he lnternet boom o f t h e 1 9 9 0 s le d ma n y e n t re p re n
e u rso t believe that they couldearn profitswell abovethose of
traditional retail storesby avoiding the high fixed costsof
brick-and-mortar retailoutlets. On line business flourished for a
wh ile , b u t wh e n t h e d o t . c o m b u b b le burst, many of
these Internetdreamsdied. Many,but not all. Consider art.com,
e-tailbusiness an that offersover 100,000 differentprints,photos,
and postersto customers rangingfrom budget-minded collegestudentsto
professional decorators searching high-end for art. Foundedin
1995,art.comhasenjoyedpositivecashflows and double-digit revenue
growth since2000.In 2003,Deloitte& Touche namedart.comone of
the fastest-growing tech companies America.lt attractsmore than a
milin lion peopleto its award-winning Web site eachmonth.
Eventhough art.comdoesn'tface the fixed costsof traditional
retailoutlets,it still incursfixed coststied to its Web site and
its customframing facilities. alsoincurs lt variable costs
eachpieceof art.The botfor tom line:e-tailor retail, everybusiness
facesfixed and variable costs, andL-r'{.ruca yavr lporeo
$earch 0ver300,0tr0 i prints:Novr ts ftrt,cofn? $tart here E x p
l o r e I 0 0 0 0 + Su b je cts . Ar cliite ctre lr ' Antm,ils r
Children . Cu ltu r e s . Edr:cati*nal , Fant.tst, *
f'lnti'/stiilndl . morE... fir"0(,rseT$0fl+ n*istr $ Addfil$ . Sali
+ l"lofiet * O'K*eff,* . Fic*ss,r + tr ** Go q h | 'rlt . n.rr)r*.
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*C,r i{ e ftio n r {,xn'rds Translars * tJinteqe0riginel Flsters .
lland C+l,lr"ed Fri*ts " Lirnit*d tditinns Fri*ti ' 5F*cinltTr
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8,ro+!se $Ele[t * lnir' tlAP rr*w, it's frg*l
Chapter7
the company,how did art.com is no exception.Beforethey launched
volumethey hadto reachto break figureout what sales art.commanagers
their target even?How did they forecastthe volume neededto achieve
to And asthe companycontinues operate,how do managers profit
levels? changing variable and fixed business conditions, respondto
fluctuating costs, and pricing pressurefrom new
competitors?Cost-volume-profit (CVP) answersuchquestions. W
helpsmanagers analysis
LearningObjectivesffi C"l.ulate the unit contributionmarginand
the contributionmarginratio
ffi ffi ffi ffi
points andtargetprofitvolumes analysis find breakeven to Ut" CVP
in business conditions to eerform sensitivity analysis response
changing for companies rina breakeven targetprofitvolumes
multiproduct and of and leverage O"t"rrine a firm'smargin safety
operating
ffinthe last chapter, we discussedcost behavior patterns and
methods managers use to determine how their costs behave. We showed
how managers use the contribution margin income statement to
separately display the firm's variable and fixed costs. In this
chapter, we show how managers identify the volume of salesnecessary
to achieve breakeven and target profit levels. !7e also look at how
changesin costs, salesprice, and volume affect the firm's profit.
Finally, we discussways to identify the firm's risk level,
including ways to gauge how easily a firm's profits could turn to
loss if salesvolume declines.
I
Analysis How Does Cost-Volume-Profit Help
Managers?Cost-volume-profit, or CVP, analysis is a powerful tool
that helps managers make important business decisions.
Cost-volume-profit analysis expressesthe relationships among
costs,volume, and profit or loss. For example, at art.com,
managersneed to determine how many pieces of art the company must
sell each month just to cover costs or to break even. CVP can
provide the answer. CVP also helps art.com's managers determine how
many pieces of art the company must sell to earn a target profit,
such as $1,000,000 per month. And if costsor salespriceschange,CVP
can help managers decide how salesvolume would need to change to
achieve the same profit level. However, to use CVP, managers need
certain data. They must also make sure the data are consistent with
the assumptions underlying CVP analysis. In addition, managersneed
a solid understanding of the contribution margin concept introduced
in the last chapter. In this section, we'll take a look at the data
requirements, assumptions, and contribution margin in more
detail.
Cost-Volume-ProfAnalysis it
361
Data Requinedfor Effective CVP AnalysisCVP analysis relies on
the interdependency of five components, or pieces of information.
shown in Exhibit 7-1.
Components CVPAnalysis of
tilill'
If you know or can estimate four of these five components, you
can use CVP analysis to compute the remaining unknown amount.
Therefore, CVP helps managers discover how changes in any of these
components will affect their business. Becausebusinessconditions
are always changing, CVP helps managers prepare for and respond to
economic changes.Now, let's review the assumptions required for CVP
analysis.
CVPAssumptionsCVP analysis assumesthat: 1. A change in volume is
the only factor that affects costs. 2, Managers can classify each
cost (or the components of mixed costs) as either variable or
fixed. These costs are linear throughout the relevant range of
volume. 3. Revenuesare linear throughout the relevant range of
volume. 4. Inventory levels will not change. 5. The sales mix of
products will not change. Salesmix is the combination of products
that make up total sales.For example, art.com may sell 157o
posters, 25Yo unframed photographs, and 60%" fuamed prints. If
profits differ across products, changesin salesmix will affect CVP
analysis. Let's start by looking at a simple firm that has only one
product. Later, we'll expand the firm to include a wider selection
of products. Kay Pak, an entrepreneur, has just started an e-tail
businessselling art posters on the Internet. Kay is a "virtual
retailer" and carries no inventory. Kay's software tabulates all
customer orders each day and then automatically places the order to
buy posters from a wholesaler. Kay buys only what she needs to fill
the prior day's sales orders. The posters cost $21 each, and Kay
sells them for $35 each. Customers pay the shipping costs, so there
are no other variable selling costs. Monthly fixed costs for server
leasing and maintenance, software, and office rental total $7,000.
Kay's relevant range extends from 0 to 2,000 posters a month.
Beyond this volume, Kay will need to hire an employee and upgrade
her \7eb site sofrware in order to handle the increased volume.
362
Chaoter7
Let's seeif Kay's businessmeets the CVP assumptions: 1.
Salesvolume is the only factor that affects her costs. 2. The $21
purchase cost for each poster is a variable cost. Thus, Kay's total
in uariable cosl increases direct proportion to the number of
posters she sells (an extra $Zt in cost for each extra poster she
sells). The $7,000 monthly server leasing and maintenance,
software, and office rental costs are fixed and do not change no
matter how many posters she sellswithin the relevant range. \7e
could graph each of these costs as a straight line, so they are
linear within the relevant range. 3. Kay's revenueis also lilear.
She sellseach poster for $35, so a graph of her revenues is a
straight line beginning at the origin (if she doesn't sell any
posters, she won't have any revenue) that slopesupward at a rate of
$35 per poster. 4. Kay has no inventory. If she did carry
inventory, she wouldn't need to worry about this assumption as long
as she didn't allow her inventory levels to fluctuate too much. 5.
Kay sells just one size poster, so her salesmix is constant at
1.0004art posters. Later, we'll expand her product line to include
two different size posters-each with a different salesprice and
variable cost. The resulting CVP modification works for any firm
that offers two or more products as long as it assumesthat salesmix
will remain constant. Kay's businessmeets all five assumptions,so
her CVP analysiswill be accurate. Becausemost business conditions
do not meet these assumptions perfectly, managers regard CVP
analysis as approximate, not exact.
$Wmn"gfiut Whm Mmf;* ffi.mrnffimffihwtfimmCalc ulat t he uni t e
contribution margin and t he c ont r ibu ti o n m ar ginr at io The
last chapter introduced the contribution margin income statement,
which separates costs by behavior rather than function. Many
managersprefer the contribution margin income statement becauseit
gives them the information for CVP analysis in a "ready-to-use"
format. On these income statements, the contribution margin is the
"dividing line"-all variable expensesgo above the line, and all
fixed expenses go below the line. The results of l(ay's first month
of operations is shown in ExhtbitT-2.
Contribution
Sa le sr e ve n ue(550 posters).... L e ss:Va r ia b l e
expenses Co n tr ib u tio n margi n............ L e ss:F ixe d
expenses.......... Op e r a tin g income.............
$
19,250 (11,550 ) 7,700 (7,000 )
$
700
Notice that the contribution margin is the excessof
salesrevenueover variable expenses.The contribution margin tells
managers how much revenue is left-after paying variable expenses-f
or contribwting toward covering fixed costs and then generating a
profit. Hence the name contribution margin.
Cost-Volume-ProfAnalvsis it
363
The contribution margin is stated as a total amount on the
contribution margin income statement. However, managers often state
the contribution margin on a per unit basis and as a percentage,or
ratio. A product's contribution margin per unitor unit contribution
margin-is the excessof the selling price per unit over the variable
cost of obtaining and sellingeach unit. Some businesses pay a
salescommission on each unit or have other variable costs, such as
shipping costs, for each unit sold. However, Kay's variable cost
per unit is simply the price she pays for each poster. Therefore,
her unit contribution margin is: price per poster... Sales Les s :V
ar iab l e c o s t p e r p o s te r... Contribution margin per
poster... .................;:; $35 (21) $;14
The unit contribution margin indicates how much profit each unit
provides before fixed costs are considered. Each unit first
contributes this profit toward covering the firm's fixed costs.
Once the company sells enough units to cover its fixed costs,the
unit contribution margin contributes directly to profit. For
example, every poster Kay sellsgenerates$14 of contribution margin
that can be used to pay for the monthly $7,000 of fixed costs.
After l(ay sells enough posters to cover fixed costs, each
additional poster she sellswill generate$14 of operating income.
Managers can use the unit contribution margin to quickly forecast
income at any volume within their relevant range. First, they
project the total contribution margin by multiplying the unit
contribution margin by the number of units sold. Then, they simply
subtract fixed costs. For example, let's assumethat Kay hopes to
sell 650 posters next month. She can project her operating income
as follows: Contributionmargin (650 postersX $14 per poster) Less:
Fixedexpenses Operating income.......... .. $9,100 (7,000)
$2,100
If Kay sells650 postersnext month, her operating income should
be $2,100.
The Ccnmtnthutf,mm gfir'n tV1an RmtimIn addition to computing
the unit contribution margin, managers often compute the
contribution margin ratio, which is the ratio of contribution
margin to salesrevenue. Kay can compute her contribution margin
ratio at the unit level as follows:q14 bJJ
Kay could also compute the contribution margin ratio using any
volume of sales.Let's use her current salesvolume, pictured
inExhlbit 7-2:
$7,700 $tq,zs0The 40% contribution margin ratio means that each
$1.00 of salesrevenuecontributes $0.40 toward fixed expenses and
profit, as shown in Exhibit 7-3.The remaining $0.60 of each
salesdollar is used to pay for variable costs.The contribution
margin ratio is the percentage of each sales dollar that is
auailable for couering fixed expenses and generatinga profit.
364
Chapter 7
Breakdown of $1 of Sales Revenue
Managers can also use the contribution margin ratio to quickly
forecast operating income within their relevant range. \7hen using
the contribution margin ratio, project income basedon sales
managers dollars rather than salesunits.For example, what will
I(ay's income be if salesrevenue reaches$70,000 one month? To find
out, simply rnultiply projected salesrevenue by the contribution
margin ratio to get the total contribution margin. Then, subtract
fixed expenses: Contribution margin ($70,000 salesX 40o/.) =
Less:Fixed expenses..... Operating income........ $28,000 (7,000)
$Z1pg0
Let's verify. If I(ay has $70,000 of salesrevenue,she has sold
2,000 posters ($70,000 + $35 price per poster).Her
completecontribution margin income statement would be calculatedas
follows: Sa l e s v e n u e(2,000 postersx $3S /poster) re
................ (2,000 posters x $21lposter)...........
Less:Variable expenses $70,000 (42,000)
C o n tri b u ti o n margi n (2,000 postersx $14l poster)
............... $28,000 Less:Fixed expenses..... Op e ra ti n gi n
c ome........ (7,000) $21,000
The contribution margin per unit and contribution margin ratio
help managers quickly and easily project income at different
salesvolumes. However, when projecting profits, managersmust keep
in mind the relevant range. For instance,if I(ay wants to project
income at a volume of 5,000 posters, she shouldn't use the existing
contribution margin and fixed costs. Her current relevant range
extends to only 2,000 postersper month. At a higher volume of
sales, her variable cost per unit may be lower than $21 (due to
volume discountsfrom her suppliers)and her monthly fixed costsmay
be higher than $7,000 (due to upgrading her systemand hiring an
employeeto handle the extra salesvolume). Rather than use
individual unit contribution margins on each of their products,
Iarge companies that offer hundreds or thousands of products (like
art.com) use their contribution margin ratio to predict profits. As
long as the salesmix remains constant (one of our CVP assumptions),
the contribution margin ratio will remain constant. 'We'veseenhow
managersuse the contribution margin to project income; but
managersuse the contribution margin for other purposestoo, such as
motivating the sales force. Salespeople who know the contribution
margin of each product can generatemore profit by
emphasizinghigh-margin products. This is why many
Cost-Vol me-Prof Analvsis u it \ companies base sales
commissions on the contribution margins produced by sales rather
than on sales revenue alone. In the next section,we'll seehow
managersuse the contribution margin in CVP analysis to determine
their breakeven point and to determine how many units they need to
sell to reach target profits.
365
UsingCVPAnalysisto Find the BreakevenPointA company's point is
the saleslevel at which operatingincomeis zero. breakeven Sales
below the breakeven point result in a loss. Sales point abovethe
breakeven provide a profit. BeforeKay startedher business, wanted
to figure out how she many posters would haveto selljust to
breakeven. she Therearethreewaysto calculate breakeven point. AII
of the approaches the are based the incomestatement, they all
reachthe sameconclusion. on so The first two methods find breakeven
termsof sales in finds breakeven wnits.Thelast approach in terms of
sales dollars. 1. The incomestatement approach 2. The shortcut
approachusing the wnit contribution margin 3. The shortcutapproach
usingthe contribution marginratio Let'sexamine these
threeapproaches detail. inUseCVPanalysis to find breakeven points
and target profit vol umes
The Income StaternentApproachThe income statement approach
simply breaks the income statement equation into smaller
components:
Let'susethis approachto find Kay's breakeven point. Recallthat
Kay sellsher postersfor $35 each and that her variablecost is $21
per poster.Kay's fixed expenses total $7,000.At the breakeven
point, operating incomeis zero.Weusethis informationto solvethe
incomestatement equationfor the numberof posters Kay must sellto
breakeven.
($:s($3s
366
Chapter 7
point in sales to Kay must sell500 posters breakeven.Her
breakeven dollarsis (500posters $35). x $17,500 the numberof units
into the You cancheckyour answerby substituting breakeven that this
levelof sales resultsin zero profit: incomestatement and checkine
(500posters $35)........ x revenue Sales (500posters $21) x
Variable expenses Less: Contributionmargin Fixedexpenses..... Less;
Operatingincome........ . $ (7,000) 0 $tZ,50O (10,500)
a equalits contributionmargin. Notice that at breakeven, firm's
fixed expenses just In other words, the firm hasgenerated
enoughcontributionmargin to coverits (but to fixed expenses not
enough generate profit). a
The ShortcutApproachUsingthe UnitMfimngf;n ffiontributimmThe
shortcut method simply rearrangesthe income statement equation and
isolates "Units sold" on the left: = income Sales revenue
Variableexpenses Fixedexpenses Operating Contributionmargin = -
Fixedexpenses Operating income= Fixed expenses+ Operating
income
(Contribution per margin unit x Unitssold)
Dividing both sidesof the equationby contributionmargin per unit
yieldsthe shortcutmethod:salesin ,rnrr,Fixgl expjnses
operatingincome + uontnDutlonmargmper unlt
Kay can use this shortcut method to find her breakeven point in
units. Kay's fixed expensestotal $7,000, and her unit contribution
margin is $14. At the breakeven point, operating income is zero.
Thus, Kay's breakevenpoint in units is: $7,000+ $0 ., satesn unrts=
l g14 = 50Spqrsters Why does this shortcut method work? Recall that
each poster provides $14 of contribution margin. To break even, Kay
must generateenough contribution margin to cover $7,000 of fixed
expenses.At the rate of $14 per poster, Kay must sell Because the
short500 posters($7,000/$14)to cover her $7,000 of fixed expenses.
method simply rearrangesthe income statement equation, the
breakevenpoint is cut the sameunder both methods (500 posters).
Cost-Volume-Profit Analvsis
367
Silotr o