limitations of break-even analysis

4.2.3 Break‑Even Analysis – Definition, Calculations, Chart & Limitations

Learning Objective

Students will be able to:

• Define the break‑even point (BEP) and related terminology.
• Calculate BEP in units and in £, the contribution margin ratio and the margin of safety.
• Construct and interpret a break‑even chart.
• Use break‑even information to answer short‑run “what‑if” questions.
• Evaluate at least three limitations of the technique (AO4).

1. Definition of the Break‑Even Point

The break‑even point (BEP) is the level of activity (units or turnover) at which total revenue equals total cost. At this point the business makes neither profit nor loss.

2. Key Concepts

3. Formulae

• Break‑even output (units) \[ \text{BEP}_{\text{units}}=\frac{FC}{SP-VC}=\frac{FC}{C} \]
• Break‑even turnover (£) \[ \text{BEP}_{\£}= \frac{FC}{\text{CMR}} \]
• Contribution margin ratio \[ \text{CMR}= \frac{SP-VC}{SP} \]
• Margin of safety – see key concepts.

4. Worked Example (AO2 – calculation)

1. Contribution per unit: \(C = 25-15 = £10\).
2. Contribution margin ratio: \(\text{CMR}= \dfrac{10}{25}=0.40\; (40\%)\).
3. Break‑even units: \(\text{BEP}_{\text{units}} = \dfrac{30 000}{10}=3 000\) units.
4. Break‑even turnover: \(\text{BEP}_{\£}= \dfrac{30 000}{0.40}=£75 000\).
5. Margin of safety (units): \(2 500-3 000 = -500\) units (a shortfall).
6. Margin of safety (%): \(\dfrac{-500}{2 500}\times100 = -20\%\).

5. Constructing a Break‑Even Chart (AO3 – interpretation)

Steps

1. Draw a vertical axis (cost / revenue in £) and a horizontal axis (output in units).
2. Plot the Fixed‑Cost line: a horizontal line at £30 000.
3. Plot the Total‑Cost (TC) line: start at £30 000 and add the variable cost slope (VC × units).
   For the example: points (0, 30 000) and (5 000, 30 000 + 5 000 × 15 = £105 000).
4. Plot the Total‑Revenue (TR) line: start at the origin and use the selling‑price slope (SP × units).
   Points (0, 0) and (5 000, 5 000 × 25 = £125 000).
5. The intersection of TC and TR is the **break‑even point** (3 000 units, £75 000). Mark it and label the axes.
6. Shade the area to the right of the BEP (profit) and to the left (loss).

6. “What‑If” Decision Scenarios (AO2/AO3)

Practice task – complete the chart

Given: FC = £30 000, SP = £25, VC = £15.

1. Calculate the total cost and total revenue for output levels 0, 1 000, 2 000, 3 000, 4 000 units.
2. Enter the values in the table below and sketch the corresponding TC and TR lines on graph paper. Mark the break‑even point.

7. Limitations of Break‑Even Analysis (AO4 – evaluation)

8. Summary Checklist for Exams

• State a concise definition of the break‑even point.
• List and define FC, VC, SP, contribution per unit, contribution margin ratio and margin of safety.
• Write the correct formulae for:
  • Break‑even units
  • Break‑even turnover (£)
  • Contribution margin ratio
  • Margin of safety (units and %)
• Show a full worked calculation (including C, CMR, BEP units, BEP £, MoS).
• Sketch a labelled break‑even chart (fixed cost, total cost, total revenue, BEP, profit/loss areas).
• Answer a “what‑if” question – change price, fixed cost or variable cost and recalculate the BEP.
• List at least three limitations, explain why each matters and comment on the likely effect on managerial decisions.

Conclusion

Break‑even analysis gives a clear, quantitative picture of the relationship between cost, volume and profit, making it valuable for short‑run pricing and production decisions. However, its reliance on simplifying assumptions (linear costs, single product, constant price, no time factor, and exclusion of qualitative factors) means that managers must use it alongside other quantitative tools and sound business judgement to reflect the complexity of real‑world environments.