Why doesn't operating cash flow after tax include change in net working capital?

So I am doing capital budgeting, and the formula given is:
Initial cash flow = fixed asset investment + working capital investment
Every year after-tax operating cash flow is: (S-C-D)*(1-T)+D
And end cashflow is the after-tax proceeds from the sale of the project

My question is, why in the calculation of every year’s after-tax operating cash flow, we do not include the change in net working capital?

Just a simple example to illustrate this:
If every year we invest all the cash inflow into inventory. So we will have 0 cash inflow every year, and our NWC will grow really large.
At the end of the project, we sell the project which includes all the inventory.

Obviously, when we are doing a DCF analysis of the project, we should deduct the change in NWC from each year’s operating cash flow, otherwise, we are basically double-counting the increase in NWC.

What am I missing here?

Um . . . no, it won’t.

You seem to be missing something about inventory. Think about it.

Hi! Thank you for your reply. but I don’t get it. If we invest all cash flow into inventories, our inventory will grow, right? And inventory is part of the working capital so our net working capital(excluding cash) will grow…What am I missing here?

I think I get it. It is because we use CASH SALES in the calculation of after-tax operating cash flow in capital budgeting, so we have already excluded the increase in AR and we are not deducting COGS so we do not need to worry about the increase in inventory.

As I wrote before: no, it won’t.

What are you selling?

So in another word, since in the formula (S-C-D)*(1-T)+D, S is cash sales and we did not deduct COGS, investment in inventories should be included in C, the cash operating cost, right??

You keep saying that you’re not deducting COGS.

C is variable cost per unit; for all intents and purposes, that’s COGS.

Thanks, Magician!!

My pleasure.