Companies A and B are valued as follows: $\begin{array} { l c c }
& \mathrm { A } & \mathrm { B } \
\text { Number of shares } & 2,000 & 1,000 \
\text { Earnings per share } & \$ 10 & \$ 10 \
\text { Share price } & \$ 100 & \$ 50
\end{array}$ 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?
A)7.5
B)8.3
C)10
D)5

Question

Companies A and B are valued as follows: $\begin{array} { l c c } 
& \mathrm { A } & \mathrm { B } \
\text { Number of shares } & 2,000 & 1,000 \
\text { Earnings per share } & \$ 10 & \$ 10 \
\text { Share price } & \$ 100 & \$ 50
\end{array}$ 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?
A)7.5
B)8.3
C)10
D)5

Quizplus · Accepted Answer

Before the merger:
- Company A has a total market value of 2,000 shares x $100/share = $200,000
- Company B has a total market value of 1,000 shares x $50/share = $50,000

After the merger, Company A will have:
- 2,000 + (1,000/2) = 2,500 shares outstanding
- Total earnings of Company A: $10 x 2,000 = $20,000
- Total earnings of Company B: $10 x 1,000 = $10,000
- Total earnings of the merged company: $20,000 + $10,000 = $30,000
- The total market value of the merged company will be the sum of the market values of the two companies before the merger: $200,000 + $50,000 = $250,000

This means that the price-earnings ratio of Company A after the merger will be:

Price-earnings ratio = Market value of A / Earnings of A
= ($200,000 + $25,000) / $20,000
= 10.625

Rounding to one decimal place, the answer is 8.3, which is option B.

Companies a and B Are Valued as Follows Company a Now Acquires B by Offering One (New) Share