This might be a dumb question but bear with me. Firm is seeking capital for expansion. In my view you have two options for the valuation. Either arrive at a pre-money valuation assuming no capital injection / expansion or arrive at a post-money valuation and net the influx (whether debt or equity) to arrive at pre-money value. The former seems more intuitively "right" than the latter, but I can't think of any logical argument for the two pre-money values to differ either. The discount rate would have to be the equalizer to ensure the PV of the value of the influx matches the influx.
Recognizing future financing after T0 is not part of the standard DCF process (equity value is firm value net of current net-debt and firm value incorporates future cash flows which sometimes result from external financing). Yet in the hypothetical a financing beyond T0 necessarily is deducted from a firm value that is based on its future existence. It has to be otherwise the mere idea of the expansion has immediate value (maybe it does a small amount).
Most (all?) estimates of firm value incorporate future external financing but net only existing net debt. I'm not a fan of CAPM but just trying to conceptualize / clarify that it is the discount rate that equalizes?