Cost of equity of the target company or the cost of equity of the financial sponsor ?

COE = Sponsor's target IRR for two reasons: i) existing shareholders are all wiped out in an LBO so the only cost of equity is the remaining investor's (sponsor's) required rate of return and ii) this model is being built from the perspective of the sponsor who would be more concerned with seeing how much he can pay for a company given his required rate of return (target IRR) not what existing shareholders are demanding. But I agree that FCFE DCFs aren't the typical way of backing out a purchase price for the purpose of an LBO - more common to reverse engineer the LBO and back out purchase price using a given IRR. FCFE DCFs are typically used by sponsors to value an existing portfolio company for reporting to LP purposes