A company sells a product which has a unit sales price of $5, unit variable cost of $3 and total fixed costs of $240,000. The number of units the company must sell to break even is
a. 120,000 units.
b. 48,000 units.
c. 480,000 units.
d. 80,000 units.
The correct answer and explanation is :
Let’s solve it carefully:
First, break-even point (in units) is calculated by the formula:
[
\text{Break-even units} = \frac{\text{Total Fixed Costs}}{\text{Unit Sales Price} – \text{Unit Variable Cost}}
]
Given:
- Unit Sales Price = $5
- Unit Variable Cost = $3
- Total Fixed Costs = $240,000
Substituting these into the formula:
[
\text{Break-even units} = \frac{240,000}{5 – 3}
]
[
= \frac{240,000}{2}
]
[
= 120,000 \text{ units}
]
✅ Therefore, the correct answer is (a) 120,000 units.
Explanation (about 300 words):
The break-even point is a crucial financial metric that tells a business how many units it must sell to cover all its costs — both fixed and variable. At the break-even point, the company is not making a profit, but it is also not losing money.
Fixed costs are expenses that remain constant regardless of how much the company produces or sells. Examples include rent, salaries, and insurance. For this company, the total fixed costs are $240,000.
Variable costs, on the other hand, change in direct proportion to production volume. Here, the variable cost per unit is $3, meaning for every additional product made or sold, it costs the company $3.
The unit contribution margin — which is the amount each unit contributes toward covering fixed costs after covering its own variable cost — is calculated as the selling price minus the variable cost. In this case:
[
\text{Contribution margin per unit} = 5 – 3 = 2 \text{ dollars}
]
This $2 from every unit sold goes toward covering the $240,000 fixed costs. To find out how many units are needed to cover all fixed costs, you simply divide total fixed costs by the contribution margin per unit:
[
\frac{240,000}{2} = 120,000 \text{ units}
]
Thus, the company must sell 120,000 units to break even. Selling fewer units would result in a loss, while selling more would start generating profit.