Cost Volume Profit (CVP)

• Cost volume profit (CVP) analysis and the
break-even point
• Graphing CVP relationships
• Target net profit
• CVP analysis for management decisions
• CVP analysis with multiple products
• Including income taxes in CVP analysis
• Assumptions underlying CVP analysis
• An activity-based approach to CVP analysis
• Financial planning models
What is Cost Volume Profit (CVP) Analysis?
• Calculates how changes in an organisation’s
sales volume affect its costs, revenue and
profit
• Provides information for management
decision making; can determine the impact
on revenue and costs quickly
• Useful for both profit-seeking and not-forprofit
organisations
The Break-Even Point
• The volume of sales where the total revenues
and costs are equal, and the operation
breaks even (no profit or loss)
• The break-even point can be calculated for
an entire organisation or for individual
projects or activities
Break-even Formulas
• Break-even point (in units):
Fixed costs
Unit contribution margin
• Break-even point (in $):
Fixed costs
Unit contribution margin ratio
Break-Even Formulas (cont.)
• Unit contribution margin:
Unit sales price – Unit variable cost
• Contribution margin ratio (percentage):
Unit contribution margin
Unit sales price
Cost Volume Profit Graph
• Shows how costs, revenues and profits
change as sales volume changes
• Break-even point is determined by the
intersection of the total revenue line and total
cost line
• Shows the relevant range
Cost Volume Profit Graph, Melbourne Theatre
Company Production, Calypso
Profit Volume (PV) Graph
• Shows the total amount of profit or loss at
different sales volumes
• The graph intercepts the vertical axis at the
amount equal to the fixed costs
• The break-even point is the point at which the
total profit/loss line crosses the horizontal
axis
Profit volume graph, Melbourne
Theatre Company production, Calypso
Target Net Profit
• Target net profit (in units):
Fixed costs + Target net profit
Unit contribution margin
• Target net profit (in $):
Fixed costs + Target net profit
Contribution margin ratio
Using CVP Analysis for Management Decision
Making
• Safety margin

• Difference between the budgeted sales revenue
  and break-even sales revenue
• The margin of safety indicates how far sales can
  fall before an operating loss results.
  • Changes in fixed costs
• Percentage changes in fixed costs will lead
  to a similar increase in the break-even point
  (in units or dollars)
  • Changes in SP and VC will affect the
  contribution margin per unit
  Using CVP Analysis for Management
  Decision Making (cont.)
  • Multiple changes in key variables
• Decreasing variable costs per unit
• Increasing selling prices
• Undertaking a new advertising campaign
• Leasing a new office
  • Incremental approach to analysis
• Focuses on the differences in the total
  contribution margin, fixed costs and profits under the
  two alternatives
  Jones Ltd provide the following information:
  Sales $45.00 per unit
  Variable Costs $25.00 per unit
  Fixed costs$ 160,000
  Required:
  1.What is the Break-even in $ and units?
  2.If they want to make $280,000 profit how many
  units must they sell?
  3.If sales are $450,000, what is their Margin of
  Safety?
  In-class Worked Example
  Sales $45.00 per unit
  VC $25,00 per unit
  CM $20.00 per unit
  FC $160,000 / 20 = 8,000 units (BE)
  BE 8,000 x $45 = $360,000
  If they wish to make $280,000 profit:
  160,000 + 280,000 = 440,000 / 20 = 22,000
  Sales are $450,000; Margin of Safety = 90,000
  ` (25%)
  Solutions
  CVP Analysis With Multiple Products
  • Sales mix
  − The relative sales proportions of each type of
  product sold by the organisation
  • Weighted average unit contribution margin
  − The average of the products’ unit contribution
  margins, weighted by the sales mix
  Break-even point (in units):
  Fixed costs
  Weighted average unit contribution margin
  Multiple Product CVP Analysis Example:
  Weighted Average Unit CM =
  P1 sales mix% x P1 Unit CM+ P2 sales mix% x P2 Unit CM
  +…………
  P1 – Product 1
  P2 – Product 2
  Multiple Product CVP Analysis Example:
  Company Information
  Marble Limited sells two products, trolleys
  and wheelchairs
  Trolleys Wheelchairs Total
  Sales 250,000 300,000 550,000
  Variable costs 150,000 135,000 285,000
  Contribution
  margin
  100,000 165,000 265,000
  Fixed costs 170,000
  Profit 95,000
  Sales mix 250,000 300,000 550,000
  Multiple Product CVP Analysis Example:
  Sales Mix and Contribution Margin Ratio
  Sales mix:
  Trolleys 45% (250,000 / 550,000)
  Wheelchairs 55% (300,000 / 550,000)
  Weighted average CM ratio=
  45% (100,000 / 250,000) + 55% (165,000 / 300,000)
  = 0.482 (rounded)
  Multiple Product CVP Analysis Example: Break-
  Even Point
  Organisational break-even point
  Break-even ($) = Total fixed costs / weighted
  average contribution margin ratio
  = 170,000 / 0.482
  = $352,697
  Break-even sales revenue for each product
  Trolleys = 352,697 * 45%
  = $158,714
  Wheelchairs = 352,697 * 55%
  = $193,983
  Profit Volume Graph With Multiple Products,
  Calypso
  Including Income Taxes in CVP Analysis
  • Sales volume required to earn net profit after
  tax:
  Fixed costs + Target net profit after tax
  (1 – t)
  Unit contribution margin
  Assumptions Underlying CVP Analysis
  • The behaviour of total revenue is linear
  • The behaviour of total costs is linear over a
  relevant range
  • Sales volume is the only cost driver for both
  variable and fixed costs
  • The sales mix remains constant over the
  relevant range
  • In manufacturing firms, the levels of
  inventory at the beginning and end of the
  period are the same
  CVP Analysis and Longer-Term Decisions
  • CVP analysis is usually regarded as a shortterm
  or tactical decision tool
  • Classification of costs as variable or fixed is
  usually based on cost behaviour over the
  short term
  • The financial impact of long-term decisions
  is best analysed using capital budgeting
  techniques
  Treating CVP Analysis With Caution
  • CVP analysis is a simplified model
  • The usefulness of CVP analysis may be
  greater in less complex, smaller firms, or for
  stand-alone projects
  • For larger, more complex firms, CVP
  analysis can be valuable as a decision tool
  for the planning stages of new projects and
  ventures
  An Activity-Based Approach to CVP Analysis
  • ABC categorises activities at unit, batch,
  product or facility level
• Batch, product and facility activities are nonvolume
  related activity costs
  • Break-even point (in units):
  Total batch, product and facility level costs
  Selling price – unit level costs
  An Activity-Based Approach to CVP Analysis (cont.)
  Limiting Assumptions of CVP Analysis Using
  Activity-Based Costs
  • Total batch level costs are dependent on the
  batch size and the break-even/target
  production level
  • Management may change the batch size at
  certain production volume levels
  • More complex models are needed where
  there are multiple products
  Including Customer-Related Costs in CVP
  Analysis
  Profit = sales revenue – (unit level costs
• batch level costs
• product level costs
• order level costs
• customer level costs
• marketing level costs
• facility level costs)
  Financial Planning Models
  • Sensitivity analysis – CVP can be run using
  different combinations of variables
  • Goal seek approaches
• The analyst specifies the outcome, and the
  software specifies the necessary inputs
  • What-if analysis
• The analyst specifies changes in assumptions
  and data to examine the effect of these changes on
  the outputs
  Profit Model for Accutime Pty Ltd Under
  Activity-Based Costing
  Summary
  • CVP analysis is a decision tool
  • The break-even point is the sales level at
  which sales revenue covers costs: there is
  zero profit
  • The break-even formula can be modified to
  calculate target profit
  • CVP analysis has several assumptions which
  limit its usefulness for decision making
  • Activity-based approaches and financial
  planning modelling can provide more
  sophisticated models