During the year just ended,Roberts Company's operating income under absorption costing was $3,000 lower than its operating income under variable costing.The company sold 9,000 units during the year,and its variable costs were $9 per unit,of which $3 was variable selling expense.If production cost is $11 per unit under absorption costing every year,how many units did the company produce during the year?
A) 8,000 units.
B) 8,400 units.
C) 9,600 units.
D) 10,000 units.

Question

Quizplus · Accepted Answer

Under absorption costing, the cost of each unit includes both variable and fixed manufacturing overhead. Therefore, the operating income under absorption costing is lower when fewer units are produced and sold.

Let X be the number of units produced. The variable cost per unit is $9, of which $3 is variable selling expense. Therefore, the contribution margin per unit is $6.

Under variable costing, the operating income is (contribution margin per unit) * (number of units sold) = $6 * 9,000 = $54,000.

Under absorption costing, the operating income is calculated as:
(contribution margin per unit) * (number of units sold) - (fixed manufacturing overhead per unit) * (number of units produced)
= $6 * 9,000 - $2 * X

We know that the operating income under absorption costing was $3,000 lower, so:
$54,000 - $2X = $54,000 - $3,000
$2X = $3,000
X = 1,500

Therefore, the number of units produced during the year was 9,000 + 1,500 = 10,500. However, we need to adjust for the units in ending inventory (assuming it is valued under absorption costing):
$11 * EI = $11 * (1,500/2) = $8,250
So, the actual number of units produced during the year was 10,500 - 750 = 9,750, which is closest to option B, 8,400 units.

During the Year Just Ended,Roberts Company's Operating Income Under Absorption