Part Two: Management Accounting

Chapter Four
Cost Volume Profit (CVP) Analysis
 4.1 Basic Cost Concept And Cost
Behaviour
4.1.1 Basic cost concept : cost and cost
terminology
• Accountants define cost as a resource sacrificed
or forgone to achieve a specific objective.
• A cost (such as direct materials or advertising) is
usually measured as the monetary amount that
must be paid to acquire goods or services.
• Terminology
1. An actual cost is the cost incurred (a historical
or past cost), as distinguished from a budgeted
cost, which is a predicted or forecasted cost (a
future cost).
2. When you think of cost, you always think of it
in the context of finding the cost of a particular
thing. We call this thing a cost object, which is
anything for which a measurement of costs is
desired.
• Classification
1.Based on management function /General
cost classification
A. Manufactured cost
i. Direct material cost : are those materials
that become an integral part of the finished
product and that can be physically and
conveniently traced to it
ii. Direct labor is that can be easily i.e.
physically and conveniently traced to
individual units of product.
Direct labor is sometimes called touch
labor, since direct labor workers typically
touch the product while it is being made
iii. Manufacturing Overhead
• Includes all costs of manufacturing except direct
materials and direct labour
 Manufacturing overhead includes items such as
 Indirect Materials
 Indirect Labour
 Maintenance and Repairs on Production
Equipment
 Heat and Light
Direct Material + Direct Labor = Prime Cost
Direct Labor + Manufacturing Overhead = Conversion
Cost
B. Non-manufacturing Costs
• Generally, non-manufacturing costs are sub classified into two categories:
I. Marketing or selling costs: include all cost categories to secure customer
orders and get the finished product or service into the hands of the
customer. These costs are often called order-getting and order filling
costs.
 Like advertising,
 shipping,
 sales travel,
 sales commissions,
 sales salaries, and costs of finished goods warehouses.
II. Administrative Costs: include all executive,
organizational associated with the general management
of an organization rather than with manufacturing,
marketing or selling.
 Like executive compensation,
 General accounting,
 Secretarial,
 Public relations, and similar costs involved in the
overall,
 General administration of the organization as a whole.
2. Accounting treatment
A. Product cost
• Product costs include all cots that are involved in
acquiring or making product- direct materials, direct
labour, and manufacturing overhead.
• Initially product costs are assigned to an inventory
account on the balance sheet. When goods are sold,
the costs are released from inventory as expenses (cost
of goods sold) and matched against revenue. For this
reason they are also known as inventoriable costs.
• Product costs are not necessarily treated
as expenses in the period in which they
are incurred. Rather they are treated as
expenses in the period in which the
related products are sold
ii. Period Costs
• Period costs are all the costs that are not
included in product costs. These costs are
expensed on the income statement in the
period, in which they are incurred, the
rules of accrual accounting.
• Period costs are not included as part of the
cost of either purchased or manufactured
goods.
Like sales commissions and
 office rent and
all selling and administrative expenses are
considered to be period costs
3. Cost Classification for Assigning Costs to Cost
Object
A. Direct Cost : A direct cost is a cost that can be
easily and conveniently traced to the particular
cost object under consideration.
• For example, the cost of steel or tires is a direct
cost of BMW X5s
• The term cost tracing is used to describe the
assignment of direct costs to a particular cost
object
B. Indirect costs of a cost object are related
to the particular cost object but cannot be
traced to it in an economically feasible (cost-
effective) way.
• For example, the salaries of plant
administrators (including the plant
manager) who oversee production of the
many different types of cars produced.
 • Cost tracing
Cost assignment

Direct cost (DM & DL)

Cost object

Indirect cost (IM cost allocation

&IL)
4. Based on cost behaviour : Analysis
Cost behaviour mans 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 rises and fall
as well or it may remain constant.
A. Variable Cost
A variable cost is a cost that varies, in total,
in direct proportion to change 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
• A good example of a variable cost is direct
materials.
• The cost of direct materials used during a
period will vary, in total, in direct
proportion to the number of units that are
produced.
• In variable cost, the total cost rises and falls
as the activity level rises and falls. One
interesting aspect of variable cost
behaviour is that a variable cost is
constant if expressed on a per unit basis.
B. 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 force, such as price changes.
E.g.:- Rent Expense
• When we say a cost is fixed, we mean it is
fixed within some relevant range.
• The relevant range is the range of activity
within which the assumptions about
variable and fixed costs are valid.
• Example: Guild Company manufactures and sells one
product. The production can vary from 20,000 to 60,000
units. A partially schedule of the company’s total and
per unit costs for the coming year follows:
Unit produced and sold
20,000 40,000 60,000
Total cost
VC Br 80,000 ?
FC Br 100,000 ? ?
TC Br 180,000 ? ?
Cost per unit
VC ? ? ?
FC ? ? ?
TC ? ? ?
4.1 Essentials of CVP Analysis
• 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.
• Basic Components/Essentials
• CVP analysis considers the interrelationships
among the components shown in
 Volume or level of activity
 Unit selling prices
 Variable cost per unit
 Total fixed costs
 Sales mix
 Assumptions of CVP analysis
The following assumptions underlie each CVP analysis.
1. The behavior of both costs and revenues is linear
throughout the relevant range of the activity index.
2. Costs can be classified accurately as either variable or
fixed.
3. Changes in activity are the only factors that affect
costs.
4. All units produced are sold.
5. When more than one type of product is sold, the sales
mix will remain constant
 CVP Income Statement
• Because CVP is so important for decision making,
management often wants this information reported
in a CVP income statement format for internal use.
• The CVP income statement classifies costs as
variable or fixed and computes a contribution
margin.
• Contribution margin is the amount of revenue
remaining after deducting variable costs. It is often
stated both as a total amount and on a per unit
basis.
• We will use ABC Video Company to
illustrate a CVP income statement. ABC
Video produces a high-end, progressive-
scan DVD player/recorder with up to 160-
hour recording capacity and MP3
playback capability. Relevant data for the
DVD players sold by this company in June
2010 are as follows.
• Assumed selling and cost data for ABC Video
• Unit selling price of DVD player $500
• Unit variable costs $300
• Total monthly fixed costs $200,000
• Units sold 1,600
• The CVP income statement for ABC Video therefore would be
reported as follows

ABC VIDEO COMPANY

CVP Income Statement
For the Month Ended June 30, 2010
Total Per unit
Sales (1,600 DVD players) $800,000 $500
Variable costs 480,000 300
Contribution margin 320,000 $200
Fixed costs 200,000
Net income $120,000
• In the applications of CVP analysis that
follow, we assume that the term “cost”
includes all costs and expenses related to
production and sale of the product.
• That is, cost includes manufacturing costs
plus selling and administrative expenses
CONTRIBUTION MARGIN PER UNIT
• ABC Video’s CVP income statement shows a
contribution margin of $320,000, and a
contribution margin per unit of $200 ($500-
$300).
• The formula for contribution margin per unit
and the computation for ABC Video are:
Unit selling price –unit variable cost
500-300 = 200
• Contribution margin per unit indicates
that for every DVD player sold, ABC has
$200 to cover fixed costs and contribute to
net income.
• Because ABC Video has fixed costs of
$200,000, it must sell 1,000 DVD players
($200,000 @ $200) before it earns any net
income. ABC CVP income statement,
assuming a zero net income, is as follow
• The CVP income statement for ABC Video therefore would be
reported as follows

ABC VIDEO COMPANY

CVP Income Statement
For the Month Ended June 30, 2010
Total Per unit
Sales (1,000 DVD players) $500,000 $500
Variable costs 300,000 300
Contribution margin 200,000 $200
Fixed costs 200,000
Net income $-0-
• It follows that for every DVD player sold
above 1,000 units, net income increases
$200. For example, assume that ABC sold
one more DVD player, for a total of 1,001
DVD players sold. In this case ABC
reports net income of $200 as shown in
below :
• The CVP income statement for ABC Video therefore would be
reported as follows

ABC VIDEO COMPANY

CVP Income Statement
For the Month Ended June 30, 2010
Total Per unit
Sales (1,001 DVD players) $500,500 $500
Variable costs 300,300 300
Contribution margin 200,200 $200
Fixed costs 200,000
Net income $200
• CONTRIBUTION MARGIN RATIO
• Some managers prefer to use a
contribution margin ratio in CVP analysis.
The contribution margin ratio is the
contribution margin per unit divided by
the unit selling price
• CMR = contribution margin per unit
the unit selling price
 200 /500= 0.4 OR 40%

 The contribution margin ratio of 40%

means that $0.40 of each sales dollar ($1
40%) is available to apply to fixed costs
and to contribute to net income.
• This expression of contribution margin is very
helpful in determining the effect of changes in
sales dollars on net income.
• For example, if sales increase $100,000, net
income will increase $40,000 (40% $100,000).
• Thus, by using the contribution margin ratio,
managers can quickly determine increases in
net income from any change in sales dollars.
 ABC VIDEO COMPANY
CVP Income Statement
For the Month Ended June 30, 2010
No change with change
Total Per unit Total Per unit
Sales (1,000 DVD $500,000 $500 600,000 500
players)
Variable costs 300,000 300 360,000 300
Contribution 200,000 $200 240,000 200
margin
Fixed costs 200,000 200,000
Net income $-0- 40,000
 4.2 Single product and Break Even
Analysis
 A key relationship in CVP analysis is the
level of activity at which total revenues
equal total costs (both fixed and variable).
This level of activity is called the break-
even point. At this volume of sales, the
company will realize no income but will
suffer no loss.
• The process of finding the breakeven point
is called break-even analysis.
• Knowledge of the break-even point is useful
to management when it decides whether to:
 introduce new product lines,
 change sales prices on established products,
or
 enter new market areas.
• The break-even point can be:
1. Computed from a mathematical
equation.
2. Computed by using contribution margin.
3. Derived from a cost-volume-profit (CVP)
graph.
• The break-even point can be expressed
either in sales units or sales dollars.
1. MATHEMATICAL EQUATION
• Sales = Vc + Fc+ Net Income
• Identifying the break-even point is a special case
of CVP analysis. Because at the break-even point
net income is zero, break-even occurs where total
sales equal variable costs plus fixed costs.
• We can compute the break-even point in units
directly from the equation by using unit selling
prices and unit variable costs. The computation
for ABC Video is:
• Sales = Vc+ Fc + Net Income
$500Q $300Q + $200,000 + $0

$200Q $200,000
Q 1,000 units
• where
• Q sales volume in units
• $500 selling price
• $300 variable cost per unit
• $200,000 total fixed costs
• Thus, ABC Video must sell 1,000 units to
break even.
• To find sales dollars required to break
even, we multiply the units sold at the
break-even point times the selling price
per unit, as shown below. 1,000 $500
$500,000 (break-even sales dollars)
2. CONTRIBUTION MARGIN TECHNIQUE
• We know that contribution margin equals
total revenues less variable costs. It follows
that at the break-even point, contribution
margin must equal total fixed costs.
• On the basis of this relationship, we can
compute the break-even point using either
the contribution margin per unit or the
contribution margin ratio.
• Break even point in unit =Fixed Cost
Contribution Margin per Unit
= $200,000 =1,000 units
$200
• One way to interpret this formula is that
ABC Video generates $200 of contribution
margin with each unit that it sells
Or the other way is by using contribution
margin ratio can compute the break even
point in dollar.
• Break-even Point in Dollars = Fixed cost
Contribution margin ratio
• Break-even Point in Dollars = $200,000 = $500,000
40%
3. GRAPHIC PRESENTATION
• An effective way to find the break-even
point is to prepare a break-even graph.
Because this graph also shows costs,
volume, and profits, it is referred to as a
cost-volume-profit (CVP) graph
 Class work
• Lombardi Company has a unit selling
price of $400, variable costs per unit of
$240, and fixed costs of $180,000. Compute
the break-even point in units using
(a) a mathematical equation and
(b) contribution margin per unit.
 4.3 Target Net Income and Income Tax

 Rather than simply “breaking even,”

management usually sets an income
objective often called target net income.
 It indicates the sales necessary to achieve a
specified level of income. Companies
determine the sales necessary to achieve
target net income by using one of the three
approaches discussed earlier.
1. MATHEMATICAL EQUATION
• We know that at the break-even point no
profit or loss results for the company. By
adding an amount for target net income to
the same basic equation, we obtain the
following formula for determining
required sales.
• Required Sales = Vc+ Fc + Target Net Income
$500Q $300Q + $200,000 + $120,000
• Required sales may be expressed in either
sales units or sales dollars.
• Assuming that target net income is
$120,000 for ABC Video, the computation
of required sales in units is as follows.
 $200Q $320,000
Q 1,600 units
• where
• Q sales volume
• $500 selling price
• $300 variable costs per unit
• $200,000 total fixed costs
• $120,000 target net income
• The sales dollars required to achieve the
target net income is found by multiplying
• the units sold by the unit selling price
[(1,600 X $500) $800,000].
2. CONTRIBUTION MARGIN TECHNIQUE
• Fc + Target Net Income =Req. Sales in unit
Contribution Margin per unit
• ($200,000 + $120,000) / $200 = 1,600 units
• This computation tells ABC that to
achieve its desired target net income of
$120,000, it must sell 1,600 DVD players.
• Or by using contribution margin ratio
• Fc + Target Net Income = Req. Sales in doll.
Contribution Margin ratio
• 320,000/40%= $800,000
• This computation tells ABC that to achieve
its desired target net income of $120,000, it
must generate sales of $800,000
3. GRAPHIC PRESENTATION
 Income tax issue
• Assume that the income tax of ABC Co. is
60%.
• So, based on the above information
compute company should be expect to sell
the number of units and dollar amounts
to reach the desired/ target net income.
• The unit is 2500
• The dollar to be sold is 1,250,00
 Using CVP Analysis for Decision Making

 We have seen how CVP analysis is useful for calculating

the units that need to be sold to break even, or to achieve
target net income.
 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 target net income.
 CVP analysis helps managers make product decisions
by estimating the expected profitability of these choices.
 Cont…
 Strategic decisions always involve 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 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 ABC Success example to illustrate how
CVP analysis can be used for strategic decisions concerning
advertising , selling price and Determining Target Prices
• Suppose ABC anticipates selling 40 units at
the fair. Operating income will be $120,000.
ABC is considering placing an advertisement
describing the product and its features in the
fair brochure. The advertisement will be a
fixed cost of $500. ABC thinks that advertising
will increase sales by 10% to 44 packages.
• Should ABC advertise? The following table
presents the CVP analysis.
 A. Decision to advertising
class work

• Suppose Emma Company anticipates selling 40 units at

the fair. Emma’s operating income will be $1,200. Emma
is considering placing an advertisement describing the
product and its features in the fair brochure. The
advertisement will be a fixed cost of $500. Emma thinks
that advertising will increase sales by 10% to 44
packages. The selling cost and variable cost per unit is $
200 and $ 120 respectively. The fixed cost is $ 2,000
• Should Emma advertise? The following table presents
the CVP analysis
 ABC VIDEO COMPANY
CVP Income Statement
For the Month Ended June 30, 2010
40 Package sold 44 Package sold with advertising
with no
advertising
Difference
Sales (40x 200, 44x 8000 8,800 800
200 )
Variable costs (120 4,800 5280 480
X40, 120 X 44 )
Contribution 3200 3520 320
margin
Fixed costs 2000 2,500 500
Net income 1200 1,020 (180)
• Operating income will decrease from
$1,200 to $1,020, so Emma should not
advertise
 B. Decision to Reduce Selling Price

• Having decided not to advertise, Emma is

expecting whether to reduce the selling price to
$175. At this price, she thinks she will sell 50
units. At this quantity, the test per-package
wholesaler who supplies GMAT Success will sell
the packages to Emma for $115 per unit instead
of $120. Should Emma reduce the selling price?
 Cont….
 Contribution margin from lowering price 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 price $(200)
• Decreasing the price will reduce
contribution margin by $200 and, because
the fixed costs of $2,000 will not change, it
will also reduce operating income by $200.
Emma should not reduce the selling price.
 C. Determining Target Prices

• Emma could also ask “At what price can I

sell 50 units (purchased at $115 per unit)
and continue to earn an operating income
of $1,200?”
• The answer is $179, as the following
calculations show.
Target operating income $1,200
Add fixed costs $ 2,000
Target contribution margin $3,200
Divided by number of units sold 50 units
Target contribution margin per unit $ 64
Add variable cost per unit $ 115
Target selling price $179
• Proof:
• Revenues, $179 per unit * 50 units $8,950
• Variable costs, $115 per unit * 50 units ($ 5,750)
• Contribution margin $3,200
• Fixed costs ($2,000)
• Operating income $1,200
• Emma should also examine the effects of other
decisions, such as simultaneously increasing
advertising costs and lowering prices.
• In each case, Emma will compare the changes
in contribution margin (through the effects on
selling prices, variable costs, and quantities of
units sold) to the changes in fixed costs, and
she will choose the alternative that provides
the highest operating income
 4.4 Sensitivity Analysis and Margin of Safety
• Before choosing strategies and plans about how to
implement strategies, managers frequently analyze the
sensitivity of their decisions to changes in underlying
assumptions.
• Sensitivity analysis is 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 variable cost
per unit increases by 10%?” Sensitivity analysis
broadens managers’ perspectives to possible
outcomes that might occur before costs are
committed.
 Number of units required to be sold at $200

Selling Price to Earn Target Operating Income of

Variable cost $ -0- $1200 $1600 $2000

Fixed cost Per unit Breakeven

point

$ 2,000 $100 20 32 36 40

$2,000 $120 25 40 45 50

$2,000 $150 40 64 72 80

$2,400 $100 24 36 40 44

$2,400 $120 30 45 50 55

$ 2,400 $150 48 72 80 88

$2,800 $100 28 40 44 48

$2,800 $120 35 50 55 60

$ 2,800 $150 56 80 88 96

Number of U. Req.to be sold= FC+ Target net income/cont. mar.per unit 2000+1200 =32
200-100
• Note
For example, 32 units must be sold to earn an operating
income of $1,200 if fixed costs are $2,000 and variable cost
per unit is $100.
Emma can also use the above Exhibit to determine that she
needs to sell 56 units to break even if fixed cost of the rental
at the Chicago fair is raised to $2,800 and if the variable cost
per unit charged by the test-prep package supplier increases
to $150.
Emma can use information about costs and sensitivity
analysis, together with realistic predictions about how much
she can sell to decide if she should rent a booth at the fair.
• Another aspect of sensitivity analysis is
margin of safety:
 Margin of Safety
• The margin of safety is another relationship
used in CVP analysis.
• Margin of safety is the difference between
actual or expected sales and sales at the break-
even point. This relationship measures the
“cushion” that management has, allowing it to
still break even if expected sales fail to
materialize.
• The margin of safety is expressed in dollars or as
a ratio.
• The formula for stating the margin of safety in dollars is
actual (or expected) sales minus break-even sales.
Assuming that actual (expected) sales for ABC Video
are $750,000, the computation is:
• Actual (Expected) sale - Break-even Sales=Margin of
Safety
• $750,000 -$500,000 = $250,000
• ABC’s margin of safety is $250,000. Its sales must fall
$250,000 before it operates at a loss.
• The margin of safety ratio is the margin of
safety in dollars divided by actual (or expected)
sales.
• The formula and computation for determining
the margin of safety ratio are:
• Margin of Safety in Dollars / Actual (Expected)
Sales= Margin of Safety
• $250,000 / $750,000= 33%
• This means that the company’s sales could fall
by 33% before it would be operating at a loss.
• The higher the dollars or the percentage,
the greater the margin of safety.
• Management continuously evaluates the
adequacy of the margin of safety in terms
of such factors as the vulnerability of the
product to competitive pressures and to
downturns in the economy.
4.5 Multiple Products and CVP Analysis / 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 Emma is
now budgeting for a subsequent college fair in
New York. She plans to sell two different test-
prep packages—GMAT Success and GRE
Guarantee—and budgets the following:
 GMAT Success GRE Total
guarantee
Expected sale 60 40 100
Revenue $200 and $100 per unit $12,000 4,000 16,000
VC $120 and $70 per unit 7,200 2,800 10,000
Contribution margin $80 and $30 $4,800 1,200 6,000
per unit
Fixed cost 4,500
Operating income 1500
• 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 Emma selling a bundle of 3
units of GMAT Success and 2 units of GRE
Guarantee. (Note that this does not mean that
Emma physically bundles the two products
together into one big package.)
• Each bundle yields a contribution margin of $300
calculated as follows:

Number of Units Contribution Contribution

of GMAT Margin per Unit Margin
Success and for GMAT of the Bundle
GRE Guarantee Success
in and GRE
Each Bundle Guarantee
GMAT 3 80 240
Success
GRE 2 30 60
Guarantee
Total 300
• To compute the breakeven point, we
calculate the number of bundles Emma
needs to sell.
• BEP bundle = FC
Contribution margin per bundle
4,500 = 15 Bundle
300
 Breakeven point in units of GMAT Success and GRE Guarantee is as
follows:
• GMAT Success: 15 bu.* 3 units of GMAT Success per bu. 45 units
• GRE Guarantee: 15 bu.* 2 units of GRE Guarantee per bu. 30 units
• Total number of units to break even 75 units
 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
 Number of Units Selling Price Revenue of the
of GMAT for GMAT Success Bundle
and GRE Guarantee
Success and
GRE Guarantee
in
Each Bundle
GMAT 3 200 600
Success
GRE 2 100 200
Guarantee
Total 800
 Contribution margin percentage for the bundle= Con.M of Bu.
Revenue of the Bu.
$ 300 =0.375 or 37.5 %
$ 800
 Break even revenue : FC 4500 = $ 12,000
Con. Margin % for the bundle 0.375

 No. of bu. Req. to be sold to BV= BERev. = 12,000 =15 Bu.

Revenue per bu. 800
• The breakeven point in units and dollars for GMAT
Success and GRE Guarantee are as 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
 4.6 CVP analysis and non profit
organization
• Service companies like Bank of America, and nonprofit
organizations like the United Way. To apply CVP analysis
in service and nonprofit organizations, we need to focus
on measuring their output, which is different from the
tangible units sold by manufacturing and merchandising
companies. Examples of output measures in various
service and nonprofit industries are as follows:
Industry Measure of Output
• Airlines Passenger miles
• Hotels/motels Room-nights occupied
• Hospitals Patient days
• Universities Student credit-hours
• Consider an agency of the Massachusetts Department of
Social Welfare with a $900,000 budget appropriation (its
revenues) for 2011. This nonprofit agency’s purpose is to
assist handicapped people seeking employment. On
average, the agency supplements each person’s income
by $5,000 annually. The agency’s only other costs are
fixed costs of rent and administrative salaries equal to
$270,000. The agency manager wants to know how
many people could be assisted in 2011. We can use CVP
analysis here by setting operating income to $0. Let Q be
the number of handicapped people to be assisted:
• Revenue –VC-FC=0
• $900,000-5,000Q-$270,000
• =$5,000Q= $900,000-$270,000= $630,000
• $5,000Q = 630,000 = 126 People
• 5,000Q 5,000Q

• Q= 630,000/5,000=126 people
• Suppose the manager is concerned that the total
budget appropriation for 2012 will be reduced
by 15% to $900,000 * (1 - 0.15) = $765,000. The
manager wants to know how many
handicapped people could be assisted with this
reduced budget. Assume the same amount of
monetary assistance per person:
• Revenue –VC-FC=0
• $765,000-5,000Q-$270,000
• =$5,000Q= $765,000-$270,000= $495,000
• $5,000Q = 495,000 = 99 People
• 5,000Q 5,000Q

• Q= 495,000/5,000=99people
• Note the following two characteristics of the
CVP relationships in this nonprofit situation:
1. The percentage drop in the number of people
assisted, (126 to 99) 126, or 21.4%, is greater
than the 15% reduction in the budget
appropriation. It is greater because the $270,000
in fixed costs still must be paid, leaving a
proportionately lower budget to assist people.
The percentage drop in service exceeds the
percentage drop in budget appropriation.
• Given the reduced budget appropriation
(revenues) of $765,000, the manager can adjust
operations to stay within this appropriation in one
or more of three basic ways:
(a) reduce the number of people assisted from the
current 126,
(b) reduce the variable cost (the extent of assistance
per person) from the current $5,000 per person, or
(c) reduce the total fixed costs from the current
$270,000.
• The end of chapter Four