The break-even point is a fundamental concept in cost accounting and business management. It represents the level of sales (in units or revenue) at which total costs equal total revenue, resulting in zero profit or loss. Understanding this point helps businesses determine the minimum sales volume required to cover all expenses.
To calculate the break-even point in units, the formula is: Fixed Costs / (Selling Price per Unit - Variable Cost per Unit). The denominator, (Selling Price per Unit - Variable Cost per Unit), is known as the contribution margin per unit, which is the amount each unit sold contributes towards covering fixed costs.
Given the data:
- Fixed Overheads (Fixed Costs) = £16,000
- Selling Price per Unit = £10
- Variable Cost per Unit = £7.50
First, calculate the contribution margin per unit: £10 - £7.50 = £2.50.
Next, apply the break-even formula: £16,000 / £2.50 = 6,400 units.
Therefore, the correct answer is A: 6,400 units. This means the company must sell 6,400 units to cover all its fixed and variable costs. Options B, C, and D are incorrect as they result from miscalculations or incorrect application of the break-even formula, such as dividing by variable cost or selling price directly.