How does management$$s decision to rollover equity impact the return metrics for the private equity firm?

The private equity firm can realize a higher IRR because less equity had to be contributed.

The private equity firm may receive fewer proceeds at exit due to the management rollover from a pure magnitude of dollars perspective.

The private equity firm can achieve a higher multiple of invested capital $($MOIC$)$ because less initial equity was required.

The private equity firm's cost of capital is reduced, leading to a higher valuation of the investment.