Consider two firms,Bob Company and Cat Enterprises,both with earnings of $10 per share and 5 million shares outstanding.Cat is a mature company with few growth opportunities and a stock price of $25 per share.Bob is a new firm with much higher growth opportunities and a stock price of $40 per share.Assume Bob acquires Cat using its own stock and the takeover adds no value.What is the change in Bob's price-earnings ratio as a result of the acquisition?
A)0
B)-2
C)4
D)-0.75
E)1.25

Question

Quizplus · Accepted Answer

Bob's initial P/E ratio is 40/10 = 4. After acquiring Cat, the combined earnings are $100 million ($50 million from each company). The total shares after the acquisition are 7.5 million (5 million from Bob and 2.5 million issued to Cat's shareholders, since $125 million worth of Bob's stock at $40/share equals 3.125 million shares, but these represent Cat's 5 million shares, so the exchange ratio is 5/3.125 = 1.6 Bob shares for each Cat share, resulting in 5 million * 1.6 = 8 million Bob shares in total, subtracting the original 5 million leaves 3 million additional shares, not 2.5 million as initially stated). The new stock price is the combined market cap ($200 million + $125 million = $325 million) divided by the total shares after acquisition (5 million + 2.5 million = 7.5 million), which equals $43.33 per share. The new P/E ratio is $43.33/$20 = 2.1667. The change in P/E ratio is 2.1667 - 4 = -1.8333, which is not an option provided, indicating a mistake in the calculation process. Correcting this: The correct total shares should be 5 million from Bob plus 5 million/2 (since Bob's stock is worth twice as much as Cat's, so for each share of Cat, 0.5 shares of Bob are issued) = 7.5 million shares. The combined earnings are $100 million, and Bob's new market cap remains $200 million (not adding Cat's market cap since the acquisition is through stock). The correct new P/E ratio calculation should be based on these corrected figures, which would actually result in a decrease in Bob's P/E ratio due to the dilution effect of issuing new shares for the acquisition, but without the exact corrected calculation, the intended correct answer choice and explanation are flawed. The initial explanation mistakenly calculated the new share count and misinterpreted the acquisition's impact on the market cap and share price.

Consider Two Firms,Bob Company and Cat Enterprises,both with Earnings of $10