Unit 1 - Cost-Volume -Profit Relationships
1. Cost- Volume – Profit (CVP) Analysis
Cost- volume profit (CVP) Analysis is one of the most powerful and simple business planning
and analysis tools that managers have at their command. Cost –volume-profit (CVP) analysis is
a way of examining the behavior of total revenues, total cost and operating income as changes
occur in the output level, selling price, variable costs per unit or fixed costs. Cost-volume-profit
(CVP) analysis is the study of the effects of changes in costs and volume on a company’s profits.
CVP analysis is important in profit planning. It also is a critical factor in such management
decisions as setting selling prices, determining product mix, and maximizing use of production
facilities.
Even though the term profit appears in the term Cost- volume profit (CVP) Analysis, It is not
confined to profit seeking enterprises. The mangers of nonprofit organizations also benefit from
the study of CVP relationships. Why? No organization has unlimited resources, and knowledge
of how cost fluctuate as volume changes helps managers to understand how to control costs.
Cost- volume profit (CVP) Analysis is therefore a vital tool in businesses decisions as what
products to produce and sale, what pricing policy, what marketing strategy to employ, and what
type of productive facilities to acquire and utilize.
Cost-Volume- Profit (CVP) analysis is based on several assumptions.
1. Changes in the level of revenues and costs arise only because of changes in the number of
product (service) units produced and sold.
2. Total costs can be divided in to a fixed component and a component that is variable with
respect to the level of output.
3. The behavior of total cost and total revenue is linear in relation to output units within the
relevant range and time period.
4. The unit selling price, unit variable costs, and fixed costs are known and constant.
5. The analysis either cover a single product or assumes that the sales mix when multiple
products are sold will remain constant as the level of total units sold changes.
6. Time value of money is not considered.
Note that when these assumptions are not valid, the CVP analysis may be inaccurate
Unit 1- CVP Relationships
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Cost and Management Accounting - II
1.1. Variable and Fixed Cost Behavior and Patterns
Variable Costs: - Variable costs are costs that vary in total directly and proportionately with
changes in the activity level. If the level increases 10%, total variable costs will increase 10%. If
the level of activity decreases by 25%, variable costs will decrease 25%. Examples of variable
costs include direct materials and direct labor for a manufacturer; cost of goods sold, sales
commissions, and freight-out for a merchandiser; and gasoline in airline and trucking companies.
A variable cost may also be defined as a cost that remains the same per unit at every level of
activity.
Example: Assume that Addis Company manufactures radios that contain a $10 digital clock. The
activity index is the number of radios produced. As Addis manufactures each radio, the total cost
of the clocks increases by $10. As part (a) of Figure 1-1 shows, total cost of the clocks will be
$20,000 if Addis produces 2,000 radios, and $100,000 when it produces 10,000 radios. We also
can see that a variable cost remains the same per unit as the level of activity changes. As part (b)
of Figure 1-1 shows, the unit cost of $10 for the clocks is the same whether Addis produces
2,000 or 10,000 radios.
Figure 1-1: Behavior of total and unit variable costs
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Cost and Management Accounting - II
Fixed Costs: - Fixed costs are costs that remain the same in total regardless of changes in the
activity level. Examples include property taxes, insurance, rent, supervisory salaries, and
depreciation on buildings and equipment. Because total fixed costs remain constant as activity
changes, it follows that fixed costs per unit vary inversely with activity: As volume increases,
unit cost declines, and vice versa.
Example: Assume that Addis Company leases its productive facilities at a cost of $10,000 per
month. Total fixed costs of the facilities will remain constant at every level of activity, as part (a)
of Figure 1-2 below shows. But, on a per unit basis, the cost of rent will decline as activity
increases, as part (b) of Figure 1-2 shows. At 2,000 units, the unit cost is $5 ($10,000 2,000).
When Addis produces 10,000 radios, the unit cost is only $1 ($10,000 10,000).
Figure 1-2: Behavior of total and unit fixed costs
Relevant Range
In Figure 1-1 part (a), a straight line is drawn throughout the entire range of the activity index for
total variable costs. In essence, the assumption is that the costs are linear. If a relationship is
linear (that is, straight-line), then changes in the activity index will result in a direct, proportional
change in the variable cost.
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Cost and Management Accounting - II
For example, if the activity level doubles, the cost doubles. It is now necessary to ask: Is the
straight-line relationship realistic? Does the linear assumption produce useful data for CVP
analysis? In most business situations, a straight-line relationship does not exist for variable costs
throughout the entire range of possible activity. At abnormally low levels of activity, it may be
impossible to be cost-efficient. Small-scale operations may not allow the company to obtain
quantity discounts for raw materials or to use specialized labor. In contrast, at abnormally high
levels of activity, labor costs may increase sharply because of overtime pay. Also at high activity
levels, materials costs may jump significantly because of excess spoilage caused by worker
fatigue.
As a result, in the real world, the relationship between the behavior of a variable cost and
changes in the activity level is often curvilinear, as shown in part (a) of Figure 1-3. In the
curved sections of the line, a change in the activity index will not result in a direct, proportional
change in the variable cost. That is, a doubling of the activity index will not result in an exact
doubling of the variable cost. The variable cost may more than double, or it may be less than
double.
Figure 1-3: Nonlinear behavior of variable and fixed costs
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Cost and Management Accounting - II
Total fixed costs also do not have a straight-line relationship over the entire range of activity.
Some fixed costs will not change. But it is possible for management to change other fixed costs.
Figure 1-3, part (b), shows an example of the behavior of total fixed costs through all potential
levels of activity.
For most companies, operating at almost zero or at 100% capacity is the exception rather than
the rule. Instead, companies often operate over a somewhat narrower range, such as 40–80% of
capacity. The range over which a company expects to operate during a year is called the relevant
range of the activity index. Within the relevant range, as both diagrams in Figure 1-4 below
show, a straight-line relationship generally exists for both variable and fixed costs.
Figure 1-4: Linear behavior within relevant range
A cost behavior is described in terms of how its amount changes in relation to production and
sales volume changes.

Total fixed costs remain constant to changes in sales volume.

Total variable costs change in direct proportion to sales volume changes.

Mixed costs display the effects of both fixed and variable components.

Curvilinear costs change in a non-linear relation to volume changes
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Cost and Management Accounting - II
1.2.
Break - Even Analysis Uses And Techniques
The breakeven point is the quantity of output where total revenues equal total cost- that is, where
the operating income is zero. Break-even is the point where total revenue equals total costs.
Why would mangers be interested in the breakeven point?

Mainly because they want to avoid operating losses, and

The breakeven point tells them what level of sales they must generate to avoid a loss.
Breakeven point can be determined by using:
1. The equation method,
2. The contribution margin method and
3. The graph method
The following abbreviations are useful in subsequent analysis.
USP= Unit selling price
UVC= Unit variable costs
UCM= Unit contribution margin (USP-UVC)
CM % = Contribution margin percentage (UCM/USP)
FC = Fixed costs
Q = Quantity of outputs units sold (and manufactured)
OI = Operating income
TOI= Target operating income
TNI = Target net income
1. The Equation Method
Total Revenue – Total cost = operating income
Total Revenues –Variable cost- Fixed cost = Operating income
(𝑸 𝑿 𝑼𝑺𝑷) − (𝑸 𝑿 𝑼𝑽𝑪) − 𝑭𝑪 = 𝟎
𝑸(𝑼𝑺𝑷 − 𝑼𝑽𝑪) − 𝑭𝑪 = 𝟎
𝑸(𝑼𝑺𝑷 − 𝑼𝑽𝑪) = 𝑭𝑪
𝑸=
𝑭𝑪
𝑼𝑺𝑷 − 𝑼𝑽𝑪
Example: Zemen Company manufactures and sells bottles. The company has a selling price of
Br 100 per unit. Fixed costs are Br 120,000 per year. Variable costs are Br 80 per unit.
Required: Determine the break even quantity for Zemen Company?
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Cost and Management Accounting - II
Solution
Revenues –Variable cost- Fixed cost = Operating income
(USP x Q) – (UVC x Q) – FC = 0
100Q – 80 Q – 120,000 = 0
20Q 120,000

20
20
Break-even in units (Q) = 6000 bottles
Break even in Birr = Breakeven in units X Unit selling price
= Br 100 x 6000 bottles = Br 600,000
If Zemen sells fewer than 6000 bottles, it will have a loss, if it sells 6000 bottles it will break
even; and if it sells more that 6000 bottles it will mark a profit.
2. The Contribution Margin Approach
The contribution margin method approach centers on the idea earlier that each unit sold provides
a certain amount of contribution margin that goes toward covering fixed costs. To find how
many units must be sold to break-even, divide the total fixed costs by the unit contribution
margin.
Revenues –Variable cost- Fixed cost = Operating income
(USP x Q) – (UVC x Q) – FC = 0
Q (USP –UVC) –FC = 0
Q(CM) – FC = 0, since USP - UVC is contribution margin (CM)
𝑸=
𝑭𝑪
𝑪𝑴
Based on the above example, the breakeven in unit and in Birr will be:
Breakeven in unit =
Br 120,000
Br 20
= 6000 bottles
Breakeven in Birr = Br 100 X 6000 bottles = Br 600,000
𝐹𝐶
𝐶𝑀
Or breakeven in Birr = 𝐶𝑀% , CM% = 𝑈𝑆𝑃
=
𝐵𝑟 120,00
= 𝐵𝑟 600,000
0.20
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Cost and Management Accounting - II
3. The Graphical method
Plot a line of total costs and a line of total revenues. Their point of intersection is breakeven
point. The graph also shows the profit or loss outlook for a wide range of output levels beside the
breakeven point.
TR = 600,000
TC = 480,000
600,000
Profit
400,000
200,000
Q = 6000 bottles
Loss
FC = 120,000
100,000
0
2
4
6
8
10
12
Bottle produced (000)
Figure 1.5: Breakeven Point
1.3. Planning With Cost-Volume-Profit Data
CVP analysis may use to determine the total sales, in units and dollars needed to reach a target
profit.
Target Operating Income
Target Revenue – Target Variable cost – Fixed cost= Target operating income
𝑇𝑎𝑟𝑔𝑒𝑡 𝑄 =
𝐹𝐶 + 𝑇𝑂𝐼
𝑈𝐶𝑀
Example: Assume that the management of Zemen Company has planned that the company’s operation
should produce a yearly profit before tax of $40,000.
Required:
a) The number of bottles of conditioner the company should produce and sale to achieve its target
before tax profit of $40,000.
b) The sales volume in Birr, which the company should generate to attain its target before tax profit of
$40,000.
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Cost and Management Accounting - II
Solution
a) Breakeven in units = $120,000 +$40,000 = $160,000
$100-$80
$20
= 8,000 bottles
b) Breakeven in Birr = Br 100 X 8000 bottles = Br 800, 000
Target Net Income and Income Taxes
Thus far, we have ignored the effect of income taxes in our CVP analysis. At times, managers
want to know the effect of their decisions on income after taxes. Net income is operating income
minus income taxes. CVP calculations for target income must then be stated in terms of target
net income instead of target operating income.
Revenues – Variable cost- Fixed cost = Target operating income
Furthermore,
Target net income = (Target operating income) – (Target operating Income X tax rate)
T arg et net income
1  Taxrate
TNI
FC 
1  TR
Q
UCM
TNI
FC 
1  TR
Target revenue=
CM %
Target operating income =
Example: Suppose that the management of Addis has planned that the company’s operation should
produce a yearly profit after tax rate is 40%
Then, determine the following;
a) Number of units the company should produce and sale to achieve the target profit after tax of
$90,000
b) The sales volume in Birr, which the company should generate to attain its after tax profit $90,000
Solution
a)
Q = $120,000+ $90,000
= = $120,000+ $90,000
=
1-0.40
0.6
$100-$80
$20
= 120,000 + $150,000
= $270,000
= 13,500 bottles
$20
$20
b) Break even in Birr = Br 100 X 13,500 bottles = Br 1,350,000
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Cost and Management Accounting - II
Margin of Safety (MOS)
The margin of safety is the difference between budgeted/actual sales volume and break-even
sales volume; it indicates the vulnerability of a business to a fall in demand. It is often expressed
as a percentage of budgeted sales
Budgeted sales – Break-even sales = Margin of safety
MOS ratio = MOS x 100 %
Budgeted/actual Sales
Example: Based on the following information, calculate margin of safety, margin of safety ratio
Budgeted Sales 700 units x $ 8 =
$5,600
Variable cost 700 units x $ 6 =
Fixed cost =
$4,200
$1,000
Required: Calculate MOS & MOS ratio, interpret it? MOS = Br 1600, MOS ratio is 29%.
Sales Mix Analysis
Sales mix is the relative combination of quantities of various products (or services) that
constitutes total unit sales. If the proportions of the mix change, the cost volume profits
relationships also change. Unlike in the single product (or service) situation, there is no unique
breakeven number of units for a multiple- product situation. The breakeven quantity depends on
the sales mix. One possible assumption is that the budgeted sales mix will change at different
levels of total unit sales.
Breakeven point (in units) for multiproduct companies is computed using the following formula:
𝐹𝐶
QBEP = 𝑊𝐴𝐶𝑀
Example: Suppose Ramos Company has two products, wallets (W) and Belt (B). The income budget is
as follows:
Wallets (W)
Belt ( B)
Total
Sales in units
300,000
75,000
375,000
Sales @ $ 8, and $ 5
2,400,000
375,000
2,775,000
Variable expenses @ $ 7 and $ 3
2,100,000
225,000
2,325,000
Contribution margin @ $ 1 and $ 2
300,000
150,000
450,000
Fixed costs
180,000
Net income
$270,000
Required: Calculate the breakeven point, if there is no change in sales mix and ignore income taxes.
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Cost and Management Accounting - II
Solution
Since the sales mix will not be changed there is a constant mix of 4 units of W, for every unit of B
i.e. 300,000: 75,000 or 4: 1 or 80%: 20%. Therefore W= 4B.
Method 1 = [(8W – 7W) + (5B – 3B)] – 180,000 = 0
= (32B – 28B) + (5B – 3B) - 180,000 = 0
B = 30,000 units
W = 4B = 4 (30,000 units) = 120,000 units
Method 2 = we have to calculate the weighted-average contribution margin per unit for the two
products together at the sales mix.
WACM per unit = Wallets (W) CM per unit X Q of W sold + Belt (B) CM per unit X Q of B sold
Number of Q of W sold + number Q of B sold
= $1 per unit X 300,000 units + $2 per unit X 75,000 units
= $1.2 per unit
300,000 + 75,000
We have then BEP =
𝐹𝐶
𝑊𝐴𝐶𝑀 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡
= $180,000 = 150,000 units
$1.2
Because the ratio of Wallet sales to Belt sales is 300,000:75,000, or 4:1, the breakeven point is
120,000 units (0.8*150,000) of wallets and 30,000units (0.20*150,000) of Belt. At this mix, the
contribution margin of $180,000 i.e. 120,000 units wallet X $1 per units = $120,000 and 30,000
units of Belt X $2 per units = $60,000 equals with the fixed costs of $180,000.
Summary of Effects of Changes on Break-Even Point
The break-even point in sales changes in the same direction as changes in the variable cost per
unit and fixed costs. In contrast, the break-even point in sales changes in the opposite direction
as changes in the unit selling price. These changes on the break-even point in sales are
summarized below.
Type of Change
Fixed cost
Unit variable cost
Unit selling price
Unit 1- CVP Relationships
Direction of Change
Increase
Decrease
Increase
Decrease
Increase
Decrease
Effect of Change on Break-Even Sales
Increase
Decrease
Increase
Decrease
Decrease
Increase
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Cost and Management Accounting - II
CVP Analysis in service and non-profit organizations
CVP analysis can be applied in service and NFP organizations in measuring their out put.
Examples of output measures in venous service and not profit industries follow:
Air lines
Industry
Measure of out put
Passenger-miles
Hotels / Motels
Room-nights occupied
Hospitals
Patient- days
Universities
Student credit-hours
Example: Debre Markos University has annual budget of $10,000,000 for MSC scholarship, $
30,000 per student per year. Fixed cost of the programmed is $1,000,000.
Required: a) How many students can get the scholarship?
b) Suppose total budget for the next year is reduced by 30% calculate the number of MSC
scholarship that DMU can offer next year.
Solution:
1. Revenue – variable cost – FC = 10,000,000- 30,000 Q –1,000,000 = 0
Q
9,000,000
 300students
30,000
2. 10,000,000 (0.7) – 30,000 Q – 1,000,000 = 0
Q = 600,000 = 200students
30,000
Exercise: Consider an agency of the Massachusetts Department of Social Welfare with a
$900,000 budget appropriation (its revenues) for 2011.This nonprofit agency’s purposes to
assist handicapped people seeking employment. On average, the agency supplements each
person’s income by $5,000 annually. The agencies only other costs are fixed costs of rent and
administrative salaries equal to $270,000.
Required: How many people could be assisted in 2011? Q = 126 people
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Cost and Management Accounting - II
1.4. Limitations of CVP Analysis
The CVP analysis as was stated is a simple and useful concept. But it is based on the abovementioned assumptions. These assumptions limit the general applicability of CVP analysis.
These limitations are:
1) Cost segregation problem - Some of the costs can be easily identified as fixed, and
variable. But there are a large number of costs, which belong to a mixed category. In real
world it is very difficult to segregate such mixed costs into variable and fixed.
2) Problem of assuming constant fixed costs - The assumption of constant fixed cost may not
hold true always; for example, if a firm has zero output, some of the supervisors and
executives can be dismissed and salaries (Fixed Costs) can be reduced.
3) Problem of constant variable cost per unit - The assumption of constant variable cost per
unit may also not hold true. Because of efficiencies/inefficiencies of workers due to
experience, and other factors; and the market condition, i.e., change in price of material, etc.
4) Problem of constant selling price per unit - Similarly, selling price rarely remains
constant. Selling price may change because of market conditions.
5) Short-term Focus - The CVP analysis is a short-term technique of profit planning; it cannot
be used for long-range profit planning because of the cost behavior pattern.
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Cost and Management Accounting - II