NPV IRR calculation for negative cashflows

Hi everyone, I wanted to request some clarification on IRR/NPV calculations as I have seen some scenarios where there appear to be different opinions on which cash flows to be considered and how the IRR should be derived.

I understand NPV compares the original investment amount in Year 0 to the discounted cash flow for each year (Y1, Y2, Y3, Y4, Y5,… plus terminal value) and the difference between the original investment amount and the total of the discounted cash flows for all the years is the NPV i.e. add up all the cash flows from Y0 to Y5.

How does this work when applied to the free cash flows (FCFE) of a new business? If the Y0 investment amount is taken as negative, and all annual cash flows are then positive, we can simply add them up since the negative amount represents cash outflow (from an investors perspective) and the annual positive amounts are excess cash flows that can be distributed back to investors.

However, if the Y1 cash flow is negative, should this be ignored in the analysis or is this still included? Considering the Y1 negative cash flow is not actually an investment into the business but rather the cash being used up in the business operations and this cash is part of the original investment amount funded into the company, which has already been included in the Y0 investment amount. Positive cash flows in subsequent years will still be added as they are FCFE so can be distributed as dividends.

So, in summary, is it correct to state that Y0 cash flow will be the investment amount (shown as negative amount), Y1 cash flow will only be included if it is positive and ignored if it is negative, and Y2 cash flow will be included if it is positive…

Alternatively, should we ignore the initial investment amount and just consider the Y1 negative cash flow as the investment amount, but this doesn’t seem accurate as the original investment may be higher to fund project startup phase, and then reduces as working capital and other items normalize during the course of the year.

Would appreciate any help on this, thanks!