CHAPTER ONE

COST-VOLUME- PROFIT RELATIONSHIP

Variable and Fixed cost behavior and patterns
It is necessary to predict how a certain cost will behave in response to a change in the level of
activity. Cost behavior means how a cost will react or respond to changes in the level of business
activity. As the activity level rises and falls, a particular cost may rise and fall as well or it may
remain constant. Knowing how costs behave in relation to a given level of business activity
enables management to maximize profitability through more effective planning and control.
Based on their behavior, costs are often classified as variable and fixed. A variable cost is a cost
that varies in total in direct proportion to changes in the level of activity (or cost driver). As the
activity level rises or falls the variable cost will rise or fall in direct proportion. The variable cost
per unit remains constant irrespective of the changes in the level of activity. A fixed cost is a cost
that remains constant in total regardless of changes in the level of activity. The fixed cost per
unit changes inversely with changes in the level of activity.
Note from the outset that an important first step in any CVP analysis is categorizing an
organization’s costs according to their cost behaviors in to fixed or variable costs.
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 helps
managers to understand the interrelation between cost, volume, and profit in an organization by
focusing on interactions between the following elements.
 Price of product
 Volume or level of activity
 Per unit variable cost
 Total fixed costs
 Mix of products sold
Cost- volume profit (CVP) Analysis is therefore a vital tool in many businesses decisions such as
what products to produce and sale, what pricing policy to follow, what marketing strategy to
employ, and what type of productive facilities to acquire and utilize.
Cost volume-profit (CVP) analysis examines the behavior of total revenue, total costs and
operating income as changes occur in the output level, the selling price, the variable cost per
unit, and/or the fixed costs of a product. More specifically, it looks at the effects on profits of
changes in such factors as variable costs, fixed costs, selling prices, volume, and mix of products
sold on profits. By studying the relationships of costs, sales, and net income, management is
better able to cope with many planning decisions.
For example, CVP analysis helps to answer the following questions:
 How much does a firm have to sell just to cover its total costs?
 How much does a firm have to sell to reach its target profit?
 How will a change in a firm’s fixed cost affect its net income?
 How much will a firm’s sales need to increase so as to cover a planned increase in
advertising budget?
 What price should a firm change to cover its cost and provide for its planned amount of
profit?
 How much should a firm actual or budgeted sales decline before it suffers a loss?

Even though the term profit appears in the term Cost- volume profit (CVP) analysis, it is not
confined to profit seeking enterprises. Managers in non profit seeking organizations also use

1|Page
CVP analysis to examine the effect of activity and other short-run changes on revenue and costs.
For example CVP analysis can be used by a social welfare agency to find out how many people
can be assisted given the agency’s’ fixed and variable costs, by a charity hospital to determine
the number of patients to be admitted, by a public school to determine the number of students to
be enrolled, and others.
Assumptions of CVP Analysis
CVP analysis is based on several assumptions. The following assumptions must be satisfied for a
CVP analysis to be valid within the relevant range.
1. The behavior of total revenue is linear (straight line). This implies that the selling price of a
product or service will not change in relation to output as sales volume varies within the
relevant range. To put it in another way the selling price is constant throughout the entire
relevant rang. Changes in the level of revenues arise only because of changes in the number
of products (or services) units produced and sold.
2. The behavior of cost is also linear over the relevant range. This implies the following more
specific assumptions:
a. Costs can be accurately divided in to variable and fixed costs. As activity changes the
variable cost is constant per unit and fixed costs are constant in total over the entire
relevant range.
b. The efficiency and productivity of the production process and workers remain constant.
3. The analysis either covers a single product or assumes the proportion of different products
When multiple products are sold the sales mix will remain constant as the level of total units
sold change (the sales mix remains constant over the relevant range).
4. In manufacturing companies inventories don’t change. The inventory levels at the beginning
and end of the period are the same. This implies the number of units produced during the
period equals the number of units sold.
5. All revenues and costs can be added or compared without taking into account the time value
of money.
6. The only revenue and cost driver is volume of production.
Some of these assumptions may be technically violated; the violations are usually not serious
enough to call in to question the basic validity of CVP analysis. For example, in most multi-
product companies, the sales mix is constant enough so that the result of CVP analysis is
reasonably valid.
May be 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. For example, a
manager might contemplate increasing the level of sales far beyond what the company has ever
experience before. However, even in these situations a manager can adjust the model to make
into account anticipated changes in selling prices, fixed costs, and the sales mix that would
otherwise violate the assumptions.

Break Even Point Analysis

Break-even point is the quantity of output sold at which total revenue equals total costs, i.e. the
quantity of output sold at which the operating income is zero. At break-even point, a company
neither incurs a loss nor earns a profit on operating activities. At break-even, the company’s
revenue simply covers its costs. Break-even analysis is the important elements of CVP analysis.

2|Page
The break-even point can be computed using three methods:
 Equation method,
 The contribution margin method, or
 Graphic methods.
1. Equation method:
This method uses an algebraic equation to make CVP analysis.
To use the equation method to determine breakeven point, the income statement is expressed as
the following equation:
Revenues – Variable Costs – Fixed Costs = Net Income/Loss
(Selling Price x Units Sold) – (VC per Unit x Units Sold) – FC = Operating Income/Loss

Where: - Q = Break even quantity

FC = Fixed costs
VC = Variable Cost
SP = Selling Price
Example: - Assume Awash Factory’s normal production capacity is 10,000 bottles of Wine
annually. Awash Factory’s fixed cost is $120,000, sales price per bottle is $100, and the variable
cost per bottle is $80. Based on this data
a) Compute the number of bottles of wine the company should produce and sale per year at
break-even.
b) Determine the break-even sales in Birr.
Solution
a) Break even in units using the equation method can be calculated as follows:

Revenues –Variable cost – Fixed costs = Operating income

(SP X Q) - (VC X Q) – FC = OI
($100XQ) – ($80 XQ)- 120,000= 0
20Q=120,000
Q=120,000
20
Q= 6,000 units
Thus, the company should produce and sell 6,000 bottles of wine per year so as to break-even.
The break-even point in units, 6,000 bottles represents 60% (i.e 6,000/10,000bottles) of its
normal capacity. If the company sells fewer than 6,000 units there will be a loss; if it sells 6,000
units it will be at breakeven; and if it sells more than 6,000 units it will make a profit.
b) Break even sales in Birr can be computed by multiplying the break-even level of units sold
by the selling price as follows:
Break even sales in Birr = Q XSP = 6,000 units X $100 = $600,000
We can check the breakeven point as follows:
Sales ($100 x 6,000 bottles) -----------------------------$600,000
Less variable costs ($80 x 6,000 bottles) -------------$480,000
Contribution margin ($20 x 6,000 bottles) -------------120,000
Less fixed cost ---------------------------------------------120,000
Operating income------------------------------------------------0

3|Page
 2. The Contribution Margin Method:
The contribution margin method centers on the idea earlier that each unit sold provides a certain
amount of contribution margin that goes toward covering fixed costs. The method is actually just
a shortcut version of the equation method.
(SP X Q) - (VCU X Q) = OI+FC
Q(SP-VCU) = OI +FC
Q(CMU) = OI+FC
OI + FC
Q=
SP−VC
But at the breakeven point operating income is zero; therefore the quantity output at the
breakeven point using the contribution margin approach can be computed as:
FC
Q=
SP−VC
a) For the above example the breakeven point in units will be computed as follows:
120,000
Q=
$ 100−$ 80
120,000
= 6,000 units
$ 20

120,000
b) Breakeven in sales Birr = = $600,000
20 %
3. Graphic Method:
Break-even point conveys useful information to management, but it fails to show how profit
changes as activity changes. To understand the relationship between profit and volume of
activity, a cost-volume-profit graph is commonly used. A cost-volume-profit (CVP) graph is,
therefore, prepared to express graphically the relationship among revenue, cost, profit, and
volume. A cost-volume-profit graph highlights CVP relationship over wide range of activity and
can give managers a perspective that can be obtained in no other way.
The following steps are used to prepare CVP graph, which is also called a break-even chart.
1. Draw the axes of the graph. Label the vertical axis in Birr and the horizontal axis in
volume of units of sales (in our case number of bottles of wine).
2. Draw a line parallel to the horizontal axis labeled in volume of units of sales to represent
the total fixed expenses. The line is parallel to the horizontal axis because fixed expenses
do not change in with activity. For our Addis Company the fixed expense is $120,000.
3. Choose some volume of sales and plot the point representing total costs (fixed and
variable costs) at the activity level you have selected. For example, if you select a volume
of 5,000 bottles, the total costs at this volume will be computed as follows:
Variable costs ($80 X 5,000 bottles) ------ $400,000
Fixed costs ------------------------------------- 120,000
Total costs --------------------------------------$520,000
4. Draw the variable cost line. This line is parallel to the total revenue line but lies below the
revenue line after the breakeven point.

4|Page
5. Choose some volume of sales and plot the point representing total sales in Birr at the
activity level you have selected. For example, if you select a volume of 5,000 bottles, the
total sales at this volume will be computed as follows:
Total sales revenue ($100 X 5,000 bottles) --------------= $500,000
6. Draw the total revenue line. This line passes through the point plotted in step 5 above and
begins from the origin (0). The revenue line crosses the origin simply because total
revenue is zero if no sales are made.
The anticipated profit or loss at any given level of sales is measured by the vertical distance
between the total revenue and total costs (variable costs plus fixed costs lines). The break-
even point is where the total revenue and total costs lines intersect. The break-even point of
6,000 bottles, which occurs at a point where total revenues and total costs are equal to
$600,000, agrees with the break-even point obtained for Addis Company in our example
computation using the equation and contribution margin methods.
Break-even point is determined by the intersection of the total revenue line and the total
costs line. Addis Company’s break-even for the year is at 6,000 bottles, or $600,000 of sales.
This result agrees with the conclusions that are reached at by the equation and contribution
methods.
Profit and loss areas;- the CVP graph discloses more information than the break-even
calculation. From the graph, a manager can see the effects on profit of changes in volume.
The vertical distance between the total revenue and total costs lines on the graph represents
the profit or loss at a particular sales volume. If Addis Company sells fewer than 6,000
bottles in a year, the organization will suffer a loss and the magnitude of the loss increase as
bottle sales decline. The company, on the other hand, will have a profit if sales exceed 6,000
bottles in a year. (Draw the Graph in the space provided below)

5|Page
Planning With Cost-Volume-Profit Data
Managers of a company will prepare different plans to be attained. It may be planned to attain a
desired level of profit before tax or profit after tax depending on the target managers want to
attain. Using CVP analysis will help managers to compute the number of units they need to
produce in order to achieve the target profit they planned.
The break-even point provides a starting point for planning further operation. Managers want to
earn operating profits rather than simply cover costs. Consequently, CVP analysis can be used to
answer the following questions;
1. How much sales volume in units and in Birr should a company generate if a fixed amount
of profit before or after tax is desired?
2. How much sales volume in units and in Birr should a company generate if a variable
amount of profit before or after tax is desired?
 Target operating income (profit before tax)
Managers use CVP analysis to determine the sales volume needed to achieve a desired profit
called target or planned profit. In making target profit analysis, we are aimed at finding a
contribution margin figure that is sufficient to cover the fixed cost and to provide the desired
profit. The problem of computing the volume of sales required to earn a particular amount of
target profit is very similar to the problem of finding the break-even point. After all, the break-
even point is the sales volume required to earn a target profit of zero.
To illustrate, assume that the management of Awash Factory has planned that the Factory’s
operation should produce a yearly profit before tax of $40,000. Then determine:
a) The number of bottles of wine 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.
The answer can be computed using the two methods discussed before.
1a) Equation Method= (SP X Q) - (VCU X Q) – FC = OI
a) ( $100XQ) – ($80XQ) – $120,000= $40,000
20Q= 120,000+40,000
20Q=160,000
QT=160,000/20
QT=8,000 Units; this is verified as follows.
Sales ($100 X 8,000 bottles) -------------------------------$800,000
Less variable expenses ($80 X 8,000 bottles) -------------640,000
Contribution Margin ($20 x 8,000 bottles) ----------------160,000
Less fixed expenses -------------------------------------------120,000
Target operating income--------------------------------------$40,000
1b) The sales volume in Birr required to achieve the target operating income of $40,000 can be
computed by multiplying the target Quantity by the selling price per unit as follows;
Target sales = 8,000 bottles X $100 = $800,000

6|Page
2a) Contribution Margin Method: QT= FC+TOI = $120,000+$40,000 = $160,000
. CMU $20 $20
=8,000 units

2b) Target sales in Birr= FC+TOI= $120,000+$40,000 =$160,000 = $ 800,000

CMR 0.2 0.2

 Target net income (Profit after tax):

Profit seeking enterprises must pay income taxes on their profits. Thus far we have ignored the
effects of income tax in our CVP analysis. Managers may want to know the effect of their
decisions on operating income after income taxes are paid.Net income is Operating income
minus income taxes. To make these evaluations CVP calculations for target income must be
stated in terms of target net income instead of target operating income.
Revenues –Variable costs- Fixed costs = Target Operating Income
Target net income = (Target operating income) – (Target operating income X Tax rate)
Target net income= Target operating income (1-Tax rate)
Target operating income= Target net income
(1-Tax rate)
(SPXQ) - (VCUXQ) - FC=Target net income
(1-Tax rate)
Now suppose that the management of Awash has planned that the company’s operation should
produce a yearly after tax profit of $ 90,000 and the income tax rate is 40%.
Then, determine the following;
a) Number of units the company should produce and sell 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.
We can use both the equation method and the contribution margin approach method to solve the
above example.
1a) The equation Method: (SPXQ) - (VCUXQ) - FC=Target net income
(1-Tax rate)
100Q-80Q-120,000= 90,000
1-0.4
20Q=150,000+120,000
20Q=270,000
Q= 270,000/20
Q=13,500 Units
1b) The sales volume in Birr required to achieve a target profit after tax of $90,000 can be
simply computed by multiplying the target quantity by the selling price per unit as follows:
Target Sales = $100 X 13,000 units= $ 1,350,000
2a) Contribution Margin method: The number of units that must be sold to attain a target after
tax profit can be computed using the following formula.

Target net income

(SPXQ) - (VCUXQ) - FC=
(1−Tax rate)

7|Page
 Target net income
Q (SP-VCU) – FC =
(1−Tax rate)
Target net income
Q (CMU) = FC +
(1−Tax rate)
FC +Target net income
Q= (1−Tax rate)
CMU
120,000+90,000
Thus for the above given example; Q = (1−0.4 )
20
270,000
= 13,500 units
20

FC +Target net income

270,000
2b) Target profit point in sales birr = ( 1−Tax rate ) = = $ 1,350,000
0.2
CMU
The above figures can be verified as follows:
Sales ($100 X 13,500) ---------------------------------------$1,350,000
Less variable expenses ($80 X 13,500) -------------------- 1,080,000
Contribution margin ($20 X 13,500) ------------------------ $270,000
Less fixed cost ----------------------------------------------------120,000
Target operating income (PBT) ------------------------------ $150,000
Less income tax (40% x $150,000) -----------------------------60,000
Target net income (PAT) ------------------------------------ $90,000
Thus to achieve a target profit after tax of $ 90,000; the company should attain a profit before tax
of $ 150,000.

 Contribution Margin per unit = Selling Price−Variable Cost per unit

Contribution Margin per unit Total Contributin Margin
 Contribution Margin ratio = or =
Selling price Net Sales
 Contribution margin can be also referred to as profit volume ratio (P/V ratio) where the term
profit signifies the amount of contribution and the term volume refers to the amount of sales
value either per unit or in total basis.
Total Contributin Margin Contribution Margin per unit
P/V ratio = or
Net Sales Selling price
Sales−Variable cost
=
Sales
Variable Cost
= 1−
Sales
 Profit-Volume ratio when profits and sales for two time period are given.
∆∈Profit
P/V ratio =
∆∈sales
 Margin of safety: The margin of safety is the excess of budgeted or actual sales over the
break-even volume of sales. It states the amount by which sales can drop before losses begin
to be incurred. The margin of safety, therefore, gives management a clue for how close

8|Page
 projected or actual operations are to the organization’s break-even point. If the actual
(budgeted) sales are significantly above the break-even sales, there is high margin of safety
and profitability can be expected even if the actual (budgeted) sales falls for one reason or
another. The margin of safety is a measure risk because it indicates the amount by which sales
can decline before a firm suffers a loss. The formula to calculate margin of safety;
MOS = Budgeted/Actual Sales – BEP Sales
MOS ∈Birr
MOS %age =
Budgeted / Actual Sales

Sales Mix and Breakeven Point

In the previous discussions of CVP analysis we assumed that the company produces and sell
only a single product. However, many companies produce and sell more than one product which
adds some complexity to CVP analysis. For organizations producing and selling multiple
products, the relative proportion of each type of product sold is called a sales mix. Managers try
to achieve the combination or mix of products that will yield the greatest amount of profits. Most
companies have several products and, often these products are not equally profitable. Hence,
profits will depend to some extent on the company’s sales mix. Profits will greater if high margin
rather than low margin items make up a relatively large proportion of total sales.
Changes in sales mix can cause interesting variations in a company’s profits. A shift in sales mix
from high margin to low margin products can cause total profits to decrease even though total
sales may increase. Conversely, a shift in the sales mix from low margin items to high margin
items can cause total profits to increase even though total sales may decrease.
If a company sells more than one product, break even analysis is somewhat complex than
discussed earlier. The reason is that different products will have different selling price, different
costs and different contribution margin. Hence, the breakeven point will depend on the mix on
which the various products are sold.
Example: Suppose XYZ Company produces and sells two type of products; called Product X
and product Y. The company has budgeted to sell 15,000 units of product X and 5,000 units of
product Y per year. This sales mix is assumed to remain constant. The company’s annual fixed
cost is estimated at $ 246,500.The following data pertains to the two products:
Product X Product Y
Selling price per unit Br. 30 Br. 10
Variable cost per unit Br. 12 Br. 6
Required:
A. Compute the total breakeven point in units for the two products.
B. Determine the number of units of each product that must be sold so as to breakeven point.
C. Compute the breakeven point in sales birr for the company as a whole and for each
product.
Solution:

9|Page
 a. to compute the breakeven point when more than one product is sold, we should first
compute the weighted average contribution margin per unit and then the breakeven
point as follows:
WACM per unit = (CMX x Wx) + (CMy x Wy)

¿ cost
Breakeven point Quantity =
WACM per unit
¿ cost
Breakeven point Sales in Br. =
WACM %
Total Contribution Margin
Where, WACM % is computed as =
Total sales
Quantity of X
Note: - the weight for a given product is Wx =
Total Sales∈units
Wx = 15,000/20,000 = 0.75
Wy = 5,000/20,000 = 0.25
WACMU= (18 x 0.75)+(4 x 0.25)
= $14.5
FC
Breakeven point in units = = $ 246,500/14.5 = 17,000 units of product X and Y.
WACMU
b. The number of units of each product; the sales mix will not change. Hence product X
represents 75% (15,000/20,000) and product Y 25 % (5,000/ 20,000) of the total units
sold. Thus break even proportion of product X and product Y sold can be computed as
follows.
Product X= 17,000 units X 75% = 12,750 Units
Product Y = 17,000 units X 25% = 4,250 Units
c. The breakeven point in sales birr for product X = 12,750 X 30 = $382,500
The breakeven point in sales birr for product Y = 4,250 X 10 = $42,500
Total breakeven point in sales Birr = $425,500
Contribution Margin Vs Gross Margin
Contribution margin refers to the difference between revenues and all variable costs.
Gross margin refers to the difference between revenue and the costs of goods sold.
Some organizations may prepare contribution income statement for managerial analysis purpose.
The following illustration shows the difference between contribution income statement and
financial accounting income statement.

Contribution income statement Financial Accounting Income Statement

(Emphasizing on Contribution Margin) (Emphasizing on Gross Profit)
Revenues xx Revenue xx
Variable Costs xx Cost of goods sold xx
Contribution Margin xx Gross Profit xx
Fixed costs xx Operating Expenses xx
Operating Income xx Operating Income xx
Illustration
Given the following data, prepare the contribution income statement and financial accounting
income statement.
Revenue Br. 1,000,000
Variable Manufacturing costs 250,000

10 | P a g e
 Variable non Manufacturing costs 270,000
Fixed Manufacturing costs 160,000
Fixed non Manufacturing costs 138,000
Solution
Contribution Income Statement
(Emphasizing on Contribution Margin)
Revenues 1,000,000
Variable Mfg Costs 250,000
Variable non Mfg Costs 270,000 520,000
Contribution Margin 480,000
Fixed Mfg costs 160,000
Fixed Non Mfg Costs 138,000 298,000
Operating Income 182,000
Financial Accounting Income Statement
(Emphasizing on Gross Profit)
Revenue 1,000,000
Cost of goods sold 410,000
Gross Profit 590,000
Operating Expenses 408,000
Operating Income 182,000
Limitations of CVP Analysis
The accuracy of CVP analysis is limited because it assumes strictly linear relationship among
the variables. True linearity among actual CVP variable is the exception rather than the norm.
For example, suppose that a business receives a volume discount on material that it purchases.
The more material it purchases, the lower its cost per unit. In this case, the cost varies but not in
direct proportion of the amount of material purchased. The relation is not linear, therefore.
Similarly, fixed cost can change. A supervisor’s salary that is thought to be fixed may change if
the supervisor receives a raise. Likewise, amounts changed for telephone, rent, insurance, taxes,
and so on may increase or decrease subjected to market conditions and government policies. In
practice, fixed costs fluctuate. Accordingly, the relationships are not strictly linear. CVP assumes
that factors such as worker efficiency are not variable over the range of activity analyzed.
Businesses frequently are able to increase productivity, thereby reducing variable or fixed costs,
but CVP formulas are not constructed to allow for such changes in efficiency.
The following are limitations of CVP analysis:
1. CVP analysis requires estimations or projections of expected sales, fixed costs, variable
costs, and any other cost that portrays both fixed and variable components.
2. CVP analysis is useful only over a limited range of activity extending not too far what a
form expects to operate within. Moving much beyond that range will require additional
capital expenditure for more floor space, more plant assets, more personnel, and the like
which will distort the estimates of fixed and variable costs.
3. It is generally accepted in basic financial theory that the appropriate way to make
investment decisions is to consider the “discounted value of the cash flows” of a
proposed project. Such an analysis focuses on the time value money to better describe the
true value of an investment. CVP does not focus on the time value of money.
4. CVP analysis assumes that the cost-revenue relationship is linear. This may or may not
hold good for any particular business. For example, many businesses experience a
reduction in fixed costs and variable costs per unit as the overall scale of the business

11 | P a g e
 increases. This refers to as the “economies of scale”. Most very small businesses do not
experience significant economies of scale.

Benefits of CVP Analysis

A manager, who exercises good judgment, will certainly find the data generated by CVP
analysis to be useful tool regardless of its limitations. In general, despite its shortcomings,
CVP analysis is a very useful tool with which to approach a variety of decisions situations.
Such questions as the cost of expansion, evaluation of sales or profit performance, estimation
of the impact of changes in CVP variables on profit, setting selling prices and financial
analysis in general are appropriately addresses using CVP analysis. CVP analysis is best used
in conjunction with other financial analysis technique or as a screening device to determine
whether more investigation is needed.

Exercise
ABC Company’s income statement for the year 2005 on production and sale of 200,000 units is
as follows:
Revenues Br. 2,600,000
Cost of Goods Sold 1,600,000
Gross profit 1,000,000
Operating Expense 1,150,000
Operating Income (150,000)
The company’s fixed manufacturing costs are Br. 500,000, and variable non manufacturing costs
are Br. 4 per unit.
Required
a. Calculate the company’s variable manufacturing cost per unit in 2005.
b. Calculate the company’s fixed non manufacturing cost in 2005.
c. Prepare contribution income statement for the year ended December 31, 2005.

12 | P a g e