3.3 — Costs and Revenues

PART A: UNDERSTANDING COSTS

Definition

Costs are the expenditures incurred by a business in producing and selling goods or services. Understanding costs is essential for pricing decisions, break-even analysis, profitability assessment, and strategic planning.

Why Understanding Costs Matters

PART B: CLASSIFICATION OF COSTS

1. Fixed Costs vs Variable Costs

This is the most fundamental cost classification for business analysis.

Fixed Costs

Definition: Costs that do NOT change with the level of output or sales in the short term. They remain constant regardless of how much is produced.

Also called: Overhead costs, indirect costs (sometimes)

Characteristics of Fixed Costs

Examples of Fixed Costs

Fixed Costs — Graphical Representation

Total Cost ($)
    │
    │
    │ ─────────────────────────── Fixed Cost (horizontal line)
    │
    │
    └────────────────────────────────── Output (units)

The total fixed cost line is horizontal — it doesn't change with output.

Fixed Cost Per Unit

Key insight: As output increases, fixed cost is spread over more units, reducing the fixed cost per unit. This is the basis of economies of scale.

Variable Costs

Definition: Costs that change in direct proportion to the level of output or sales. If output doubles, total variable costs double.

Also called: Direct costs (often, but not always the same)

Characteristics of Variable Costs

Examples of Variable Costs

Variable Costs — Graphical Representation

Total Cost ($)
    │                            /
    │                          /
    │                        /
    │                      / Variable Cost (upward sloping line from origin)
    │                    /
    │                  /
    │                /
    │              /
    │            /
    │          /
    │        /
    │      /
    │    /
    │  /
    │/
    └────────────────────────────────── Output (units)

The total variable cost line starts at the origin and slopes upward proportionally.

Variable Cost Per Unit

Key insight: Variable cost per unit remains constant; total variable cost increases proportionally with output.

Fixed vs Variable Costs — Summary

Semi-Variable (Mixed) Costs

Definition: Costs that have both a fixed and variable component. They change with output but not in direct proportion.

Also called: Semi-fixed costs, mixed costs

Examples of Semi-Variable Costs

Semi-Variable Costs — Graphical Representation

Total Cost ($)
    │                            /
    │                          /
    │                        /
    │                      /
    │                    /
    │──────────────────/──────── Fixed component
    │                /
    │              /
    │            /
    │          /
    │        /
    │      /
    │    /
    │  /
    │/
    └────────────────────────────────── Output (units)

The line starts above zero (fixed component) and slopes upward (variable component).

Stepped Fixed Costs

Definition: Costs that are fixed within a certain range of output but increase in steps when capacity thresholds are crossed.

Examples of Stepped Fixed Costs

Stepped Fixed Costs — Graphical Representation

Total Cost ($)
    │                              ┌──────────
    │                              │
    │                    ┌─────────┘
    │                    │
    │          ┌─────────┘
    │          │
    │ ─────────┘
    │
    └────────────────────────────────── Output (units)

Costs are fixed within ranges but jump up at capacity thresholds.

2. Direct Costs vs Indirect Costs

This classification focuses on whether costs can be directly traced to specific products, services, or departments.

Direct Costs

Definition: Costs that can be directly attributed and traced to a specific product, service, job, or cost centre.

Examples of Direct Costs

Characteristics

Indirect Costs

Definition: Costs that cannot be directly traced to a specific product or service; they support the business overall.

Also called: Overhead costs

Examples of Indirect Costs

Types of Overheads

Characteristics

Direct vs Indirect — Summary

Relationship Between Classifications

Note: The two classifications (fixed/variable and direct/indirect) are independent. A cost can be:

• Direct and Variable (raw materials)

• Direct and Fixed (salary of worker dedicated to one product)

• Indirect and Fixed (factory rent)

• Indirect and Variable (factory electricity based on usage)

PART C: TOTAL COSTS

Calculating Total Costs

Total Cost = Fixed Costs + Variable Costs

Or equivalently:

Total Cost = Fixed Costs + (Variable Cost Per Unit × Quantity)

$TC = FC + (VC \times Q)$

Where:

• TC = Total Cost

• FC = Total Fixed Costs

• VC = Variable Cost per unit

• Q = Quantity produced

Example Calculation

A business has:

• Fixed costs: $50,000 per month

• Variable cost per unit: $8

• Production: 10,000 units

Total Cost = $50,000 + ($8 × 10,000) Total Cost = $50,000 + $80,000 Total Cost = $130,000

Total Cost — Graphical Representation

Total Cost ($)
    │                                    /
    │                                  /
    │                                /
    │                              /
    │                            / Total Cost
    │                          /
    │                        /
    │                      /
    │                    /
    │                  /
    │                /
    │              /
    │            / Variable Costs
    │          /
    │        /
    │      /
    │────/───────────────────────────── Fixed Costs
    │  /
    │/
    └────────────────────────────────── Output (units)

The total cost line:

• Starts at the level of fixed costs (not at zero)

• Slopes upward at the rate of variable cost per unit

Average Cost (Cost Per Unit)

Average Cost = Total Cost ÷ Quantity

$AC = \frac{TC}{Q} = \frac{FC + (VC \times Q)}{Q} = \frac{FC}{Q} + VC$

Example Calculation

Using the previous example:

• Total Cost = $130,000

• Quantity = 10,000 units

Average Cost = $130,000 ÷ 10,000 = $13.00 per unit

Breaking it down:

• Fixed cost per unit = $50,000 ÷ 10,000 = $5.00

• Variable cost per unit = $8.00

• Average cost per unit = $5.00 + $8.00 = $13.00

How Average Cost Changes with Output

Key insight: Average cost falls as output increases because fixed costs are spread over more units. This is the source of economies of scale.

PART D: REVENUE

Definition

Revenue (also called sales revenue, turnover, or sales) is the total income received by a business from selling its goods or services.

Calculating Revenue

Total Revenue = Selling Price × Quantity Sold

$TR = P \times Q$

Where:

• TR = Total Revenue

• P = Selling Price per unit

• Q = Quantity sold

Example Calculation

A business sells:

• 10,000 units

• At $20 each

Total Revenue = $20 × 10,000 = $200,000

Revenue — Graphical Representation

Revenue ($)
    │                                    /
    │                                  /
    │                                /
    │                              /
    │                            / Total Revenue
    │                          /
    │                        /
    │                      /
    │                    /
    │                  /
    │                /
    │              /
    │            /
    │          /
    │        /
    │      /
    │    /
    │  /
    │/
    └────────────────────────────────── Quantity Sold

The revenue line:

• Starts at the origin (zero sales = zero revenue)

• Slopes upward at the rate of the selling price

Types of Revenue

Revenue Streams

Many businesses have multiple revenue streams:

Revenue Recognition

Key principle: Revenue should be recognised when it is earned, not necessarily when cash is received.

PART E: PROFIT

Basic Profit Calculation

Profit = Total Revenue − Total Costs

$Profit = TR - TC$

Or:

$Profit = (P \times Q) - FC - (VC \times Q)$

Example Calculation

Using previous examples:

• Revenue = $200,000 (10,000 units × $20)

• Total Costs = $130,000 (FC $50,000 + VC $80,000)

Profit = $200,000 − $130,000 = $70,000

Contribution

Definition: The amount each unit sold contributes toward covering fixed costs and generating profit.

Contribution per unit = Selling Price − Variable Cost per unit

$Contribution = P - VC$

Total Contribution = Contribution per unit × Quantity

Or:

Total Contribution = Total Revenue − Total Variable Costs

Example

• Selling price = $20

• Variable cost = $8

Contribution per unit = $20 − $8 = $12

For 10,000 units: Total Contribution = $12 × 10,000 = $120,000

Contribution and Profit

Profit = Total Contribution − Fixed Costs

From the example: Profit = $120,000 − $50,000 = $70,000 ✓

Why Contribution Matters

PART F: COST-VOLUME-PROFIT RELATIONSHIPS

Key Relationships

Combined Graph

$ 
    │                              / TR (Revenue)
    │                            /
    │                          /
    │                        / ←── Profit zone
    │                      /
    │                    /
    │                  / ←────────── Break-even point
    │                /
    │              /╱ TC (Total Cost)
    │            /╱
    │          /╱ ←── Loss zone
    │        /╱
    │      /╱
    │    /╱
    │──/╱─────────────────────────── FC (Fixed Cost)
    │/╱
    │/
    └────────────────────────────────── Output/Sales (units)

• Below break-even: Loss (TC > TR)

• At break-even: Neither profit nor loss (TC = TR)

• Above break-even: Profit (TR > TC)

PART G: PRACTICAL APPLICATIONS

Cost Behaviour and Decision-Making

Cost Control Strategies

Margin of Safety

Definition: The amount by which actual or expected sales exceed break-even sales.

Margin of Safety = Actual Sales − Break-even Sales

Margin of Safety % = (Margin of Safety ÷ Actual Sales) × 100%

Covered in detail in Unit 5.5 (Break-even analysis)

PART H: EXAM APPLICATION

Potential Exam Questions

1. "Analyse the difference between fixed costs and variable costs." (10 marks)

2. "Evaluate the importance of understanding cost behaviour for business decision-making." (10 marks)

3. "Discuss how a business might use contribution analysis to make product decisions." (10 marks)

4. "Examine the relationship between output levels and average cost per unit." (10 marks)

5. "To what extent should a business accept a special order priced below full cost?" (10 marks)

6. "Analyse the difference between direct and indirect costs." (10 marks)

Key Definitions to Memorise

Key Formulas

Evaluation Frameworks

When discussing costs:

• "The behaviour of costs depends on the time horizon — in the long run, all costs are variable..."

• "Understanding cost behaviour is essential for accurate pricing and profitability..."

• "The classification of costs depends on the purpose of the analysis..."

• "Fixed costs create risk — they must be paid regardless of sales..."

When discussing contribution:

• "Contribution analysis is useful for short-term decisions but ignores fixed costs..."

• "A product with positive contribution adds value, even if not covering full costs..."

• "In the short term, any contribution above variable cost helps cover fixed costs..."