Why might a private equity firm allot some of a company’s new equity in an LBO to a management option pool, and how would this affect the model?

This is done for the same reason you have an Earnout in an M&A deal: the PE firm wants to incentivize the management team and keep everyone on-board until they exit the investment.

The difference is that there’s no technical limit on how much management might receive from such an option pool: if they hit it out of the park, maybe they’ll all become millionaires.

In your LBO model, you would need to calculate a per-share purchase price when the PE firm exits the investment, and then calculate how much of the proceeds go to the management team based on the Treasury Stock Method.

An option pool by itself would reduce the PE firm’s return, but this is offset by the fact that the company should perform better with this incentive in place.