CostVolumeProfit Analysis
CVP Analysis is a way to quickly answer a number of important
questions about the profitability of a company's products or services. CVP
Analysis can be used with either a product or service. Our examples will usually
involve businesses that produce products, since they are often more complex
situations. Service businesses (health care, accounting, barbers & beauty shops,
auto repair, etc.) can also use CVP Analysis.
It involves three elements:
 Cost  the cost of making the product or providing a
service
 Volume  the number of units of products produced or
hours/units of service delivered
 Profit  Selling Price of product/service  Cost to make
product/provide service = Operating Profit
The first two items are information available to business
managers, about their own business, products and services. This type of
information is not generally available to those outside the business. They
constitute important operating information that can help managers asses past
performance, plan for the future, and monitor current progress. As for the third
item, a business can't stay in business very long without profits.
It is important to know whether the company is profitable as
a whole. It is also important to know if a particular product is profitable. A
business that sells 100 or more different products may lose sight of a single
product. If that product becomes unprofitable (selling for less than the cost to
produce & sell), the company will lose money on each and every sale of that
product. The company might raise the selling price, cut production costs or
discontinue the product entirely. Building a business with 100 products we know
are profitable is good management. CVP & variable costing provide the tools to
make this happen in a real business.
A successful business can be built around a single profitable
product. It can also be built around hundreds or thousands of profitable
products. Many businesses start small and grow over time, adding products as
they gain experience and are able to identify and/or develop new markets and
products. No matter the size of the business or the number of products, the same
rules apply. Each product must "carry its own weight" for the business to be
profitable.
Using CVP Analysis we can analyze a single product, a group
of products, or evaluate the entire business as a whole. The ability to work
across the entire product line in this way gives us a powerful tool to analyze
financial information. It provides us with daytoday techniques that are easy
to understand and easy to use. The concepts parallel the real world, so they are
easy to visualize and use. The math is very simple  no complex formulae or
techniques. Just simple formulae that can be easily modified to analyze a large
variety of situations.
Quiz Yourself
CVP Analysis is important because:
a. the teacher says so.
b. it sounds cool to say "see vee pee".
c. it is a good way to analyze the profitability of a company's
products or services.
d. I haven't a clue.
Answer
CVP Analysis is important because:
a. the teacher says so.
b. it sounds cool to say "see vee pee".
c. it is a good way to analyze the profitability of a
company's products or services.
d. I haven't a clue.
CVP Relationships
Cost  product cost, consisting of materials, labor, overhead,
etc.
Volume  number of units of product sold in a given period of
time
Profit  Selling Price minus Cost, per unit or in total
The greater the volume, the greater the TOTAL profit.
Approaches to product costs
Full Costing is used in financial accounting. The full
cost of a product includes materials, labor and manufacturing overhead. Not
included: Selling and administrative costs.
Variable Costing is used in managerial accounting.
Costs are classified as either Variable or Fixed, depending on their Cost
Behavior.
Cost Behavior
Costs are classified according to how they behave, in relation
to units of production.
CAUTION: Cost behavior can be viewed in terms of
total costs or unit costs. Both approaches will be used, but they are
not interchangeable.
Fixed Costs
Total Fixed Costs  stay essentially the same month to
month, regardless of the number of units produced.
Unit Fixed Costs  goes down as production goes up
Variable Costs
Total Variable Costs  go up and down in direct
proportion to units produced.
Unit Variable Costs  stay the same regardless of how
many units are produced.
Accounting information is captured once by the accounting
system. In Accounting I you learned how to analyze transactions, record journal
entries, post to the ledger accounts and prepare financial statements for use by
those outside the company. That is one way to organize accounting information,
but it is not the only way. That same information can be organized in many
different ways. In this section we are going to simplify the process greatly.
Our topic is CostVolumeProfit, so we will focus on income statement accounts,
Revenues and Expenses. For now we can ignore balance sheet accounts.
Managers focus on income statement accounts because these are
the ones affected by daytoday operating activities. Companies produce/purchase
and sell products or services. Companies may uses hundreds of income statement
accounts to track all their different types of revenues and expenses. We are
going to simplify the income statement by dividing all expenses into one of two
categories: Variable and Fixed. To master this material you need to master these
two concepts.
VARIABLE COSTING  in general
CVP Analysis uses Variable Costing concepts. In this context we
will divide ALL costs into one of two categories: Variable or Fixed. We refer to
this as "cost behavior." In CVP Analysis cost behavior will be discussed on BOTH
a total cost and per unit basis. The facts will remain the same,
but the behavior will appear different, depending on the context. Read
carefully, especially on exams and in problems, so you understand the context of
the question/problem: total cost or per unit. Since CVP Analysis can
answer questions about both, we will switch back and forth frequently in our
discussion. Tighten you "thinking bolts" and read carefully in this section.
In CVP Analysis we assume that the number of units produced
equals the number of units sold. In other words, we factor out changes in
inventory during a production period. In the "real world" managers often include
inventory changes & income taxes in CVP Analysis. In this course we will ignore
both inventory changes and income taxes. Here, you should gain a basic working
knowledge of CVP Analysis fundamentals.
VARIABLE COSTS (VC)
Total Variable Costs increase in direct proportion to
production/sales.
Unit Variable Costs stay the same as production fluctuates
within the relevant range.
EXAMPLE: Mike's Bikes builds the XRacer from its inventory
of parts. Each bicycle is made up of the following parts:
 frame (1)
 seat (1)
 handlebars (1)
 wheels (2)
 tires (2)
 gears & shifting system (1)
 brakes & braking system (1)
Parts prices vary over time. Currently the cost to produce one
bicycle is $70.
UNITS of Product : XRacer 
Cost Per Unit 
Total Costs 

1 bicycle = $70 
1 bicycle @ $70
= $70 

1 bicycle = $70 
2 bicycles @ $70
= $140 

1 bicycle = $70 
3 bicycles @ $70
= $210 
Per Unit costs stay the same; total costs increase in direct
proportion to the number of units produced or sold (sales or production volume).
The Relevant Range is the number of units that can be produced or sold
under normal circumstances. That might vary due to seasonal demand or factory
capacity. To go beyond the relevant range would generally require the additional
of more equipment, buildings, personnel, etc. and that would cause a change in
all costs. We presume that we are working within the relevant range when doing
CVP Analysis. This makes the task much easier. It also helps us understand when
we will need to address the need to expand our business.
Variable Costs include any total cost that varies
in direct proportion to volume. These commonly include:
 component parts, packaging, etc.
 production labor
 sales commissions (percentage or per unit basis)
 other costs allocated on a per unit basis
FIXED COSTS (FC)
Total Fixed Costs (FC) do not change as production/sales
increases.
Unit Fixed Costs decrease as production increases within the
relevant range.
Ask yourself this question: Would a cost be zero if
production was zero? If the answer is NO, you are looking at a fixed cost. A
common example would be rent on a building. The company must pay rent on the
building even if it sells no products in a given month! Some other common
costs that follow this pattern are:
 managers & executives salaries
 insurance
 advertising
 real estate & property taxes
 security service
 cleaning & maintenance costs
 depreciation expense on buildings, vehicles & equipment
EXAMPLE: Mike's Bikes spends $5,000 per month in fixed costs.
If they make X bicycles per month.... 
their fixed costs PER UNIT will be...... 
1,000 bicycles 
$5,000 / 1,000 bicycles = $5.00 per bicycle 
2,000 bicycles 
$5,000 / 2,000 bicycles = $2.50 per bicycle 
3,000 bicycles 
$5,000 / 3,000 bicycles = $1.67 per bicycle 
4,000 bicycles 
????????? Quick Quiz try these on your own 
5,000 bicycles 
????????? 
Answer:
$5,000 / 4,000 bicycles = $1.25 per bicycle
$5,000 / 5,000 bicycles = $1.00 per bicycle
Quick Quiz
Do Total Fixed Costs change as production goes up?
Answer:
NO.
Total Fixed Costs stay the same as production goes up.
Unit Fixed Costs decrease as productions goes up.
Since Fixed Cost per Unit goes down as sales/production go
up, it is always a good idea to sell/produce more units. In the real world,
companies try to produce approximately the same number of units they expect to
sell in a given period of time. If you think about the computer industry you
will see how important this can be. If a computer company manufactures too many
units it may have a stock of merchandise that is hard to sell as new computer
chips are introduced to the market. It may have to sell its products at a
discount or even at a loss to liquidate its inventory. Chapter 8 discusses "Just
In Time" (JIT) inventory management, which is used to help reduce inventory
costs, by having parts delivered "just in time" to go into production. JIT
inventory systems are commonly used in automobile assembly plants. Using JIT
reduces a company's risk of carrying a stock of parts that may quickly become
obsolete.
MIXED COSTS
Mixed costs change somewhat in relation to production, but not
proportionately like Variable Costs do. Mixed costs generally have a fixed
portion and a variable portion. We deal with these costs by separating them into
these two parts  so we are back to only 2 types of cost behavior.
A common example of a mixed cost would be a rental car. You
might rent a car for a weekend for $20, for up to a total of 200 miles. You will
be charged $ .10 for each additional mile you drive. The flat rate of $20
represents the fixed component; the $ .10 per mile represents the variable
component. If you drive 300 miles you will pay:
Fixed component 
$20.00 
Variable component 
$10.00 (100 extra miles @ $ .10) 
Total cost 
$30.00 
We have a couple of simple ways to separate costs into their
fixed and variable components. One way is called the HighLow Method. It looks
at the highest & lowest costs over a period of several months to come up with a
simple formula that can be used to calculate the variable & fixed costs.
Separating mixed costs into their parts is an inexact practice. At best it is
an estimate, or approximation, that is only as accurate as the method we use.
This is not usually a significant issue, since all costs are eventually included
in our equations. However, if mixed costs constitute a percentage of total
costs, it is necessary to be as accurate as possible. More sophisticated methods
should be used when a higher level of accuracy is needed.
Contribution Margin
The Contribution Margin (CM) is one of the most essential parts
of variable costing and managerial accounting.
CM = Selling Price  Variable Costs
It can be calculated as either unit CM or total CM.
CM is the profit available to cover fixed costs and provide
net income to the owners.
Break Even analysis
One of the first uses of variable costing is calculating the
break even point. This is the point at which sales exactly equals total costs.
It can be expressed as either units or sales dollars.
Break Even Units (BE units) the number of units needed to
cover fixed costs for a given period of time.

BE units example:
XYZ Co. has monthly fixed costs of $2,000. They sell a single
product for $30 each. Variable costs are $10 per unit. They sell about 200 units
per month. Calculate the break even point in units.
1) Calculate CM
Selling price 
$ 30

Variable costs 
10

Contribution margin (CM) 
$ 20

2) Calculate BE units
BE Units 
= 
Total Fixed Costs
Unit CM 
= 
2000
20 
= 
100 units to break even

proof:
Contribution margin 100 units @ $20 
$ 2000

less Total Fixed Costs 
2000

Profit (loss) 
$ 0

When sales are below the Break Even point a company is
operating at a loss; Above the BE point they will be operating at a profit. The
company is selling 200 units per month, well above the break even point, so they
are operating at a profit.
How much profit will they make by selling 200 units per
month?
Contribution margin 200 units @ $20 
$ 4000

less Total Fixed Costs 
2000

Profit at 200 units per month 
$ 2000


Example 2:
XYZ is facing fierce competition from a new company, and
management decides to lower the selling price of their product to $20 per unit.
They also decide to take out advertising at a cost of $400 per month.
Recalculate their Break Even point given the new information:
1) Calculate CM
Selling price 
$ 20

Variable costs 
10

Contribution margin 
$ 10

2) Calculate BE units
The $400 advertising costs will increase total fixed costs; add
it to the numerator (top number).
BE Units 
= 
Total Fixed Costs
Unit CM 
= 
2400
10 
= 
240 units at break even 
This will be a problem for the company. Their new break even
point is higher than their normal monthly sales. They will be operating at a
loss under these conditions, and must reevaluate the decision.
proof:
Contribution margin 200 units @ $10 
$ 2000

less Total Fixed Costs 
2400

Profit (loss) 
($ 600)


Example 3:
We can work the formula in reverse. Assume they include the
advertising costs of $400 per month, and sell 200 units. What selling price will
put them at the break even point?
CM Unit at BE 
= 
$2400
200 
= 
$12 CM 
They must reverse the calculation, and add variable costs to
CM to arrive at the new selling price.
Contribution margin 
$ 12

Variable costs 
+ 10

Selling price 
$ 22

Proof:
Selling price 
$ 22

Variable costs 
10

Contribution margin 
$ 12

BE Units 
= 
Total Fixed Costs
Unit CM 
= 
2400
12 
= 
200 units at break even 
proof:
Contribution margin 200 units @ $12 
$ 2400

less Total Fixed Costs 
2400

Profit (loss) 
$ 0

CM Ratio and BE sales volume
The CM can also be viewed as a percentage or ratio. To calculate
the CM ratio, divide CM by the Selling Price (SP).
ABC Co. has monthly fixed costs of $2,400. They sell a single
product for $40 each. Variable costs are $24 per unit. They sell about 250 units
per month. Calculate their break even point in sales dollars (also called sales
volume).
Selling price 
$ 40

Variable costs 
24

Contribution margin 
$ 16

Their CM Ratio is CM/SP = 16/40 = .40 or 40%
(In accounting we usually carry calculations out to 4 decimal
places).
Break Even Sales Volume
Total Fixed Costs / CM Ratio = 2400/.40 = $6000 in sales per
month
proof:
$6000 / $40 SP per unit = 150 units to break even, or:
BE Units 
= 
2400
16 
= 
150 units at break even 
When do we use CM Ratio and BE sales volume?
We can use these calculations anytime. They are especially
useful when the company sells a large number of different products  in other
words a large sales mix. Take for example a convenience store. They might sell
200 different items, or more. Each item carries its own selling price, and
contribution margin per unit.
Calculating all those contribution margins would be a huge
job. And with a sales mix, the company would have to carefully track each and
every product. It is much easier to consider the merchandise as a large group,
and use the CM Ratio.
QuikMart operates a convenience store, and their CM Ratio is
approximately 42%. Their monthly overhead (fixed costs) is $2604. What sales
volume is needed to break even?
BE volume = TFC / CM Ratio = $2604 / .42 = $6200 per month in
sales volume
It is not necessary for the owner to know exactly how many
Snickers bars, Milky Way, cans of Coke etc. will be sold each month. That will
depend on the what the customers want to buy. The owner will stock a variety of
products. By using CM Ratio we don't need to know each item individually.
Of course, in the real world not all products will earn the
same CM Ratio. Some products face stiff competition, and the company will charge
accordingly. For instance, they will sell milk at a price similar to grocery
stores, earning a rather small CM. But the neat trinkets that adorn the front
counter will be sold for twice, three, four times or more their cost, greatly
improving the company's overall profit margin. A few high profit items can make
up for the "loss leaders" in a company's product mix.
[Loss leaders are products sold at a low price, sometimes at
a loss, to attract customers, and get them to shop in your store. Free items,
2fer sales, 1 cent sales, etc. are all examples of the loss leader strategy
used by grocery stores to get your business. They hope you will buy some of the
high profit items while you are shopping in their store. Sometimes they will
require a minimum purchase, or limit the number of loss leader items a customer
can buy.]
CVP Graphs
CVP relationships and the break even formula can all be
illustrated with a simple graph. CVP graphs are a great way to convey
information. They are especially useful in presenting alternatives to decision
makers, many of whom may more easily grasp the concepts with a visual
presentation, rather than page full of numbers.
