ch04 cost volume profit analysis

7/23/2019 Ch04 Cost Volume Profit Analysis

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Chapter 4 Cost-Volume-Profit Analysis 71

CHAPTER 4

COST-VOLUME-PROFIT ANALYSIS

CHAPTER INTRODUCTION

Te analysis of o! "osts an# $rofit "an%e !en &olume "an%es is referre# to as cost-volume-profit

(CVP) analysis' In tis "a$ter( tools are #e&elo$e# to ena)le mana%ers to ans!er *uestions relatin% to

$lannin%( "ontrol( an# #e"ision ma+in%'

Objectives, Terms, and Discussions

LO1 Identify common cost behavior patterns.

COMMON COST ,EAVIOR PATTERNS

To $erform "ost-&olume-$rofit analysis .CVP/( you nee# to +no! o! "osts )ea&e !en )usinessa"ti&ity .e'%'( $ro#u"tion &olume or sales &olume/ "an%es' Tis se"tion #es"ri)es some "ommon

$atterns of "ost )ea&ior'

Variable costs are "osts tat "an%e in $ro$ortion to "an%es in &olume or a"ti&ity' For

e0am$le( if $ro#u"tion &olume in"reases )y 12 $er"ent( #ire"t materials are e0$e"te# to in"rease in

total )y 12 $er"ent' E0am$les of &aria)le "osts are #ire"t material( #ire"t la)or( in#ire"t material( an#

sales "ommissions' Te &aria)le "ost per unit #oes not "an%e !en &olume or a"ti&ity "an%es'

E0a"tly o! a"ti&ity soul# )e measure# in analy3in% a &aria)le "ost #e$en#s on te situation' For

e0am$le( a "aterer4s foo# "ost .#ire"t material/ &aries !it num)er of %uests ser&e# !ile an airline4s

fuel "ost &aries !it te num)er of miles flo!n'

Fie! costsare "osts tat #o not "an%e in res$onse to "an%es in a"ti&ity le&els' E0am$les of

fi0e# "osts are #e$re"iation( su$er&isory salaries( )uil#in% maintenan"e( an# rent' For e0am$le( if fi0e#

"osts total 567(222 for te $erio#( !ate&er te num)er of units $ro#u"e#( te amount of fi0e# "osts

remains at 567(222' o!e&er( te amount of fi0e# "ost $er unit #oes "an%e !it te le&el of a"ti&ity'

For e0am$le( if 1(222 units are $ro#u"e#( fi0e# "ost $er unit is 567 .567(22281(222 units/( )ut if

$ro#u"tion in"reases to 9(222 units( fi0e# "ost $er unit #e"reases to 57: .567(22289(222 units/'

In te sort-run( some fi0e# "osts "an )e "an%e# !ile oters "annot' "iscretionary fie!

costs are tose fi0e# "osts tat mana%ement "an easily "an%e in te sort-run' E0am$les in"lu#e

a#&ertisin%( resear" an# #e&elo$ment( an# re$air an# maintenan"e' Committe! fie! costs are tose


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7# $tu!y %ui!eto a""om$any ;iam)al&oManagerial Accounting

fi0e# "osts tat "annot )e easily "an%e# in te sort-run' Su" "osts in"lu#e rent( #e$re"iation of

)uil#in%s an# e*ui$ment( an# insuran"e relate# to )uil#in%s an# e*ui$ment'

&ie! costs.also referre# to as semivariable costs/ are "osts tat "ontain )ot a &aria)le "ost

element an# a fi0e# "ost element' For e0am$le( if a sales$erson is $ai# 5


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Chapter 4 Cost-Volume-Profit Analysis 7*

estimate of total fi0e# "ost' Te slo$e is e*ual to te "an%e in "ost #i&i#e# )y te "an%e in a"ti&ity'

Tus te estimate of &aria)le "ost .te slo$e/ is "al"ulate# as>

Estimate of Varia)le Cost B Can%e in "ost

Can%e in a"ti&ity

Estimate ofVaria)le Cost

BCost at i%est le&el of a"ti&ity @ Cost at lo!est le&el of a"ti&ity i%est le&el of a"ti&ity @ Lo!est le&el of a"ti&ity

Te fi0e# "ost e*uals te #ifferen"e )et!een total "ost an# estimate# total &aria)le "ost at

eiter te i% or lo! $oint' Fi0e# "osts !ill )e te same !eter "al"ulate# usin% te i%est le&el of

a"ti&ity or te lo!est le&el of a"ti&ity' Te i%-lo! meto# is sim$le to #o( )ut not relia)le' ,e"ause

only te i%est an# lo!est measures of a"ti&ity are use#( tese may not )e re$resentati&e of te ty$i"al

"ost )ea&ior'

+e'ression analysisis a statisti"al te"ni*ue tat uses all te a&aila)le #ata $oints to estimate

te inter"e$t an# slo$e of a "ost e*uation' Te line fitte# to te #ata )y re%ression is te )est strai%t-

line fit to te #ata' Te formulas use# in "on#u"tin% re%ression analysis are "om$le0' o!e&er(

soft!are $ro%rams tat $erform re%ression analysis are !i#ely a&aila)le' o! to use E0"el to"on#u"t re%ression analysis is e0$laine# in te a$$en#i0 to tis "a$ter' Re%ression analysis is "o&ere#

in intro#u"tory statisti"s "lasses' Te a$$li"ation of re%ression analysis yiel#s te follo!in% e*uation>

Total "ost B Fi0e# "ost D .Varia)le "ost $er unit 0 a"ti&ity le&el in units/

Estimates of fi0e# an# &aria)le "osts are only &ali# for a limite# ran%e of a"ti&ity' Te rele&ant

ran%e is te ran%e of a"ti&ity for !i" estimates an# $re#i"tions are e0$e"te# to )e a""urate' Outsi#e

te rele&ant ran%e( estimates of fi0e# an# &aria)le "osts may not )e &ery useful' Often( mana%ers are

not "onfi#ent usin% estimates of fi0e# an# &aria)le "osts in ma+in% $re#i"tions for a"ti&ity le&els tat

a&e not )een en"ountere# in te $ast' Sin"e te a"ti&ity le&els a&e not )een en"ountere# in te $ast(

$ast relations )et!een "ost an# a"ti&ity may not )e a useful )asis for estimatin% "osts in tis situation'

In some "ases( a"tual "osts )ea&e in a manner tat is #ifferent from te "ost )ea&ior $atterns#is"usse# a)o&e' All tose $atterns im$ly linear .strai%t line/ relations )et!een "ost an# a"ti&ity' In te

real !orl#( some "osts are nonlinear'

LO* Perform cost-volume-profit analysis for single products.

COST-VOLUME-PROFIT ANALYSIS

,he Profit .uation /On"e fi0e# an# &aria)le "osts a&e )een estimate#( "ost-&olume-$rofit .CVP/

analysis "an )e "on#u"te#' CVP analysis is any analysis tat e0$lores te relations amon% "ost( &olume

or a"ti&ity le&els( an# $rofit' Fun#amental to CVP analysis is te profit e.uation!i" states tat

$rofit is e*ual to re&enue .sellin% $ri"e times *uantity/ minus &aria)le "ost .&aria)le "ost $er unit times

*uantity/ minus total fi0e# "ost'

Profit 0 $P() / VC() / ,FC

ere 0 B uantity of units $ro#u"e# an# sol#

SP B Sellin% $ri"e $er unit

VC B Varia)le "ost $er unit

TFC B Total fi0e# "ost


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74 $tu!y %ui!eto a""om$any ;iam)al&oManagerial Accounting

rea2-ven Point /One of te $rimary uses of CVP analysis is to "al"ulate te brea2-even

point3Te )rea+-e&en $oint is te num)er of units tat must )e sol# for a "om$any to )rea+ e&enGto

neiter earn a $rofit nor in"ur a loss'

To "al"ulate te )rea+-e&en $oint( !e set te $rofit e*uation e*ual to 3ero' Ten !e insert te

a$$ro$riate sellin% $ri"e( &aria)le "ost( an# fi0e# "ost information an# sol&e for te *uantity (x)' For

e0am$le( su$$ose Co#eConne"t $ro#u"es a $ro#u"t tat sells for 5922 $er unit( &aria)le "osts are

estimate# to )e 562'


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Unit sales .K/ nee#e#

to attain s$e"ifie#

$rofit

BProfit D TFC

SP @ VC

Unit sales .K/ nee#e# to

attain s$e"ifie# $rofitB

Profit D TFC

Contri)ution mar%in $er unit

Te contribution mar'in ratiomeasures te amount of in"remental $rofit %enerate# )y an

a##itional #ollar of sales' It is e*ual to te "ontri)ution mar%in $er unit #i&i#e# )y te sellin% $ri"e'

Contri)ution mar%in ratio BSP @ VC

SP

e "an e0$ress te $rofit e*uation in terms of te "ontri)ution mar%in ratio as>

=ollar sales nee#e# to

attain s$e"ifie# $rofitB

Profit D TFC

Contri)ution mar%in ratio

Te $rofit e*uation also "an so! o! $rofit !ill )e affe"te# )y &arious o$tions un#er

"onsi#eration )y mana%ement' Su" analysis is sometimes referre# to as 6hat if analysis)e"ause it

e0amines what!ill a$$en ifa $arti"ular a"tion is ta+en'

LO4 Perform cost-volume-profit analysis for multiple products.

MULTIPLEPRO=UCT ANALYSIS

Contribution &ar'in pproach@ CVP analysis "an )e e0ten#e# to "o&er multi$le $ro#u"ts' If te

$ro#u"ts a "om$any sells are similar .e'%' &arious fla&ors of i"e "ream( &arious mo#els of similar

)oats/( te !ei%te# a&era%e "ontri)ution mar%in $er unit "an )e use# in CVP analysis' Te !ei%te#

a&era%e "ontri)ution mar%in $er unit is "al"ulate# e0a"tly te same as "ontri)ution mar%in $er unit fora sin%le $ro#u"t e0"e$t tat o&erall fi%ures are use#'

Contribution &ar'in +atio pproach @ If te $ro#u"ts tat a "om$any sells are su)stantially

#ifferent( CVP analysis soul# )e $erforme# usin% te "ontri)ution mar%in ratio' en a "om$any sells

many #ifferent $ro#u"ts( o! many units must )e sol# to )rea+ e&en or ma+e a $rofit is not

a$$ro$riate' A more a$$ro$riate measure is o! mu" salesmust )e ma#e to )rea+ e&en or %enerate a

$rofit' To "al"ulate o! mu" sales #ollars are nee#e#( te "ontri)ution mar%in ratio( rater tan te

"ontri)ution mar%in $er unit( soul# )e use#' Te "ontri)ution mar%in ratio "an also )e use# to analy3e

te effe"t on net in"ome of a "an%e in total "om$any sales'

ASSUMPTIONS IN CVP ANALYSIS

ene&er CVP analysis is $erforme#( a num)er of assum$tions are ma#e tat affe"t te &ali#ity of te

analysis>

Costs "an )e a""urately se$arate# into teir fi0e# an# &aria)le "om$onents'

Fi0e# "osts remain fi0e#'

Varia)le "osts $er unit #o not "an%e o&er te a"ti&ity le&els of interest'

en $erformin% multi$ro#u"t CVP analysis( it is assume# tat te mi0 remains "onstant'

Sellin% $ri"e $er unit #oes not "an%e'


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78 $tu!y %ui!eto a""om$any ;iam)al&oManagerial Accounting

LO5 Discuss the effect of operating leverage.

OPERATIN LEVERAE

Operatin' levera'erelates to te le&el of fi0e# &ersus &aria)le "osts in a firm4s "ost stru"ture' Firms

tat a&e relati&ely i% le&els of fi0e# "ost are sai# to a&e i% o$eratin% le&era%e' Te le&el of

o$eratin% le&era%e is im$ortant )e"ause it affe"ts te "an%e in $rofit !en sales "an%e' Firms tat

a&e i% o$eratin% le&era%es are %enerally tou%t to )e more ris+y )e"ause tey ten# to a&e lar%e

flu"tuations in $rofit !en sales flu"tuate'

,e"ause of fi0e# "osts in te "ost stru"ture( !en sales in"rease )y say 12 $er"ent( $rofit !ill

in"rease )y more tan 12 $er"ent' Te only time $rofit !ill in"rease )y te same $er"ent as sales is

!en all "osts are &aria)le' If all "osts &ary in $ro$ortion to sales .i'e'( all "osts are &aria)le/( ten

$rofit !ill &ary in $ro$ortion to sales'

LO8 Use the contribution margin per unit of the constraint to analyze situations involving a

resource constraint.

CONSTRAINTS

In many "ases tere are "onstraints on o! many items "an )e $ro#u"e# or o! mu" ser&i"e "an )e

$ro&i#e#' E0am$les of "onstraints fa"e# )y mana%ers in"lu#e sorta%es of s$a"e( e*ui$ment( or la)or'

In su" "ases( te fo"us sifts from te contribution mar'in per unitto te contribution mar'in per

unit of the constraint3 For e0am$le( su$$ose a "om$any "an $ro#u"e eiter Pro#u"t A or Pro#u"t ,

usin% te same e*ui$ment' Te "ontri)ution mar%in of A is 5922' Te "ontri)ution mar%in of , is 5122'

Assume only 1(222 ma"ine ours are a&aila)le an# Pro#u"t A re*uires 12 ours of ma"ine time to

$ro#u"e one unit !ile Pro#u"t , re*uires only 9 ours $er unit' Te "om$any !oul# only $ro#u"e

Pro#u"t ,' Altou% its "ontri)ution mar%in is smaller( it "ontri)utes 5J2 $er ma"ine our( !ereas

Pro#u"t A "ontri)utes only 592 $er ma"ine our' it 1(222 ma"ine ours a&aila)le( Pro#u"t A "an

%enerate 592(222 of "ontri)ution mar%in !ile , "an %enerate 5J2(222 of "ontri)ution mar%in'

PP9":; Using Regression in Ecel ! to Estimate "ied and #ariable $osts.

Te a$$en#i0 uses #ata for Co#eConne"t $resente# in Illustration 7-: in te te0t)oo+ to illustrate te

Re%ression fun"tion in E0"el' Te s$rea#seet $ro%ram ma+esperforming re%ression analysis &ery

easy' o!e&er( it #oes not ma+e understandingre%ression analysis easy

On"e you a&e installe# te #ata analysis $ro%rams( o$en a s$rea#seet an# enter te

$ro#u"tion an# "ost #ata from Illustration 7-:' No! %o un#er Data ta) an# s"roll #o!n to Data

Analysis' Ten s"roll #o!n toRegressionan# "li"+ O' Un#erInput Y( s"roll #o!n from ,1 to ,1H

.note tat tis in"lu#es te ea#in% Cost)' Un#erInput X,s"roll #o!n from A1 to A1H .tis in"lu#es te

ea#in% Pro!uction/' Cli"+ on La)els !i" in#i"ates tat you a&e la)els in Pro#u"tion an# Cost #ata

"olumns' Un#er output options( "li"+ onew wor!"oo!' Un#er residuals( "li"+ on#ine fit plot' Tisin#i"ates tat you !ant a $lot of #ata an# te re%ression line'

Inter$retation of "riti"al elements .te $lot( R S*uare( Inter"e$t an# Slo$e of te Re%ression

Line( an# P-Value/ of te re%ression out$ut is im$ortant' ,he plotof te #ata an# te $lot of te

re%ression line in#i"ate tat te #ata line u$ *uite "lose to te re%ression line' Tis su%%ests tat a

strai%t line fit to te #ata !ill )e *uite su""essful' + $.uareis a statisti"al measure of o! !ell te

re%ression line fits te #ata' R S*uare ran%es from a lo! of 2( in#i"atin% tat tere is no linear relation

)et!een "ost an# $ro#u"tion( to a i% of 1( in#i"atin% tat tere is a $erfe"t linear relation )et!een


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"ost an# $ro#u"tion' Te intercept of the re'ressionline is inter$rete# as te estimate of fi0e# "ost

!ile te slope of the re'ression line is inter$rete# as te &aria)le "ost $er unit' Te p-values

"orres$on#in% to te inter"e$t an# te slo$e measure te $ro)a)ility of o)ser&in% &alues as lar%e as te

estimate# "oeffi"ients !en te true &alues are 3ero'


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7< $tu!y %ui!eto a""om$any ;iam)al&oManagerial Accounting

Review o !e" Terms

ccount analysis= A meto# of estimatin% "ost)ea&ior !i" re*uires $rofessional?u#%ment to "lassify "osts as eiter fi0e# or&aria)le' Te total of te "osts "lassifie# as

&aria)le are #i&i#e# )y a measure of a"ti&ityto "al"ulate te &aria)le "ost $er unit ofa"ti&ity' Te total of te "osts "lassifie# asfi0e# $ro&i#es te estimate of fi0e# "ost'.19H/

rea2-even point= Te num)er of units a"om$any must sell to earn a 3ero $rofit'.1H2/

Committe! fie! costs= Tose fi0e# "osts tat"annot )e easily "an%e# in te sort-run'.199/

Contribution mar'in= Te #ifferen"e )et!eensales an# &aria)le "osts' .1H9/

Contribution mar'in ratio= Te "ontri)ution

mar%in #i&i#e# )y sales or te "ontri)utionmar%in $er unit #i&i#e# )y te sellin% $ri"e'.1HH/

Cost-volume-profit (CVP)= Te analysis ofo! "osts an# $rofit "an%e !en &olume"an%es' .116/

"iscretionary fie! costs= Tose fi0e# "oststat mana%ement "an easily "an%e in tesort-run' .191/

Fie! cost= Costs tat #o not "an%e !entere is a "an%e in )usiness a"ti&ity' .192/

>i'h-lo metho!= A meto# of estimatin%fi0e# an# &aria)le "ost "om$onents in !i"a strai%t line is fitte# to te #ata $oints

re$resentin% te i%est an# lo!est le&els ofa"ti&ity' .19/&ar'in of safety= Te #ifferen"e )et!een te

e0$e"te# le&el of sales an# )rea+-e&en sales'.1H1/

&ie! cost= Costs tat "ontain )ot &aria)lean# fi0e# "ost elements' .199/Operatin' levera'e= Le&el of fi0e# &ersus

&aria)le "osts in a firm4s "ost stru"ture'

Firms tat a&e relati&ely i% le&els of fi0e#"ost are sai# to a&e i% o$eratin% le&era%e'.172/

Profit e.uation= E*uation tat states tat$rofit is e*ual to re&enue .sellin% $ri"e times*uantity/ minus &aria)le "ost .&aria)le "ost$er unit times *uantity/ minus total fi0e#"ost' .1H2/

+e'ression analysis= A statisti"al te"ni*ueuse# to estimate te inter"e$t .an estimate offi0e# "ost/ an# te slo$e .an estimate of&aria)le "ost/ of a "ost e*uation' .19


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Chapter 4 Cost-Volume-Profit Analysis 7@

C#a$ter 4 % True&'a(se

1' T!o "ommon fi0e# "osts are rent an# sales "ommissions'

9' Varia)le "osts( in total( "an%e in&ersely !it "an%es in a"ti&ity'

H' Mi0e# "osts "ontain elements of )ot #ire"t material an# #ire"t la)or'

7' Te a""ount analysis meto# is su)?e"ti&e in tat #ifferent mana%ers usin% te same

set of fa"ts may rea" #ifferent "on"lusions re%ar#in% te "lassifi"ation of "osts into

fi0e# an# &aria)le "om$onents'

J' Usin% te i%-lo! meto# to "lassify "osts as fi0e# or &aria)le( te slo$e of te line is

te estimate of &aria)le "ost'

' Te le&el of o$eratin% le&era%e is im$ortant )e"ause it affe"ts te "an%e in $rofit

!en sales "an%e'

:' To "al"ulate te )rea+-e&en $oint( te $rofit e*uation is set to 51( an# ten te

a$$ro$riate sellin% $ri"e( &aria)le "ost( an# fi0e# "ost information are inserte# into te

e*uation'


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a' A""ount analysis %' O$eratin% le&era%e

)' ,rea+-e&en $oint ' Profit e*uation

"' Contri)ution mar%in i' Re%ression analysis#' i%-lo! meto# ?' S"atter%ra$

e' Mi0e# "ost +' Ste$ "osts

f' Mar%in of safety l' at if analysis

1' A %ra$ of "osts at &arious a"ti&ity le&els'

9' E*uation tat states tat $rofit is e*ual to re&enue .sellin% $ri"e times *uantity/ minus

&aria)le "ost .&aria)le "ost $er unit times *uantity/ minus total fi0e# "ost'

H' An e0amination of te results of &arious "ourses of a"tion'

7' Te num)er of units a "om$any must sell to earn a 3ero $rofit'

J' Costs tat "ontain )ot &aria)le an# fi0e# elements'

' A meto# of estimatin% "ost )ea&ior !i" re*uires $rofessional ?u#%ment to "lassify

"osts as eiter fi0e# or &aria)le'

:' Te #ifferen"e )et!een sales an# &aria)le "osts'


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Chapter 4 Cost-Volume-Profit Analysis

a' 12'

)' 1H'

"' 1

a' 519(222'

)' 51J(22'

"' 591(22'

#' 5H2(222'

:' Te "ontri)ution mar%in ratio is>

a' 96'2'

)' 71':'

"' J


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a' sellin% $ri"e $er unit( &aria)le "ost $er unit( an# fi0e# "ost $er unit'

)' total re&enue( total &aria)le "osts$er unit( an# total fi0e# "ost'

"' sellin% $ri"e $er unit( &aria)le "ost $er unit( an# total fi0e# "osts'

#' sellin% $ri"e $er unit( total &aria)le "osts( an# fi0e# "ost $er unit'

12' Te "ontri)ution mar%in ratio $ro&i#es a measure of>

a' te "ontri)ution of e&ery sales #ollar to "o&erin% fi0e# "ost an# %eneratin% a $rofit'

)' te "ontri)ution of e&ery sales #ollar to "o&erin% &aria)le "ost an# %eneratin% a $rofit'

"' te "ontri)ution of e&ery sales #ollar to "o&erin% &aria)le an# fi0e# "osts an# %eneratin% a

$rofit'

#' none of te a)o&e'

11' i" of te follo!in% assum$tions ma#e !en usin% CVP analysis mi%t affe"t te &ali#ity of

te analysisQ

a' Costs "an )e a""urately se$arate# into teir fi0e# an# &aria)le "om$onents'

)' Fi0e# "osts remain fi0e# an# &aria)le "osts $er unit #o not "an%e o&er te a"ti&ity le&els

of interest'

"' ,ot a an# )'

#' Neiter a nor )'

19' =alton Com$any "an $ro#u"e Pro#u"t A an# Pro#u"t , usin% te same e*ui$ment' Te

"ontri)ution mar%in for A is 5922 !ile te "ontri)ution mar%in for , is 51J2' =alton as only

1(222 ours of ma"ine time a&aila)le' Pro#u"t A re*uires 1 ma"ine our to $ro#u"e one unit!ile Pro#u"t , re*uires 189 ma"ine our to $ro#u"e one unit' i" of te follo!in% units

soul# =alton $ro#u"eQ

a' Pro#u"t A )e"ause te "ontri)ution mar%in of 5922 is %reater tan te "ontri)ution mar%in

of 51J2 for Pro#u"t ,'

)' Pro#u"t , )e"ause te "ontri)ution mar%in $er "onstraint of 5H22 is %reater tan te

"ontri)ution mar%in $er "onstraint of 5922 for Pro#u"t A'

"' Pro#u"t A an# Pro#u"t , $ro$ortionately a""or#in% to teir res$e"ti&e "ontri)ution

mar%ins'

#' Pro#u"t A an# Pro#u"t , e*ually'


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&onth 9umber of Cupca2es tilities pense

;anuary H(J22 5 622

Fe)ruary J(722 1(H92

Mar" 7(622 1(


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16/21


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18/21

&onth 9umber of Cupca2es tilities pense

;anuary H(J22 5 622

Fe)ruary J(722 1(H92

Mar" 7(622 1(


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@A $tu!y %ui!eto a""om$any ;iam)al&oManagerial Accounting

0o(ution %

E+ercise 4 . / For se&eral years( ,ella%io4s Restaurant as offere# a lun"s$e"ial for 5:'22' Montly fi0e# e0$enses a&e )een 57(922' Te &aria)le "ost of a meal as )een

59'12' Antony ,ella%io( te o!ner( )elie&es tat )y remo#elin% te restaurant an# u$%ra#in% te foo#

ser&i"es( e "an in"rease te $ri"e of te lun" s$e"ial to 5:'72' Montly fi0e# e0$enses !oul# in"rease

to 57(


21/21

Chapter 4 Cost-Volume-Profit Analysis @1

0o(ution % Prob(em 4 % 4 o%an Manufa"turin% Com$any ma+es an# sells a sin%le$ro#u"t' Te "om$anys sales an# e0$enses for te most re"ent mont are %i&en )elo!>

,otal Per nit

5

Sales 5J22(222 9J 122

Less &aria)le e0$enses H72(222 1:

ch04 cost volume profit analysis

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