FCInv = ending gross PP&E - beginning gross PP&E - gain on sale
FCInv = ending net PP&E - beginning net PP&E + depreciation - gain on sale
where gain on sale = proceeds from sale - book value of asset sold
With IS information given:
FCInv = CAPEX - proceeds from the asset sale
However, for me it is still not clear why I only consider the proceeds from the asset sale (and not the gain) using IS information. Because the gain is based on accrual accounting? Maybe anyone could explain the differences for all formulas with a little example?
Let’s say i own 1mm of equipment at the start of the year, i buy 2mm of equipment during the course of the year and also sell 200k of equipment for a 300k gain (i.e. book value of 200k is sold for 500k proceeds to net 300k profit). So my ending gross PPE is: 1mm starting balance + 2mm purchases - 200k book value sold = 2.8mm
FCInv = gross PPE end of year - gross PPE begining of year - gain on sale = 2.8mm - 1mm - 300k = 1.5mm
CAPEX = 2mm (this is how much equipment i bought during the year)
FCInv = CAPEX - proceeds from asset sale = 2mm - 500k = 1.5mm
This is basically just explaining balance sheet carrying value changes via cash flows.
The “trick” is that the book value of assets sold is already(!) included in the ending gross PP&E and, so, I only have to consider the gain on the assets sold and not the entire proceeds from that sale. Therefore, both equations have—of course–the same result.