Croft Corporation produces a single product. Last year, the company had a net operating income of $93,800 using absorption costing and $81,600 using variable costing. The fixed manufacturing overhead cost was $10 per unit. There were no beginning inventories. If 28,000 units were produced last year, then sales last year were:
A) 15,800 units
B) 26,780 units
C) 29,220 units
D) 40,200 units

Question

Quizplus · Accepted Answer

Under absorption costing, fixed manufacturing overhead costs are included in the cost of each unit produced, whereas under variable costing, fixed manufacturing overhead costs are treated as a period cost and are expensed in the period incurred.

To reconcile the difference in net operating incomes between the two costing methods, we need to determine the difference in the fixed manufacturing overhead costs that were expensed under variable costing but capitalized under absorption costing.

The fixed manufacturing overhead cost per unit is given as $10. Therefore, the difference in fixed manufacturing overhead costs between the two methods is:

$10 x 28,000 units = $280,000

This means that $280,000 in fixed manufacturing overhead costs were capitalized under absorption costing but expensed under variable costing.

To determine sales, we need to first calculate the cost of goods sold under each method.

Under absorption costing:
Cost of goods sold = (28,000 units x $50 per unit) = $1,400,000
($50 per unit includes $40 variable manufacturing cost + $10 fixed manufacturing overhead cost per unit)

Under variable costing:
Cost of goods sold = (28,000 units x $40 per unit) = $1,120,000

To find sales, we need to add the gross profit to cost of goods sold under each method and equate it to the net operating income for that method:

Under absorption costing:

Sales - Cost of goods sold = Gross profit = $1,400,000 - $93,800 = $1,306,200

Under variable costing:

Sales - Cost of goods sold = Gross profit = $1,120,000 - $81,600 = $1,038,400

We know that the difference in net operating incomes between the two methods is $12,200 ($93,800 - $81,600). Therefore:

$1,306,200 - $1,038,400 = $267,800 = $280,000 - $12,200

This means that $267,800 is the additional fixed manufacturing overhead cost that was expensed under variable costing but capitalized under absorption costing.

To find sales, we can use the contribution margin ratio under variable costing:

Contribution margin ratio = (Sales - Variable expenses) ÷ Sales

We know that variable expenses per unit are $40 and that 28,000 units were produced. Therefore,

Variable expenses = 28,000 units x $40 per unit = $1,120,000

Contribution margin ratio = ($1,306,200 - $1,120,000) ÷ $1,306,200 = 0.1427

This means that the contribution margin per unit is:

Contribution margin per unit = ($1 - 0.1427) x $40 = $34.49

To find sales, we can use the following equation:

Sales = Fixed expenses ÷ Contribution margin ratio

Fixed expenses under variable costing = $81,600 + $267,800 (additional fixed manufacturing overhead costs expensed under variable costing) = $349,400

Sales = $349,400 ÷ 0.1427 = $2,445,180

Finally, we can determine the number of units sold by dividing sales by the selling price per unit under either costing method:

Number of units sold = Sales ÷ Selling price per unit

Under absorption costing:

Number of units sold = $2,445,180 ÷ $50 per unit = 48,904 units

Under variable costing:

Number of units sold = $2,445,180 ÷ $40 per unit = 61,130 units

Since there were no beginning inventories, the number of units sold equals the number of units produced. Therefore, sales last year were 26,780 units (option B).

Croft Corporation Produces a Single Product