payoff to different holders of an investment

So I think I understand well enough kind of how to calculate a residual value from an investment buy an LBO firm. Usually the residual value comes out to something like:

  • we expect to sell the company for 10mi - loan principal or whatever is left to be paid off - preferred payoff which is the preferred equity investment grown at the divident rate = residual value
    • and then usually the private equity holders get say 90% of this and management gets 10%

This all makes sense to me but I think I got confused in going through some problems so to clarify

  • if asked to calculated the payoff to ‘the private EQ firm’- what payoff would be appropriate? I think it would be BOTH the common EQ holder’s payoff (ie the 90% above) plus the preferred EQ holders payoff. But is that right?