Cost – Volume – Profit Analysis Notes

Module Overview

  • Module Title: Cost – Volume – Profit Analysis

  • Prepared by: Wahseem Soobratty, Faculty of Business and Law

  • Objectives of the Module:

    • Identify different types of costs: fixed, variable, mixed

    • Prepare a Cost-Volume-Profit (CVP) analysis for entities

    • Explain key assumptions underlying CVP analysis

    • Discuss uses of break-even data

    • Understand resource optimization concerning limiting factors

Introduction to CVP Analysis

  • CVP analysis deals with how profits change in response to changes in sales volume, costs, and prices.

  • Key questions addressed:

    • How many units must be sold to break even?

    • What is the profit impact of changing cost mixes?

    • How many units must be sold to achieve target profits?

    • What is the effect on profits of cost increases?

Cost Behaviour

  • Definition: Cost behaviour looks at how costs change with activity levels, influenced by various factors.

  • Cost Classifications:

    • Fixed Costs: Remain constant within a certain range of activity.

    • Examples: lease payments, depreciation.

    • Total fixed costs stay the same; fixed cost per unit decreases as output increases.

    • Variable Costs: Change in total with activity levels.

    • Examples: materials, labor costs.

    • Can be analyzed on total or per unit basis.

    • Mixed Costs: Combination of fixed and variable costs which change partially with activity.

Understanding Fixed and Variable Costs

  • Fixed Costs:

    • Do not change with production levels within a relevant range.

    • Total remains the same, but per unit cost decreases with increased output.

  • Variable Costs:

    • Change in total as the production level varies.

    • Depending on sales volume:

    • Total variable costs increase; variable costs per unit typically remain constant.

Break-even Analysis

  • Break-even occurs when total revenue equals total costs, resulting in zero profit.

  • Break-even Formula:

    • $SP(X) = FC + VC(X)$

    • When profit $P = 0$:

    • Break-even units = $ rac{FC}{CM}$

    • Break-even dollars = Break-even units × Selling Price

  • Contribution Margin (CM):

    • For unit: $CM = SP - VC$

    • For total: $Total CM = SP(X) - VC(X)$

  • Significance:

    • Assists in identifying the number of units needed to meet profit targets and evaluating impacts of cost changes.

Practical Applications and Examples

  • Example calculating break-even for single-product:

    • Selling price: $25

    • Fixed costs: $28,000 + $10,600 + $6,400 = $45,000

    • Variable costs per unit: $14 + $1 = $15

    • Contribution Margin per unit: $25 - $15 = $10

    • Required units to break even: $ rac{45000}{10} = 4500$ units

  • Impact of increased variable costs or changed fixed costs on break-even calculation:

    • Example: If VC increases to $17, new CM = $25 - $17 = $8

    • New Break-even = $ rac{32000}{8} = 4000$ units

Contribution Margin Ratio

  • Indicates profit for every dollar of sales.

  • If CM Ratio = 0.4, profit for every dollar = $0.40

  • Example: Selling $40,000 with a CM Ratio of 0.05 results in a profit of $2,000

Break-even and Taxes

  • Pre-tax profit:

    • Formula: Pre-tax profit = After-tax profit / (1 - tax rate)

    • Example: expected after-tax profit = $50,000, with tax rate 30% results in pre-tax of $71,428

Margin of Safety

  • Indicates how much revenue can decline before reaching break-even point.

  • Margin of safety in units = Actual or estimated units - Break-even units

  • Margin of safety in dollars = Actual or estimated revenue - Revenue at break-even

Contribution Margin Per Limiting Factor

  • Assess profitability based on limited resource availability.

  • Example analysis with three products (B101, C101, D101) considering contribution margin per unit and limited hours available shows B101 is most profitable, followed by D101, then C101 preserving resource allocation.

  • Conclusion:
    Understanding CVP analysis and embracing a strategic approach to cost management can significantly influence business decision-making, profitability, and resource optimization.