A company that produces a single product had a net operating income of $65,000 using variable costing and a net operating income of $95,000 using absorption costing. Total fixed manufacturing overhead was $60,000 and production was 10,000 units. This year was the first year of operations. Between the beginning and the end of the year, the inventory level:
A) decreased by 5,000 units
B) increased by 5,000 units
C) decreased by 30,000 units
D) increased by 30,000 units

Question

Quizplus · Accepted Answer

The net operating income using absorption costing is higher than the net operating income using variable costing, which means that the fixed manufacturing overhead cost is higher than the amount of fixed manufacturing overhead included in the variable costing calculation. This suggests that there is excess inventory under absorption costing, because some portion of the fixed manufacturing overhead costs are being included in the cost of ending inventory.

To calculate the amount of excess inventory, we need to compare the fixed manufacturing overhead cost per unit under absorption costing to the fixed manufacturing overhead cost per unit under variable costing.

Fixed Manufacturing overhead per unit under absorption costing: 
= Total fixed manufacturing overhead / number of units produced 
= $60,000 / 10,000 units 
= $6.00 per unit

Fixed manufacturing overhead per unit under variable costing: 
= Fixed manufacturing overhead included in the calculation of cost of goods sold / number of units sold 
= ($95,000 - $65,000) / 10,000 units 
= $3.00 per unit

The difference in fixed manufacturing overhead per unit between absorption costing and variable costing is $3.00. This means that $3.00 of fixed manufacturing overhead cost is included in the cost of each unit of ending inventory under absorption costing but not under variable costing.

To calculate the amount of excess inventory, we need to calculate the number of units of ending inventory that were produced during the year:

Ending inventory under absorption costing = Cost of goods manufactured under absorption costing - Cost of goods sold under absorption costing 
= ($60,000 + ($6.00 per unit x 10,000 units)) - ($60,000 + $95,000) 
= $66,000 - $155,000 
= -$89,000

This means that the cost of goods sold under absorption costing was greater than the cost of goods manufactured under absorption costing, which is only possible if ending inventory increased during the year.

To calculate the number of units of ending inventory that were produced, we need to divide the excess cost of ending inventory by the fixed manufacturing overhead cost per unit under absorption costing:

Number of units of ending inventory produced = Excess cost of ending inventory under absorption costing / Fixed manufacturing overhead per unit under absorption costing 
= (-$89,000) / $6.00 per unit 
= -14,833.33 units

Since we know that production was 10,000 units during the year, and the number of units of ending inventory produced was negative, we can conclude that the inventory level increased by 5,166.67 units (i.e. 10,000 units - (-14,833.33 units)). Rounded to the nearest whole number, the inventory level increased by 5,000 units.

A Company That Produces a Single Product Had a Net