Roberts Company Produces A Single Product This Year

Roberts Company Produces a Single Product This Year The Companys Ne

Roberts Company produces a single product. This year, the company's net operating income under absorption costing was $2,000 lower than under variable costing. The company sold 8,000 units during the year, and its variable costs were $8 per unit, of which $2 was variable selling and administrative expense. If production cost was $10 per unit under absorption costing, then how many units did the company produce during the year? (The company produced the same number of units last year.)

Paper For Above instruction

Understanding the relationship between absorption costing and variable costing is essential in managerial accounting, especially when analyzing how production levels influence net income. In this paper, the focus is to compute the number of units produced during the year given the specific cost and income information provided by Roberts Company.

Absorption costing includes all manufacturing costs—both fixed and variable—in the cost of each unit produced, whereas variable costing includes only variable manufacturing costs. The difference in net operating income between these two costing methods arises mainly due to the handling of fixed manufacturing overhead costs, which can be deferred or released depending on whether production exceeds sales or vice versa.

From the problem, the company sold 8,000 units, and variable costs were $8 per unit, of which $2 was variable selling and administrative expenses. The production cost per unit was $10 under absorption costing. The net operating income under absorption costing was $2,000 lower than under variable costing. The task is to determine the number of units produced during the year.

The first step is to understand the cost components and their impact on income differences. Since fixed manufacturing overhead costs are spread over the units produced, the difference between absorption and variable costing net incomes depends on how many fixed overhead costs are deferred in inventory. If production exceeds sales, some fixed manufacturing costs are stored in inventory under absorption costing, increasing net income compared to variable costing. Conversely, if sales exceed production, the fixed costs are released from inventory, decreasing net income under absorption costing relative to variable costing.

Mathematically, the difference in net income can be expressed as:

\[ \text{Difference} = ( \text{Units produced} - \text{Units sold} ) \times \text{Fixed manufacturing overhead per unit} \]

Since the fixed manufacturing overhead is part of the absorption cost of $10 per unit, and variable manufacturing costs are $8 per unit, the fixed overhead per unit is:

\[ \text{Fixed manufacturing overhead per unit} = \text{Absorption cost per unit} - \text{Variable manufacturing cost} \]

\[ = 10 - (8 - 2) \]

But note that variable costs include total variable manufacturing and variable selling/admin expenses: $8 per unit, with $2 being applying to selling/admin expenses, which are not part of manufacturing costs. Therefore, the manufacturing variable cost per unit is:

\[ 8 - 2 = 6 \]

then, the fixed manufacturing overhead per unit is:

\[ 10 - 6 = 4 \]

since $4 accounts for fixed manufacturing overhead per unit.

The difference in net operating income due to changes in inventory levels related to fixed manufacturing overhead is:

\[ \text{Net income difference} = (\text{Units produced} - \text{Units sold}) \times \text{Fixed manufacturing overhead per unit} \]

Substituting known values:

\[ 2000 = (\text{Units produced} - 8000) \times 4 \]

Rearranged:

\[ \text{Units produced} - 8000 = \frac{2000}{4} = 500 \]

\[ \text{Units produced} = 8500 \]

Hence, Roberts Company produced 8,500 units during the year.

This production volume aligns with the provided options, confirming the calculations. Producing more units than sold creates an inventory of fixed manufacturing costs on the balance sheet, increasing net income under absorption costing compared to variable costing. The analysis underlines the significance of understanding inventory management and cost behavior in managerial decision-making.

In conclusion, Roberts Company produced 8,500 units during the year to account for the $2,000 difference in net operating income between absorption and variable costing methods.

References

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