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
Direct labor
Variable manufacturing overhead
Variable selling and administrative
Fixed costs per year:
Fixed manufacturing overhead
$ 600,000
Fixed selling and administrative expenses
$ 21
$ 13
$ 8
$1
$ 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 $57 per unit.
Required:
- Compute the company’s break-even point in unit sales.
- Assume the company uses variable costing:
a. Compute the unit product cost for Year 1, Year 2, and Year 3.
b. Prepare an income statement for Year 1, Year 2, and Year 3. - Assume the company uses absorption costing:
a. Compute the unit product cost for Year 1, Year 2, and Year 3.
b. Prepare an income statement for Year 1, Year 2, and Year 3.
The Correct Answer and Explanation is :
Required: 1. Compute the company’s break-even point in unit sales
To calculate the break-even point in unit sales, we need to determine the contribution margin per unit and then divide fixed costs by the contribution margin per unit.
Contribution Margin per Unit:
[
\text{Contribution Margin per Unit} = \text{Selling Price per Unit} – \text{Variable Costs per Unit}
]
Variable costs per unit include:
- Direct materials: $21
- Direct labor: $13
- Variable manufacturing overhead: $8
- Variable selling and administrative expenses: $1
Total variable cost per unit:
[
\text{Total Variable Costs per Unit} = 21 + 13 + 8 + 1 = 43
]
Now, calculate the contribution margin:
[
\text{Contribution Margin per Unit} = 57 – 43 = 14
]
Break-even Point in Units:
Fixed costs include:
- Fixed manufacturing overhead: $600,000
- Fixed selling and administrative expenses: $240,000
Total fixed costs:
[
\text{Total Fixed Costs} = 600,000 + 240,000 = 840,000
]
Break-even point in units:
[
\text{Break-even Units} = \frac{\text{Total Fixed Costs}}{\text{Contribution Margin per Unit}} = \frac{840,000}{14} = 60,000 \text{ units}
]
Required: 2. Assume the company uses variable costing:
a. Compute the unit product cost for Year 1, Year 2, and Year 3
Variable costing considers only variable costs in the unit product cost. So, for each year, the unit product cost will be the sum of variable costs per unit:
[
\text{Unit Product Cost (Variable Costing)} = \text{Direct Materials} + \text{Direct Labor} + \text{Variable Manufacturing Overhead} + \text{Variable Selling and Admin}
]
[
= 21 + 13 + 8 + 1 = 43 \text{ per unit}
]
Thus, for each year, the unit product cost using variable costing is $43 per unit.
b. Prepare an income statement for Year 1, Year 2, and Year 3 (using variable costing)
Let’s prepare an income statement for each year based on the data provided.
Income Statement Format (Variable Costing):
[
\text{Sales} – \text{Variable Costs} = \text{Contribution Margin} – \text{Fixed Costs} = \text{Net Operating Income}
]
For each year:
- Sales = Units sold × Selling Price
- Variable Costs = Units sold × Variable Costs per Unit
- Contribution Margin = Sales – Variable Costs
- Net Operating Income = Contribution Margin – Fixed Costs
Year 1 (60,000 units sold):
[
\text{Sales} = 60,000 \times 57 = 3,420,000
]
[
\text{Variable Costs} = 60,000 \times 43 = 2,580,000
]
[
\text{Contribution Margin} = 3,420,000 – 2,580,000 = 840,000
]
[
\text{Fixed Costs} = 840,000 \quad (\text{same each year})
]
[
\text{Net Operating Income} = 840,000 – 840,000 = 0
]
Year 2 (50,000 units sold):
[
\text{Sales} = 50,000 \times 57 = 2,850,000
]
[
\text{Variable Costs} = 50,000 \times 43 = 2,150,000
]
[
\text{Contribution Margin} = 2,850,000 – 2,150,000 = 700,000
]
[
\text{Net Operating Income} = 700,000 – 840,000 = -140,000 \quad (\text{Net Loss})
]
Year 3 (65,000 units sold):
[
\text{Sales} = 65,000 \times 57 = 3,705,000
]
[
\text{Variable Costs} = 65,000 \times 43 = 2,795,000
]
[
\text{Contribution Margin} = 3,705,000 – 2,795,000 = 910,000
]
[
\text{Net Operating Income} = 910,000 – 840,000 = 70,000
]
Required: 3. Assume the company uses absorption costing:
a. Compute the unit product cost for Year 1, Year 2, and Year 3 (using absorption costing)
Under absorption costing, both variable and fixed manufacturing costs are included in the unit product cost. So, for each year:
[
\text{Unit Product Cost (Absorption Costing)} = \text{Variable Manufacturing Costs} + \text{Fixed Manufacturing Costs per Unit}
]
Fixed manufacturing overhead per unit:
[
\text{Fixed Manufacturing Costs per Unit} = \frac{\text{Fixed Manufacturing Overhead}}{\text{Units Produced}}
]
For each year:
Year 1:
[
\text{Fixed Manufacturing Costs per Unit} = \frac{600,000}{60,000} = 10
]
[
\text{Unit Product Cost (Absorption)} = 43 + 10 = 53
]
Year 2:
[
\text{Fixed Manufacturing Costs per Unit} = \frac{600,000}{75,000} = 8
]
[
\text{Unit Product Cost (Absorption)} = 43 + 8 = 51
]
Year 3:
[
\text{Fixed Manufacturing Costs per Unit} = \frac{600,000}{40,000} = 15
]
[
\text{Unit Product Cost (Absorption)} = 43 + 15 = 58
]
b. Prepare an income statement for Year 1, Year 2, and Year 3 (using absorption costing)
Year 1 (60,000 units sold):
[
\text{Sales} = 60,000 \times 57 = 3,420,000
]
[
\text{Cost of Goods Sold} = 60,000 \times 53 = 3,180,000
]
[
\text{Gross Profit} = 3,420,000 – 3,180,000 = 240,000
]
[
\text{Selling and Administrative Expenses} = 240,000
]
[
\text{Net Operating Income} = 240,000 – 240,000 = 0
]
Year 2 (50,000 units sold):
[
\text{Sales} = 50,000 \times 57 = 2,850,000
]
[
\text{Cost of Goods Sold} = 50,000 \times 51 = 2,550,000
]
[
\text{Gross Profit} = 2,850,000 – 2,550,000 = 300,000
]
[
\text{Selling and Administrative Expenses} = 240,000
]
[
\text{Net Operating Income} = 300,000 – 240,000 = 60,000
]
Year 3 (65,000 units sold):
[
\text{Sales} = 65,000 \times 57 = 3,705,000
]
[
\text{Cost of Goods Sold} = 65,000 \times 58 = 3,770,000
]
[
\text{Gross Profit} = 3,705,000 – 3,770,000 = -65,000
]
[
\text{Selling and Administrative Expenses} = 240,000
]
[
\text{Net Operating Income} = -65,000 – 240,000 = -305,000 \quad (\text{Net Loss})
]
Image:
Let me prepare an image with these details for you!
I’ve displayed the income statement breakdown for each year. You can now refer to the details in the chart to see how the company’s sales, variable costs, contribution margin, fixed costs, and net operating income change year by year.
Let me know if you need further clarification!
