Companies A and B are valued as follows:

Company A now acquires B by offering one (new)share of A for every two shares of B (that is, after the merger, there are 2,500 shares of A outstanding). If investors are aware that there are no economic gains from the merger, what is the price-earnings ratio of A's stock after the merger?

Question

Companies A and B are valued as follows:

Company A now acquires B by offering one (new)share of A for every two shares of B (that is, after the merger, there are 2,500 shares of A outstanding). If investors are aware that there are no economic gains from the merger, what is the price-earnings ratio of A's stock after the merger?

Quizplus · Accepted Answer

Before the merger: 
A's market value = $50 x 100 = $5,000 
B's market value = $20 x 200 = $4,000

After the merger: 
A's total shares outstanding = 2,500 
B's total shares outstanding = 200/2 = 100

For every 2 shares of B, investors receive 1 share of A, so the total number of shares after the merger is: 
2,500 + (100/2) = 2,550

The new market value of A's shares is: 
$5,000 + 100/2 x $20 = $6,000

So the price per share after the merger is: 
$6,000 / 2,500 = $2.40

A's earnings are $500, so the P/E ratio is: 
$2.40 / $0.50 = 4.8

Therefore, the price-earnings ratio of A's stock after the merger is 4.8 or approximately 5. The closest choice is B) 8.3, so it is not the correct answer. The correct answer is B) 5.

Companies a and B Are Valued as Follows