Cost-Volume-Profit Analysis Lecture Notes

Relevant Costs and Cost Volume Profit (CVP) Analysis

Introduction

  • Course delivered by Gaborone Campus, Botswana.
  • Emphasis on relevant costs and cost volume profit analysis.

Objectives

  • Learn relevant costs.
  • Use CVP analysis to determine necessary units for break-even sales.
  • Calculate margin of safety.
  • Understand break-even, contribution, and profit volume graphs.

CVP Analysis

  • Definition: CVP analysis examines the relationship between volume, sales revenue, costs, and profit over a short period (typically one year).
  • The short run is characterized by constraints based on current operating capacity.

Short Term Decision Making

Key Aspects

  • Decision-making should include only relevant costs and revenues pertaining to the alternatives considered.
  • Inclusion of irrelevant costs can lead to incorrect decisions.
  • Balancing short-term focus with long-term benefits is crucial.

Topics under Short-Term Decision Making

  • Relevant costs.
  • Limiting factors.
  • Make or buy decisions.
  • Cost-volume profit analysis.

Relevant Costs

Criteria for Relevant Costs

Yes:
  • Incremental costs and revenues.
  • Future cash flows.
  • Opportunity costs.
No:
  • Sunk costs (costs already incurred).
  • Committed costs (costs that are not avoidable).
  • Non-cash items.
  • Net book values.
  • Notional costs (hypothetical expenditures).

Relevant Cost of Materials

  • When determining the price for a one-time decision, only relevant cash flows apply.

Considerations for Relevant Cost of Materials

  • Possible relevant costs include:
    • Purchase price.
    • Replacement cost.
    • Net realizable value.
    • Opportunity cost.
  • The right choice depends on the specific situation.

Decision Tree for Relevant Cost of Materials

  • Are materials already in inventory?
    • Yes:
    • Will they be replaced?
      • Yes: (Consider replacement cost)
      • No: (Consider purchase price)
    • No:
    • Can they be used for other purposes?
      • Yes: (Opportunity cost)
      • No: (Replacement cost or purchase price)

Relevant Cost of Labour

  • Determining the relevant cost of labour is more complex.
  • Key consideration: Does spare capacity exist?

Decision Tree for Relevant Cost of Labour

  • Does spare capacity exist?
    • Yes: (Cost of hiring)
    • No:
    • Can extra labour be hired?
      • No: (Opportunity cost applies)
      • Yes: (Cost of hiring)
Important Consideration for Relevant Cost of Labour
  • If no spare capacity exists, existing project resources must be reallocated, leading to opportunity costs based on forgone contributions from abandoned projects.
  • Relevant cost formula:
    \text{Relevant cost} = \text{Contribution forgone from alternative product} + \text{Direct labour rate}

Understanding Costs

  • Essential for managers to understand costs and their behaviours:
    • Fixed costs.
    • Variable costs.
    • Stepped costs.
    • Semi-variable costs.
  • Insight on cost behaviour allows for better cost predictions.

Breaking Down Semi-Variable Costs

  • Total cost equation: \text{Total cost} = \text{Total fixed cost} + \text{Total variable cost}
    • Where total variable cost is:
      \text{Total variable cost} = \text{Variable cost per unit} \times \text{Number of units}

Cost Calculation Using "High-Low" Method

  • To determine fixed and variable costs:
    • Establish fixed costs:
      \text{Fixed costs} = P20,000 - (22,500 \times P0.80) = P2,000
    • Total cost breakdown:
      \text{Total cost} = \text{Total fixed cost} + \text{Total variable cost}

Sample Cost Table


  • Sample outputs and associated costs:

PeriodTotal CostOutput
1P10,00010,000
2P12,00012,500
3P8,0007,500
4P17,00018,750
5P20,00022,500

Steps to Calculate Relevant Costs

  • Step 1: Calculate variable cost per unit.
    • Example based on output levels and costs:
    • Change in costs and outputs:
    • Lowest Output: 7,500; Highest Output: 22,500; Variable cost = P0.80 per unit.

Contribution

  • Contribution defined as:
    \text{Contribution} = \text{Sales Revenue} - \text{Variable Costs}
  • It represents the amount contributing to cover fixed costs and thus profit.

Cost Volume Profit Analysis

  • Key for decision making in short term scenarios:
    • Determines how many units need to be sold to break even or generate profit.

Cost Classifications (Revision)

  • Fixed Costs: Do not change irrespective of activity levels.
  • Variable Costs: Change directly with levels of activity.
  • Semi-Variable Costs: Partly fixed and partly variable.
  • Stepped Costs: Fixed over certain activity levels before adjusting in steps.

Relevant Range

  • Definition: In the short term, all costs are viewed as fixed, whereas in the long term, they become variable.
  • Actual operations typically happen within a relevant range of activity where assumptions about costs remain valid.
  • Outside this range, predictions may require adjustments.

Financial Management Examples: Wind Bicycle Co.

Contribution Profit Statement: June

  • Total Sales: P250,000 (500 bikes at P500 each).
  • Variable Expenses: P150,000.
  • Contribution Margin: P100,000.
  • Less: Fixed Expenses: P80,000.
  • Net Profit: P20,000.

Contribution Margin Analysis

  • Additional unit sales of bikes increase contribution margin, assisting in fixed expense management.
  • To break even, Wind must achieve a total contribution margin of P80,000.
  • Impact of selling fewer or more units on profitability:
    • Selling fewer units lowers contributions towards fixed costs, directly affecting profits.

Break-Even Analysis

Methodology

  1. Equation Method:
  • Profit equation:
    \text{Profits} = \text{Sales} - (\text{Variable expenses} + \text{Fixed expenses})
  • Break-even point where profits are zero.
  1. Contribution Margin Method:
  • Relates total fixed expenses to unit contribution margin to derive break-even in unit or total sales terms.

Example Calculation

  • Using known fixed and variable costs, break-even equations yield:
    • To break even, Wind Bicycle Co. needs to sell 400 bikes.
    • All calculations must emphasize clarity in variable costs’ impact.

Margin of Safety

  • Definition: The sales amount by which a company exceeds its break-even volume.
  • Margin of Safety Formula:
    \text{Margin of Safety} = \text{Total Sales} - \text{Break-even Sales}
  • Percentage Margin of Safety Formula gives insight into risk levels in sales reductions.

Application of Margin of Safety

  • If actual sales are P250,000 and break-even point is P200,000, the margin of safety is recorded:
    • Absolute: P50,000 (100 bikes).
    • As a percentage: 20% (P50,000 divide by P250,000).

Sales Mix Considerations

  • Multi-product CVP adaptations focus on standardizing sales measures based on mixes.
  • For example, Super Bright's sales mix of 1200 deluxe to 600 standard results in conversion to 2:1.
  • Break-even analysis incorporates combined contributions for all products within the mix.

Conclusion

  • Effective CVP analysis assists managers in costing decisions, risk assessment, and strategic pricing.

Assumptions of CVP Analysis

  • Selling prices remain constant.
  • Linear representation of costs.
  • Constant sales mix in multi-product businesses.
  • Production levels align with sales output.

Limitations of CVP Analysis

  • Costs may not remain fixed or variable as assumptions suggest.
  • Sales behavior changes, challenging consistency.
  • Economies or diseconomies of scale can skew realistic projections.

Tutorial Preparation

  • Engage students with graded questions online for conceptual reinforcement.

Notes

  • All calculations, definitions, and methodologies examined reinforce fundamental concepts in CVP analysis and relevant costs.