I have omitted an R superscript from everything, and put the subscript indicating time period in square brackets. The form of this equation that is familiar to me is:
FCF = NOPLAT + NCC - Change in NWC - Capex
There are so many things I don't get about the first expression:
1) What is the intuition for the term (1 - g[t]/ROIC[t])?
2) Where are the noncash charges?
3) Where is the capex?
4) I get the adjustment to last period's NWC, but shouldn't that be netted against the current period NWC?