A firm with a P/E ratio of 25 wants to take over a firm that is half its size (in market capitalization)that has a P/E ratio of 40. What would be the P/E ratio of the merged firm?

Question

Quizplus · Accepted Answer

First, we need to calculate the weighted average of the P/E ratios:

Weighted average P/E ratio = (P/E ratio of Firm A x Market cap of Firm A) + (P/E ratio of Firm B x Market cap of Firm B) / (Total market cap of both firms)

Let's assume firm A has a market cap of 100 and firm B has a market cap of 50.

Weighted average P/E ratio = (25 x 100) + (40 x 50) / (100+50) = 30

Therefore, the P/E ratio of the merged firm would be 30. The P/E ratio of the merged firm can be calculated as a weighted average of the P/E ratios of the two firms, based on their market capitalizations.

Let's assume that the larger firm has a market capitalization of X, and the smaller firm has a market capitalization of 0.5X.

Then, the P/E ratio of the merged firm can be calculated as follows:

P/E merged = (P/E larger firm * X + P/E smaller firm * 0.5X) / (X + 0.5X)

P/E merged = (25X + 40(0.5X)) / (1.5X)

P/E merged = (25X + 20X) / (1.5X)

P/E merged = 45 / 3

P/E merged = 15

Therefore, the P/E ratio of the merged firm would be 15. However, this option is not among the answer choices.

To choose the best answer, we need to select the option that is closest to this calculated value.

Option B is the closest, with a calculated P/E ratio of 14.29. This is reasonable, as the P/E ratio of the smaller firm (40) is much higher than that of the larger firm (25), and the resulting merged firm would likely have a P/E ratio that is closer to the lower end of this range.

A Firm with a P/E Ratio of 25 Wants to Take