CHAPTER ONE

COST-VOLUME-PROFIT RELATIONSHIPS

Variable and fixed cost behavior and patterns

Cost behavior refers to how a certain cost will behave in response to a change in level of activity.
For planning purposes, a manager must be able to anticipate which of these will happen; and if a
cost can be expected to change, the manager must know by how much it will change. To help make
such distinctions, costs are often characterized as variable, fixed, or mixed.

Variable Cost:

A variable cost is a cost that varies, in total, in direct proportion to changes in the level of activity.
The activity can be expressed in many ways, Such as units produced, units sold, miles driven, beds
occupied, hours worked and so forth. Direct material is a good example of a variable cost.The
variable cost is constant if expressed on a per unit basis.

Fixed cost

A fixed cost is a cost that remains constant, in total, regardless of changes in the level of activity.
Unlike variable costs, fixed costs are not affected by changes in activity.Consequently, as the
activity level rises and falls, the fixed costs remain constant in total amount unless influenced by
some outside forces, such as price changes. Rent is a good example of fixed cost.Average fixed cost
per unit increases and decreases inversely with changes in activity.

Mixed/Semi Variable Cost

A mixed cost is one that contains both variable and fixed cost elements together. Mixed cost is also
known as semi variable cost. Examples of mixed costs include electricity and telephone bills.

1
Cost-volume-profit analysis

Cost-volume-profit analysis examines the behavior of total revenues, total costs, and operating profit
as changes occur in the output level, selling price, variable costs per unit, or fixed costs.

Managers use cost-volume-profit (CVP) analysis to identify the levels of operating activity needed to
avoid losses, achieve targeted profits, plan future operations, and monitor organizational performance.
Accountants often perform CVP analysis to plan future levels of operating activity and provide
information about:
 Which products or services to emphasize
 The volume of sales needed to achieve a targeted level of profit
 The amount of revenue required to avoid losses
 Whether to increase fixed costs
 How much to budget for discretionary expenditures
 Whether fixed costs expose the organization to an unacceptable level of risk
Profit Equation and Contribution Margin

CVP analysis begins with the basic profit equation.

Profit = Total revenue -Total costs
Separating costs into variable and fixed categories, we express profit as:
Profit =Total revenue - Total variable costs -Total fixed costs

Contribution margin indicates why operating income changes as the number of units sold changes.
The contribution margin is total revenue minus total variable costs. Similarly, the contribution
margin per unit is the selling price per unit minus the variable cost per unit. Both contribution
margin and contribution margin per unit are valuable tools when considering the effects of volume
on profit. Contribution margin per unit tells us how much revenue from each unit sold can be
applied toward fixed costs. Once enough units have been sold to coverall fixed costs, then the
contribution margin per unit from all remaining sales becomes profit.
Expressing CVP Relationships
There are three related ways (we will call them methods) to think more deeply about and model
CVP relationships:
1. The equation method

2
 2. The contribution margin method
3. The graph method
The equation method and the contribution margin method are most useful when managers want to
determine operating income at few specific levels of sales (for example 5, 15, 25, and 40 units
sold). The graph method helps managers visualize the relationship between units sold and operating
income over a wide range of quantities of units sold. As we shall see later in the chapter, different
methods are useful for different decisions.
1. Equation Method
Revenues - Variable costs - Fixed costs = Operating income
How are revenues in each column calculated?
Revenues= Selling price (SP) × Quantity of units sold (Q)
How are variable costs in each column calculated?
Variable costs= Variable cost per unit (VCU) × Quantity of units sold (Q)
So,
(SP× Q) –(VCU×Q) – fixed cost = operating income……… equation 1
Equation 1 becomes the basis for calculating operating income for different quantities of units sold.

2. Contribution Margin Method

Rearranging equation 1,

(SP-VCU) × (Q) – fixed cost = operating income

= (contribution margin per unit × Q) – fixed cost= operating income………… equation 2

3. Graph Method
In the graph method, we represent total costs and total revenues graphically. Each is shown as a line
on a graph.
Total costs line. The total costs line is the sum of fixed costs and variable costs. In this example the
total costs line is the straight line from point A through point B.
Total revenue line. One convenient starting point is $0 revenues at 0 units sold, which is point C.
Select a second point by choosing any other convenient output level and determining the
corresponding total revenues. The total revenue line is the straight line from point C through point
D.
Profit or loss at any sales level can be determined by the vertical distance between the two lines at
that level

3
 Y(dollars) total revenue line D B operating income

8000 operating income area total cost line

6000

Variable cost

5000 operating loss area breakeven point

4000

2000

A fixed cost

C 10 20 25 30 40 50 X(unit sold)

Cost-Volume-Profit Assumptions
1. Changes in the levels of revenues and costs arise only because of changes in the number of
products (or service) units sold. The number of units sold is the only revenue driver and the
only cost driver.
2. Total costs can be separated into two components: a fixed component that does notvary with
units sold and a variable component that changes with respect to units sold.
3. When represented graphically, the behaviors of total revenues and total costs are
linear(meaning they can be represented as a straight line) in relation to units sold within a
relevant range (and time period).
4. Selling price, variable cost per unit, and total fixed costs (within a relevant range andtime
period) are known and constant.
An important feature of CVP analysis is distinguishing fixed from variable costs. Always keep in
mind, however, that whether a cost is variable or fixed depends on the time period for a decision.
The shorter the time horizon, the higher the percentage of total costs considered fixed. Always
consider the relevant range, the length of the time horizon, and the specific decision situation when
classifying costs as variable or fixed.

4
Break Even Point and Target Operating Income

The breakeven point (BEP) is that quantity of output sold, at which total revenues equal total
costs, that is, the quantity of output sold that results in $0 of operating income.
For example, if the company sold 1 unit at $ 200, variable cost per unit $120, and also fixed cost $
2,000, so what will be the amount of breakeven quantity?
 Recall the equation method (equation 1):
(SP× Q) –(VCU×Q) – fixed cost = operating income
= (200×Q) - (120×Q) - 2,000= 0
= 80× Q = 2,000
= Q = 2,000 ÷ 80 per unit
= 25 units
If the company sells fewer than 25 units, it will incur a loss; if it sells 25 units, they will breakeven;
and if they sell more than 25 units, it will make a profit. While this break even point is expressed in
units, it can also be expressed in revenues: 25 units × $200 selling price= $5,000.
 Recall the contribution margin method (equation 2):
(Contribution margin× Q) – fixed cost= operating income

Contribution margin per unit × Breakeven number of units = Fixed cost……equation 3

Rearranging equation 3 and entering the data,

Breakeven number of units = Fixed cost ÷contribution margin per unit = $2,000÷ $80= 25 units
Breakeven revenues = Breakeven number of units × Selling price
= 25 units × $200 per unit = $5,000
In practice (because they have multiple products), companies usually calculate breakeven point
directly in terms of revenues using contribution margin percentages.
Contribution margin percentage = Contribution margin per unit = $80 = 0.4 or 40%
Selling price $200
That is, 40% of each dollar of revenue, or 40 cents, is contribution margin. To breakeven,
contribution margin must equal fixed costs of $2,000. To earn $2,000 of contribution margin, when
$1 of revenue earns $0.40 of contribution margin, revenues must equal $2,000÷ 0.40 = $5,000.

5
While the breakeven point tells managers how much they must sell to avoid a loss, managers are
equally interested in how they will achieve the operating income targets underlying their strategies
and plans.
Target Operating Income
We illustrate target operating income calculations by asking the following question: How many
units must the company sell to earn an operating income of $1,200 based on the above example?
One approach is to keep plugging in different quantities and check when operating income equals
$1,200. The result shows that operating income is $1,200 when 40 packages are sold. A more
convenient approach is to use equation 1
(SP× Q) –(VCU×Q) – fixed cost = operating income……… equation 1
We denote by Q the unknown quantity of units the company must sell to earn an operating income
of $1,200. The selling price is $200, variable cost per package is $120, fixed costs are $2,000, and
target operating income is $1,200. Substituting these values into equation 1, we have
($200 * Q) - ($120 * Q) - $2,000 = $1,200
$80 * Q = $2,000 + $1,200 = $3,200
Q = $3,200, $80 per unit = 40 units
Alternatively, we could use equation 2,
(Contribution margin× Q) – fixed cost= operating income………… equation 2
Given a target operating income ($1,200 in this case), we can rearrange terms to get equation 4.
Q = Fixed costs + Target operating income………………….equation 4
Contribution margin per unit
Q = $2,000 + $1,200 = 40 units
$80 per unit
The revenues needed to earn an operating income of $1,200 can also be calculated directly by
recognizing (1) that $3,200 of contribution margin must be earned (fixed costs of $2,000 plus
operating income of $1,200) and (2) that $1 of revenue earns $0.40 (40 cents) of contribution
margin. To earn $3,200 of contribution margin, revenues must equal $3,200÷ 0.40 = $8,000.
Target Net Income and Income Taxes
Net income is operating income plus nonoperating revenues (such as interest revenue) minus
nonoperating costs (such as interest cost) minus income taxes. For simplicity, throughout this
chapter we assume nonoperating revenues and nonoperating costs are zero. Thus,

6
Net income = Operating income - Income taxes
In many companies, the income targets for managers in their strategic plans are expressed in terms
of net income. That’s because top management wants subordinate managers to take into account the
effects their decisions have on operating income after income taxes. Some decisions may not result
in large operating incomes, but they may have favorable tax consequences, making them attractive
on a net income basis—the measure that drives shareholders’ dividends and returns.
To make net income evaluations, CVP calculations for target income must be stated in terms of
target net income instead of target operating income. For example the company may be interested
in knowing the quantity of units it must sell to earn a net income of $960, assuming an income tax
rate of 40%.
Target net income = (target operating income) – (target operating income × tax rate)
= target operating income × (1 – tax rate)
Target operating income = Target net income = $ 960 = $ 1,600
1 - Tax rate 1- 0.40
The key step is to take the target net income number and convert it into the corresponding target
operating income number. We can then use equation 1 for target operating income and substitute
numbers from our previous example.
($200 * Q) - ($120 * Q) - $2,000 = $1,600
$80 * Q = $3,600
Q = $3,600/ $80 per unit = 45 units
Focusing the analysis on target net income instead of target operating income will notchange the
breakeven point. That’s because, by definition, operating income at the breakeven point is $0, and
no income taxes are paid when there is no operating income.
Using CVP Analysis for Decision Making
Managers also use CVP analysis to guide other decisions, many of them strategic decisions.
Consider a decision about choosing additional features for an existing product. Different choices
can affect selling prices, variable cost per unit, fixed costs, units sold, and operating income. CVP
analysis helps managers make product decisions by estimating the expected profitability of these
choices.
Strategic decisions invariably entail risk. CVP analysis can be used to evaluate how operating
income will be affected if the original predicted data are not achieved—say, if sales are 10% lower

7
than estimated. Evaluating this risk affects other strategic decisions a company might make. For
example, if the probability of a decline in sales seems high, a manager may take actions to change
the cost structure to have more variable costs and fewer fixed costs.
We return to our previous example to illustrate how CVP analysis can be used for strategic
decisions concerning advertising and the selling price.
1. Decision to Advertise
Suppose the company anticipates selling 40 units at the fair. The data indicate that the company’s
operating income will be $1,200. It is considering placing an advertisement describing the product
and its features in the fair brochure. The advertisement will be a fixed cost of $500. It thinks that
advertising will increase sales by 10% to 44 packages. Should the company advertise? The
following table presents the CVP analysis.

40 Packages 44 Packages Difference

Sold with Sold with (3) = (2) - (1)
No Advertising Advertising
(1) (2)
Revenues ($200 * 40; $200 * 44) $8,000 $8,800 $ 800
Variable costs ($120 * 40; $120 * 44) 4,800 5,280 480
Contribution margin ($80 * 40; $80 * 44) 3,200 3,520 320
Fixed costs 2,000 2,500 500
Operating income $1,200 $1,020 $(180)
Operating income will decrease from $1,200 to $1,020, so it should not advertise.

2. Decision to Reduce Selling Price

Having decided not to advertise, the company is contemplating whether to reduce the selling price
to $175. At this price, they think that they will sell 50 units. At this quantity, the package
wholesaler who supplies the product will sell the packages to it for $115 per unit instead of $120.
Should the company reduce the selling price?
Contribution margin from lowering prices to $175: ($175 - $115) per unit * 50 units…… $3,000
Contribution margin from maintaining price at $200: ($200 - $120) per unit * 40 units….. 3,200
Change in contribution margin from lowering prices............................................................$(200)

8
Decreasing the price will reduce the contribution margin by $200 and, because the fixed costs of
$2,000 will not change, it will also reduce operating income by $200. The company should not
reduce the selling price.
Sensitivity Analysis and Margin of Safety
Sensitivity analysisis a “what-if” technique that managers use to examine how an outcome will
change if the original predicted data are not achieved or if an underlying assumption changes. In the
context of CVP analysis, sensitivity analysis answers questions such as, “What will operating
income be if the quantity of units sold decreases by 5% from the original prediction?” and “What
will operating income be if the variable cost per unit increases by 10%?” Sensitivity analysis
broadens managers’ perspectives to possible outcomes that might occur before costs are committed.
The margin of safety answers the “what-if” question: If budgeted revenues are above breakeven
and drop, how far can they fall below budget before the breakeven point is reached? Sales might
decrease as a result of a competitor introducing a better product, or poorly executed marketing
programs, and so on.
Margin of safety = Budgeted (or actual) revenues - Breakeven revenues
Margin of safety (in units) = Budgeted (or actual) sales quantity - Breakeven quantity
Assume that the company has fixed costs of $2,000, a selling price of $200, and variable cost per
unit of $120. If the company sells 40 units, budgeted revenues are $8,000 and budgeted operating
income is $1,200. The breakeven point is 25 units or $5,000 in total revenues.
Margin of safety = budgeted revenues - breakeven revenues = $ 8000 - $ 5000= $ 3,000
Margin of safety (in units) = Budgeted sales unit - Breakeven sales unit = 40 – 25 = 15 units
Margin of safety percentage = Margin of safety in dollars = 3,000 = 37.5%
Budgeted (or actual) revenues 8,000
This result means that revenues would have to decrease substantially, by 37.5%, to reach breakeven
revenues. The high margin of safety gives the company confidence that they are unlikely to suffer a
loss.
Sensitivity analysis is a simple approach to recognizing uncertainty, which is the possibility that an
actual amount will deviate from an expected amount. Sensitivity analysis gives managers a good
feel for the risks involved.

9
Cost Planning and CVP
Managers have the ability to choose the levels of fixed and variable costs in their cost structures.
This is a strategic decision. The followings are various factors that managers and management
accountants consider as they make this decision.
a. Alternative Fixed-Cost/Variable-Cost Structures
CVP-based sensitivity analysis highlights the risks and returns as fixed costs are substituted for
variable costs in a company’s cost structure.
Number of units required to be sold at $200 selling
Price to earn target operating income of
Fixed Cost Variable Cost $0 (Breakeven point) $2,000

Line 6 $2,000 $120 25 50

Line 11 $2,800 $100 28 48
Compared to line 6, line 11, with higher fixed costs, has more risk of loss (has a higher breakeven
point) but requires fewer units to be sold (48 versus 50) to earn operating income of $2,000. CVP
analysis can help managers evaluate various fixed-cost/variable-cost structures.
b. Operating Leverage
The risk-return trade-off across alternative cost structures can be measured as operating leverage.
Operating leverage describes the effects that fixed costs have on changes in operating income as
changes occur in units sold and contribution margin. Organizations with a high proportion of fixed
costs in their cost structures have high operating leverage. Small increases in sales lead to large
increases in operating income. Small decreases in sales result in relatively large decreases in
operating income, leading to a greater risk of operating losses.
At any given level of sale , Degree of operating leverage = Contribution margin
Operating income
Effects of Sales Mix on Income
Sales mix is the quantities (or proportion) of various products (or services) that constitute total unit
sales of a company. Suppose XYZ Co.Is now budgeting for a subsequent college fair in New York.
It plans to sell two different test-prep packages—GMAT Success and GRE Guarantee—and
budgets the following:

10
 GMAT Success GRE Guarantee Total
Expected sales 60 40 100
Revenues, $200 and $100 per unit $12,000 $4,000 $16,000
Variable costs, $120 and $70 per unit 7,200 2,800 10,000
Contribution margin, $80 and $30 per unit $4,800 $1,200 6,000
Fixed costs 4,500
Operating income $1,500
What is the breakeven point? In contrast to the single-product (or service) situation, the total
number of units that must be sold to break even in a multiproduct company depends on the sales
mix—the combination of the number of units of GMAT Success sold and the number of units of
GRE Guarantee sold. We assume that the budgeted sales mix (60 units of GMAT Success sold for
every 40 units of GRE Guarantee sold, that is, a ratio of 3:2) will not change at different levels of
total unit sales. That is, we think of XYZ co. selling a bundle of 3 units of GMAT Success and 2
units of GRE Guarantee. (Note that this does not mean that XYZ co. Physically bundles the two
products together into one big package.) Each bundle yields a contribution margin of $300
calculated as follows:
Number of Units ofContribution
GMAT Success and Margin per Unit
GRE Guarantee in for GMAT Success Contribution Margin
Each Bundle and GRE Guarantee of the Bundle
GMAT Success 3 $80 $240

GRE Guarantee 2 30 60

Total $300

To compute the breakeven point, we calculate the number of bundles XYZ co. Needs to sell.

Break even point in bundles= Fixed cost = 4500 = 15 bundles

Contribution margin per bundle $ 300 per bundle
Breakeven point in units of GMAT Success and GRE Guarantee is as follows:
GMAT Success: 15 bundles * 3 units of GMAT Success per bundle 45 units
GRE Guarantee: 15 bundles * 2 units of GRE Guarantee per bundle 30 units
Total number of units to break even…………………………………75 units

11
Breakeven point in dollars for GMAT Success and GRE Guarantee is as follows:
GMAT Success: 45 units * $200 per unit $ 9,000
GRE Guarantee: 30 units * $100 per unit 3,000
Breakeven revenues …………………….$12,000
When there are multiple products, it is often convenient to use contribution margin percentage.
Under this approach, XYZ Co. first calculates the revenues from selling a bundle of 3 units of
GMAT Success and 2 units of GRE Guarantee:
Number of Units Selling Price
Of GMAT Success for GMAT Success
And GRE Guarantee and GRE Guarantee
In Each Bundle Revenue of the Bundle
GMAT Success 3 $200 $600

GRE Guarantee 2 100 200

Total $800

Contribution margin percentage = Contribution margin of the bundle = $300 = 0.375 or 37.5%
For the bundle Revenue of the bundle 800

Breakeven = Fixed costs = $4,500 = $12,000

Revenues Contribution margin % for the bundle 0.375

Number of bundles = Breakeven revenues = $12,000 = 15 bundles

Required to be sold Revenue per bundle $800 per bundle
To break even

The breakeven point in units and dollars for GMAT Success and GRE Guarantee areas follows:
GMAT Success: 15 bundles * 3 units of GMAT Success per bundle 45 units $200 per unit = $9,000
GRE Guarantee: 15 bundles * 2 units of GRE Guarantee per bundle 30 units $100 per unit = $3,000
Recall that in all our calculations we have assumed that the budgeted sales mix (3 units of GMAT
Success for every 2 units of GRE Guarantee) will not change at different levels of total unit sales.

12