5.5 Break-even Analysis

5.5 Break-even Analysis – Detailed Revision Notes

Contribution Analysis

What is Contribution?

• Contribution refers to the amount of money from sales that remains after variable costs have been deducted.

• It shows how much is available to cover fixed costs and, once those are paid, to generate profit.

• Contribution analysis is a valuable decision-making tool used in pricing, make-or-buy choices, and special order decisions.

Unit Contribution

• Formula: Unit Contribution = Selling Price per unit – Variable Cost per unit.

• This tells us how much each unit contributes toward covering fixed costs.

• Example: Bea’s Candles sells at $1.50, with variable costs of $0.50. Contribution per candle = $1.

• Interpretation: Each candle sold contributes $1 towards paying off fixed costs.

Total Contribution

• Formula: Total Contribution = Fixed Costs ÷ Unit Contribution.

• This shows how many units need to be sold to cover all fixed costs.

• Example: Bea’s fixed costs are $100. With unit contribution of $1, she needs to sell 100 candles to break even.

Purpose of Contribution Analysis

• Helps set pricing strategies by showing how much flexibility exists for discounts or promotions.

• Prioritizes high-contribution products in a portfolio.

• Aids in make-or-buy analysis and special order decisions.

• Essential step in calculating the break-even point.

Break-even Analysis

Definition

• Break-even occurs when Total Revenue (TR) = Total Costs (TC).

• At this point, the business is making neither profit nor loss.

• It shows the minimum level of sales required to avoid losses.

Methods of Break-even Calculation

• Unit Contribution Method

• Break-even = Fixed Costs ÷ Unit Contribution.

• Simple, quick, and widely used.

• Example: Bea’s Candles → $100 ÷ $1 = 100 units.

• TR = TC Method

• Break-even found algebraically by setting Total Revenue = Total Costs.

• TR = Price × Quantity; TC = Fixed Costs + (Variable Costs × Quantity).

• Example: 1.5Q = 100 + 0.5Q → Q = 100 units.

• Break-even Chart Method

• Graphical method showing FC, TC, and TR.

• BEP is where TR and TC intersect.

• Beyond BEP, profit is earned; below BEP, a loss occurs.

Profit or Loss

• Break-even charts clearly display profit and loss regions.

• Above BEP: Revenue exceeds costs → firm makes a profit.

• Below BEP: Costs exceed revenue → firm incurs a loss.

• Managers use this to visualize risk and reward under different sales volumes.

Margin of Safety (MOS)

Definition

• The difference between actual sales (or demand) and the break-even quantity.

• Shows how much sales can fall before the firm starts making a loss.

Formula

• Margin of Safety = Actual Demand – Break-even Quantity.

Example

• Bea’s Candles demand = 250 units, BEP = 100 units.

• MOS = 250 – 100 = 150 units.

• Interpretation: Sales can drop by 150 units before losses occur.

Importance

• Larger MOS = safer position for the business.

• Smaller MOS = higher risk, as even slight drops in sales can cause losses.

Target Profit Analysis

• Target Profit Output

• Formula: Target Profit Quantity = (Fixed Costs + Target Profit) ÷ (Price – Variable Cost).

• Shows how many units must be sold to reach a desired profit.

•  Target Profit

• Once actual sales are known, profit = TR – TC.

• Example: If Bea sells 300 candles, her profit can be calculated directly.

• Target Price

• If output is limited, firms calculate the selling price needed to reach a desired profit.

• Formula involves rearranging TR and TC equations to solve for price.

Application

• Guides firms in goal-setting and helps ensure pricing and production plans align with financial objectives.

Effects of Changes in Price or Cost

Price Changes

• A higher selling price lowers the break-even quantity, increases the MOS, and raises potential profits.

• A lower selling price increases the break-even quantity, reduces the MOS, and lowers profitability.

Cost Changes

• Rising variable costs raise the break-even point, squeezing profit margins.

• Higher fixed costs also push up the break-even level, requiring more sales to cover costs.

• Cost reductions (through efficiency or technology) lower the break-even point.

External Influences

• Seasonal demand, economic changes, new competitors, or innovation can all shift break-even analysis outcomes.

• Riskier projects usually demand a higher break-even output to justify investment.

Limitations of Break-even Analysis

• Assumptions of Linearity

• Assumes costs and revenues are linear, which may not hold true in reality (e.g., bulk discounts, stepped costs).

• Static Model

• Provides a snapshot, not reflecting dynamic changes in markets, trends, or consumer demand.

• Data Sensitivity (GIGO – Garbage In, Garbage Out)

• If input data (costs, prices, demand) are inaccurate, results will be misleading.

• Excludes Qualitative Factors

• Ignores customer behavior, competitor strategies, and brand value.

• Limited to Single-Product Firms

• More complex and less useful for multi-product firms, as it cannot account for varied contribution margins.

• Practical Limitations

Not sufficient on its own; must be combined with other decision-making tools.