Equity Portion of WACC in an IPO

There was a recent question about valuation methods for an IPO and the involvement of WACC. It got me thinking about the equity portion of WACC in such a situation. Considering it is an IPO, does that mean that the only type of equity that can exist is unregistered private placement or are there other possibilities? Also, is there any differential treatment for registered and unregistered stock with regards to calculating WACC (assuming a company has done both private placement and an IPO), or are they lumped together as outstanding shares?

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