HA355 : The Class : Financial Statement : CVP Analysis : Lesson231 
CostVolumeProfit, (CVP), Analysis: A Definition.
CVP is a management tool that expresses relationships among sales volume, costs
and profits. CVP can be used in the form of a graph or an equation. Costvolumeprofit
analysis can answer a number of analytical questions, such as:
What is the breakeven revenue of a restaurant?
How much revenue does a restaurant need to achieve a given profit?
What level of price change is needed to achieve a given profit?
What is the effect of cost changes on the profitability of an operation?
Many other "what if" type of questions
Variable versus fixed costs:
In order to use CVP analysis, Managers need to divide operating costs in to
two categories. Variable expenses are those cost that vary with changes in sales
volume. Fixed cost are those cost that remain constant with changes in sales
volume. Quite often we run into expenses that are of a mixed nature; in this
case managers needs to breakout the cost, as best they can, into its fixed and
variable components.
Management may also designate fixed and variable expenses within their accounting
system. In addition there are various other ways of breaking out cost. Consider
the following analysis of a restaurant operation's high and low months:
High month  Low month  Change  Variable 


Meals  8,000  15,000  7,000  Per meal  High month  Low month 
Sales  $ 80,000  $ 150,000  
Cost of Sales  (24,000)  (45,000)  (21,000)  (3.00)     
Wages  (22,000)  (32,500)  (10,500)  (1.50)  (10,000)  (10,000) 
Other Controllable  __(24,000)  __(27,500)  (3,500)  (0.50)  (20,000)  (20,000) 
Operating Income  $ 10,000  $ 45,000  
________  
Variable  (5.00)  _________  _________  
Fixed  (30,000)  (30,000) 
By comparing a high and low months, estimates can be made of variable and fixed
costs. Consider Wages. The difference between the two months is $10,500. By
dividing this amount by the change in meals, 7,000 meals, results in an estimated
variable wage cost of $1.50 per meal. We can then estimate the fixed cost by
looking at either the high or the low month. For the high month variable wages
are $22,500 ($1.50x 15,000 meals). Deducting the $22,500 from total wages of
$32,500 equals an estimated fixed costs of $10,000. Applying this technique
to the low month will give the same results. Try it yourself!
Applying this procedure to all three expense categories results in total variable
expense of $5.00 per meal and total fixed costs of $30,000. The relationship
between sales, variable expense, fixed expenses and income can then be reflected
in a simple formula. For the high month this is:
$150,000($5.00x15, 000 meals)$30,000=$45,000
For the low month this is:
$80,000($5.00x8, 000 meals)$30,000=$10,000
CVP Model
We are now going look at a larger example and use it to learn some concepts
and see how CVP analysis can be applied. The following table shows an income
statement of the NAU Grill with expenses broken out into variable and fixed:
NAU Grill


Income Statement

Expense  Variable Cost  
Amount  Variable  Fixed  Ratio  Per meal  
Sales  

$ 1,000,000  

____200,000  _______  _______  

1,200,000  100.0%  12.00  
Cost of Sales  

310,000  $ 310,000  25.8%  3.10  

_____46,000  46,000  3.8%  0.46  

____356,000  
Gross profit  844,000  
Controllable Expenses  

348,000  148,000  $ 200,000  12.3%  1.48 

72,000  22,000  50,000  1.8%  0.22 

40,000  13,000  27,000  1.1%  0.13 

25,000    25,000  0.0%   

28,000  13,000  15,000  1.1%  0.13 

_____50,000    50,000  0.0%   
Total controllable  

____563,000  
Operating profit  281,000  
Noncontrollable expenses  

60,000    60,000  

15,000    15,000  

35,000    35,000  

______3,000    3,000  
Total noncontrollable  

____113,000  
Income before income taxes  168,000  
Provision for income taxes @17%  _____28,560  
Net income  $ 139,440  
Meals sold  100,000  
Total variable costs  $ 552,000  46.0%  5.52  
Total fixed costs  $ 480,000 
The NAU Grill has total fixed costs of $480,000. Variable cost is $552,000,
which when divided by meals sold give a variable cost per meal of $5.52. Variable
cost can also be expressed as a ratio of 46%. To facilitate looking at a number
of "what if" situations, we have condensed the income statement in
the following manner:
NAU Grill  
Income Statement  Variable Cost  
Amount  Ratio  Per meal  
Sales  $1 ,200,000  100.0%  12.00 
Variable Costs  ____552,000  ___46.0%  _____5.52 
Contribution Margin  648,000  54.0%  6.48 
Fixed Costs  ____480,000  
Income before income taxes  168,000  
Provision for income taxes  _____28,560  
Net income  $ 139,440 
You will note a new term in our statement: "contribution margin."
Contribution margin is defined as the excess of revenues over variable
cost. The term contribution margin is used since this is the amount that
is to cover fixed costs and provide a profit. NAU Grill's contribution margin
ratio is 54%. Contribution margin per meal is $6.48 per meal.
To continue our analysis, we will be using two equations where
S= sales,
F= fixed costs
I= income before taxes
CMm= contribution margin per meal
CMR= contribution margin ratio
M= number of meals
To determine sales:
S = 
F + I
CMR 
=

480,000 + 168,000
54% 
= 1,200,000

To determine meals:
M = 
F + I
CMm 
=

480,000 + 168,000
6.48 
= 10,000 meals 
We can now determine the breakeven point for the NAU Grill. In terms of sales
it is:
S =  F + I CMR 
=  480,000 + 0 54% 
= 888,889

In terms of meals it is:
M =  F + I CMm 
=  480,000 + 0 6.48 
= 7,074meals

From this point on we will be using the meal formula only since it is more
flexible to use when dealing with different scenarios.
The column titled "Breakeven" shows the breakeven income statement:
Start

Breakeven


Sales  $ 1,200,000  $ 888,889 
Variable Costs  $ 552,000  ____408,889 
Contribution Margin  648,000  480,000 
Fixed Costs  ____480,000  ____480,000 
Income before income taxes  168,000   
Provision for income taxes @ 17%  _____28,560   
Net income  $ 139,440  $  
Meals sold  100,000  74,074 
Per Meal  
Sales  12.00  12.00 
Variable Costs  ______5.52  ______5.52 
Contribution Margin  6.48  6.48 
CVP analysis can also be visualized by means of a CVP graph:
The point where revenue and total cost meet is the breakeven point; to the left
the difference between the two lines is the loss; to the right it is the income
before taxes. However, in order to obtain precise numbers we will need to use
formulas
Let us look at two more situations. How many meals do we need to earn $150,000
before taxes?
M =

F + I
CMm 
=

480,000 + 150,000
6.48 
= 97,222meals

Then, lets consider $150,000 in net income. To do that we first need to calculate
before tax income:
I =

____N___
(100%  T) 
=

__150,000__
(100%  17%) 
= 180,723 
Where:
N=net income
I= income before taxes
T=tax rate
Then we can calculate the required number of meals :
M =

F + I
CMm 
=

480,000 + 180,723
6.48 
= 101,963meals 
The condensed income statement for these two cases is as follows:
Before Tax

Net Income


Sales  $ 1,166,667  $1,223,561 
Variable Costs  ______536,667  ______562,838 
Contribution Margin  630,000  660,723 
Fixed Costs  ______480,000  ______480,000 
Income before income taxes  150,000  180,723 
Provision for income taxes @ 17%  _______25,500  _______30,723 
Net income  $ 124,500  $ 150,000 
Meals sold  97,222  101,963 
Per Meal  
Sales  12.00  12.00 
Variable Costs  _________5.52  _________5.52 
Contribution Margin  6.48  6.48 
Two more cases and then we finished! Let's assume that NAU Grill experiences
some costs increases: fixed expense go up by $20,000 to $500,000 and variable
expense go from $5.52 to $6.82 per meal. Under these circumstances how many
additional meals over the 101,963 need to be sold in order to maintain net income
at $150,000? Using the meal formula we can quickly calculate the requirement:
M =

F + I
CMm 
=

500,000 + 180,723
5.18 
= 131,414meals 
Cost increase example


Sales  $ 1,576,964 
Variable Costs  _________896,241 
Contribution Margin  680,723 
Fixed Costs  _________500,000 
Income before income taxes  180,723 
Provision for income taxes @ 17%  __________30,723 
Net income  $ 150,000 
Meals sold  131,414 
Per Meal  
Sales 
12.00 
Variable Costs  ____________6.82 
Contribution Margin  5.18 
Let's assume that 131,000 meals is beyond reasonable expectations. Another
approach would be a price increase in menu items. What average price per meal
do we need in order to achieve net income of $150,000 serving 100,000 meals?
To calculate this we need to manipulate our formula in order to solve for the
contribution margin per meal:
M = 
F + I
CMm 
Then we solve for CMm:
CMm =

F + I
M 
=

500,000 + 180,723
100,000 
= 6.80723 
We can then solve for the required average price per meal:
Where:
P= Average price per meal
Vm= Variable cost per meal=$6.82
CMm= contribution per meal=$6.81
P = Vm + Cm = 6.82 + 6.80723 = 13.62723
The condensed income statement will now be as follows:
Price increase example


Sales  $ 1,362,723 
Variable Costs  ____________682,000 
Contribution Margin  680,723 
Fixed Costs  ____________500,000 
Income before income taxes  180,723 
Provision for income taxes @ 17%  _____________30,723 
Net income  $ 150,000 
Meals sold  100,000 
Per Meal  
Sales  13.62723 
Variable Costs  ____________6.82000 
Contribution Margin  6.80723 
What if management wanted to take a look at the effect of different price increases
on the required number of meals needed to achieve a net income of $150,000?
One way to do this would be to try different prices in the above analysis and
have the computer calculate the required number of meals. Spreadsheet programs,
such as Excel, can simplify this task by use of a "table" feature.
We have prepared such a table relating average meal prices in a range of $12.60
to $13.70 to the required number of meals in order to produce a net income of
$150,000. A graph was produced from the table showing the relationship in a
graphic forme:
Table for $150K Net Income  
Price

Meals

12.00

131,414

12.10

128,925

12.20

126,528

12.30

124,220

12.40

121,993

12.50

119,846

12.60

117,772

12.70

115,796

12.80

113,833

12.90

111,961

13.00

110,149

13.10

108,395

13.20

106,696

13.30

105,050

13.40

103, 453

13.50

101,905

13.60

100,401

13.70

98,942

There are many other ways to apply CVP analysis. Spreadsheet programs are well
suited for this task. To experiment with the file used for the examples in this
section, download here.
Are there any disadvantages to CVP analysis?
Yes. Some of the shortcomings are:
Cost volume profit analysis can get complicated when applying it to a multiproduct operation, which is usually the case with restaurant operations. Each of the menu items on the restaurant's menu can have different variable cost ratios. To get around this problem an average variable cost ratio is used; this needs to be recognized when interpreting the analysis results.
Variable cost and fixed cost may differ from assumptions if the analysis is applied over a wide range of potential sales. Consequently the analysis technique needs to be restricted to a narrow range of sales volumes.
Cost volume profit analysis only provides approximate answers. In addition to quantitative studies, such as CVP analysis, management needs to investigate operations directly and to exercise judgement before making any changes to operations.
Go back to CostVolumeProfit Analysis
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