Opening + purchases − ending = COGS, and the sign falls out
◈ 7 cardsTracing an ending-inventory error and a purchase cut-off error through two periods with the COGS identity, so the sign is computed rather than guessed.
Run the identity, do not reason it out
Every inventory error question is solved by one line:
Learners who try to reason the effect ("less inventory means… less profit?") get the sign wrong about half the time. Learners who push the error through the identity, line by line, do not. Ending inventory is subtracted, so an error in it moves COGS the opposite way; and this year's ending inventory is next year's opening inventory, so the same error moves next year's COGS the same way as the original error. That is the whole theory. The rest is bookkeeping.
Worked example — Boreal Bikes misses a rack of frames
At the 31 December 2024 count Boreal Bikes Ltd. missed a rack of frames costing $30,000. The purchase invoice was recorded correctly; only the count is wrong. Ending inventory is understated by 30,000.
2024. Ending inventory understated → it is subtracted → COGS overstated 30,000 → gross profit and net income understated 30,000 → at 31 December 2024, retained earnings understated 30,000 and total assets (inventory) understated 30,000. The balance sheet is wrong on both sides by the same amount.
2025. The understated 2024 ending inventory becomes the understated 2025 opening inventory. Opening inventory is added → COGS understated 30,000 → 2025 net income overstated 30,000. Retained earnings at 31 December 2025: understated 30,000 from 2024, overstated 30,000 from 2025 — correct. The 2025 count was right, so inventory and total assets are correct too. The error has self-corrected over two periods.
"Self-correcting" does not mean harmless. Two years of income are each wrong by $30,000 in opposite directions; the 2024 balance sheet was wrong; any covenant ratio computed on it — current ratio, debt-to-equity — was wrong; and when the error is found, the 2024 comparatives must still be restated.
Overstated instead
Run an ending inventory overstated by 12,000 through the same line and every sign flips: 2024 COGS understated, net income overstated, retained earnings and assets overstated 12,000; 2025 COGS overstated, net income understated; retained earnings correct at the end of 2025.
The cut-off error — where the identity really earns its keep
On 29 December 2024 a supplier shipped $18,000 of frames to Boreal FOB shipping point. Title passed when the goods left the supplier's dock, so at 31 December they are Boreal's inventory — but they were in transit at the count and the invoice had not arrived, so they were excluded from ending inventory and not recorded as a purchase.
Run it: purchases understated 18,000 and ending inventory understated 18,000. In the identity, one is added and one is subtracted, so COGS is correct, and so is net income. What is wrong is the balance sheet: inventory understated 18,000 and accounts payable understated 18,000. Equity is right; the current ratio is not (both current assets and current liabilities are short by the same amount, which moves the ratio unless it happened to be exactly 1.0). Had the terms been FOB destination, title would not pass until delivery in January, and excluding the goods would have been correct.