Unit 5.3 — Bases of cost allocation (costing & break-even)
Learning outcomes (from the 9587 syllabus). This note is complete when every bullet below is covered.
Learning outcomes
- Classification of costs: fixed and variable; direct and indirect
- Importance of costing: pricing decisions, calculating profits, determining resource requirements at different output levels, make-or-buy decisions
- Approaches to costing: full costing (uses and limitations); marginal costing (explanation, situations used, limitations)
- Break-even analysis: calculation and interpretation of break-even quantity, break-even point, margin of safety and profit; uses and limitations
Running example: Swift Logistics charges $10 per parcel delivery. Variable cost per delivery is $4; fixed costs are $120,000 a month.
Big picture
In plain English: costing is knowing how much it costs to make each unit, so the business can set prices, measure profit and make decisions. Break-even analysis finds the sales level where the business just covers its costs (no profit, no loss).
Analogy: break-even is the point where your income exactly equals your spending — like a stall that must sell 50 drinks to cover the day’s rent and ingredients before it starts making money.
Core content
1. Classifying costs
| Classification | Meaning | Example |
|---|---|---|
| Fixed costs | Do not change with output | Rent, salaries, van leases |
| Variable costs | Change directly with output | Fuel, packaging, delivery wages per parcel |
| Direct costs | Directly traceable to a product | Ingredients, delivery fuel |
| Indirect costs (overheads) | Cannot be traced to one product | Rent, admin salaries, electricity |
Swift’s fixed costs are its depot rent and manager salaries (same whether it delivers 1,000 or 10,000 parcels). Its variable costs are fuel and packaging (rise with each parcel). Fuel for delivery is a direct cost; the depot’s electricity is an indirect cost.
2. The importance of costing
Cost information is used for:
- Pricing decisions — price must cover costs.
- Calculating profits — profit = revenue − costs.
- Determining resource needs at different output levels — how much money, staff and materials are needed.
- Make-or-buy decisions — whether to make a component or buy it in.
3. Approaches to costing
- Full costing — allocates all costs
(fixed + variable) to the product, so price covers everything.
- Uses: pricing to cover total costs, measuring full profit.
- Limitations: allocating fixed (overhead) costs to products is somewhat arbitrary.
- Marginal (contribution) costing — charges only
variable costs to the product; the
contribution is what each unit contributes toward fixed
costs and profit.
- Contribution per unit = selling price − variable cost per unit
- Uses: short-term decisions — special orders, make-or-buy, whether to accept a low-price order.
- Limitations: ignores fixed costs, so it is unsuitable for long-term pricing.
Swift’s delivery: price $10, variable cost $4, so contribution = $6 per parcel. For a special one-off bulk order at $6 per parcel, marginal costing says accept it (it still adds $2 contribution above variable cost), even though it does not cover fixed costs — a short-term decision.
4. Break-even analysis
Break-even point = the output where total revenue = total cost (zero profit).
- Break-even quantity = Fixed costs ÷ Contribution per unit
- Margin of safety = actual output − break-even output (how far sales can fall before a loss).
- Profit = Total contribution − Fixed costs (or total revenue − total cost).
Swift: contribution $6 per parcel, fixed costs $120,000. - Break-even quantity = 120,000 ÷ 6 = 20,000 parcels/month. - If actual deliveries are 30,000, margin of safety = 30,000 − 20,000 = 10,000 parcels. - Profit = (30,000 × $6) − $120,000 = $180,000 − $120,000 = $60,000.
Uses and limitations of break-even:
- Uses: simple to understand; helps set sales targets and prices; shows margin of safety.
- Limitations: assumes costs and prices stay the same (linear), assumes all output is sold, and is less accurate with multiple products.
Analysis & evaluation points (AO3/AO4)
- Full vs marginal costing trade-off: full costing is right for long-term pricing, marginal costing for short-term decisions — using the wrong one leads to bad decisions.
- Break-even is a simplification — real costs are not perfectly fixed or variable, and prices change.
- A high margin of safety is reassuring but may mean the business is not being ambitious enough.
- Lowering price raises break-even — cutting price increases sales needed to break even.
Language bank: however · on balance · it depends on · trade-off ·
Worked examples (PEEL)
PEEL = Point → Explain → Example → Link. Use this structure for every written answer. For calculations, always show the formula first.
Worked example 1 — “Calculate” (6 marks)
Question: A business has fixed costs of $80,000, a selling price of $20 and variable cost of $12 per unit. Calculate the break-even quantity.
- Formula: Break-even quantity = Fixed costs ÷ (Price − Variable cost)
- Substitute: = 80,000 ÷ (20 − 12) = 80,000 ÷ 8
- Answer: = 10,000 units
- Interpret: The business must sell 10,000 units to cover all its costs.
Worked example 2 — “Evaluate” (10 marks)
Question: Evaluate the usefulness of break-even analysis to a business.
- P (Point): Break-even analysis helps set targets and prices.
- E (Explain): It shows the minimum sales needed to avoid a loss and the margin of safety, so managers can set sales targets and judge whether a price covers costs.
- E (Example): Swift knows it must deliver at least 20,000 parcels a month to break even, and targets 30,000 for a safety margin.
- L (Link): This guides planning and reduces risk.
- Evaluate (AO4): However, break-even relies on simplifying assumptions — constant prices and costs, and all output sold — which rarely hold in reality. On balance, it is a useful planning tool but must be used with judgement and updated as costs and prices change.
Application bank (Singapore quick reference)
| Idea | Singapore example |
|---|---|
| Costing for pricing | Hawkers pricing dishes to cover ingredient and rental costs |
| Make-or-buy | Restaurants deciding whether to make or buy sauces |
| Break-even | New F&B outlets calculating the daily sales needed to cover rent |
| Fixed vs variable | F&B: rent (fixed) vs ingredients (variable) |
Exam technique
- How it appears: a data-response or case study gives cost/price data and asks for break-even, margin of safety or profit — or asks which costing approach to use.
- Model skeleton for calculations: formula → substitute → answer → interpret in the business’s context.
- Common pitfalls: confusing fixed and variable costs; forgetting to subtract variable cost to get contribution; not interpreting the answer.
Self-test checklist
Essay practice: “Evaluate the view that break-even analysis is of little value to a modern business.” (25 marks)