GrowFast currently sells at a priceearnings multiple of 10 T

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?

Solution

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.