Chapter Four
Cost Volume Profit
Analysis
Cost Behavior
A cost is classified as either
fixed or variable, according to
whether the total amount of the
cost changes as activity
changes.
Activity is a general term
denoting anything that the
company does; examples: units
of product sold or produced,
hours worked, invoices
prepared, and parts inspected.
Volume is a common measure
of activity.
Definitions
Variable costs change, in total, in direct proportion
to changes in volume.
Fixed costs remain the same in total over a wide
range of volume.
Total Costs = Fixed costs + Variable costs
Classification of Cost by Cost Behavior
Total Fixed Cost
Behavior
$
Relevant Range
Number of Units Produced
Total Variable Cost
Behavior
$
Number of Units Produced
Cost per Unit
Variable
Fixed
Mixed Cost
A mixed cost is a cost that has a fixed and
a variable element
 Example would be utilities in a factory
 Can separate mixed costs into fixed and
variable by:

 Regression
 Scatter
Diagram
 Account analysis
 High-low method
High-Low Method Example
Assume power costs at 10,000 units
produced are $20,000 and at 12,000 units
produced are $21,000.
 Is power a fixed, variable or mixed cost?
 If mixed, how much is fixed and how much
is variable

It’s Mixed!
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We know that it is mixed because it is increasing
in total and decreasing per unit as activity
increases
To find variable component divide the change in
cost by the change in activity
(21,000 - 20,000)/(12,000 - 10,000) = $0.50 per
unit
total cost - total variable cost = Fixed cost
21,000 - (12,000 *$0.50) = $15,000 fixed cost
Total cost = $15,000 + $0.50 per unit
Definitions
Cost-volume-profit (CVP) analysis is a
method for analyzing the relationships
among costs, volume, and profits.
Contribution margin per unit (CMU) is the
difference between selling price per unit
and variable cost per unit.
Definitions
Contribution margin ratio (CMR)is per-unit
contribution margin divided by selling
price, or total contribution margin divided
by total sales dollars.
Variable cost ratio is per-unit variable cost
divided by selling price, or total variable
costs divided by total sales dollars.
Contribution margin ratio plus variable cost
ratio equals 100 percent.
Cost Behavior Example
Selling price per backpack
$20.00
Cost of backpacks
10.00
Variable cost to pack and ship
1.00
Sales commission (5% of sales)
1.00
Total unit variable costs
$12.00
Monthly fixed costs
$40,000
CVP Equation
The CVP equation can be used to solve
many CVP problems
 Sales - variable costs - fixed costs = profit
 If x = quantity sold; SP = selling price and
VCU = variable cost per unit equation
becomes:
 SPx - VCUx - FC = profit

Contribution Margin Income
Statements at Various Sales
Levels
5,000 units 6,000 units 7,000 units
Sales ($20 per unit)
$100,000 $120,000 $140,000
Variable costs ($12/unit) 60,000
72,000
84,000
Contribution margin ($8 /unit)$40,000$48,000
$56,000
Fixed costs
40,000
40,000
40,000
Income
$0
$8,000
$16,000
Cost-Volume-Profit Graph
Dollar
s $160,000
Total
Revenues
$140,000
$120,000
Profit
Area
$100,000
$80,000
Total
Cost
Loss
Area
Break-even point,
5,000 units, $100,000
$60,000
$40,000
$20,000
$0
2,000
4,000
6,000
Unit Sales
8,000
10,000
Break-Even Point
Break-even point is the point at which profits
are zero because total revenues equal
total costs, or where the profit equals 0
SPx - VCUx - FC = 0
Break-Even Sales
BEP in units
BEP in sales $
=
Total fixed costs
--------------------CMU
=
Total fixed costs
--------------------CMR
Break-Even Sales
BEP in units =
$40,000
----------- = 5,000 units
$20 - $12
BEP in sales $=
$40,000
---------- = $100,000
$8 / $20
Target Profit Equation
The equations that follow to find target
profit come from the CVP equation
 SPx - VCUx - FC = target profit
 Solving this for x you get:

x
= (FC + target profit)/(SP - VCU)
 SP - VCU = CMU which is contribution
margin per unit
Target Profit
=
FC + Target profit
---------------------------CMU
In sales dollars=
FC + Target profit
---------------------------CMR
In units
Target Profit of $5,000
in units
=
$40,000 + $5,000
--------------------- = 5,625 units
$20 - $12
$40,000 + $5,000
In sales dollars=--------------------- = $112,500
$8 / $20
Indifference Point
•
•
•
The indifference point is the level of
volume at which total costs, and hence
profits, are the same under both cost
structures.
Suppose that you currently have variable
costs of $7 per unit and fixed costs of
$40,000. A new technology will lower vcu
to $4 and increase fixed costs to $95,000.
Above what volume does this make
sense?
Indifference Point Solution
$40,000 + $7X = $95,000 + $4X
X = 18,333 units (rounded)
This means that at any volume above 18,333
you would be better off with the lower variable
cost and the higher fixed cost
Example of using equation
Using our original information, assume that
management would like to know what
price would need to be charged to earn a
income of 20% of sales at a sales level of
7,000 units
The equation becomes
7,000*SP - 7,000*11 - 0.05*7,000*SP 40,000 = .2*7,000*SP
.75*7,000*SP = 117,000
SP = $22.86
Margin of Safety
The difference in volume from the expected
level of sales to the break-even point is
called the margin of safety (MOS).
If actual sales are 6,000 units, the margin of
safety is 1,000 units (6,000 - 5,000).
If actual sales are $120,000, the margin of
safety is $20,000 ($120,000 - $100,000).
Multiple Products
For multiple products, must assume that
they are sold in a constant mix to do CVP
 Calculate a weighted average contribution
margin per unit or contribution margin ratio
and then proceed with CVP as normal.

Multiple Product Example
Product A sells for $8 per unit and has
variable costs of $5 per unit; Product B sells
for $9 per unit and has Variable cost of $5
per unit.
 The sales mix is 3:2, meaning that for every
3 units of A that are sold, 2 units of B are
sold
 Fixed costs are $170,000 per year.
 How many of each must be sold to
breakeven?
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Calculation of Average CMU
A
B
Selling Price
$8.00
$9.00
Variable Cost
$5.00
$5.00
Contribution Margin
$3.00
$4.00
Mix
Total CM
3
$9.00
2
$8.00
Units
Average CMU
Overall
$17.00
5
$ 3.40
Multiple Product Break Even
Point
Fixed costs are $170,000
 Weighted average CMU is $3.40
 Breakeven point is $170,000/3/40 =
50,000 units
 That makes 30,000 units of A and
20,000 of B (in the 3:2 mix)
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Assumptions and Limitations of
CVP Analysis
Selling price, per-unit variable cost, and
total fixed costs must be constant
throughout the relevant range.
 The company sells only one product, or
the sales of each product in a multiproduct
company are a constant percentage of
sales.
 Production equals sales in units.
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Relevant Range
Relevant range is the
range of volume over
which it can
reasonably expect
selling price, per-unit
variable cost, and
total fixed costs to be
constant.
Do Fixed Costs Add Risk?
Fixed costs cannot be reduced quickly
 When sales fall off, fixed costs remain
 When sales rise, fixed costs also remain
the same
 Do fixed costs add risk?
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Operating Leverage
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Firm’s with high levels of fixed costs are said to
have high operating leverage.
Their profit will move faster (up or down) in
response to a change in sales.
The ratio of CM/profit will tell you how many
multiples a % change in sales will have on
profits
For example if a firm has CM of 30,000 and
profit of 10,000, a 10% increase in sales gives a
30% increase in profits!! Try it out.
Constraints
A constraint exists when a supply of a
resource (labor, material, processing time)
is inadequate to meet demand
 Demand itself is also a constraint
 Need to get the most out of each unit of a
constrained input
 Do this by calculating a contribution
margin per unit of the constrained
resource
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Constraints Example
Assume that there are only 800 labor
hours available, product A needs 2 hours
per unit, product B needs 3 hours per unit.
 Product A has a CMU of $5.00, B is $6.00
 Demand for each product is 200 units
 How many units of each product should
you produce?
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