5.3 — Break-Even Analysis

PART A: INTRODUCTION TO BREAK-EVEN ANALYSIS

Definition

Break-even analysis is a technique used to determine the point at which total revenue equals total costs — the point at which a business makes neither profit nor loss.

Purpose of Break-Even Analysis

Key Assumptions

Break-even analysis relies on several simplifying assumptions:

PART B: COST CONCEPTS REVIEW

Fixed Costs (FC)

Definition: Costs that do not change with the level of output in the short term.

Variable Costs (VC)

Definition: Costs that change in direct proportion to the level of output.

Total Costs (TC)

Definition: The sum of all fixed and variable costs.

$Total\ Costs = Fixed\ Costs + Total\ Variable\ Costs$

$TC = FC + (VC\ per\ unit \times Quantity)$

Revenue

Definition: The income received from selling goods or services.

$Total\ Revenue = Selling\ Price \times Quantity\ Sold$

$TR = P \times Q$

Profit

Definition: The surplus remaining after total costs are deducted from total revenue.

$Profit = Total\ Revenue - Total\ Costs$

$Profit = TR - TC$

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

PART C: CONTRIBUTION

Definition

Contribution is the amount each unit sold contributes toward covering fixed costs and then generating profit.

Contribution Per Unit

$Contribution\ Per\ Unit = Selling\ Price - Variable\ Cost\ Per\ Unit$

$Contribution = P - VC$

Total Contribution

$Total\ Contribution = Contribution\ Per\ Unit \times Quantity\ Sold$

$Total\ Contribution = (P - VC) \times Q$

Relationship to Profit

$Profit = Total\ Contribution - Fixed\ Costs$

Why Contribution Matters

Example: Contribution Calculation

Interpretation: Each unit sold contributes $20 toward fixed costs and profit.

PART D: BREAK-EVEN POINT CALCULATION

Break-Even Point (BEP)

Definition: The level of output (or sales) at which total revenue equals total costs — no profit, no loss.

At break-even: $Total\ Revenue = Total\ Costs$ $Profit = 0$

Break-Even Formula (Units)

$Break\text{-}Even\ Point\ (units) = \frac{Fixed\ Costs}{Contribution\ Per\ Unit}$

$BEP = \frac{FC}{P - VC}$

Break-Even Formula (Revenue)

$Break\text{-}Even\ Revenue = Break\text{-}Even\ Units \times Selling\ Price$

Or:

$Break\text{-}Even\ Revenue = \frac{Fixed\ Costs}{Contribution\ Margin\ Ratio}$

Where:

$Contribution\ Margin\ Ratio = \frac{Contribution\ Per\ Unit}{Selling\ Price}$

Example: Break-Even Calculation

Step 1: Calculate Contribution Per Unit

Contribution = 50 - 30 = $20

Step 2: Calculate Break-Even Point

$BEP = \frac{100,000}{20} = 5,000\ units$

Step 3: Calculate Break-Even Revenue

Break\text{-}Even\ Revenue = 5,000 \times 50 = $250,000

Interpretation: The business must sell 5,000 units (or generate $250,000 in revenue) to break even.

Verification

PART E: TARGET PROFIT

Definition

Target profit analysis calculates the output level needed to achieve a specific profit goal.

Formula

$Units\ for\ Target\ Profit = \frac{Fixed\ Costs + Target\ Profit}{Contribution\ Per\ Unit}$

Example: Target Profit Calculation

Using the previous example, if the business wants to earn $50,000 profit:

$Units = \frac{100,000 + 50,000}{20} = \frac{150,000}{20} = 7,500\ units$

Verification:

PART F: MARGIN OF SAFETY

Definition

The margin of safety is the difference between actual (or expected) sales and the break-even point — how much sales can fall before losses occur.

Formulas

In units:

$Margin\ of\ Safety\ (units) = Actual\ Sales - Break\text{-}Even\ Sales$

In revenue:

Margin\ of\ Safety\ ($) = Actual\ Revenue - Break\text{-}Even\ Revenue

As a percentage:

$Margin\ of\ Safety\ ($

Example: Margin of Safety

Margin of Safety (units):

$MoS = 7,000 - 5,000 = 2,000\ units$

Margin of Safety (%):

$MoS\$

Interpretation: Sales can fall by 2,000 units (28.6%) before the business makes a loss.

Interpreting Margin of Safety

PART G: BREAK-EVEN CHARTS

Definition

A break-even chart is a graphical representation of the relationship between costs, revenue, and output, showing the break-even point visually.

Components of a Break-Even Chart

Drawing a Break-Even Chart

Revenue/
Costs ($)
    │
    │                              TR (Total Revenue)
    │                            /
    │                          /   PROFIT
    │                        /     AREA
    │                      / •────────── Break-Even Point
    │                    /  /
    │                  /  / TC (Total Costs)
    │                /  /
    │              /  /
    │            /  /
    │          /  /
    │        /  /    LOSS
    │      /  /      AREA
    │    /  /
    │  /  /
    │/ ──────────────────────────── FC (Fixed Costs)
    │
    └──────────────────────────────────────────► Output (units)
                        ↑
                   Break-Even
                    Quantity

Steps to Draw a Break-Even Chart

Example: Plotting Key Points

Plotting Points:

Reading a Break-Even Chart

Profit-Volume Chart (Alternative)

A simpler chart showing profit/loss directly:

Profit ($)
    │
    │                    /
    │                  /
    │                /
    │──────────────•─────────────────► Output (units)
    │            /  ↑
    │          /    Break-Even Point
    │        /
    │      /
    │    /
Loss ($)

PART H: CHANGES IN VARIABLES

Impact of Changes on Break-Even Point

Example: Impact of Price Change

Original situation:

• Fixed costs: $100,000

• Variable cost: $30

• Selling price: $50

• Contribution: $20

• BEP: 5,000 units

If price increases to $55:

• New contribution: $55 − $30 = $25

• New BEP: $100,000 ÷ $25 = 4,000 units

If price decreases to $45:

• New contribution: $45 − $30 = $15

• New BEP: $100,000 ÷ $15 = 6,667 units

Example: Impact of Cost Change

If fixed costs increase to $120,000:

• BEP: $120,000 ÷ $20 = 6,000 units

If variable costs increase to $35:

• New contribution: $50 − $35 = $15

• BEP: $100,000 ÷ $15 = 6,667 units

Showing Changes on a Break-Even Chart

When variables change, lines shift:

PART I: LIMITATIONS OF BREAK-EVEN ANALYSIS

Key Limitations

Overcoming Limitations

PART J: EXAM APPLICATION

Potential Exam Questions

1. "Calculate the break-even point and margin of safety for the proposed product." (10 marks)

2. "Analyse the impact of a 10% increase in variable costs on the break-even point." (10 marks)

3. "Evaluate the usefulness of break-even analysis for a new business." (10 marks)

4. "Discuss the limitations of break-even analysis for decision-making." (10 marks)

5. "Using a break-even chart, explain the effect of increasing fixed costs." (10 marks)

6. "Calculate the number of units needed to achieve a target profit of $X." (10 marks)

Key Definitions to Memorise

Key Formulas

Exam Calculation Tips

Evaluation Frameworks

When discussing break-even analysis:

• "Break-even is a useful planning tool but has significant limitations..."

• "The accuracy depends on the reliability of cost and price estimates..."

• "Break-even should be used alongside other decision-making tools..."

• "The margin of safety indicates the risk level of the business..."

When analysing changes:

• "An increase in fixed costs raises the break-even point, increasing risk..."

• "Higher contribution (from price increase or cost reduction) lowers break-even..."

• "Businesses should seek ways to improve contribution and reduce fixed costs..."

Sample Exam Question with Solution

Question: A business has the following data:

• Fixed costs: $80,000

• Variable cost per unit: $12

• Selling price: $20

• Expected sales: 15,000 units

Calculate: (a) Contribution per unit (b) Break-even point in units (c) Break-even revenue (d) Margin of safety in units and as a percentage (e) Expected profit

Solution:

(a) Contribution per unit Contribution = $20 - $12 = $8

(b) Break-even point (units) BEP = \frac{$80,000}{$8} = 10,000\ units

(c) Break-even revenue BEP\ Revenue = 10,000 \times $20 = $200,000

(d) Margin of safety

Units: $MoS = 15,000 - 10,000 = 5,000\ units$

Percentage: $MoS\$

(e) Expected profit Profit = (15,000 \times $8) - $80,000 Profit = $120,000 - $80,000 = $40,000

Or: Profit = 5,000\ units \times $8 = $40,000 (Margin of safety units × contribution = profit)