FIFO and Weighted-Average Inventory Costing

Why Inventory Costing Methods Matter

When a business buys identical goods at different prices, it must assign dollar costs to the units it sells and the units it still holds. The physical units may be indistinguishable, but their recorded costs need not be. As a result, the cost assigned to ending inventory—and the cost assigned to goods sold—depends on the inventory-costing method.

This tutorial uses the periodic approach: at the end of the accounting period, the business uses total units and costs available, together with the number of units sold, to calculate cost of goods sold and ending inventory. Two methods are considered: first-in, first-out (FIFO) and weighted average. The examples assume there are no returns, losses, or other inventory adjustments.

Definition: Goods available for sale are the beginning inventory plus purchases during the period. Ending inventory is the cost assigned to units remaining at period-end. Cost of goods sold (COGS) is the cost assigned to units sold during the period. Under either method, when all goods available are accounted for, $$ \text{Cost of goods available for sale}=\text{COGS}+\text{Ending inventory}. $$

Periodic FIFO

FIFO means first-in, first-out. Under periodic FIFO, the cost of the earliest goods available is assigned to the units sold first. Thus, the units remaining in ending inventory are costed from the most recent purchases, moving backward through the cost layers only if needed. The method describes a cost-assignment assumption; it does not require that a business physically ship its oldest goods first.

To calculate periodic FIFO, first determine units available and units sold. Assign the earliest cost layers to the sold units. The costs left over belong to ending inventory. Alternatively, assign the latest layers to ending inventory and obtain COGS by subtracting ending inventory from total cost available. Both approaches should give the same result.

Worked Example: FIFO and Weighted Average With Rising Costs

A retailer begins the month with 12 units costing $9 each. It purchases 8 units at $10 each and later purchases 10 units at $12 each. It sells 18 units. Calculate ending inventory and COGS under periodic FIFO and periodic weighted average. Then compare the reported inventory balances.

Method. First calculate total units and total cost available; then apply each cost-assignment rule. This avoids a common mistake: calculating COGS independently and failing to reconcile it to the goods available for sale.

Step 1: Total units and cost available. Beginning inventory is $12\times \$9=\$108$. The first purchase costs $8\times \$10=\$80$, and the second costs $10\times \$12=\$120$. Therefore:

\begin{aligned} \text{Units available}&=12+8+10=30,\\ \text{Cost available}&=\$108+\$80+\$120=\$308,\\ \text{Units in ending inventory}&=30-18=12. \end{aligned}

Step 2: FIFO. The 18 units sold are assigned the oldest costs: 12 units at $9 and 6 units at $10. Thus COGS is $12\times \$9+6\times \$10=\$108+\$60=\$168$. The 12 units remaining consist of 2 units at $10 and 10 units at $12, so ending inventory is $2\times \$10+10\times \$12=\$20+\$120=\$140$.

Step 3: Weighted average. The periodic average cost per unit is $\$308/30=\$10.266666\ldots$. Using the unrounded average, COGS is $18\times(\$308/30)=\$184.80$, and ending inventory is $12\times(\$308/30)=\$123.20$. Round dollar amounts to the nearest cent.

Check and comparison. Under FIFO, $\$168+\$140=\$308$. Under weighted average, $\$184.80+\$123.20=\$308$. FIFO ending inventory is $\$140-\$123.20=\$16.80$ higher, and FIFO COGS is $16.80 lower. The two methods assign the same total cost, but divide it differently between goods sold and goods still held.

Periodic Weighted-Average Costing

Under periodic weighted-average costing, the business pools the cost of all units available for sale during the period. It divides total cost available by total units available to obtain one average cost per unit. That average is assigned to both units sold and units remaining.

Formula: For a periodic inventory calculation, let $C$ be total cost of goods available, $Q$ the total units available, and $Q_E$ the units in ending inventory. Then the weighted-average cost per unit is $C/Q$. Ending inventory is $Q_E(C/Q)$, and COGS is $(Q-Q_E)(C/Q)$.

The average is weighted by units, not found by taking an unweighted average of the listed purchase prices. If different quantities were purchased at different prices, each price must contribute in proportion to the number of units purchased at that price.

The reconciliation follows directly from the formula. Since units sold are $Q-Q_E$, the sum of COGS and ending inventory is:

(Q-Q_E)\frac{C}{Q}+Q_E\frac{C}{Q} =Q\frac{C}{Q} =C.

This establishes why the average-cost calculation allocates the entire cost available between sold and remaining units. It is also a useful arithmetic check: if COGS plus ending inventory does not equal total cost available, there is an error in the unit counts, cost layers, or arithmetic.

Worked Example: Finding Ending Inventory From the Remaining Units

A parts distributor has 20 units at $15 each at the start of a period. It purchases 10 units at $18 and 15 units at $20. It sells 25 units. Find ending inventory and COGS under FIFO and periodic weighted average. Round dollar amounts to the nearest cent.

Method. Calculate total available units and cost first. For FIFO, identify the 20 units left from the latest cost layers. For weighted average, apply one average cost per unit to both the 20 remaining units and the 25 sold units.

Step 1: Available units and cost. Beginning inventory costs $20\times \$15=\$300$. The purchases cost $10\times \$18=\$180$ and $15\times \$20=\$300$. Therefore, units available are $20+10+15=45$, and total cost available is $\$300+\$180+\$300=\$780$. Ending units are $45-25=20$.

Step 2: FIFO. Ending inventory takes the latest costs first. It consists of all 15 units at $20 and 5 of the 10 units at $18. Therefore, ending inventory is $15\times \$20+5\times \$18=\$300+\$90=\$390$. COGS is $\$780-\$390=\$390$. Equivalently, the 25 sold units cost $20\times \$15+5\times \$18=\$300+\$90=\$390$.

Step 3: Weighted average. The average cost is $\$780/45=\$17.333333\ldots$ per unit. Ending inventory is $20\times(\$780/45)=\$346.6666\ldots$, or $346.67. COGS is $25\times(\$780/45)=\$433.3333\ldots$, or $433.33.

Check and interpretation. FIFO gives $\$390+\$390=\$780$. Weighted average gives $\$346.67+\$433.33=\$780$ after rounding. With rising purchase prices, FIFO leaves more recent, higher-priced units in inventory; here FIFO ending inventory exceeds weighted-average ending inventory by $\$390-\$346.67=\$43.33$. The COGS difference is also $43.33 in the opposite direction.

A Sale Between Purchases: Periodic Versus Moving Average

The timing of purchases and sales matters when identifying which weighted-average method is being used. Periodic weighted average pools the costs of all goods available over the period, including purchases made after an earlier sale. A perpetual moving-average system instead recalculates the average after each purchase and uses the current average when a sale occurs. These methods can produce different answers when prices change during the period.

Worked Example: A Purchase Made After an Earlier Sale

A shop begins with 10 units at $4 each. It purchases 10 units at $10, sells 10 units, then purchases 10 units at $16 and sells 5 more units. Calculate ending inventory and COGS under periodic FIFO and periodic weighted average. Then calculate the moving-average result to show why the timing convention matters.

Method. For periodic methods, combine the entire period’s goods available before assigning costs. For moving average, recalculate inventory cost per unit after each purchase, and use the then-current average for each sale. A common mistake is to apply the periodic average after every transaction, which is not the moving-average method.

Step 1: Total available and ending units. Beginning inventory costs $10\times \$4=\$40$. Purchases cost $10\times \$10=\$100$ and $10\times \$16=\$160$. Total cost available is $\$40+\$100+\$160=\$300$, and total units available are 30. Total sales are $10+5=15$ units, so ending inventory is 15 units.

Step 2: Periodic FIFO. The 15 units sold are costed from the oldest layers: 10 units at $4 and 5 units at $10. COGS is $10\times \$4+5\times \$10=\$40+\$50=\$90$. Ending inventory consists of the remaining 5 units at $10 and 10 units at $16, for $5\times \$10+10\times \$16=\$50+\$160=\$210$. The check is $\$90+\$210=\$300$.

Step 3: Periodic weighted average. The average cost is $\$300/30=\$10$ per unit. COGS is $15\times \$10=\$150$, and ending inventory is $15\times \$10=\$150$. The check is $\$150+\$150=\$300$.

Step 4: Perpetual moving average. After the first purchase, the shop has 20 units costing $\$40+\$100=\$140$, so the average is $\$140/20=\$7$. The first sale costs $10\times \$7=\$70$, leaving 10 units costing $\$70$. After the second purchase, inventory is 20 units costing $\$70+\$160=\$230$, and the new average is $\$230/20=\$11.50$. The second sale costs $5\times \$11.50=\$57.50$. Moving-average COGS is therefore $\$70+\$57.50=\$127.50$, and ending inventory is $15\times \$11.50=\$172.50$. The check is $\$127.50+\$172.50=\$300$.

The periodic and moving-average calculations both reconcile to $300, but they do not produce the same allocation: periodic weighted average gives $150 of ending inventory, while moving average gives $172.50. The difference arises because periodic average includes the later $16 purchase when assigning costs to the earlier sale; moving average does not.

Balance-Sheet and Income-Statement Effects

Ending inventory is reported as an asset on the balance sheet. COGS is an expense in determining income for the period. Because total cost available is fixed, assigning more cost to ending inventory assigns less to COGS, and vice versa. Before considering taxes or other effects, lower COGS means higher income; higher ending inventory means higher assets and, through the income effect, higher equity.

When purchase costs are rising, FIFO commonly produces higher ending inventory and lower COGS than weighted average, because the latest, higher unit costs remain in ending inventory. The examples show this relationship. It is not a universal rule for every price sequence: if costs are falling, or fluctuate, the comparison depends on the actual layers. If all unit costs are equal, the methods produce the same allocation.

Do not interpret this comparison as a change in the amount of goods physically held or the total cost available. The methods change the accounting assignment of costs. For a complete analysis, keep the inventory method consistent with the stated facts and period; do not substitute a moving-average calculation for a periodic weighted average unless the problem specifies a perpetual system.

Common Mistakes and a Reliable Check

A frequent error is to calculate ending inventory correctly and then report COGS as though it were the same amount or as though it came from a separate total. COGS must be the cost of units sold, and the two assigned amounts must add to cost available. For instance, in the first worked example, FIFO ending inventory is $140 and total cost available is $308. A claimed COGS of $240 would be wrong because $\$140+\$240=\$380$, not $308. The correct COGS is $\$308-\$140=\$168$.

Do not count units sold as ending inventory. Compute ending units as units available minus units sold.
Do not average prices without weighting by quantities. Divide total cost by total units, not the sum of the listed prices by the number of price layers.
Do not mix periodic and moving-average rules. Periodic weighted average uses all goods available in the period; moving average recalculates after purchases.
Always perform the cost reconciliation. Verify that COGS plus ending inventory equals total cost available.

Key takeaway: FIFO assigns the earliest costs to units sold and leaves the latest cost layers in ending inventory. Periodic weighted average pools the cost of all units available and assigns one average unit cost to both sold and remaining units. Both methods must allocate exactly the total cost available.

Check Your Understanding

For each problem, calculate the requested amounts under the stated periodic methods and check that COGS plus ending inventory equals total cost available.

A store has 10 units at $6, buys 10 more at $8, and sells 12 units. Find FIFO ending inventory and COGS, then find periodic weighted-average ending inventory and COGS. (Answer: FIFO ending inventory $64 and COGS $76; weighted-average ending inventory $56 and COGS $84.)
A repair supplier begins with 5 units at $20, buys 7 at $22 and 8 at $25, and sells 9 units. Find ending inventory and COGS under FIFO and periodic weighted average. (Answer: FIFO ending inventory $266 and COGS $188; weighted-average ending inventory $249.70 and COGS $204.30.)
A seller begins with 30 units at $4, buys 10 at $7 and 10 at $10, and sells 35 units. Calculate FIFO and periodic weighted-average COGS and ending inventory. (Answer: FIFO COGS $155 and ending inventory $135; weighted-average COGS $203 and ending inventory $87.)
A business has 8 units at $11, purchases 12 units at $14, and sells 10 units. Calculate both periodic methods and state which gives higher ending inventory. (Answer: FIFO ending inventory $140 and COGS $116; weighted-average ending inventory $128 and COGS $128; FIFO ending inventory is higher by $12.)
A shop begins with 4 units at $30, purchases 6 at $24, and sells 5 units. Calculate FIFO and periodic weighted-average ending inventory and COGS. (Answer: FIFO COGS $144 and ending inventory $120; weighted-average COGS $132 and ending inventory $132.)

What You'll Learn