An inventory error affects two periods because 1) the ending inventory of one period will become the beginning inventory for the following period, and 2) the calculation of the cost of goods sold is beginning inventory + purchases - ending inventory.
We will demonstrate this with some amounts. Let's assume that a company began on December 1. During the month of December it purchased or manufactured $100,000 of goods. At the end of December 31, the company reported that its ending inventory was $15,000. As a result, its balance sheet will report inventory of $15,000 and its income statement will report cost of goods sold of $85,000. In January it purchases $130,000 of goods and at the end of January 31 it reports inventory of $20,000. It will report January's cost of goods sold as $125,000 (beginning inventory of $15,000 plus purchases of $130,000 minus ending inventory of $20,000).
Now let's assume that only one error occurred and it involved the calculation of the December 31 ending inventory. Instead of the $15,000 that had been reported, the true amount of inventory was $19,000. That meant the December 31 balance sheet understated the true cost of inventory by $4,000. It also meant that the income statement's cost of goods sold was not $85,000. Rather, the true cost of goods sold was $81,000 ($100,000 minus $19,000 of inventory). In January, the true cost of goods sold is $129,000 (beginning inventory of $19,000 plus the purchases of $130,000 minus the January 31 inventory of $20,000).
To recap, the December 31 balance sheet reported the incorrect ending inventory and the December and January income statements reported the incorrect cost of goods sold, and gross profit and net income. The true cost of goods sold for December was $81,000—not the $85,000 that was reported. The true cost of goods sold for January was $129,000—not the $125,000 that was reported. That one error in calculating the December 31 inventory cost resulted in December's cost of goods sold being too high and January's cost of goods sold being too low. That in turn meant that the reported gross profit for December was $4,000 too low and January's reported profit was $4,000 too high.
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