Hi dig,
By definition, cash carried forward is:
Cash balance brought forward,
plus profit or less loss with non-cash items removed (so in your 1, normally items like R&D and COS are cash-related - things like salaries and hotel expenses and suchlike - but items like stock based compensation and depreciation are fished out),
adjusted for changes in working capital balances (things like AR, AP etc), which don't go through the P&L (- this deals with your concern in 2),
adjusted for things like purchases of fixed assets and assumption of debts, which also don't go through the P&L,
and adjusted for things like warrant redemptions and pipe receipts, which also also don't go through the P&L.
This doesn't result in an approximation. It results in a cash balance carried forward which is accurate to the penny if you have all the numbers.
Unfortunately, we do not have much of this info for Q4. We don't know anything from changes in working capital balances downwards, except we have a bead on warrants.
The bits that are not cash balances in this equation represent all of the cash flows in the period. The cash flows from operations are the P&L less the non-cash items, plus the adjustments to working capital. The whole thing is part of the debit and credit system from which the P&L and the balance sheet are also derived.
I think your method maybe has some double counting issues.
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