The key difference between M&A and PE would be one being more of a strategic while the other latter being a financial buyer. As a result, for M&A, you would be asking more about synergies for the acquiror that justifies the acquisition and price. Cases with HF is not typical but I have seen a few where its important to clarify the investment strategy (e.g., long/short, event driven, credit, etc.) as that will shape what to discuss in the case.
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A litte more detail below:
M&A: in a case context is typically one corporate acquiring another public/private corporate (or a carve-out of it) and so there is more of a strategic intention (e.g., synergies) than purely financial which is often why a corporate acquiror could be willing to pay more than a pure financial investor
PE: generally would be the acquisition of either controlling (buyout) or minority (growth equity) stake of a private (or public that will go through a management buyout and become private). The investment thesis is largely around the returns over the funds investment period of plus/minus 5 years where they typically aim for an IRR of 15-20%. Occassionally, they will also make bolt-on acquisitions to inorganically grow their existing portfolio company but otherwise the intention is largely financial
HF: although they do cover more asset classes (e.g., private credit), will generally acquire stake in public companies either for growth/return as well as to hedge that the share price will go down (i.e., shorting the stock). The key considerations are highly depednent on the fund's investment style (e.g., long/short, event-driven, credit, macro-driven, etc.)