Rollover Equity - LBO

Coming across some conflicting stuff online about how to model rollover equity in LBO tests for interviews, would appreciate some help here.

For simplicity, let’s say a company has a purchase EV of $100, no existing debt or cash (making purchase equity value also = $100), and PE firm is using $50 in debt to finance the transaction. No fees or any other uses except purchase equity value. Management rollover is 20%.

I’ve seen 2 different ways of calculating this:

1. Management rollover would just be 20%*Purchase Equity Value = $20.

2. To calculate management rollover, you set uses = sources=100. From here, in sources, you subtract out the debt used to finance the transaction to get to the transaction equity. (100-50=50). You multiply THIS value by 20%, and get management rollover of 20%*$50=10.

Obviously you get 2 totally different numbers here which would significantly impact initial investment from sponsor and therefore returns.

The first way makes more intuitive sense to me because if management is rolling over its equity, wouldn’t equity value be the management’s preexisting equity and not the equity used to finance the transaction (as is the case in method 2)?

Peak Frameworks seems to stick exclusively to Method 2, though. Maybe it depends on how the question is worded? I.e. if it says management rolls over 20% of its existing ownership, then it’d be method 1, but in other cases, it’d be method 2? Honestly don’t see any situations where method 2 would be accurate, but PF must have some rationale here…