Final answer:
To calculate the P/E ratio of the merged firm, calculate the market values of both companies and the projected earnings of the merged firm. Then, divide the combined market value by the projected earnings. The P/E ratio of the merged firm is approximately 2.95.
Step-by-step explanation:
To calculate the price-earnings ratio (P/E ratio) for the merged firm, we need to first calculate the market value of each company. The market value of Winterbourne is calculated by multiplying the number of shares outstanding (18 million) by the share price ($56), which gives a market value of $1,008 million. The market value of Monkton is calculated in the same way, giving a market value of $364 million.
The combined market value of the merged firm is the sum of the market values of Winterbourne and Monkton, which is $1,008 million + $364 million = $1,372 million.
The projected earnings of the merged firm is the sum of the merger gains ($65 million) and the earnings of Winterbourne and Monkton. To calculate the earnings of each company, we multiply the number of shares outstanding by the respective P/E ratios. The earnings of Winterbourne is 18 million * 15 = $270 million, and the earnings of Monkton is 13 million * 10 = $130 million. Therefore, the projected earnings of the merged firm is $65 million + $270 million + $130 million = $465 million.
Finally, we can calculate the P/E ratio of the merged firm by dividing the combined market value ($1,372 million) by the projected earnings ($465 million). The P/E ratio is $1,372 million / $465 million = 2.95. Therefore, the P/E ratio of the merged firm is approximately 2.95.