cost of the cash offer?
3. What is the NPV of the acquisition under the cash offer?

9. Stock versus Cash Offers. Suppose that instead of making a cash offer as in Problem 8, Velcro Saddles considers offering Pogo shareholders a 50 percent holding in Velcro Saddles.
1. What is the value of the stock in the merged company held by the original Pogo shareholders?
2. What is the cost of the stock alternative?
3. What is its NPV under the stock offer?

10. Merger Gains. Immense Appetite, Inc., believes that it can acquire Sleepy Industries and improve efficiency to the extent that the market value of Sleepy will increase by \$5 million. Sleepy currently sells for \$20 a share, and there are 1 million shares outstanding.
1. Sleepy's management is willing to accept a cash offer of \$25 a share. Can the merger be accomplished on a friendly basis?
2. What will happen if Sleepy's management holds out for an offer of \$28 a share?

****Note***** : I would like to see all calculations (either written out in Word or with Excel formulas).