Which has the higher expected valuation - LBO or Trading Comps?

I’m not sure I agree. An LBO could be a precedent in your transaction comps set. Precedent transactions are used to assess the premiums paid for businesses in the past, but the acquirer does not need to be a public company.

I can agree most PE transactions occur in private markets, but that’s not why it’s called private equity. It’s called private equity because the POST transaction companies acquired are not publicly traded, thus the owners are “private” equity holders.

OP, you are right. Sponsors pay a premium over the equity (obviously, if not the current shareholders wouldn’t sell the business) for control, but this is offset by the illiquidity of the investment. So, while they pay a premium for control, the take into account the illiquidity of the investment by running their IRR analysis over a defined time horizon (i.e., they know they won’t be able to exit or monetize the investment for at least a few years).

Generally, you run LBOs not so much to show aN explicit “floor price.” I know that’s what the M&I and similar guides say, but it’s not entirely true. You generally run LBOs to understand what is the price that someone who is just trying to squeeze returns can pay. To make this clear, imagine the following real life scenario:

CEO of, let’s say, Forg Motors communicates to, let’s say, Lizard that they want to sell the business. MD at Lizard is trying to understand and manage expectations of Forg CEO. Lizard MD would ask poor Lizard monkey to run an LBO. Let’s say LBO spits out an implied 20% premium if you target a 25% IRR. Now, Lizard MD can go to Forg motors CEO and say, “listen, even if we go to a sponsor who would just buy you out with leverage, run your business and try to keep it at steady state to then exit in 5 years, we should get a 20% premium. So, when we go to our set of potential buyers, let’s tell them this is a home run even in a no synergy-steady state scenario at 20%. Thus, after having Lizard Monkey do 100 iterations of cost saves analysis, we think you should give us credit for synergies and pay us an ever higher value.”

What I mean is, yes, sure, it sets a “floor price.” But it’s not really a floor price, it’s just more a way to understand what the business would be worth at steady state after financially engineering their capital structure. So any efficiencies you can identify beyond that allow you to argue for a higher price. It’s more a rhetoric tool than an actual number.