Cost Of Goods Sold And Gross Profit

From Inventory Costs to Gross Profit

A merchandising company earns revenue by selling goods it has purchased for resale. To measure the result of those sales, the income statement separates the cost of the goods sold from the revenue earned on them. The difference is gross profit, a subtotal that shows how much remains from net sales after accounting for the cost assigned to the goods sold.

The amount assigned to goods sold depends on both the inventory count and the method used to assign costs to units. Under a periodic inventory system, a company determines ending inventory at the end of the period and uses it, together with beginning inventory and purchases, to calculate cost of goods sold. The examples below state when they use this system and identify the cost-flow assumption used.

Definition: Cost of goods sold (COGS) is the cost assigned to inventory sold during the reporting period. Gross profit is net sales less COGS. In a merchandising income statement, gross profit is a subtotal before operating expenses; it is not net income.

The Periodic Inventory Calculation

In a periodic system, inventory records do not necessarily determine the cost of each sale as it occurs. Instead, the company counts the goods remaining at period-end and calculates COGS from the inventory cost rollforward. Assume the count is accurate, the inventory consists of goods held for resale, and the cost of all goods available is allocated between the units sold and those remaining.

\begin{aligned} \text{Net purchases} &= \text{Purchases} - \text{Purchase returns and allowances} - \text{Purchase discounts} + \text{Freight-in},\\ \text{Goods available for sale} &= \text{Beginning inventory} + \text{Net purchases},\\ \text{COGS} &= \text{Goods available for sale} - \text{Ending inventory},\\ \text{Gross profit} &= \text{Net sales} - \text{COGS}. \end{aligned}

The calculation follows from dividing the cost available during the period into two destinations: the cost of goods still on hand and the cost of goods sold. Rearranging that inventory rollforward gives the COGS formula.

\begin{aligned} \text{Beginning inventory} + \text{Net purchases} &= \text{Ending inventory} + \text{COGS},\\ \text{COGS} &= \text{Beginning inventory} + \text{Net purchases} - \text{Ending inventory}. \end{aligned}

This is a cost allocation, not a calculation of cash paid. Purchases may be made on credit, and freight-in is included because it is a cost of bringing goods to the place and condition in which they are available for sale. Purchase returns and discounts reduce the cost of purchases. Costs such as advertising or store rent are not part of inventory cost in these calculations.

Net sales are sales revenue after applicable sales returns, allowances, and discounts, as covered in the earlier material on net sales. A sales allowance or discount reduces net sales; it does not, by itself, change the cost assigned to inventory. If physical goods are returned and restored to saleable inventory, the inventory count and cost records must reflect that fact as well.

Worked Example: Periodic Weighted-Average Cost

A hypothetical shop begins the month with 120 units costing $8 each. It buys 80 more units at $10 each, returns 10 of those units to the supplier, and pays $50 freight-in on the purchases. A period-end count finds 70 units. Net sales for the month are $2,400. Using periodic weighted-average costing, calculate ending inventory, COGS, and gross profit.

Method and assumptions. This is a periodic inventory calculation. The 10 returned units cost $10 each, and the freight-in cost is included in the cost of the units retained. Under periodic weighted average, divide the total cost of goods available by the total units available to obtain one average unit cost.

Beginning inventory cost is $120 \times \$8 = \$960$. The original purchase cost is $80 \times \$10 = \$800$, and the purchase return reduces it by $10 \times \$10 = \$100$. Net purchases, including freight-in, are therefore $\$800 - \$100 + \$50 = \$750$.

The number of units available is $120 + 80 - 10 = 190$. Goods available for sale cost $\$960 + \$750 = \$1,710$, so the weighted-average cost is $\$1,710 \div 190 = \$9$ per unit.

Ending inventory is $70 \times \$9 = \$630$. COGS is $\$1,710 - \$630 = \$1,080$. Gross profit is $\$2,400 - \$1,080 = \$1,320$.

Check. The 120 units sold cost $120 \times \$9 = \$1,080$, and the 70 units remaining cost $70 \times \$9 = \$630$. Together they account for all 190 units and $\$1,710$ of available cost. The common mistake avoided is excluding freight-in from the cost pool.

Assigning Costs to Units

The inventory count tells a company how many units remain, but an inventory-cost assumption determines which costs are assigned to those units. Two common methods are FIFO and weighted average. Under FIFO (first-in, first-out), the earliest costs are assigned to goods sold first; in a periodic calculation, ending inventory is assigned the most recent costs. Under periodic weighted average, all units and costs available during the period are combined to calculate one average cost per unit.

These are cost-flow assumptions: they specify how recorded costs are allocated, not necessarily the physical order in which goods moved. For FIFO, use the stated purchase layers and the ending unit count. For weighted average, use total available cost divided by total available units. Do not mix the methods within a single calculation.

Worked Example: FIFO With Freight-In

A hypothetical retailer begins a period with 60 units costing $12 each. It purchases 140 units at $15 each and pays $280 freight-in on that shipment. It sells 150 units, and net sales are $5,250. Under periodic FIFO, calculate ending inventory, COGS, and gross profit.

Method and assumptions. Treat the freight-in as part of the purchased inventory cost and spread it evenly over the 140 purchased units. Apply periodic FIFO to the 200 units available; the 50 units left at period-end are assigned the newest costs.

Freight-in per purchased unit is $\$280 \div 140 = \$2$. Each purchased unit therefore costs $\$15 + \$2 = \$17$. Beginning inventory cost is $60 \times \$12 = \$720$, and purchase cost including freight-in is $140 \times \$17 = \$2,380$. Total goods available cost $\$720 + \$2,380 = \$3,100$.

Units remaining are $60 + 140 - 150 = 50$. Since the most recent costs are assigned to ending inventory under periodic FIFO, ending inventory is $50 \times \$17 = \$850$. COGS is $\$3,100 - \$850 = \$2,250$, and gross profit is $\$5,250 - \$2,250 = \$3,000$.

Check. FIFO assigns all 60 beginning units and 90 purchased units to the 150 units sold. Their cost is $(60 \times \$12) + (90 \times \$17) = \$720 + \$1,530 = \$2,250$. Adding COGS of $2,250 to ending inventory of $850 recovers the $3,100 available cost. The common mistake avoided is valuing the 50 ending units at the older $12 cost; periodic FIFO assigns them the newer $17 cost.

Worked Example: Purchase Returns and Gross Profit

A hypothetical distributor begins a period with 100 units costing $20 each. It purchases 200 units at $24 each, returns 20 units to the supplier, and pays $120 freight-in. At period-end, 80 units remain. Gross sales are $8,500, sales allowances are $300, and sales discounts are $200; there are no physical customer returns. Using periodic weighted-average costing, find net sales, ending inventory, COGS, and gross profit.

Method and assumptions. Use the physical count of 80 units and include freight-in in inventory cost. The 20 returned units cost $24 each. Since there are no returned goods to add back to inventory, the stated sales allowances and discounts reduce net sales only.

Net sales are $\$8,500 - \$300 - \$200 = \$8,000$. Beginning inventory cost is $100 \times \$20 = \$2,000$. Purchase cost is $200 \times \$24 = \$4,800$, and the supplier return reduces it by $20 \times \$24 = \$480$. Net purchases including freight-in are $\$4,800 - \$480 + \$120 = \$4,440$.

Units available are $100 + 200 - 20 = 280$. Goods available cost $\$2,000 + \$4,440 = \$6,440$, so average cost per unit is $\$6,440 \div 280 = \$23$. Ending inventory is $80 \times \$23 = \$1,840$. COGS is $\$6,440 - \$1,840 = \$4,600$, and gross profit is $\$8,000 - \$4,600 = \$3,400$.

Check. The units sold are $280 - 80 = 200$; at $23 each, their cost is $4,600. The 200 units sold and 80 units remaining account for all 280 units. The common mistake avoided is subtracting purchase returns from sales revenue rather than from purchases.

Why the Subtotal Matters—and Common Traps

Gross profit measures the amount of net sales remaining after the cost of the merchandise sold is deducted. It is useful for assessing the relationship between selling revenue and inventory cost, but it does not include operating expenses or other income-statement items. A positive gross profit therefore does not, by itself, establish that the company has positive operating income or net income.

Inventory errors flow through the gross-profit calculation because ending inventory is subtracted to determine COGS. If ending inventory is overstated by $700 while all other amounts are correct, COGS is understated by $700 and gross profit is overstated by $700. Conversely, an ending inventory understatement makes COGS too high and gross profit too low by the same amount. This direction follows directly from $\text{COGS} = \text{goods available} - \text{ending inventory}$.

Do not confuse purchases with COGS. Purchases are added to beginning inventory; ending inventory must still be deducted.
Do not omit freight-in. In these examples it is an inventory acquisition cost, not a selling expense.
Do not confuse purchase returns with sales returns. Purchase returns reduce net purchases; sales returns reduce net sales and may also affect inventory if goods are restored to saleable stock.
Do not apply FIFO in reverse. Under periodic FIFO, the newest costs remain in ending inventory; the earlier costs are assigned to goods sold first.
Do not call gross profit net income. Gross profit is calculated before expenses and other income-statement items not covered here.

Key takeaway: Under a periodic system, begin with beginning inventory, add net purchases to determine goods available, and subtract ending inventory to obtain COGS. Then subtract COGS from net sales to obtain gross profit. Check that ending inventory and COGS together equal the cost of goods available.

Check Your Understanding

For each problem, use the stated inventory method and verify that ending inventory plus COGS equals goods available for sale.

A shop has beginning inventory of $4,200, net purchases of $11,100, and ending inventory of $3,600. Net sales are $18,500. Find goods available, COGS, and gross profit. (Answer: Goods available = $15,300; COGS = $11,700; gross profit = $6,800.)
A retailer begins with 60 units at $12 each, buys 140 units at $15 each, and pays $280 freight-in. It sells 150 units and has net sales of $5,250. Under periodic FIFO, find ending inventory, COGS, and gross profit. (Answer: Ending inventory = $850; COGS = $2,250; gross profit = $3,000.)
A distributor has 50 units at $30 each, then buys 150 units at $34 each. It returns 10 purchased units and pays $100 freight-in. Ending inventory is 40 units, and net sales are $7,200. Under periodic weighted average, calculate ending inventory, COGS, and gross profit, rounding money to the nearest cent. (Answer: Ending inventory = $1,338.95; COGS = $5,021.05; gross profit = $2,178.95.)
Goods available for sale cost $30,000 and net sales are $50,000. Actual ending inventory is $5,000, but the company reports $5,700. Calculate reported and correct COGS and gross profit, and state the direction of each error. (Answer: Reported COGS = $24,300 and reported gross profit = $25,700; correct COGS = $25,000 and correct gross profit = $25,000; reported COGS is understated and reported gross profit is overstated by $700.)
A company has beginning inventory of $6,000, purchases of $18,000, purchase returns of $1,200, freight-in of $600, and ending inventory of $7,400. Net sales are $24,000. Calculate net purchases, goods available, COGS, and gross profit. (Answer: Net purchases = $17,400; goods available = $23,400; COGS = $16,000; gross profit = $8,000.)

What You'll Learn