Break-even Analysis

Introduction

• Your friend owns an ice-cream shop.
• She is concerned because two more shops have opened in the same area.
• Some customers may shift to these new shops.
• She wants to know how many units she must sell to avoid losses.

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Ice Cream Shop Case: Break-Even Sales

• Ice creams sold at ₹10 to ₹40, average commission = 20% on sales.
• Monthly fixed expenses = ₹10,000 (rent, electricity, salaries, taxes).
• For every ₹100 in sales, she earns ₹20 as commission.

Calculation:

Sales (₹)	Commission (₹)
10,000	2,000
50,000	10,000

• She must earn ₹10,000 commission to cover expenses.
• Hence, Break-even Sales = ₹50,000.

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Marginal Costing & Contribution Concepts

Chemical Company Example:

• Selling Price = ₹100/kg
• Variable Cost = ₹60/kg
• Contribution = ₹40/kg
• Contribution Margin Ratio = 40%
• Fixed Cost = ₹10,000

Break-Even Computation:

• Break-even Quantity = Fixed Cost / Contribution
  • ₹10,000 / ₹40 = 250 kg
• Break-even Sales = Fixed Cost / Contribution Margin Ratio
  • ₹10,000 / 40% = ₹25,000

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Capacity-Based Break-Even

• Maximum capacity = 1000 kg
• Break-even volume = 250 kg
• Break-even Capacity = 25%
  • If the firm operates at 25% capacity, it avoids loss.

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Margin of Safety (MOS)

• Current Sales = 600 kg
• Break-even Sales = 250 kg
• MOS = 600 - 250 = 350 kg

The firm is in a comfortable position with high MOS.
It’s less likely to incur losses due to volume decline.

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Understanding Profit Beyond BEP

• At Break-even Point (BEP):
  • Firm covers variable + fixed costs.
• Any additional unit beyond BEP = profit.

Profit Formula:

Profit = Margin of Safety (units) × Contribution per unit
       = 350 × ₹40
       = ₹14,000

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Profit Tub Analogy

• Imagine two tubs:
  1. Fixed Cost Tub
  2. Profit Tub
• Contribution from sales first fills the fixed cost tub (250 kg).
• Remaining contribution flows into the profit tub.
• At 600 kg sales:
  • Contribution for 350 kg = ₹14,000 → Profit

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Sales vs Profit Table & Trend

Sales Volume (kg)	Sales Value (₹)	Profit (₹)
250	₹25,000	₹0 (BEP)
400	₹40,000	₹6,000
500	₹50,000	₹10,000

• From 400 to 500 kg:
  • Volume ↑ 25%
  • Profit ↑ 66%

After BEP, profit grows faster than volume.

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