CVP-ANALYSIS
COST-VOLUME-PROFIT
ANALYSIS
Saganga Kapaya; PhD, CPA(T).
Department of Accounting and Finance
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Study Objectives
1. Determine the number of units that must be sold to
break even or to earn a targeted profit.
2. Calculate the amount of revenue required to break even
or to earn a targeted profit.
3. Apply cost-volume-profit analysis in a multiple-product
setting.
4. Prepare a profit-volume graph and a cost-volume-profit
graph, and explain the meaning of each.
5. Explain the impact of risk, uncertainty, and changing
variables on cost-volume-profit analysis.
6. Discuss the impact of activity-based costing on costvolume-profit analysis.
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Objectives of CVP analysis
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Earning of profit depends on the efficient management of cost because each unit sold has
its specific cost controlling of cost through efficient management; on the other hand, it
depends on the quantum of output.
The main objective of the cost-volume-profit analysis is to help management make
important decisions revealing the interrelationship among the volume of output and sales,
cost, and profit.
In other words, cost-volume-profit analysis is an important tool through which the
management can have an insight into the effects on profit due to variations in cost and
volume of sales for taking appropriate decisions.
The objectives achieved by such analysis may also be identified as its benefits. These
objectives or advantages of cost-volume-profit analysis are as follows:
Profit planning;
Help in preparation of flexible budgets;
Ascertainment of no profit and no loss level;
Ascertainment of optimum product mix;
Taking pricing decisions;
Production planning;
Taking other managerial decisions;
Help in controlling cost;
Achieving efficiency;
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Assumptions of CVP
• Basic Assumptions of CVP Analysis
• Several assumptions commonly underlie CVP analysis:
• The selling price is constant. The price of a product or service will
not change as volume changes.
• Costs are linear and can be accurately divided into variable and
fixed elements. The variable element is constant per unit, and the
fixed element is constant in total over the entire relevant range.
• In multiproduct companies, the sales mix is constant.
• In manufacturing companies, inventories do not change. The
number of units produced equals the number of units sold.
• While these assumptions may be violated in practice, the results of
CVP analysis are often “good enough” to be quite useful.
• Perhaps the greatest danger lies in relying on simple CVP analysis
when a manager is contemplating a large change in volume that lies
outside of the relevant range.
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Assumptions of CVP…
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More Assumptions of CVP Analysis
The technique of cost-volume-profit analysis rests on a set of assumptions.
These assumptions may be identified as the fundamental base of such analysis. The
assumptions underlying the cost-volume-profit analysis are discussed below:
All costs can be divided into fixed and variable elements.
The selling price is constant. So total revenue will change direction and proportionately with
the output, and the TR curve will be linear.
Total fixed costs remain constant.
Prices of factors of production e.g., material price wage rates, etc. are constant.
The variable cost per unit is also constant. Therefore total variable costs are directly
proportioned to volume.
There will be no change in the firm’s efficiency or productivity.
For a multiproduct firm, product-mix is constant.
The volume of output is the only revenue and cost driver.
There will no be any significant change in the inventory level at the beginning and the end
of the year.
The firm is assumed to analyze the short run.
The analysis will be effective for a limited range of operations over which the firm was
operating the past and is expected to operate in the future. It is known as a relevant range.
No risk or uncertainty is involved, and the analysis is deterministic.
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Limitations of CVP
• Despite being considered as an important tool for decision
making and planning the cost-volume-profit analysis, the
technique has the following limitations:
• Problems in identifying fixed and variable costs.
• Fixed costs not always fixed.
• Proportionate relation between variable cost and volume of
output not always effective.
• Unit selling price not always constant.
• Not suitable for a multiproduct firm.
• Ignoring the influence of other factors on cost and profit.
• Presence of inventory.
• Not effective in the long run.
• More emphasis on sales.
• A statistic tool.
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Uses or application of CVP
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The cost-volume-profit analysis enables the management to reach planning and
policymaking decisions more -intelligently.
Examples of specific uses to which information derived from cost-volume-profit analysis
can be put are given below:
Sales and Pricing Policies.
Determination of profit which will result from any given volume of sales.
Analysis of the effect of changes in selling price.
Effect of changes in the product mixture.
Additional sales volume needed to support additional expenditure.
The lowest price at which business may be accepted to utilize facilities and contribute
something towards net profit.
The particular products to be emphasized to reflect the highest net profit.
Financial and Production Problems.
Interpretation of proposed or alternative budgets and effect of suggested cost and other
changes when the goals are not satisfactory to management.
Determination of unit costs at various volume levels.
Determination of the probable effect of investment in new plant and equipment.
Determination of the most profitable use of scarce materials.
Assistance in the choice between the make or buys decisions.
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The Break-Even Point in Units
The controller of More-Power Company has prepared the
following projected income statement:
Sales (72,500 units @ $40)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$2,900,000
1,740,000
$1,160,000
800,000
$ 360,000
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The Break-Even Point in Units
Operating Income Approach
0 = ($40 x Units) – ($24 x Units) – $800,000
0 = ($16 x Units) – $800,000
$1,740,000 ÷ 72,500
($16 x Units) = $800,000
Units = 50,000
Proof
Sales (50,000 units @ $40)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$2,000,000
1,200,000
$ 800,000
800,000
$
0
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The Break-Even Point in Units
Contribution Margin Approach
Number of units = $800,000 ÷ ($40 - $24)
= $800,000 ÷ $16 contribution margin per unit
= 50,000
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The Break-Even Point in Units
Target Income as a Dollar Amount
$424,000 = ($40 x Units) – ($24 x Units) – $800,000
$1,224,000 = $16 x Units
Units = $1,224,000 ÷ $16
= 76,500
Proof
Sales (76,500 units @ $40)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$3,060,000
1,836,000
$1,224,000
800,000
$ 424,000
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The Break-Even Point in Units
Target Income as a Percentage of Sales Revenue
More-Power Company wants to know the number of sanders that
must be sold in order to earn a profit equal to 15 percent of sales
revenue.
0.15($40)(Units) = ($40 x Units) – ($24 x Units) – $800,000
$6 x Units = ($40 x Units) – ($24 x Units) – $800,000
$6 x Units = ($16 x Units) – $800,000
$10 x Units = $800,000
Units = 80,000
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The Break-Even Point in Units
After-Tax Profit Targets
Net income = Operating income – Income taxes
= Operating income – (Tax rate × Operating income)
= Operating income × (1 – Tax rate)
Or
Net income
Operating income =
(1 - Tax rate)
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The Break-Even Point in Units
After-Tax Profit Targets
More-Power Company wants to achieve net income of
$487,500 and its income tax rate is 35 percent.
$487,500 = Operating income – 0.35(Operating income)
$487,500 = 0.65(Operating income)
$750,000 = Operating income
Units = ($800,000 + $750,000) ÷ $16
= $1,550,000 ÷ $16
= $96,875
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Break-Even Point in Sales Dollars
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Break-Even Point in Sales Dollars
The following More-Power Company contribution margin
income statement is shown for sales of 72,500 sanders.
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$2,900,000
1,740,000
$1,160,000
800,000
$ 360,000
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Break-Even Point in Sales Dollars
To determine the break-even in sales dollars, the contribution
margin ratio must be determined ($1,160,000 ÷ $2,900,000)
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$2,900,000
1,740,000
$1,160,000
800,000
$ 360,000
100%
60%
40%
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Break-Even Point in Sales Dollars
Operating income = Sales – Variable costs – Fixed Costs
0 = Sales – (Variable cost ratio × Sales) – Fixed costs
0 = Sales × (1 – Variable cost ratio) – Fixed costs
0 = Sales × (1 – .60) – $800,000
Sales × 0.40 = $800,000
Sales = $2,000,000
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Break-Even Point in Sales Dollars
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Break-Even Point in Sales Dollars
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Break-Even Point in Sales Dollars
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Break-Even Point in Sales Dollars
Profit Targets
How much sales revenue must More-Power generate to earn a
before-tax profit of $424,000?
Sales = ($800,000 + $424,000) ÷ 0.40
= $1,224,000 ÷ 0.40
= $3,060,000
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Multiple-Product Analysis
More-Power plans on selling 75,000 regular sanders and
30,000 mini-sanders. The sales mix is 5:2
Sales
Less: Variable expenses
Contribution margin
Less: Direct fixed expenses
Product margin
Less: Common fixed exp.
Operating income
Regular
MiniSander
Sander
Total
$3,000,000 $1,800,000 $4,800,000
1,800,000
900,000 2,700,000
$1,200,000 $ 900,000 $2,100,000
250,000
450,000
700,000
$ 950,000 $ 450,000 $1,400,000
600,000
$ 800,000
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Multiple-Product Analysis
Break-Even Point in Units
Regular sander break-even units
= Fixed costs ÷ (Price – Unit variable)
= $250,000 ÷ $16
= 15,625 units
Mini-sander break-even units
= Fixed costs ÷ (Price – Unit variable)
= $450,000 ÷ $30
= 15,000 units
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Multiple-Product Analysis
Sales Mix and CVP Analysis
Product
Regular Sander
Mini sander
Unit
Unit
Package Unit
Variable Contribution Sales Contribution
Price Cost
Margin
Mix
Margin
$40
60
$24
30
$16
30
Package total
Package break-even units
= Fixed costs ÷ Package contribution margin
= $1,300,000 ÷ $140
= 9,285.71 units
Sales volume for break-even
Regular sander: 46,429 units
Mini sander: 18,571 units
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2
$80
60
$140
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Multiple-Product Analysis
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Multiple-Product Analysis
Sales Dollar Approach
Projected Income:
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$4,800,000
2,700,000
$2,100,000
1,300,000
$ 800,000
0.4375
Break-even sales = Fixed costs ÷ contribution margin ratio
= 1,300,000 ÷ 0.4375
= $2,971,429
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Graphical Representation of
CVP Relationships
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Graphical Representation of
CVP Relationships
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Graphical Representation of
CVP Relationships
Assumptions of C-V-P Analysis
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The analysis assumes a linear revenue function and
a linear cost function.
The analysis assumes that price, total fixed costs,
and unit variable costs can be accurately identified
and remain constant over the relevant range.
The analysis assumes that what is produced is sold.
For multiple-product analysis, the sales mix is
assumed to be known.
The selling price and costs are assumed to be
known with certainty.
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Changes in the CVP Variables
Alternative 1: If advertising expenditures increase by
$48,000, sales will increase from 72,500 units to
75,000 units.
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Changes in the CVP Variables
Alternative 2: A price decrease from $40 per sander
to $38 would increase sales from 72,500 units to
80,000 units.
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Changes in the CVP Variables
Alternative 3: Decreasing price to $38 and increasing
advertising expenditures by $48,000 will increase sales
from 72,500 units to 90,000 units.
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Changes in the CVP Variables
Margin of safety
– The excess of units sold over break-even
units
– The excess of revenue earned over breakeven sales
Current sales
Break-even volume
Margin of safety
(in units)
500
200
300
Current revenue
$350,000
Break-even volume 200,000
Margin of safety
(in dollars)
$150,000
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Changes in the CVP Variables
Operating Leverage
Automated
System
Manual
System
Sales (10,000 units)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$1,000,000
500,000
$ 500,000
375,000
$ 125,000
$1,000,000
800,000
$ 200,000
100,000
$ 100,000
Unit selling price
Unit variable cost
Unit contribution margin
$100
50
50
$100
80
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DOL of 4
$500,000 ÷ $125,000
DOL of 2
$200,000 ÷ $100,000
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Changes in the CVP Variables
Operating Leverage
Assume a 40% increase in sales
Increase in sales
Degree of operating leverage
Increase in operating income
Sales (14,000 units)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
Automated
System
40%
×4
160%
$1,400,000
700,000
$ 700,000
375,000
$ 325,000
Manual
System
40%
×2
80%
$1,400,000
1,120,000
$ 280,000
100,000
$ 180,000
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CVP Analysis and
Activity-Based Costing
The ABC Cost Equation:
+
+
+
=
Fixed costs
Unit variable cost × number of units
Setup cost × number of setups
Engineering cost × number of
engineering hours
Total cost
Operating Income:
Total revenue
– Total Cost
= Operating income
Break-Even in Units:
 Fixed Costs
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 + (Setup cost  number of setups)
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Break-even  + (Engineering cost  number of engineering hours) 
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in
= 
Price - unit variable cost 
Units
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CVP Analysis and
Activity-Based Costing
• Differences between ABC break-even and
conventional break-even
– Fixed costs differ
• Costs by vary with non-unit cost drivers
– The numerator of the ABC break-even
equation has two nonunit-variable cost terms
• Batch-related activities
• Product-sustaining activities
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CVP Analysis and
Activity-Based Costing
Example Comparing Conventional and ABC Analysis
Cost Driver
Unit Variable Cost
Level of Cost Driver
Units sold
$ 10
Setups
1,000
Engineering hours
30
Other data:
Total fixed costs (conventional) $100,000
Total fixed costs (ABC)
50,000
Unit selling price
20
-20
1,000
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CVP Analysis and
Activity-Based Costing
Example Comparing Conventional and ABC Analysis
Units to be sold to earn a before-tax profit of $20,000:
Units =
=
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=
(Targeted income + Fixed costs) ÷ (Price – Unit variable cost)
($20,000 + $100,000) ÷ ($20 – $10)
$120,000 ÷ $10
12,000
Same data using the ABC
Units = ($20,000 + $50,000 + $20,000 + $30,000) ÷ ($20 – $10)
= $120,000 ÷ $10
= 12,000
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CVP Analysis and
Activity-Based Costing
Example Comparing Conventional and ABC Analysis
Suppose that marketing indicates that only 10,000 units can
be sold. A new design reduces direct labor by $2 (thus, the
new variable cost is $8). The new break-even is :
Units = Fixed costs ÷ (Price – Unit variable cost)
= $100,000 ÷ ($20 – $8)
= 8,333
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CVP Analysis and
Activity-Based Costing
Example Comparing Conventional and ABC Analysis
Projected income if 10,000 units are sold:
Sales ($20 × 10,000)
Less: Variable expenses ($8 × 10,000)
Contribution margin
Less: Fixed expenses
Operating income
$200,000
80,000
$120,000
100,000
$ 20,000
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CVP Analysis and
Activity-Based Costing
Example Comparing Conventional and ABC Analysis
Suppose that the new design requires a more complex
setup, increasing the cost per setup from $1,000 to $1,600.
Also, suppose that the new design requires a 40 percent
increase in engineering support.
New cost equation:
$50,000 (fixed costs)
+ ($8 × units)
+ ($1,600 × setups)
+ ($30 × engineering hours)
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CVP Analysis and
Activity-Based Costing
Example Comparing Conventional and ABC Analysis
Break-even point using the ABC equation:
 $50,000 
 + $1,600  20 
Break-even  + $30  1,400 
  10,333
in
= 
 $20 - $8 
Units
This exceeds the firm’s sales capacity!
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