Croft Corporation produces a single product. Last year, the company had a net operating income of $160,000 using absorption costing and $149,000 using variable costing. The fixed manufacturing overhead cost was $10 per unit. There were no beginning inventories. If 43,000 units were produced last year, then sales last year were:
A) 32,000 units
B) 40,000 units
C) 41,900 units
D) 54,000 units

Question

Quizplus · Accepted Answer

Net operating income using absorption costing = Sales - Cost of goods sold - Fixed manufacturing overhead
$160,000 = Sales - [(Variable manufacturing cost per unit + Fixed manufacturing overhead per unit) × Units sold] - (Fixed manufacturing overhead per unit × Units produced)
$160,000 = Sales - [(variable cost per unit + $10) × 43,000] - ($10 × 43,000)
$160,000 = Sales - ($760,000)
Sales = $920,000

Net operating income using variable costing = Contribution margin - Fixed manufacturing overhead
$149,000 = (Sales - Variable manufacturing cost per unit × Units sold) - (Fixed manufacturing overhead per unit × Units produced)
$149,000 = (Sales - Variable cost per unit × 43,000) - ($10 × 43,000)
$149,000 = Sales - $430,000
Sales = $579,000

Using absorption costing, the fixed manufacturing overhead is treated as a product cost and is included in the cost of goods sold. Using variable costing, the fixed manufacturing overhead is treated as a period cost and is deducted from the contribution margin.

To calculate the number of units sold, we must use the variable costing method since it separates the fixed overhead cost from the cost of goods sold.

Contribution margin per unit = Sales price per unit - Variable manufacturing cost per unit
Contribution margin per unit = $579,000 ÷ 43,000 units = $13.47 per unit

We know that the fixed manufacturing overhead per unit is $10, so the variable manufacturing cost per unit is:
Variable manufacturing cost per unit = Sales price per unit - Contribution margin per unit - Fixed manufacturing overhead per unit
Variable manufacturing cost per unit = $10 + $13.47 - $10 = $13.47 per unit

Using this information, we can calculate the number of units sold:
Sales - Variable manufacturing cost per unit × Units sold = Contribution margin - Fixed manufacturing overhead
$579,000 - ($13.47 × Units sold) = $149,000 + ($10 × 43,000)
$579,000 - ($13.47 × Units sold) = $589,000
($13.47 × Units sold) = $10,000
Units sold = 741 units

Since there were no beginning inventories and 43,000 units were produced, the sales last year were:
Sales = 43,000 - 741 = 41,900 units.

Therefore, the best choice is (C).

Croft Corporation Produces a Single Product