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 2500 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 2500 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:

- Company A's stock price is $80 per share and the earnings per share (EPS) is $10. 
- Therefore, the price-earnings (P/E) ratio of A's stock is 8 ($80/$10).

- Company B's stock price is $50 per share and the EPS is $5. 
- Therefore, the P/E ratio of B's stock is also 10 ($50/$5).

After the merger:

- Company A has offered 1 new share for every 2 shares of B.
- As a result, there are 2500 shares of A outstanding (since there were originally 5000 shares of B outstanding and they have been exchanged for 2500 new shares of A).

- Company A's earnings have also increased after the merger, since they have acquired the earnings of Company B. The new EPS is $15.

- Therefore, the new stock price of A can be calculated as: 
New stock price = New EPS x P/E ratio 
New stock price = $15 x 8.3 (since the total market capitalization before and after the merger remains the same) 
New stock price = $124.50

- Therefore, the P/E ratio of A's stock after the merger is 8.3 ($124.50/$15), which is the closest answer choice to our calculation.

Companies a and B Are Valued as Follows