Study Notes on Cost-Volume-Profit Analysis

Loughborough Business School Lecture 5: Cost-Volume-Profit (CVP) Analysis

Overview of Lecture

  • Title: Accounting for Decision Making - HANDOUT

  • Presenter: Dr. Anna Raffoni

  • Email: A.Raffoni@lboro.ac.uk

  • Date: 29th October

Learning Objectives

  • At the end of the lecture, students should be able to:

    • Explain and analyze mixed costs using the high-low method.

    • Define and calculate contribution and break-even point.

    • Utilize CVP formulas for “what if” analyses.

    • Assess the costs and benefits of short-term decision making.

  • Focus of Workbook 8 activities:

    • High-low method

    • CVP Analysis

    • Short-term decision making

  • Reading Assignments:

    • Chapters 3 & 6 from Seal, Rohde, Garrison, and Noreen (6th Edition)

    • Chapter 10 (pages 375-388) for examples of short-term decision making

  • Online Tutorial: No tutorial this week, but check Tutorial 2 questions on Learn.

Cost Variability

  • Key Considerations in Cost Behavior:

    1. The specific cost

    2. The activity base or cost driver: Factor causing variable costs

    3. The relevant range: Range of activity within which cost behavior assumptions hold

    4. Time period of analysis: Short-term perspective

Cost Classification

  • Fixed Costs:

    • Remain constant over a wide range of activity for a specified time period.

  • Variable Costs:

    • Vary with the volume of activity.

  • Mixed Costs:

    • Exhibit both fixed and variable behavior.

    • Types of Mixed Costs:

    • Semi-fixed (semi-variable) costs

    • Step-fixed costs

Example of Variable Costs

  • Transportation Cost Example:

    • Cost: £10 per unit

    • As production volume increases, total variable costs increase proportionally.

    • Graph Analysis:

      • x-axis: Volume of production (units)

      • y-axis: Total variable cost (€)

    • Total variable costs at different output levels:

    • 0 units: €0

    • 1 unit: €10

    • 2 units: €20

    • 3 units: €30

    • 4 units: €40

    • 5 units: €50

    • 6 units: €60

Example of Fixed Costs

  • Fixed Cost per Unit Interpretation:

    • Fixed costs only interpreted relative to the specific volume considered.

    • Rent Cost Example:

    • Total Fixed Cost Graph:

      • x-axis: Volume of production (units)

      • y-axis: Total fixed cost (€):

    • As volume increases, fixed cost per unit decreases:

      • 1 unit: €10,000

      • 2 units: €5,000

      • 3 units: €3,333

      • 4 units: €2,500

      • 5 units: €2,000

      • 6 units: €1,667

Activity Total Cost and Relevant Range

  • Cost Behavior Assumptions:

    • Consistent relationships within the relevant range

    • Utilizes constant unit variable cost approximation

    • Differences between Accountant's Straight-Line Approximation versus Economist’s Curvilinear Cost Function for analyzing variable costs within the relevant range.

Mixed Costs Analysis

  • Mixed costs include both fixed (F) and variable components (v*Q), expressed in the equation:
    C = F + v imes Q

  • Example: Utilities costs with fixed fees and variable components based on usage.

Cost Separation: High-Low Method

  • High-low method example focused on Campus Catering Services Ltd.

  • Objective: Determine fixed vs variable components in total catering costs.

  • Required Analysis:

    • Calculate variable cost per unit

    • Calculate fixed cost

    • Express costs in the form:
      Y = a + bX

Cost-Volume-Profit (CVP) Analysis

  • CVP Analysis Defined:

    • Analyzes the interrelationships among costs, volume, and profits by focusing on five variables:

    • Prices of products/services

    • Volume or level of activity

    • Per unit variable costs

    • Total fixed costs

    • Mix of products sold

  • Impacts of variable costs, fixed costs, selling price per unit, and activity level on operating profit.

CVP Application

  • Critical questions answered by CVP:

    • What sales level is needed to cover all costs (break-even point)?

    • What sales level is needed to achieve a target profit?

    • How many additional sales are needed for price reduction recovery?

    • How much sales level can drop before incurring losses?

    • Sensitivity of profits to sales fluctuations.

Operating Profit Formula

  • Formula presentation:
    Profit = p imes Q - (v imes Q + TFC)

  • Rearrangement yields Contribution Margin per Unit (CMu):
    Profit = (p-v) imes Q - TFC

Contribution Margin (CM)

  • Contribution Margin (CM) represents the remaining amount from sales revenues after deducting variable expenses to cover fixed expenses.

Break-even Point (BEP)

  • Established via:
    Profit = CMu imes Q - TFC

  • Break-even is reached when total revenues equal total costs.

    • Q^ (Break-even point quantity) is calculated by: CMu imes Q^ = TFC

Margin of Safety (MS)

  • Definition:

    • Difference between actual/budgeted units or revenues and BEP, showing how much sales can drop before losses occur.

  • Calculating Margin of Safety (MS):

    • In units or as a percentage:
      MS/Q or MS/Revenue.

Contribution Margin Ratio

  • Contribution margin expressed as a percentage of revenue:

    • ext{Profit/volume ratio (%CM) = } rac{ ext{Contribution}}{ ext{Revenue}} imes 100

  • Used for estimating BEP in terms of revenue:

    • R^* = rac{ ext{Total fixed costs}}{ ext{Contribution margin ratio}}

Target Profit Analysis

  • Formula to reach Target Profit:
    Q^* = rac{ ext{Target Profit + Fixed Costs}}{p-v}

  • Rearranged for units sold required to achieve target profit.

Short-term Decision Making

  • Focus on differential costs/revenue that change between alternatives.

  • Classification:

    • Relevant costs/revenue: Differential cost and revenue

    • Irrelevant costs/revenue: Sunk costs that do not affect decisions.

General Approach to Differential Analysis

  • Decision-making framework:

    • Assess total benefits against total costs.

    • Accept decisions when benefits exceed costs.

Operating Leverage

  • Definition: Sensitivity of operating profit to percentage changes in sales volume.

  • Higher operating leverage means a small sales increase can lead to significantly larger profit increases.

Operating Leverage Example

  • Summary Table of Sales Changes and Profit Impact Across Firms:

    • Firm A:

    • Sales +20% leads to a profit change of +£6

    • Sales -20% leads to a profit change of -£6

    • Firm B:

    • Similar calculations yield different profit sensitivity outcomes.

Key Takeaways

  • CVP is vital for understanding how changes in sales volume, costs, and prices affect profits within a short-term and relevant range.

  • Underlying assumptions:

    • Constant selling price, linear costs within the relevant range, stable sales mix in multi-product scenarios, and constant stock levels in manufacturing.