Circle K Furniture has a contribution margin ratio of 16%. If fixed costs are $176,800, how many dollars of revenue must the company generate in order to reach the break-even point?
The Correct Answer and Explanation is :
To find the revenue required to reach the break-even point, we use the break-even formula:
[
\text{Break-even revenue} = \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}}
]
Step-by-step calculation:
- Fixed Costs ((FC)):
[
FC = 176,800
] - Contribution Margin Ratio ((CMR)):
[
CMR = 16\% = 0.16
] - Break-even Revenue ((R)):
[
R = \frac{FC}{CMR} = \frac{176,800}{0.16} = 1,105,000
]
Thus, Circle K Furniture must generate $1,105,000 in revenue to reach the break-even point.
Explanation:
The break-even point is where a company’s total revenue equals its total expenses, meaning no profit or loss is incurred. For Circle K Furniture, we need to cover fixed costs using the contribution margin generated from sales.
- Contribution Margin Ratio: The ratio of contribution margin (sales revenue minus variable costs) to sales revenue. Here, every dollar of revenue contributes $0.16 toward fixed costs after covering variable costs.
- Fixed Costs: These are the company’s expenses that do not change with sales volume, such as rent, salaries, and utilities. Circle K Furniture has fixed costs of $176,800.
- Break-even Revenue: This is the revenue needed to ensure that the contribution margin fully covers fixed costs. Beyond this point, the company starts making a profit.
By dividing the fixed costs by the contribution margin ratio, we calculate the sales revenue required to offset the fixed costs. The calculation assumes all other factors, such as the contribution margin ratio, remain constant.
In summary, Circle K Furniture needs $1,105,000 in sales revenue to break even, ensuring fixed costs are covered without incurring a loss.