Chapter 18
Cost volume profit analysis
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Outline
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What is CVP analysis?
The break-even point
Graphing CVP relationships
Target net profit
Using CVP analysis for management decisions
CVP analysis with multiple products
Including income taxes in CVP analysis
Practical issues in CVP analysis
An activity-based approach to CVP analysis
Financial planning models
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Cost volume profit (CVP) analysis
• A technique used to determine the effects of
changes in an organisation’s sales volume on its
costs, revenue and profit
• Can be used in profit-seeking organisations and
not-for-profit organisations
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The break-even point
• The volume of sales where the total revenues and
costs are equal, and the operation breaks even
• At this level of sales, there is no profit or loss
• Can be calculated for an entire organisation or for
individual projects
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Break-even formulas
Fixed costs
Break - even point (in units) =
Unit contributi on margin
Break - even point (in sales dollar) =
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Fixed costs
Unit contributi on margin ratio
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Terminology
• Contribution margin (or variable costing)
statement
– An income statement that separates fixed and variable
costs and calculates a contribution margin
• Total contribution margin
– The difference between the total sales revenue and the
total variable costs
– The amount available to cover fixed costs and then
contribute to profits
• Unit contribution margin
– The difference between the sales price per unit and the
variable cost per unit
(cont.)
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Terminology (cont.)
• Contribution margin ratio
– The unit contribution margin divided by the unit sales
price
– The proportion of each sales dollar available to cover
fixed costs and earn a profit
• Contribution margin percentage
– The contribution margin ratio multiplied by 100
– The percentage of each sales dollar available to cover
fixed costs and earn a profit
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Graphing cost volume profit
relationships
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•
Shows how costs, revenue and profits change as
sales volume changes
Five steps
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2.
3.
4.
5.
Draw the axes of the graph
Draw the fixed cost line
Draw the total cost line
Draw the total revenue line
Break-even point—where the total revenue and total
cost lines intersect
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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
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Target net profit
• A desired profit level determined by management
• The break-even formula can be sued to determine
the target profit
Fixed costs + target profit
Target sales volume =
Unit contributi on margin
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Using CVP analysis for
management decision making
• Safety margin
– Difference between the budgeted sales revenue and
break-even sales revenue
– Gives a feel for how close projected operations are to the
break-even point
• Changes in fixed costs
– Percentage change in fixed costs will lead to a similar
increase in the break-even point (in units or dollars)
– Different fixed costs may apply to different levels of
sales/production volume, and provide more than one
break-even point
(cont.)
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Using CVP analysis for
management decision making
(cont.)
• Changes in the unit contribution margin
– Change in unit variable costs, leads to new
– unit contribution margin and new break-even point
– An increase in unit variable costs will increase the breakeven point
– An increase in unit price will lower the break-even point
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Multiple changes in key variables
• May involve, for example
–
–
–
–
Increasing unit prices
Increasing selling prices
Undertaking a new advertising campaign
Leasing a new office
• An incremental approach to analysis
– Focuses on the differences in the total contribution
margin, fixed costs and profits under the two alternatives
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CVP analysis with multiple
products
• Sales mix
– The relative 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
Fixed costs
Break - even point =
Weighted average unit contribution margin
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Including income taxes in CVP
analysis
Sales volume required to earn target after - tax profit
target net profit after tax
Fixed costs +
=
(1 - t )
unit contribution margin
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Assumptions underlying CVP
analysis
• The behaviour of total revenue is linear
• The behaviour of total costs is linear over a
relevant range
– Costs can be categorised as fixed, variable or
semivariable
– Labour productivity, production technology and market
conditions do not change
– There are no capacity changes during the period under
consideration
(cont.)
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Assumptions underlying CVP
analysis (cont.)
• For both variable and fixed costs, sales volume is
the only cost driver
• 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
– Thus, the number of units produced and sold during a
period are equal
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CVP analysis and longer-term
decisions
• CVP analysis is usually regarded as a short-term
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
– Takes into account the time value of money
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Treating CVP analysis with
caution
• CVP analysis is merely a simplified model
• The usefulness of CVP analysis may be greater in
less complex smaller firms, or stand-alone
projects
• For larger firms, CVP analysis can be valuable as
a decision tool for the planning stages of new
projects and ventures
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An activity-based approach to CVP
analysis
• ABC categorises activities as unit, batch, product
or facility level
– Facility, product and batch activities are non-volume
activity costs
Total batch, product and facility level costs
Break - even point =
Selling price per unit - costs per unit
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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 and this will
change the break-even volume
• More complex models are needed where there
are multiple products
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Financial planning models
• Sensitivity analysis and CVP analysis
– An approach that examines how an outcome may change if
there are variations in the predicted data or underlying
assumptions
• Can be run using spreadsheet software, such as Excel
• 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
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Summary
• CVP analysis is a decision tool that can be used to
assess the effects on changes in profit of changes in
sales volume, sales price, sales mix and costs
• The break-even point is the sales level at which sales
covers costs—there are zero profits
• The break-even formula can be modified to calculate
target profit, and to include sales mix and income
taxes
• CVP analysis has several assumptions which limit its
usefulness for decision making
• Activity-based approaches and financial planning
modelling can provide more sophisticated models
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