well, the question is very unconcrete and the case could go into a million directions. But here is a fundamental line of thinking that should be employed:
I would start by making explicit the relationship between return rate and inherent risk of an investment class. So determining its own risk appetite is a central precondition for the PE fund in order to set a reasonable target return rate. Then, for its given risk appetite, the market return rate of comparable assets in the same risk bracket needs to be researched and should form a "floor level" of expected returns. This can then be transformed into a "decision grid" for each investment opportunity to come to a go or no-go decision.
But a I said - the actual case and the required analysis dirung the case can branch off into many different directions.