Costs, scale of production and break-even analysis
| Example |
|---|
| Rent, insurance, salaries of permanent staff. |
| Raw materials, packaging, direct labour (if paid per unit). |
| TC = FC + VC |
| AC = \frac{TC}{Q} |
Contribution (C) is the amount of money left over from sales revenue after variable costs have been deducted. This remainder contributes towards paying off fixed costs and then generating profit.
Formula:
C = P - V
Where:
- P = Selling Price per unit
- V = Variable Cost per unit
Correct Reasoning: A business should continue production as long as the selling price (P) is greater than the variable cost per unit (V). Even if the business is making an overall loss (because P < AC), continuing to produce allows it to generate a positive contribution (C > 0). This contribution helps pay for some of the fixed costs, reducing the total loss compared to shutting down completely (where the loss would equal all fixed costs).
Examiner Acceptance: Look for phrases like 'price covers variable costs' or 'positive contribution reduces losses'. Examiners accept this because it demonstrates an understanding that fixed costs are unavoidable in the short term, so the focus must be on maximizing cash flow from sales.
The Correction: In the short term, a business should only stop if P < V (i.e., contribution is negative). If P > V, the business loses less money by continuing to produce than by shutting down. Do not confuse long-term viability with short-term cash flow decisions.
Diseconomies of scale occur when the long-run average cost per unit (AC) rises as the business grows too large.
| Explanation & Example |
|---|
| Large businesses buy raw materials in bulk, negotiating bulk discounts or lower prices per unit from suppliers. |
| Large firms can afford expensive, specialized machinery that increases efficiency and lowers the average cost per unit (e.g., automated assembly lines). |
| Large businesses are seen as less risky by banks and investors, allowing them to borrow money at lower interest rates than small businesses. |
| Large firms can employ specialist managers (e.g., a dedicated marketing director or IT expert) who improve efficiency, whereas small firms rely on generalists. |
| The cost of advertising is spread over a larger number of units. A large campaign costs the same regardless of whether they sell 1,000 or 10,000 units, lowering the average marketing cost per unit. |
| As layers of management are added, information takes longer to pass down and feedback takes longer to reach top management. This leads to delays and errors in decision-making. |
| Different departments (e.g., production and sales) may work at cross-purposes or fail to coordinate effectively, leading to duplication of effort or stockouts. |
| Employees in very large firms may feel like a 'small cog in a big machine'. This leads to lower motivation, higher staff turnover, and reduced productivity. |
Break-even output is the level of production and sales where Total Revenue (TR) equals Total Costs (TC). At this point, the business makes neither profit nor loss.
Formula:
Q_{BE} = \frac{FC}{P - V}
Where:
- Q_{BE} = Break-even quantity (units)
- FC = Total Fixed Costs
- P = Selling Price per unit
- V = Variable Cost per unit
- (P - V) = Contribution per unit
A break-even chart visually represents the relationship between costs and revenue.
Key Lines to Draw:
- Fixed Cost Line: A horizontal straight line at the value of FC (it does not change with output).
- Total Cost Line: Starts at the fixed cost level on the Y-axis and slopes upwards. The slope is determined by the variable cost per unit (V). Formula: TC = FC + (V \times Q).
- Total Revenue Line: Starts at the origin (0,0) and slopes upwards. The slope is determined by the selling price (P). Formula: TR = P \times Q.
Interpretation:
- The point where the Total Revenue line crosses the Total Cost line is the Break-Even Point.
- To the right of this point, the business makes a Profit (TR > TC).
- To the left of this point, the business makes a Loss (TC > TR).
Margin of Safety is the amount by which current (or expected) sales exceed the break-even output. It measures the risk level; a larger margin means lower risk.
Formula:
\text{Margin of Safety} = Q_{current} - Q_{BE}
Where:
- Q_{current} = Current or expected sales output
- Q_{BE} = Break-even output
Correct Reasoning:
- Higher Price (P increases): Contribution (P-V) increases. This lowers the break-even output (Q_{BE}), meaning the business needs to sell fewer units to cover costs. However, it may reduce demand.
- Lower Variable Costs (V decreases): Contribution (P-V) increases. This also lowers the break-even output and increases profit per unit.
Examiner Acceptance: Examiners look for the phrase 'break-even point shifts to the left' or 'lower break-even quantity'. They accept this because it directly links the mathematical change in variables to the strategic outcome of reduced risk.
The Correction: Break-even output is measured in units (quantity). Break-even revenue is measured in currency. Ensure you read the command word carefully: 'Calculate break-even output' requires units, not money.
- Assumes all output is sold: It ignores inventory holding costs and the risk of unsold stock.
- Fixed costs are constant: In reality, fixed costs may step up (e.g., needing a new factory) if production exceeds a certain capacity.
(a) The break-even output.
(b) The margin of safety if current sales are 800 units. [4]
Q_{BE} = \frac{10,000}{50 - 30} = \frac{10,000}{20} = 500 \text{ units}
(b) Margin of Safety:
\text{Margin} = 800 - 500 = 300 \text{ units}
The business should choose Product B.
Justification:
- Product B has a lower break-even output (500 vs 1,000 units).
- This means Product B requires fewer sales to cover costs, reducing the risk of loss.
- It also implies a higher margin of safety for any given level of sales compared to Product A.