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Chapter 2
Introduction to Cost Behavior
and Cost-Volume Relationships
LEARNING OBJECIVE!"
When your students have fnished studying this chapter, they should beable to:
1. Explain how activity cost drivers aect cost behavior.
2. Show how changes in costdriver levels aect variable and fxedcosts.
!. "alculate brea#even sales volu$e in total dollars and total units.
%. "reate a costvolu$eproft graph and understand the assu$ptionsbehind it.
&. "alculate sales volu$e in total dollars and total units to reach atarget proft.
'. (ierentiate between contribution $argin and gross $argin.
). Explain the eects o* sales $ix on profts +A##EN$I% 2A.
-. "o$pute costvolu$eproft relationships on an a*tertax basis+A##EN$I% 2B.
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C&A#ER 2" A!!IGN'EN!
CRIICAL &IN(ING E%ERCI!E!
2%. ar#eting /unction o* 0alue"hain and "ost ehavior2&. roduction /unction o* 0alue"hain and "ost ehavior2'. 3enneco 4uto$otive5s 0alue "hain
E%ERCI!E!
2). 6denti*ying "ost (rivers2-. asic 7eview Exercises28. 0ariable and /ixed"ost ehavior!9. 0ariable and /ixed"ost ehavior!1. asic 7eview Exercises!2. asic "ost0olu$e raph!!. asic "ost0olu$e raph!%. asic "ost0olu$e raphs!&. asic "ost0olu$e raphs!'. ;ospital "osts and ricing!). "ost0olu$eroft at a ;ospital!-. otel 7entals!8. 0ariable "ost to rea# Even%9. Salesix 4nalysis%1. 6nco$e 3axes%2. 6nco$e 3axes and "ost0olu$eroft 4nalysis
#ROBLE'!
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&!. ingo and ?everage&%. ?everage at eay&&. 4dding a roduct&'. overn$ent @rganiAation&). ross argin and "ontribution argin
&-. "hoosing EBuip$ent *or (ierent 0olu$es&8. Sales "o$pensation, 0ariableC/ixed "osts, and Ethics'9. Salesix 4nalysis'1. ;ospital atient ix'2. 6nco$e 3axes on ;otels'!. 3ax Eects, ultiple "hoice
CA!E!
'%. ;ospital "osts
'&. "0 in a odern anu*acturing Environ$ent''. ultiproduct rea#Even in a 7estaurant'). Eects o* "hanges in "osts, 6ncluding 3ax Eects'-. @perating ?everage
E%CEL A##LICAION E%ERCI!E
'8. "0 and rea#Even
COLLABORAIVE LEARNING E%ERCI!E
)9. "0 *or a S$all usiness
INERNE E%ERCI!E
)1. "ost ehavior at Southwest 4irlines+http:CCwww.southwest.co$
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C&A#ER 2" O)LINE
I* Identi+,in Resources. Activities. Costs. and Cost
$rivers {L. O. 1}
Cost $rivers - @utput $easures o* resources and activities.E%&IBI 2-/shows the traditional and activitybased views o* costbehavior. 3o apply the activitybased view, we $ust identi*y theresources used by each activity and the cost driver *or eachresource.
@rganiAations can have $any cost drivers. 6n this chapter,volu$ebased cost drivers are used in order to exa$ine costbehavior. See E%&IBI 2-2*or exa$ples o* costs and potential
cost drivers *or valuechain *unctions.
II* Varia0le and 1ied Costs {L. O. 2}
0ariable and fxed costs re*er to how cost behaves with respect tochanges in a particular cost driver.
Varia0le Cost - a cost that changes in direct proportion tochanges in the cost driver level +i.e., costs per unit do not change,total costs do change. Exa$ples include the costs o* $aterials,
$erchandise, parts, supplies, co$$issions, and $any types o*labor.
1ied Cost - a cost that is not i$$ediately aected by changes inthe cost driver level +i.e., costs per unit do change, total costs donot change within the relevant range. Exa$ples include realestate taxes, real estate insurance, $any executive salaries, andspace rentals. E%&IBI 2-3 su$$ariAes the relationship betweenfxed and variable costs. See E%&IBI 2-4 *or the relationshipbetween the receiving activity and the costs o* the *uel and
eBuip$ent resources. See E%&IBI 2-5*or the total cost lines *ortotal *uel and eBuip$ent lease costs.
A* Relevant Rane
Relevant Rane -the li$its +i.e., ti$e period andCor activityo* costdriver activity within which a specifc relationship
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between costs and the cost driver is valid. See E%&IBI 2-6*or a graph o* fxed cost behavior within a relevant range.
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B* $i7erences in Classi+,in Costs
"osts $ay not act in a linear $anner with volu$ebased costdrivers.Exa$ples: when learning aects the production ti$e, and
there*ore the labor cost o* units o* productD so$e costs $aybe aected by $ore than one cost driverD and whether costsare variable or fxed o*ten depends on the decision situation.
III* Cost-Volume-#ro8t Anal,sis {L. O. 3}
Cost-Volume-#ro8t 9CV#: Anal,sis -the study o* the eects o*output volu$e on revenue +sales, expenses +costs, and netinco$e +net proft. 3he $aor si$pli*ying assu$ption is to classi*y
costs as either variable or fxed with respect to the volu$e o*output activity. 4 "0 scenario *ollows.
A* Computin the Brea;-Even #oint
Brea;-Even #oint 9BE#: - the level o* sales at whichrevenues eBual expenses and net inco$e is Aero. @ne directuse o* the E is to assess possible ris#. y co$paringplanned sales with the E, $anagers can deter$ine a'arin o+ !a+et, - how *ar sales can *all below the planned
level be*ore losses occur.
Margin of Safety = planned unit sales - break-even unitsales
/* Contri0ution-'arin 'ethod* Contri0ution'arin 9C': #er )nit - the sales price per unit $inusthe variable expenses per unit. 3he E is reachedwhen total contribution $argin eBuals total fxed costs.(ividing total fxed costs by the " per unit gives theE in nu$ber o* units.
C' #ercentaeor Ratio - the portion o* every salesdollar that contributes to covering fxed costs and,hope*ully, provides *or proft +divide total contribution$argin by total sales. (ividing total fxed costs by the" percentage +total contribution $argin C total salesyields the sales dollars needed to brea# even. 3he use
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o* the " percentage is necessary when a fr$ produces$ore than one product.
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2* E
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B* Graphin the Brea;-Even #oint {L. O. 4}
3he E can also be *ound by graphing the cost and revenuerelationships. 3he process ta#es the *ollowing steps.
!tep /" (raw the axes. 3hehoriAontal axis G sales volu$e, and the verticalaxis G dollars o* cost and revenue.
!tep 2" lot sales volu$e. Select a convenient salesvolu$e and plot a point *or total sales dollars atthat volu$e. 3hen draw a line between the originand the point.
!tep 3" lot the fxed expenses. 6t should be ahoriAontal line intersecting the vertical axis at thelevel o* fxed costs.
!tep 4" lot variable expenses. (eter$ine thevariable expenses at a convenient level o* activity.4dd this a$ount to fxed expenses and plot thepoint. 3hen draw a line *ro$ the intersection o*the vertical axis to this point. 3his line representstotal expenses, and the dierence between thefxed expense line and this new line represents thevariable expenses.
!tep 5" ?ocate the brea#even point. 3he brea#even point is where the total expense line crossesthe sales line.
See E%&IBI 2-> *or an illustration o* a "0 graph. "0graphs show profts over a wide volu$e range easier thannu$erical exhibits.
4l$ost all brea#even graphs show revenue and cost linesextending bac# to the vertical axis. 3his approach $isleadsbecause the relationships depicted are only valid within therelevant range.
3he assu$ptions used in constructing the typical brea#evengraph include the *ollowing:
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1. Expenses $ay be classifed into variable and fxedcategories.
2. 3he behavior o* revenues and expenses is accurately
portrayed and is linear over the relevant range.
!. EHciency and productivity will be unchanged.
%. !ales 'i+i.e., the relative proportions or co$binationso* Buantities o* products that constitute total sales isconstant. ISee A##EN$I% 2A *or $ore on sales$ixes.J
&. 3he dierence in inventory level at the beginning and
end o* a period is insignifcant.
C* Chanes in 1ied Epenses
6ncreases +decreases in fxed expenses increase +decreasethe E.
$* Chanes in )nit Contri0ution 'arin
6ncreases +decreases in the " per unit decrease +increase
the E.
E* aret Net #ro8t and an Incremental Approach
{L. O. 5}
"0 analysis can be used to deter$ine the target sales, inunits and dollars, needed to earn a target proft. Ksing eitherthe contribution $argin or eBuation techniBues results in the*ollowing shortcut eBuations.
target sales volume in units = xed expenses ! target netincome
M per unit
target sales volume in dollars = xed expenses ! targetnet income
M ratio
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3he Incremental Approach+i.e., the change in total resultsunder a new condition in co$parison with so$e given or#nown condition can be used. (ivide the target net inco$eby the " per unit and add the result to the unit E to get
the target sales volu$e in units. ?i#ewise, divide the targetnet inco$e by the " ratio and add the result to the dollarE to get the target sales volu$e in dollars.
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1* 'ultiple Chanes in (e, 1actors
ultiple *actor changes can be de$onstrated by constructinginco$e state$ents reLecting the changes and co$paringbe*ore change and a*ter change results. 4lso, an incre$ental
approach can be used to isolate ust the eects o* thechanges and eli$inates irrelevant and potentially con*usingdata.
G* CV# Anal,sis and Computer-Based !preadsheets
Fu$erous co$binations o* fxed expenses, selling prices,variable expenses, and target inco$e levels can be analyAedBuic#ly using these co$puteriAed spreadsheets. SeeE%&IBI 2-?*or an exa$ple o* spreadsheet analysis*
IV* Additional )ses o+ Cost-Volume Anal,sis
A* Best Cost !tructure
"o$panies try to fnd their $ost desirable co$bination o*fxed and variablecost *actors. So$e choose to increasetheir " ratios and fxed costs by auto$ating, while others$ay choose to lower their fxed costs and lower their "ratios by putting their sales *orce on co$$issions rather than
paying salaries.
When the " percentage o* sales is low, great increases involu$e are necessary be*ore signifcant i$prove$ents in netprofts are possible. 4s sales exceed the E, a high "percentage increases profts *aster than a low " percentage.
B* Operatin Leverae
Operatin Leverae -the fr$=s ratio o* fxed and variable
costs. 6n highly leveraged fr$s, +i.e., those with high fxedcosts and low variable costs s$all changes in sales volu$ewill result in large changes in net inco$e. ?ess leveragedfr$s show s$aller changes in net inco$e with changes insales volu$e. 4bove the E, net inco$e increases *aster *orhighly leveraged fr$s. ;owever, below the E, losses$ount $ore rapidly. See E%&IBI 2-@*or a graph co$paring
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high versus low operating leverage.
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C* 'arin o+ !a+et,
3he marin o+ sa+et,shows how *ar sales can *all below theplanned level o* sales be*ore losses occur. 6t co$pares thelevel o* planned sales with the brea#even point:
marin o+ sa+et, planned unit sales 0rea;-evenunit sales
4 s$all $argin o* sa*ety $ay indicate a $ore ris#y situation.
$* Contri0ution 'arin and Gross 'arin {L. O.6}
Gross 'arin 9or Gross #ro8t: the excess o* sales overthe Cost o+ Goods !old +i.e., cost o* the acBuired or$anu*actured $erchandise to be sold. Contri0ution'arinis the excess o* sales over all variable expenses. SeeE%&IBI 2-/which shows costs divided on two dierentdi$ensions: gross $argin and contribution $argin.
V* Nonpro8t Application
Fonproft organiAations, such as govern$ent agencies, can use the
principles o* "0 analysis to deter$ine how $any individuals theycan serve with li$ited budgets and to assess the i$pact o* changesin the level o* *unding andCor costs on their ability to provideservices. See E%&IBI 2-//*or a graphical presentation o* thenonproft analysis.
VI* Appendi 2A" !ales-'i Anal,sis {L. O. 7}
!ales 'i - the relative proportions or co$binations o* Buantities
o* products that co$prise total sales. 6* the proportions o* the $ixchange, the "0 relationships $ay also change. enerally, sellinga higher +lower proportion o* high " products than anticipatedresults in higher +lower net inco$e. /actors other than " per unito* product +e.g., " per unit o* ti$e can be use*ul in $a#ing sales$ix decisions +see Chapter 5*or *urther explanation.
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VII* Appendi 2B" Impact o+ Income aes {L. O. 8}
3he target sales eBuation can be altered to the *ollowing:
target sales - variable expenses - fxed expenses =
target ater-tax in!"#e $ %1 - taxrate&
?etting F G the nu$ber o* units o* sales necessary to achieve thedesired a*tertax inco$e and substituting values *or the selling priceper unit, variable expenses per unit, fxed expenses, target a*tertaxinco$e, and the tax rate into the eBuation, F can be solved.4lternatively, the *ollowing shortcut *or$ula $ay be used:
!'ange in net in!"#e =
%!'ange in v"l(#e in (nits& x %)* per (nit& x %1 -tax rate&
Each unit beyond the E adds to a*tertax net proft at the unit "$ultiplied by +1 inco$e tax rate.
When incorporating inco$e taxes in "0 analysis, the E does notchange because the E is the point o* Aero profts. 3here*ore,
there are no taxes on Aero profts.
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C&A#ER 2" DuiF$emonstrationEercises
Learnin O0ective /
1. "ost drivers MMMMM.
a. can be volu$e basedb. aect the total level o* costs incurred by co$paniesc. are activities that cause costs to be incurredd. all o* these
2. roduction is one o* the valuechain *unctions. Which one o* the*ollowing is not an exa$ple o* a cost driver *or production costsN
a. labor hoursb. nu$ber o* people supervisedc. sales dollarsd. $achine hours
Learnin O0ective 2
!. Which o* the *ollowing will not re$ain constant, i* the level o*costdriver activity increases within the relevant rangeN
a. variable cost per unitb. total variable costsc. total fxed costsd. total costse. 4 and ".*. , ", and (
%. 3he li$its o* costdriver activity within which a specifcrelationship between costs and the cost driver is valid is called
MMMMM.
a. variable rangeb. total rangec. relevant ranged. valid range
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Learnin O0ective 3
Items 5 and 6 are 0ased on the +ollo=in data"
aple, 6nc., produces and sells the fnest Buality pool tables in all
o* 4la$eda "ounty, "ali*ornia. 3he co$pany expects the*ollowing sales and expenses in 2911 *or its tables:
Sales +1,999 tables O P%99 per table P %99,9990ariable expenses 299,999/ixed expenses 129,999
&. ;ow $any tables $ust be sold in order *or ;ardwood, 6nc., to brea#evenN
a. 299 b. %99 c. '99d. -99
'. What dollar a$ount o* sales o* tables is necessary to brea# evenN
a. P'9,999 b. P129,999 c. P1&9,999 d.P2%9,999
Learnin O0ective 4
). Which o* the *ollowing is not an assumptiono* costvolu$eproftanalysisN
a. 3he behavior o* revenues and expenses is accuratelyportrayed and is linear over the relevant range.
b. Expenses can be classifed into variable and fxed categories.c. Sales $ix will be constant.d. EHciency and productivity will both increase.e. 3he inventory level at the end o* the period will be
insignifcantly dierent *ro$ that at the beginning.
-. 6ncrease in contribution $argin per unit MMMMM.
a. increases brea#even pointb. decreases brea#even pointc. does not change brea#even point
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d. $eans there is a change in fxed cost per unit
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Learnin O0ective 5
Items @ and / are 0ased on the +ollo=in data 9inore incometaes:"
apple, 6nc., $anu*actures and sells 6peds. 4 proected inco$estate$ent *or the expected sales volu$e o* 199,999 6peds is as*ollows:
Sales P),&99,9990ariable expenses !,999,999"ontribution $argin P%,&99,999/ixed expenses 2,&99,999e*oretax proft P2,999,999
8. ;ow $any 6peds would need to be sold to have a be*oretax profto* P2,899,999N
a. 119,999 d. 1%9,999b. 129,999 e. 199,999c. 1!9,999 *. none o* the above
19. What dollar sales volu$e would be reBuired to achieve P!,&99,999o* be*oretax proftN
a. P),999,999 b. P),&99,999 c. P8,&99,999d. P19,999,999e. so$e other a$ount
Learnin O0ective 6
11. 3he dierence between sales and cost o* goods sold is co$$onlycalled MMMMM.
a. contribution $argin b. operating inco$ec. gross proft d. excess sales
12. 6* variable selling expenses increase, then contribution $argin+assu$ing all else constant $ust MMMMM.
a. stay the sa$e
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b. increasec. decreased. need $ore in*or$ation
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Learnin O0ective >
1!. 3win"o produces and sells two products. roduct 4 sells *or P- andhas variable expenses o* P!. roduct sells *or P1- and hasvariable expenses o* P19. 6t predicts sales o* 29,999 units o* 4 and
19,999 units o* . /ixed expenses are P199,999 per $onth.4ssu$e that 3win"o hits its sales goal *or /ebruary o* P'99,999,and exceeds its expected be*oretax proft o* P)9,999. What hashappenedN
a. 3win"o sold %9,999 units o* product 4 and no product .b. 3win"o sold $ore o* both products 4 and than expected.c. 3win"o sold $ore o* product 4 and less o* product than
expected.d. 3win"o sold $ore o* product and less o* product 4 than
expected.
1%. rea#even in units *or a $ultiproduct fr$ is calculated as fxedcosts divided by MMMMM.
a. the su$ o* the contribution $argin percentages *or eachproduct
b. the weighted average contribution $argin o* all the productsc. the su$ o* the individual product contribution $arginsd. it is not possible to calculate brea#even in units *or a $ulti
product fr$
Learnin O0ective ?
1&. Re+er to the data provided +or 'apple. Inc*. in pro0lems @and /* Fow assu$e that apple, 6nc., is subect to a %9Q tax.;ow $any 6peds $ust it sell to achieve an a*tertax inco$e o*P1,&99,999N
a. 111,111
b. !!!,!!!c. '','''d. 1%2,-&)
1'. 4*tertax proft eBuals be*oretax proft MMMMM.
a. $ultiplied by the tax rate
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b. $ultiplied by 1 $inus the tax ratec. divided by the tax rated. divided by 1 $inus the tax rate
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C&A#ER 2" !olutions toDuiF$emonstration Eercises
/*+d, 2*+!, 3*+e, 4*+!,
5*+!, 3he " per unit $ust be co$puted. 6n this case, it isP299 +P%99,999 P299,999C1999 tables. (ividing theP129,999 fxed expenses by the P299 per unit " gives '99sets.
6*+d, Either $ultiplying the unit E by the unit selling priceor by dividing the fxed expenses by the " ratio. Ksing the
frst $ethod, '99 tables $ultiplied by a price o* P%99 pertable gives P2%9,999 o* sales to brea# even. With the second$ethod, P129,999 o* fxed expenses divided by .&9 +P299,999"CP%99,999 Sales also yields P2%9,999 to brea# even.
>*+d, ?*+b,
@*+b, 4dd the be*oretax desired proft to the fxed expensesand divide the result by the " per unit. 6n this case,P2,899,999 R P2,&99,999 G P&,%99,999 C +P%,&99,999 C
199,999 cases gives 129,999 cases.
/*+d, (ivide the su$ o* the target be*oretax inco$e and the fxedexpenses by the " percentage. 6n this case that isP',999,999 IP!,&99,999 R P2,&99,999J divided by .'9IP%,&99,999CP),&99,999J G P19,999,999.
//*+!, /2*+!,
/3*+!, 3he " ratios *or the two products are '2.&Q *or 4 and%%.%Q *or . When the sales $ix shi*ts to products withhigher " ratios, profts increase.
/4*+b,
/5*+a, 3o solve this proble$ it is necessary to convert the a*tertax inco$e desired to the be*oretax inco$e necessary.
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(ividing P1,&99,999 by .'9 +1 tax rate gives P2,&99,999 inbe*oretax inco$e reBuired. 4dding this to the P2,&99,999 infxed expenses yields a reBuired contribution $argin o*P&,999,999. Ksing the data provided *or 199,999 6peds, theselling price per 6ped is P)&.99 and the variable expenses per
6ped are P!9.99. 3his gives a " per unit o* P%&.99, whichcan be divided into the P&,999,999 total contribution $arginto give 111,111 6peds needed to sell to get P1,&99,999 a*tertax proft.
/6.+b,