Haas Company manufactures and sells one product. The following information pertains to each of the company’s first three years of operations: Variable costs per unit: Manufacturing: Direct materials
12 Variable manufacturing overhead
2 Fixed costs per year: Fixed manufacturing overhead
240,000 During its first year of operations, Haas produced 60,000 units and sold 60,000 units. During its second year of operations, it produced 75,000 units and sold 50,000 units. In its third year, Haas produced 40,000 units and sold 65,000 units. The selling price of the company’s product is
1,000,000 1. How many units must be sold? 2. What is the total sales in dollars required? Question 4: Assume the company uses variable costing: 1. Compute the unit product cost for year 1, year 2, and year 3. Question 5: Assume the company uses absorption costing: 1. Compute the unit product cost for year 1, year 2, and year 3
The Correct Answer and Explanation is:
Let’s break this down step by step for both variable costing and absorption costing.
Given Data:
- Variable costs per unit:
- Direct materials: 12
- Variable manufacturing overhead: 2
- Total Variable Manufacturing Cost per unit = 12 + 2 = 14
- Fixed costs per year:
- Fixed manufacturing overhead: 240,000
- Selling price per unit = 1,000,000
1. Units to be sold for break-even:
To find the break-even units, we need to calculate the contribution margin per unit and divide the fixed costs by this margin.
- Contribution margin per unit = Selling price per unit – Variable cost per unit
Contribution margin = 1,000,000 – 14 = 999,986
Now, the break-even units are calculated as:
- Break-even units = Fixed costs / Contribution margin per unit
Break-even units = 240,000 / 999,986 ≈ 0.24 units
This indicates that, practically, very few units need to be sold to break even due to the extremely high selling price compared to the variable cost.
2. Total sales in dollars required:
The total sales required can be found by multiplying the break-even units by the selling price per unit.
- Total sales required = Break-even units * Selling price per unit
Total sales = 0.24 * 1,000,000 ≈ 240,000 dollars
3. Unit Product Cost using Variable Costing:
Under variable costing, we only include variable manufacturing costs in the unit product cost.
Year 1:
- Variable costing unit product cost = Direct materials + Variable manufacturing overhead
Variable costing unit cost = 12 + 2 = 14
Year 2:
- Variable costing unit product cost = 12 + 2 = 14 (same as year 1, as variable costs don’t change)
Year 3:
- Variable costing unit product cost = 12 + 2 = 14 (same as year 1 and 2)
4. Unit Product Cost using Absorption Costing:
Absorption costing includes both variable and fixed manufacturing costs in the unit product cost. The fixed costs are allocated to each unit produced.
Year 1:
- Absorption costing unit product cost = Variable costs per unit + (Fixed manufacturing overhead / Units produced)
Absorption costing unit cost = 14 + (240,000 / 60,000) = 14 + 4 = 18
Year 2:
- Absorption costing unit product cost = Variable costs per unit + (Fixed manufacturing overhead / Units produced)
Absorption costing unit cost = 14 + (240,000 / 75,000) = 14 + 3.2 = 17.2
Year 3:
- Absorption costing unit product cost = Variable costs per unit + (Fixed manufacturing overhead / Units produced)
Absorption costing unit cost = 14 + (240,000 / 40,000) = 14 + 6 = 20
Summary:
- Units to break even ≈ 0.24 units
- Total sales required ≈ 240,000 dollars
- Variable costing unit cost for all years = 14
- Absorption costing unit costs:
- Year 1: 18
- Year 2: 17.2
- Year 3: 20
The difference in unit costs between variable and absorption costing comes from the allocation of fixed manufacturing overhead. In variable costing, only variable costs are considered, while in absorption costing, the fixed overhead is distributed over the number of units produced, leading to a higher unit product cost in years where production is low.
