Martin’s ltd produce high quality kitchen titles. The firm has a modern factory which can produce a maximum output of 90 000 boxes of tiles a year ear when the factory is operating at full capacity. Last year the firm produced and sold 80 000 boxes at a price of $12 per box. The firm incurred the following costs. Annual fixed costs (overheads) were $240 000 whilst the variable cost of producing each box was £8. (i) Draw a break-even chart to illustrate last year’s financial situation (ii) State and illustrate the break-even point on the chart you have just drawn.(iii) Identify the firm’s break-even revenue.
The Correct Answer and Explanation is :
To analyze Martin’s Ltd’s financial performance, we’ll construct a break-even chart, identify the break-even point, and determine the break-even revenue.
i) Break-Even Chart:
A break-even chart visually represents the relationship between costs, revenue, and profit at varying production levels. The horizontal axis (X-axis) denotes the number of units (boxes of tiles), while the vertical axis (Y-axis) represents the monetary values (costs and revenues).
To create the chart:
- Fixed Costs Line: Plot a horizontal line at $240,000, representing the annual fixed costs, which remain constant regardless of production volume.
- Total Costs Line: Start this line at the fixed costs level ($240,000) and add variable costs ($8 per box) for each unit produced. The slope of this line reflects the variable cost per unit.
- Total Revenue Line: Begin at the origin (0,0) and plot the revenue generated by selling each box at $12. The slope of this line corresponds to the selling price per unit.
The point where the Total Revenue Line intersects the Total Costs Line is the break-even point.
ii) Break-Even Point:
The break-even point is where total revenue equals total costs, resulting in neither profit nor loss.
To calculate:
- Contribution Margin per Unit: Selling Price per Unit – Variable Cost per Unit = $12 – $8 = $4
- Break-Even Quantity: Fixed Costs ÷ Contribution Margin per Unit = $240,000 ÷ $4 = 60,000 boxes
Thus, Martin’s Ltd needs to produce and sell 60,000 boxes to break even. On the chart, this is the intersection point of the Total Revenue and Total Costs lines at 60,000 units.
iii) Break-Even Revenue:
Break-even revenue is the amount of sales dollars required to cover all fixed and variable costs.
To calculate:
- Break-Even Revenue: Break-Even Quantity × Selling Price per Unit = 60,000 boxes × $12 = $720,000
Therefore, the firm must achieve $720,000 in sales to break even. This value can also be determined using the contribution margin ratio:
- Contribution Margin Ratio: Contribution Margin per Unit ÷ Selling Price per Unit = $4 ÷ $12 ≈ 0.3333 (or 33.33%)
- Break-Even Revenue: Fixed Costs ÷ Contribution Margin Ratio = $240,000 ÷ 0.3333 ≈ $720,000
Understanding the break-even point is crucial for Martin’s Ltd as it indicates the minimum sales volume needed to cover all costs. Producing and selling more than 60,000 boxes will result in a profit, while falling short will lead to a loss. This analysis aids in setting sales targets, pricing strategies, and cost management to ensure financial stability and profitability.