GrowFast currently sells at a price-earnings multiple of 10. The firm has 2 mill
ID: 2826729 • Letter: G
Question
GrowFast 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. Steady & Stable has a P/E multiple of 8, has 1 million shares outstanding, and sells at a price per share of $20.
a. If GrowFast acquires the other firm by exchanging one of its shares for every two of Steady & Stable's, what will be the earnings per share of the merged firm?
b. If the merger has no economic gain, what will be the P/E of the new firm? What will happen to GrowFast's price per share? Will any of the shareholders experience a change in wealth?
c. What will happen to GrowFast's price per share if the market does not realize that the P/E ratio of the merged firm ought to differ from GrowFast's premerger ratio? Who gains and by how much in this case?
Explanation / Answer
a. If GrowFast acquires the other firm by exchanging one of its shares for every two of Steady & Stable's
Then the earnings per share of the merged firm, will be:
Formula for earnings per share = Total earnings / number of outstanding shares
Here Total earnings = earnings before merger + earnings at the time of exchange
= (Price per share/ PE multiple) * number of shares + (Price per share/ PE multiple) * number of shares
= ($40/10)*2million shares + ($20/8)*1million shares
= $8million + $2.5million = $10.5million
number of outstanding shares= 2million + (0.5million) = 2.5million
Therefore, EPS = 10.5million / 2.5million = $4.20.
b. If the merger has no economic gain,
The P/E of the new firm = Value of the firm / total earnings
= (2million*$40) +( 1million* $20)+ $10.5million
= $100million / $10.5 million = 9.524
The P/E of the new firm will be in between the P/E's of the 2 firms.
GrowFast's price per share= Value of the firm / number of outstanding shares
= 100million / 2.5million = $40 per share.
There is no change in wealth.
c. What will happen to GrowFast's price per share if the market does not realize that the P/E ratio of the merged firm ought to differ from GrowFast's premerger ratio? Who gains and by how much in this case?
Solution:
If the P/E of GrowFast remains at 10, then the new firm will sell a share for $4.20 x 10 = $42
The firm is thus worth: $42 x 2.5 = $105 million
Here, the combined market value of the old firms as per the above calculation it shows only $100 million.
Then, the Gain can be calculated as = $102- $100million = $2million
Gain = 2million x 2 million shares = $4 million
Therefore, Gain to Steady & Stable:
Gain = Value of new shares - Original value of firm
= (0.5 million x $42) - $20 million = $1 million
The total gain = $4 + $1million = $5 million
Thus, increase in the combined market value of the firms.
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