Periodic Inventory Costing — Roberts Company: 23-Ind-B7 Financial and Managerial Accounting, May 2013, Q7

Question 7: Periodic Inventory Costing — Roberts Company (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Periodic-system unit flow: beginning inventory 1,600@$90; purchase 2,400@$92; sale 2,800 units; purchase 2,000@$97; sale 800 units; sales return of 8 units (from the 800-unit sale).

Find. (a) Ending inventory and COGS under weighted-average; (b) ending inventory and COGS under FIFO.

Approach. Under a periodic system, cost is assigned only once, at year-end, from the full pool of goods available for sale — find total units/cost available and net units sold first, then apply each costing method to that single pool (a single weighted-average rate for the whole year; FIFO layers from the oldest purchase forward).

Layer	Units	Unit cost	Total cost
Beginning inventory	1,600	$90	$144,000
Nov 9 purchase	2,400	$92	220,800
Jun 7 purchase	2,000	$97	194,000
Goods available for sale	6,000		$558,800

Net units sold and ending-inventory units. $2{,}800+800-8_{\text{return}}=\boxed{3{,}592\ \text{units sold}}$; ending inventory $=6{,}000-3{,}592=\boxed{2{,}408\ \text{units}}$.
(a) Weighted-average (periodic — one annual average). $$\bar{c}=\frac{558{,}800}{6{,}000}=\boxed{\$93.1333/\text{unit}}.$$ $$\text{Ending inventory}=2{,}408\times93.1333=\boxed{\$224{,}265.07},\qquad \text{COGS}=558{,}800-224{,}265.07=\boxed{\$334{,}534.93}.$$
(b) FIFO. The 3,592 units sold are costed from the oldest layers first: all 1,600 beginning-inventory units, then $3{,}592-1{,}600=1{,}992$ units from the Nov 9 purchase. $$\text{COGS}_{\text{FIFO}}=1{,}600(90)+1{,}992(92)=144{,}000+183{,}264=\boxed{\$327{,}264}.$$ Ending inventory is the remaining $2{,}400-1{,}992=408$ units of the Nov 9 layer, plus all 2,000 units of the Jun 7 layer: $$\text{Ending inventory}_{\text{FIFO}}=408(92)+2{,}000(97)=37{,}536+194{,}000=\boxed{\$231{,}536}.$$ Check: $327{,}264+231{,}536=558{,}800$, matching total goods available.

Method	Ending inventory	Cost of goods sold
(a) Weighted-average (periodic)	$224,265.07	$334,534.93
(b) FIFO	$231,536	$327,264

Concept & Theory

Topic. Periodic-system inventory costing under weighted-average and FIFO.

Key relations. Goods available for sale = Beginning inventory + Purchases; Ending inventory + COGS = Goods available for sale; weighted-average rate $=\dfrac{\text{total cost available}}{\text{total units available}}$; FIFO assumes the earliest-acquired units are sold first, leaving the most recent purchases in ending inventory.

Why this works. In a period of rising unit costs ($90 → $92 → $97 here), FIFO leaves the newest, most expensive layers in ending inventory and expenses the oldest, cheapest units as COGS — this is exactly why FIFO's ending inventory ($231,536) is higher, and its COGS lower, than the smoothed weighted-average result: the average blends in the cheaper early-year costs that FIFO keeps entirely out of COGS.

Common pitfall. Forgetting that the 8-unit sales return reduces net units sold (not ending inventory units directly, and not treated as a purchase) — the returned units effectively never left the goods-available pool; applying a perpetual (moving-average / running FIFO) technique instead of the single year-end pool a periodic system requires (the two coincide for FIFO but not for weighted-average).

Source. Libby, Libby & Short, Financial Accounting (Canadian ed.), ch. on inventory costing methods (FIFO, weighted-average, periodic vs. perpetual systems).

Question 7 of 7: Periodic Inventory Costing — Roberts Company

Question 7: Periodic Inventory Costing — Roberts Company (10 marks)