Final answer:
In a perfect capital market, Bob must offer 3.125 million shares to the shareholders of Cat in exchange for their shares.
Step-by-step explanation:
In order to determine how many shares Bob must offer the shareholders of Cat in exchange for their shares, we need to consider the stock prices and earnings of both companies.
Bob's stock price is $40 per share and Cat's stock price is $25 per share.
We can calculate the number of shares Bob must offer using the formula:
Number of shares = (Stock price of Cat / Stock price of Bob) x Number of shares outstanding of Cat
Plugging in the values, we get:
Number of shares = (25 / 40) x 5 million
= 3.125 million shares
Therefore, Bob must offer 3.125 million shares to the shareholders of Cat in exchange for their shares.