classify and calculate costs using examples, e.g. fixed, variable, average and total

4.4.1 Identify, Classify and Use Costs

Learning Objectives

• Define the main types of costs used in business decision‑making.
• Classify costs as fixed, variable, average or total.
• Calculate total and average costs from given data.
• Explain economies and diseconomies of scale.
• Perform a break‑even analysis (including margin of safety and limitations).
• Apply cost classification to real‑world business decisions.

Quick‑Reference Box (Cambridge wording)

Key Definitions & Formulae

• Fixed Cost (FC) – unchanged as output varies (within the relevant range).
• Variable Cost (VC) – changes in direct proportion to the number of units produced.
• Total Cost (TC) – sum of all costs incurred in producing a given level of output.
  TC = FC + VC
• Average Cost (AC) – cost per unit of output.
  AC = TC ÷ Q
• Contribution per unit – price less variable cost per unit.
  Contribution = P – VC per unit
• Break‑Even Point (BEP) – output at which total revenue equals total cost.
  BEP = FC ÷ Contribution
• Margin of Safety (MoS) – how far sales can fall before the business reaches the BEP.
  MoS = (Expected sales – BEP) ÷ Expected sales × 100 %
• Economies of Scale – fall in AC as output rises, usually because fixed costs are spread over more units or because of bulk purchasing, specialised equipment, etc.
• Diseconomies of Scale – rise in AC when output becomes very large, often due to coordination problems, bureaucracy, or over‑use of resources.

Classification Table (Manufacturing Example)

Note (Extension)

Semi‑variable (mixed) costs contain a fixed component plus a variable component (e.g., telephone bill = £30 fixed + £0.02 per minute). They are useful for deeper analysis but are not required for the core IGCSE syllabus.

Worked Example 1 – Total and Average Cost

Scenario: ABC Ltd produces T‑shirts. Monthly cost data:

• Fixed rent: £4,000
• Variable cost per T‑shirt (fabric + labour): £3
• Electricity (semi‑variable): £200 fixed + £0.05 per T‑shirt

Calculate total cost and average cost for 2,000 T‑shirts.

Solution

1. Variable cost: VC = £3 × 2,000 = £6,000
2. Electricity (treated as semi‑variable): SC = £200 + (£0.05 × 2,000) = £300
3. Total cost: TC = FC + VC + SC = £4,000 + £6,000 + £300 = £10,300
4. Average cost per T‑shirt: AC = £10,300 ÷ 2,000 = £5.15

Worked Example 2 – Break‑Even Analysis

Scenario: XYZ Co. sells a handmade candle for £12 each.

• Fixed costs per month: £3,600 (rent, salaries, depreciation)
• Variable cost per candle: £5 (wax, wick, labour)

Determine:

• Break‑even output
• Margin of safety if the company expects to sell 800 candles
• One limitation of the analysis

Solution

1. Contribution per unit = £12 – £5 = £7
2. Break‑even output: BEP = £3,600 ÷ £7 ≈ 514 units
3. Margin of safety (units) = 800 – 514 = 286 units
4. Margin of safety (%) = 286 ÷ 800 × 100 ≈ 35.8 %
5. Limitation: The calculation assumes that both the selling price and the variable cost per unit remain constant. In reality they may change (e.g., bulk discounts, price promotions).

Decision‑Making Case Study (Use of Cost Data)

Company: GreenTech Ltd manufactures solar‑powered garden lights.

Situation: The business is considering whether to introduce a new “deluxe” model that uses a larger battery. The management team has the following cost information:

Task for students:

1. Calculate the total cost of producing 1,000 standard units and 1,000 deluxe units.
2. Assuming the selling price is £12 for the standard model and £15 for the deluxe model, compute the contribution per unit for each.
3. Identify which model gives the higher contribution margin and discuss what this tells the manager about which product to prioritise.
4. Explain one non‑financial factor (e.g., brand image, production complexity) that could affect the final decision.

This case study links the classification of costs directly to a realistic business decision – a requirement of the syllabus.

Economies & Diseconomies of Scale

When a business expands output, the average cost per unit can change:

• Economies of scale (costs fall)
  • Bulk buying of raw materials → lower per‑unit purchase price.
  • Specialised machinery that produces more units faster.
  • Spreading administrative overhead over a larger output.
• Diseconomies of scale (costs rise)
  • More supervisory layers → higher admin cost per unit.
  • Longer communication lines causing delays.
  • Over‑use of equipment leading to more breakdowns and maintenance.

Practice Item – Scale of Production

“A small bakery buys flour at £0.30 per kg when it purchases 100 kg a month. When it increases purchases to 500 kg, the price falls to £0.25 per kg. Explain which type of scale this illustrates and why it matters for pricing decisions.”

Using Cost Data for Decision‑Making (Summary)

Cost classification helps managers answer questions such as:

• Should we increase production to achieve economies of scale?
• Is a new product financially viable (break‑even analysis)?
• Which costs can be reduced without affecting output (focus on variable costs)?
• How does the margin of safety affect risk assessment?

Practice Questions

1. Classify each cost as Fixed, Variable or Semi‑Variable:
   • Insurance premium of £1,200 per year.
   • Wages paid at £8 per hour, with 5 hours required to make one unit.
   • Telephone bill: £30 fixed + £0.02 per minute of call.
2. A bakery incurs the following costs in a week:
   • Rent: £800
   • Flour: £0.40 per loaf
   • Electricity: £150 fixed + £0.10 per loaf
   If the bakery produces 1,500 loaves, calculate:
   • Total cost
   • Average cost per loaf
3. Using the candle data from Worked Example 2, calculate the break‑even point if the selling price is reduced to £10 while the variable cost remains £5.
4. Explain one possible diseconomy of scale that a fast‑growing clothing manufacturer might face.

Answers to Practice Questions

1. • Insurance premium – Fixed
   • Wages – Variable (cost varies with the number of units produced)
   • Telephone bill – Semi‑Variable

2. Variable cost (flour): VC = £0.40 × 1,500 = £600

   Semi‑variable electricity: SC = £150 + (£0.10 × 1,500) = £150 + £150 = £300

   Total cost: TC = £800 + £600 + £300 = £1,700

   Average cost per loaf: AC = £1,700 ÷ 1,500 ≈ £1.13

3. New contribution per unit = £10 – £5 = £5

   Break‑even output = £3,600 ÷ £5 = 720 units

4. Example of diseconomy: As output rises, the clothing manufacturer may need several supervisory layers, leading to slower decision‑making and higher administrative cost per unit.

Suggested Diagram

Summary Checklist

• Fixed costs remain unchanged as output varies (within the relevant range).
• Variable costs change in direct proportion to output.
• Total Cost = Fixed Cost + Variable Cost.
• Average Cost = Total Cost ÷ Quantity produced.
• Break‑Even Point = Fixed Cost ÷ (Price per unit – Variable cost per unit).
• Margin of safety shows how far sales can fall before a loss occurs.
• Economies of scale lower average cost; diseconomies of scale raise it.
• Cost data underpin pricing, production, and expansion decisions.

Extension Activity

Using real data from a small business (e.g., a local café, online shop, or family‑run workshop), create a table that classifies at least six different cost items as fixed or variable. Then:

1. Calculate total and average cost for a chosen level of output.
2. Perform a break‑even analysis based on a realistic selling price.
3. Write a brief paragraph discussing how the cost structure influences the business’s pricing strategy and its ability to achieve economies of scale.