Math Problem Statement

Gabuat Corporation, which has only one product, has provided the following data concerning its most recent month of operations:

Selling price

Units in beginning inventory O

Units produced

Units sold

$ 106

2,600

2,200

Units in ending inventory 400

Variable costs per unit:

•Direct materials

Direct labor

Variable manufacturing overhead

$46

$ 28

$2

Variable selling and administrative expense $ 7

Fixed costs:

Fixed manufacturing overhead

$33,800

Fixed selling and administrative expense $ 8,800

The total contribution margin for the month under variable costing is:

O $16,800

O $37,400

O $50,600

O $66,000

Solution

To calculate the total contribution margin under variable costing, we need to understand and apply the following steps:

1. Calculate Sales Revenue

The revenue is based on the units sold multiplied by the selling price per unit.

Sales Revenue=Units Sold×Selling Price per Unit=2,200×106=233,200\text{Sales Revenue} = \text{Units Sold} \times \text{Selling Price per Unit} = 2,200 \times 106 = 233,200

2. Calculate Total Variable Costs

Variable costs include direct materials, direct labor, variable manufacturing overhead, and variable selling and administrative expense.

  • Direct materials cost per unit = $46
  • Direct labor cost per unit = $28
  • Variable manufacturing overhead per unit = $2
  • Variable selling and administrative expense per unit = $7

The total variable cost per unit is the sum of these values:

Total Variable Cost per Unit=46+28+2+7=83\text{Total Variable Cost per Unit} = 46 + 28 + 2 + 7 = 83

Now, we calculate the total variable costs for the units sold:

Total Variable Costs=Total Variable Cost per Unit×Units Sold=83×2,200=182,600\text{Total Variable Costs} = \text{Total Variable Cost per Unit} \times \text{Units Sold} = 83 \times 2,200 = 182,600

3. Calculate Contribution Margin

The contribution margin is the difference between sales revenue and total variable costs.

Contribution Margin=Sales RevenueTotal Variable Costs=233,200182,600=50,600\text{Contribution Margin} = \text{Sales Revenue} - \text{Total Variable Costs} = 233,200 - 182,600 = 50,600

Answer

The total contribution margin for the month under variable costing is:

50,600\boxed{50,600}

Correct Answer

Option: $50,600


Would you like further details on variable costing, contribution margin calculations, or additional examples? Here are some related questions:

  1. How do fixed costs affect the contribution margin in variable costing?
  2. What is the purpose of calculating contribution margin in managerial accounting?
  3. How does absorption costing differ from variable costing?
  4. How would the contribution margin change if sales volume increased?
  5. What impact do variable selling expenses have on the break-even point?

Tip: In variable costing, only variable costs are considered in the cost of goods sold, making it easier to assess the impact of changes in sales volume.

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Math Problem Analysis

Mathematical Concepts

Cost Accounting
Contribution Margin
Variable Costing

Formulas

Sales Revenue = Units Sold × Selling Price per Unit
Total Variable Costs = Total Variable Cost per Unit × Units Sold
Contribution Margin = Sales Revenue - Total Variable Costs

Theorems

-

Suitable Grade Level

Grades 11-12