Here’s an example:
Company A (a high-growth, high-P/E company) acquires Company B (a low-growth, low-P/E company).
Company A has 100,000 shares outstanding at a market price of $50/share; its earnings are $250,000, so its P/E ratio is $50 × 100,000 ÷ $250,000 = 20.
Company B has 10,000 shares outstanding at a market price of $20/share; its earnings are $20,000, so its P/E ratio is $20 × 10,000 ÷ $20,000 = 10.
Company A issues 4,000 shares of stock for Company B’s shares:
$20/sh × 10,000 shares = $200,000
$200,000 ÷ $50/sh = 4,000 shares.
Before the acquisition, Company A’s EPS was:
$250,000 ÷ 100,000 shares = $2.50/sh.
Before the acquisition, Company B’s EPS was:
$20,000 ÷ 10,000 shares = $2.00/sh.
After the acquisition, Company A’s EPS is:
($250,000 + $20,000) ÷ (100,000 shares + 4,000 shares) = $2.60/sh.
Note that Company A’s EPS increased from $2.50/sh to $2.60/sh.
The reason is that because Company A’s P/E ratio was higher than Company B’s, Company A got a greater percentage increase in earnings than the corresponding increase in its shares outstanding: its earnings rose by $20,000/$250,000 = 8%; its shares outstanding rose by only 4,000/100,000 = 4%.