5.4 Costs – Break‑Even Analysis
Objective
To understand what break‑even analysis is, why every business needs a break‑even point, and how to calculate and interpret it for effective decision‑making.
1. Meaning & Importance of Break‑Even Analysis
- Definition: A financial technique that shows the level of sales (either units or value) at which total revenue equals total cost, giving a profit of zero. This level is called the break‑even point (BEP) or the break‑even level of output.
- Why it matters: It provides a clear target for budgeting, performance measurement and risk assessment – the sales level that must be achieved before any profit can be earned.
- Key uses (as required by the Cambridge syllabus):
- Setting an appropriate selling price.
- Evaluating the effect of a new product launch or a change to an existing product line.
- Controlling costs and assessing the impact of cost changes.
2. Key Concepts
| Concept | Explanation / Formula |
|---|
| Fixed Costs (FC) |
Costs that do not vary with output (e.g., rent, salaries). |
| Variable Cost per unit (VC) |
Cost that varies directly with each unit produced (e.g., raw material, direct labour). |
| Total Cost (TC) |
TC = FC + VC × Q |
| Selling Price per unit (P) |
Price at which each unit is sold. |
| Total Revenue (TR) |
TR = P × Q |
| Contribution Margin per unit (CM) |
CM = P − VC |
| Total Contribution (TCM) |
TCM = CM × Q (the amount that contributes to covering fixed costs and profit) |
| Contribution Margin Ratio (CMR) |
CMR = CM ÷ P (usually expressed as a %) |
3. Underlying Assumptions
- Cost and revenue relationships are linear within the relevant range.
- Fixed costs remain constant regardless of output.
- Variable cost per unit and selling price are constant.
- The analysis is short‑run (capacity is not a limiting factor).
- Only one product is considered, or an average product‑mix is used.
4. Calculating the Break‑Even Point
Two equivalent forms are required by the syllabus:
- Break‑even level of output (units): BEPunits = FC ÷ CM
- Break‑even sales value (£): BEPvalue = FC ÷ CMR
5. Margin of Safety (MOS)
The MOS shows how far current or projected sales can fall before the business reaches the break‑even point.
- Formula (using units): MOS = (Actual Q − BEPunits) ÷ Actual Q × 100 %
- Formula (using sales value): MOS = (Actual £ − BEPvalue) ÷ Actual £ × 100 %
- Interpretation: A larger MOS indicates a lower risk of loss; a small or negative MOS signals that the business is close to, or already below, the break‑even level.
6. Profit at Different Levels of Output
Once the contribution per unit is known, profit for any output level can be calculated:
- Profit formula: Profit = (CM × Q) − FC = TCM − FC
- Positive profit occurs when Q > BEPunits; a loss occurs when Q < BEPunits.
7. Worked Example (including MOS and profit)
| Item | Amount (£) |
|---|
| Fixed Costs (FC) | 120,000 |
| Selling Price per unit (P) | 30 |
| Variable Cost per unit (VC) | 18 |
| Projected sales for the period | 150,000 units |
Step 1 – Contribution margin per unit
$$CM = P - VC = 30 - 18 = £12$$
Step 2 – Break‑even level of output (units)
$$\text{BEP}_{units} = \frac{FC}{CM} = \frac{120,000}{12} = 10,000\ \text{units}$$
Step 3 – Break‑even sales value
$$CMR = \frac{12}{30} = 0.40\;(40\%)$$
$$\text{BEP}_{value} = \frac{120,000}{0.40} = £300,000$$
Step 4 – Margin of safety (units)
$$\text{MOS} = \frac{150,000 - 10,000}{150,000}\times100 = 93.3\%$$
Interpretation: sales could fall by up to 93 % before a loss would be incurred – a very comfortable safety margin.
Step 5 – Profit at the projected sales level
$$\text{Profit} = (CM \times Q) - FC = (12 \times 150,000) - 120,000 = £1,680,000$$
8. Break‑Even Chart (Key Features to Sketch)
- Axes: Horizontal – Quantity (Q); Vertical – £ (costs / revenue).
- Fixed‑Cost line (FC): Horizontal line at £120,000.
- Total‑Cost line (TC): Starts at the FC line and slopes upward with a gradient equal to the variable cost per unit (£18).
- Total‑Revenue line (TR): Starts at the origin and slopes upward with a gradient equal to the selling price (£30).
- Break‑even point (BEP): Intersection of TC and TR – mark the coordinates (10,000 units, £300,000).
- Profit area: Shade the region above the TC line and below the TR line to the right of the BEP – this represents the profit that would be earned at any output above the break‑even level.
- Margin of safety area: Shade the portion of the TR line between the actual sales level (150,000 units) and the BEP – this visually shows the MOS.
9. Uses of Break‑Even Analysis (Cambridge Syllabus)
- To set a selling price that will cover costs and deliver a desired profit.
- To assess the financial viability of launching a new product or altering an existing product line.
- To evaluate the effect of changes in fixed or variable costs and to aid cost‑control decisions.
10. Limitations
- Assumes linear cost and revenue relationships; real‑world curves may be non‑linear.
- Ignores the time value of money and cash‑flow timing.
- Based on a single product or an average product mix – not ideal for highly diversified ranges.
- Does not consider external factors such as market demand, competition, or macro‑economic conditions.
- Overlooks economies of scale and capacity utilisation effects.
11. Summary Checklist
- Identify all fixed costs (FC) and the variable cost per unit (VC).
- Determine the selling price per unit (P).
- Calculate contribution margin per unit (CM) and contribution margin ratio (CMR).
- Apply the BEP formulas to find the break‑even level of output (units) and the break‑even sales value (£).
- Calculate the margin of safety (units or £) and interpret its significance.
- Use the profit formula to estimate profit at any expected output level.
- Sketch a break‑even chart, clearly labeling the BEP, profit area, and margin‑of‑safety area.
- Remember the assumptions and limitations before using the results for decision‑making.