calculation and interpretation of break-even level of output, contribution, margin of safety and level of profit in numeric and graphic form

5.4 Costs – Break‑even Analysis

5.4.1 Break‑even Point

When a business covers all its fixed costs but earns no profit, it’s at the break‑even point.

Formula: \$BE = \dfrac{FC}{CM}\$

where FC = Fixed Costs and CM = Contribution Margin per unit.

Example – T‑shirt shop:

• Fixed costs (rent, salaries): $10,000
• Variable cost per T‑shirt: $20
• Selling price per T‑shirt: $50
• Contribution margin: \$50 - \$20 = $30
• Break‑even units: \$10,000 ÷ \$30 ≈ 333.33 → 334 units (round up)

5.4.2 Contribution Margin

The amount each unit contributes to covering fixed costs and generating profit.

Contribution per unit: \$CM = SP - VC\$

Contribution ratio: \$CR = \dfrac{CM}{SP}\$

Using the T‑shirt example:

CM = \$30, CR = \$30 ÷ $50 = 0.60 or 60 %.

5.4.3 Margin of Safety

Shows how far sales can fall before the business starts losing money.

Margin of Safety (units): \$MoS = Actual\_Sales - BE\$

Margin of Safety (percentage): \$MoS\% = \dfrac{Actual\Sales - BE}{Actual\Sales}\$

Example – Actual sales = 500 units:

MoS = 500 – 334 = 166 units

MoS% = 166 ÷ 500 = 0.332 → 33.2 %.

5.4.4 Level of Profit

Profit can be calculated in two equivalent ways.

1. Profit = (Actual sales – BE) × CM
2. Profit = (Actual sales × CM) – FC

Example – 500 units sold:

Profit = (500 – 334) × \$30 = 166 × \$30 = $4,980

or Profit = (500 × \$30) – \$10,000 = \$15,000 – \$10,000 = $5,000 (rounded).

Visual Summary – 📊 Simple Bar Chart

Analogy – Lemonade Stand

Imagine you run a lemonade stand:

• Fixed costs: stall rent ($50 per day)
• Variable cost per cup: lemons, sugar, cups ($0.50)
• Price per cup: $1.00
• Contribution per cup: $0.50
• Break‑even cups: \$50 ÷ \$0.50 = 100 cups

If you sell 150 cups, you’ve covered the rent and earned \$25 profit (150 × \$0.50 – $50).

Quick Check – 5‑Minute Quiz

1. What is the contribution margin if the selling price is \$80 and the variable cost is \$45?
2. If fixed costs are \$12,000 and the contribution margin per unit is \$30, how many units must be sold to break even?
3. Calculate the margin of safety percentage if actual sales are 600 units and the break‑even point is 400 units.