Recompute at every purchase, never at a sale; carry the decimals

One cost for every unit on the shelf

The weighted-average formula refuses to say which pair of trail shoes left first. Every unit on hand is assumed to cost the same — the total cost on hand divided by the total units on hand — and every sale is costed at that average. The word weighted matters: it is not the average of the prices (52, 55, 58) but the average weighted by how many were bought at each.

Moving average — the perpetual version

Under a perpetual system the average is recomputed every time a purchase changes it, and never at a sale — a sale removes units at the current average, which leaves the average unchanged. Bramble Lane's March again (1 Mar 40 @ 52 · 8 Mar buy 60 @ 55 · 12 Mar sell 70 · 20 Mar buy 50 @ 58 · 27 Mar sell 45):

After 8 March: 100 units, cost 2,080 + 3,300 = 5,380. Average $5,380÷100=53.80$.

12 March, sell 70: $70\times 53.80=3,766$. Left: 30 units, 5,380 − 3,766 = 1,614 — still 53.80 each.

After 20 March: 80 units, cost 1,614 + 2,900 = 4,514. Average $4,514÷80=56.425$.

27 March, sell 45: $45\times 56.425=2,539.125$, reported as 2,539.13. Left: 35 units, 4,514 − 2,539.125 = 1,974.875, reported as 1,974.88.

Cost of goods sold, March     3,766.00 + 2,539.13 = 6,305.13
Ending inventory, 31 March    35 × 56.425         = 1,974.88

Notice that 56.425 was carried, not rounded to 56.43. Had it been, the 27 March sale would be 2,539.35 and the ending inventory 1,974.65 — 23 cents adrift on one line, and the drift compounds across a year of purchases. Keep four decimals, or work in totals (units left × the unrounded average = the unrounded balance) and round only what you report.

Periodic weighted average — one average for the month

A periodic store strikes the average once, over everything available: $8,280÷150=55.20$. Ending inventory = 35 × 55.20 = 1,932; cost of goods sold = 115 × 55.20 = 6,348 (or 8,280 − 1,932).

Different from the moving average's 1,974.88 and 6,305.13 — and this is the property FIFO did not have. The periodic average lets the 20 March purchase at 58 pull up the cost of the 70 pairs sold on 12 March, before that purchase existed. The moving average costs the 12 March sale at what was actually on hand that day. The two averages differ whenever purchases and sales interleave and agree only if all purchases precede all sales.

Rising costs, three formulas

March's costs rose. On the same 8,280 of goods:

FIFO charged the oldest, cheapest costs to the income statement and left the newest on the balance sheet — highest gross profit, highest inventory. The averages blend old and new, so they sit below FIFO on both. When costs fall, every sign reverses — a case that says "FIFO always reports higher income" is wrong by half. What s.3031 requires, once a formula is chosen, is consistency: the same formula for all inventories of a similar nature and use, period after period, so that two years' gross margins are comparable.