Fastest way to estimate sponsor equity at entry in a paper LBO?

How to answer

Entry EV = entry multiple x EBITDA, then equity = EV - net debt raised (plus fees/cash needs). Simplified: equity check = EV x (1 - leverage %). So 10x on $100M = $1,000M EV at 60% debt gives a $400M check. If debt is quoted in turns (e.g., 6x), debt = $600M and equity = EV - $600M = $400M — the same answer stated differently.

Key idea: Confusing 'leverage as % of EV' with 'leverage as turns of EBITDA.' 6x debt on a 10x EV is 60%; confirm which the interviewer gave you.