Moyas Corporation sells a single product for $20 per unit. Last year, the company’s sales revenue was $300,000 and its net operating income was $24,000. If fixed expenses totaled $96,000 for the year, the break-even point in unit sales was:
14,100 units
9,900 units
15,000 units
12,000 units
The correct answer and explanation is :
To find the break-even point in unit sales, we can use the following formula:
[
\text{Break-even point (in units)} = \frac{\text{Fixed Expenses}}{\text{Contribution Margin per Unit}}
]
Where:
- Fixed Expenses = $96,000 (given)
- Contribution Margin per Unit is calculated as the selling price per unit minus the variable cost per unit.
Step 1: Find the Contribution Margin per Unit
First, we need to calculate the contribution margin per unit. The contribution margin is the difference between sales revenue and total variable costs. However, we don’t have the variable cost per unit directly, so we will first derive the variable cost using the available information.
From the income statement, we know:
- Sales Revenue = $300,000
- Net Operating Income = $24,000
- Fixed Expenses = $96,000
We can use the following relationship:
[
\text{Net Operating Income} = \text{Sales Revenue} – \text{Total Variable Costs} – \text{Fixed Expenses}
]
Rearranging this formula to find the total variable costs:
[
\text{Total Variable Costs} = \text{Sales Revenue} – \text{Net Operating Income} – \text{Fixed Expenses}
]
Substituting the given values:
[
\text{Total Variable Costs} = 300,000 – 24,000 – 96,000 = 180,000
]
Step 2: Calculate the Contribution Margin Ratio
Now that we know the total variable costs, we can calculate the contribution margin. The contribution margin per unit is the difference between the selling price and the variable cost per unit.
We know:
- Selling Price per Unit = $20
- Total Variable Costs = $180,000
To find the variable cost per unit, divide the total variable costs by the number of units sold. The total number of units sold is:
[
\text{Number of units sold} = \frac{\text{Sales Revenue}}{\text{Selling Price per Unit}} = \frac{300,000}{20} = 15,000 \text{ units}
]
Now, we calculate the variable cost per unit:
[
\text{Variable Cost per Unit} = \frac{180,000}{15,000} = 12
]
Thus, the contribution margin per unit is:
[
\text{Contribution Margin per Unit} = \text{Selling Price per Unit} – \text{Variable Cost per Unit} = 20 – 12 = 8
]
Step 3: Calculate the Break-Even Point
Finally, we can calculate the break-even point in units:
[
\text{Break-even point (in units)} = \frac{96,000}{8} = 12,000 \text{ units}
]
Answer:
The break-even point in unit sales is 12,000 units. Therefore, the correct answer is 12,000 units.