Ch04 Cost Volume Profit Analysis

Cost -Volume-Pro lume-Profit fit Analysis Chapter 4 Cost-Vo

CHAPTER

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4

COST-VOLUME-PROFIT ANALYSIS

CHAPTER INTRODUCTION Te analysis of o! "osts an# $rofit "an%e !en &olume "an%es is referre# to as cost-volume-profit (CVP) analysis' In tis "a$ter( tools are #e&elo$e# to ena)le mana%ers to ans!er *uestions relatin% to $lannin%( $lannin%( "ontrol( "ontrol( an# #e"isio #e"ision n ma+in%' ma+in%'

Objectives, Terms, and Discussions LO1

Identify common common cost behavior patterns. patterns.

COMMON COST ,EAVIOR ,EAVIOR PATTERNS PATTERNS To $erform "ost-&olume-$rofit analysis .CVP/( you nee# to +no! o! "osts )ea&e !en )usiness a"ti&ity .e'%'( $ro#u"tion &olume or sales &olume/ "an%es' Tis se"tion #es"ri)es some "ommon $atterns of "ost )ea&io )ea&ior' r' Variable costs are "osts tat "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 sales "ommi "ommissi ssions ons'' Te &aria)le &aria)le "ost per unit #oes not "an%e !en &olume or a"ti&ity "an%es' E0a"tly o! a"ti&ity soul# )e measure# in analy3in% a &aria)le "ost #e$en#s on te situation' For e0am$le( a "aterer4s foo# "ost .#ire"t material/ &aries !it num)er of %uests ser&e# !ile an airline4s fuel "ost &aries !it te num)er of miles flo!n' Fie! costs are "osts tat #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 te $erio#( !ate&er te num)er of units $ro#u"e#( te amount of fi0e# "osts remains at 567(222' o!e&er( te amount of fi0e# "ost $er unit #oes "an%e !it te le&el of a"ti&ity' For e0am$le( if 1(222 units are $ro#u"e#( fi0e# "ost $er unit is 567 .567(22281(222 units/( )ut if $ro#u"tion $ro#u"tion in"reases in"reases to 9(222 units( units( fi0e# "ost "ost $er unit #e"reases #e"reases to 57: .567(22289(222 units/' In te sort-run( some fi0e# "osts "an )e "an%e# "an%e# !ile oters oters "annot' "iscretionary fie! costs are tose fi0e# "osts tat mana%ement "an easily "an%e in te sort-run' E0am$les in"lu#e a#&ertisin%( resear" an# #e&elo$ment( an# re$air an# maintenan"e' Committe! fie! costs are tose

7#

$tu!y %ui!e to a""om$any ;iam)al&o Managerial Accounting Accounting

fi0e# "osts tat "annot )e easily "an%e# in te sort-run' Su" "osts in"lu#e rent( #e$re"iation of )uil#in%s )uil#in%s an# an# e*ui$men e*ui$ment( t( an# insuran"e insuran"e relate# relate# to )uil#in%s )uil#in%s an# e*ui$me e*ui$ment' nt' &ie! costs .also referre# to as semivariable costs/ are "osts tat "ontain )ot a &aria)le "ost element an# a fi0e# "ost element' For e0am$le( if a sales$erson is $ai# 5<2(222 $er year .fi0e# "ost/ $lus a "ommissio "ommission n e*ual to 1 $er"ent of sales .&aria)le "ost/( te sales$erson4s sales$erson4s total "om$ensatio "om$ensation n is a mi0e# "ost' Note es$e"ially tat total pro!uction cost is also a mie! cost sin"e it "ontains material( la)or( an# )ot &aria)le an# fi0e# o&erea# "osts' $tep costs are tose "osts tat are fi0e# for a ran%e of &alue )ut in"rease to a i%er le&el !en te u$$er )oun# of te ran%e is e0"ee#e#' At tat $oint te "osts a%ain remain fi0e# until anoter u$$er )oun# is e0"ee#e#' Ste$ "osts are often "lassifie# as eiter ste$ &aria)le or ste$ fi0e# "osts #e$en#in% on te ran%e of a"ti&ity for !i" te "ost remains fi0e#' If te ran%e is relati&ely lar%e( te "ost is "onsi#er "onsi#ere# e# to )e a ste$ fi0e# fi0e# "ost' Te relevant ran'e is te ran%e of a"ti&ity for !i" assum$tions as to o! a "ost )ea&es are reasona)le &ali#' LO#

Estimate the relation between cost and activity using account analysis and the high-low method.

COST ESTIMATION METO=S To $re#i"t o! mu" "ost !ill )e in"urre# at &arious le&els of a"ti&ity( o! mu" of te total "ost is fi0e# an# o! mu" is &aria)le must )e #etermine#' Fre*uently "ost information is not )ro+en out in terms of fi0e# an# &aria)le "ost "om$onents' Terefore( te amount of fi0e# an# &aria)le "ost must )e estimate#' In tis "a$ter( tree te"ni*ues are $resente# for estimatin% te amount of fi0e# an# &aria)le "ost> a""ount analysis( te i%-lo! meto#( an# re%ression analysis' ccount analysis is te most "ommon a$$roa" to estimatin% fi0e# an# &aria)le "osts' Tis meto# meto# re*uires re*uires tat te mana%er mana%er use $rofess $rofession ional al ?u#%e ?u#%eme ment nt to "lassify "lassify "osts as eiter eiter fi0e# or &aria)le' Te total of te "osts "lassifie# as &aria)le "an )e #i&i#e# )y a measure of a"ti&ity to "al"ulate te &aria)le "ost $er unit of a"ti&ity' Te total of te "osts "lassifie# as fi0e# $ro&i#es te estimate of fi0e# "ost' Te a""ount analysis a$$roa" is su)?e"ti&e in tat #ifferent mana%ers usin% te same set of fa"ts may rea" #ifferent "on"lusions re%ar#in% te "lassifi"ation of "osts into fi0e# an# &aria)le "om$onents' Illustrations 7-: an# 7-< in te te0t)oo+ $ro&i#e e0am$les of estimatin% fi0e# an# &aria)le "osts usin% a""ount analysis' $catter'raphs @ In some "ases( a mana%er may a&e "ost information from se&eral re$ortin% $erio#s $erio#s a&aila)le to estimate estimate o! "osts "an%e in res$onse to "an%es "an%es in a"ti&ity' a"ti&ity' A mana%er mana%er "an %ain insi%t into te relationsi$ )et!een $ro#u"tion "ost an# a"ti&ity )y $lottin% "osts an# a"ti&ity le&els' Te $lot of te #ata is referre# to as a scatter'raph' enerally( s"atter%ra$s are $re$are# !it "ost measure# on te &erti"al a0is an# a"ti&ity le&el measure# on te ori3ontal a0is' Ea" $oint in te s"atter%ra$ re$resents one $air of "ost an# a"ti&ity &alues' Te $re$aration of s"atter%ra$s is a sim$le $ro"e#ure usin% te %ra$i"al features in s$rea#seet $ro%rams' To ma+e $re#i"tions( mana%ers &isually fit a line to te #ata $oints !it te %eneral i#ea to try to minimi3e te #e&iations of te #ata $oints from te fitte# line' Te meto#s meto#s !e use to estimate estimate "ost )ea&ior )ea&ior assume tat "osts are linear' linear' In oter !or#s( tey assume tat "osts are !ell re$resente# )y strai%t lines' A s"atter%ra$ is useful in assessin% !eter tis assum$tion is reasona)le' Te s"atter%ra$ is also useful in assessin% !eter tere are any outliers .#ata $oints tat are mar+e#ly at o##s !it te tren# of oter #ata $oints/' Illustrations 7-6 an# 7-12 in te te0t)oo+ %i&e an e0am$le of estimatin% fi0e# an# &aria)le "ost usin% te s"atter%ra$ a$$roa"' Te hi'h-lo metho! fits a strai%t line to te #ata $oints re$resentin% te i%est an# lo!est le&els of a"ti&ity' Te slo$e of te line is te estimate of &aria)le "ost .)e"ause te slo$e measures te "an%e in "ost $er unit "an%e in a"ti&ity/( an# te inter"e$t .!ere te line meets te "ost a0is/ is te

Chapter 4 Cost-Volume-Profit Analysis

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estimate of total fi0e# "ost' Te slo$e is e*ual to te "an%e in "ost #i&i#e# )y te "an%e in a"ti&ity' Tus te estimate of &aria)le "ost .te slo$e/ is "al"ulate# as> Estimate of Varia)le Cost B Estimate of Varia)le Cost

B

Can%e in "ost Can%e in a"ti&ity

Cost 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

Te fi0e# "ost e*uals te #ifferen"e )et!een total "ost an# estimate# total &aria)le "ost at eiter te i% or lo! $oint' Fi0e# "osts !ill )e te same !eter "al"ulate# usin% te i%est le&el of a"ti&ity or te lo!est le&el of a"ti&ity' Te i%-lo! meto# is sim$le to #o( )ut not relia)le' ,e"ause only te i%est an# lo!est measures of a"ti&ity are use#( tese may not )e re$resentati&e of te ty$i"al "ost )ea&ior' +e'ression analysis is a statisti"al te"ni*ue tat uses all te a&aila)le #ata $oints to estimate te inter"e$t an# slo$e of a "ost e*uation' Te line fitte# to te #ata )y re%ression is te )est strai%tline fit to te #ata' Te formulas use# in "on#u"tin% re%ression analysis are "om$le0' o!e&er( soft!are $ro%rams tat $erform re%ression analysis are !i#ely a&aila)le' o! to use E0"el  to "on#u"t re%ression analysis is e0$laine# in te a$$en#i0 to tis "a$ter' Re%ression analysis is "o&ere# in intro#u"tory statisti"s "lasses' Te a$$li"ation of re%ression analysis yiel#s te 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' Te rele&ant ran%e is te ran%e of a"ti&ity for !i" estimates an# $re#i"tions are e0$e"te# to )e a""urate' Outsi#e te 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 tat a&e not )een en"ountere# in te $ast' Sin"e te a"ti&ity le&els a&e not )een en"ountere# in te $ast( $ast relations )et!een "ost an# a"ti&ity may not )e a useful )asis for estimatin% "osts in tis situation' In some "ases( a"tual "osts )ea&e in a manner tat is #ifferent from te "ost )ea&ior $atterns #is"usse# a)o&e' All tose $atterns im$ly linear .strai%t line/ relations )et!een "ost an# a"ti&ity' In te 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-$rofit .CVP/ analysis "an )e "on#u"te#' CVP analysis is any analysis tat e0$lores te relations amon% "ost( &olume or a"ti&ity le&els( an# $rofit' Fun#amental to CVP analysis is te profit e.uation !i" states tat $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 ere 0 SP VC TFC

0 $P() / VC() / ,FC B uantity of units $ro#u"e# an# sol# B Sellin% $ri"e $er unit B Varia)le "ost $er unit B Total fi0e# "ost

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$tu!y %ui!e to a""om$any ;iam)al&o Managerial Accounting

rea2-ven Point / One of te $rimary uses of CVP analysis is to "al"ulate te brea2-even point3 Te )rea+-e&en $oint is te num)er of units tat must )e sol# for a "om$any to )rea+ e&enGto neiter earn a $rofit nor in"ur a loss' To "al"ulate te )rea+-e&en $oint( !e set te $rofit e*uation e*ual to 3ero' Ten !e insert te a$$ro$riate sellin% $ri"e( &aria)le "ost( an# fi0e# "ost information an# sol&e for te *uantity (x)' For e0am$le( su$$ose Co#eConne"t $ro#u"es a $ro#u"t tat sells for 5922 $er unit( &aria)le "osts are estimate# to )e 562'
2 2 5126'1:0 0

B 5922.0/ - 562'
Sol&in% for x yiel#s a )rea+-e&en *uantity of 1(7< units' To e0$ress te )rea+-e&en in #ollars of sales rater tan units( te *uantity is sim$ly multi$lie# )y te sellin% $ri"e of 5922 to yiel# 596H(22' &ar'in of $afety / To e0$ress o! "lose mana%ers e0$e"t to )e to te )rea+-e&en le&el( tey may "al"ulate te mar%in of safety' Te mar'in of safety is te #ifferen"e )et!een te e0$e"te# le&el of sales an# )rea+-e&en sales' For e0am$le( if )rea+-e&en sales are 596H(22 an# mana%ement e0$e"ts to a&e sales of 5HJ2(222( te mar%in of safety is 5J(722 .5HJ2(222 - 596H(22/' &ar'in of $afety 0 pecte! sales / rea2-even sales

Te mar%in of safety "an also )e e0$resse# as a ratio "alle# te mar%in of safety ratio' It is e*ual to te mar%in of safety #i&i#e# )y e0$e"te# sales' Mar%in of Safety Ratio

B

Mar%in of Safety E0$e"te# Sales

Contribution &ar'in / Te $rofit e*uation "an )e re!ritten )y "om)inin% te terms !it x in tem to yiel# te contribution mar'in per unit3 Te "ontri)ution mar%in is #efine# as te #ifferen"e )et!een te sellin% $ri"e $er unit .SP/ an# &aria)le "ost $er unit .VC/' Profit is ten "al"ulate# as te #ifferen"e )et!een te "ontri)ution mar%in times te le&el of a"ti&ity an# te total fi0e# "osts .TFC/'

Profit B SP.0/ @ VC.0/ @ TFC Profit B .SP-VC/.0/ @ TFC Profit B Contri)ution mar%in $er unit .0/ @ TFC Te "ontri)ution mar%in $er unit measures te amount of in"remental $rofit %enerate# )y sellin% an a##itional unit' en sales an# $ro#u"tion in"rease )y one unit te "om$any )enefits from re&enue .sellin% $ri"e/( )ut tat )enefit is re#u"e# )y &aria)le "ost $er unit' Fi0e# "osts #o not affe"t te incremental $rofit asso"iate# !it sellin% an a##itional unit )e"ause fi0e# "osts are not affe"te# )y "an%es in &olume' Note tat if !e multi$ly te "ontri)ution mar%in $er unit )y te num)er of units sol#( !e o)tain te total in"remental $rofit relate# to te units sol#' nits nee!e! to chieve Profit ,ar'et / If !e sol&e te $rofit e*uation for te sales *uantity in units( !e %et a formula for "al"ulatin% te )rea+-e&en for te le&el of sales in units or for "al"ulatin% te num)er of units nee#e# to a"ie&e a s$e"ifie# or tar%et le&el of $rofit'


Unit sales .K/ nee#e# to attain s$e"ifie# $rofit

B

Unit sales .K/ nee#e# to attain s$e"ifie# $rofit

B

75

Profit D TFC SP @ VC Profit D TFC Contri)ution mar%in $er unit

Te contribution mar'in ratio measures te amount of in"remental $rofit %enerate# )y an a##itional #ollar of sales' It is e*ual to te "ontri)ution mar%in $er unit #i&i#e# )y te sellin% $ri"e' Contri)ution mar%in ratio B

SP @ VC SP

e "an e0$ress te $rofit e*uation in terms of te "ontri)ution mar%in ratio as> =ollar sales nee#e# to attain s$e"ifie# $rofit

B

Profit D TFC Contri)ution mar%in ratio

Te $rofit e*uation also "an so! o! $rofit !ill )e affe"te# )y &arious o$tions un#er "onsi#eration )y mana%ement' Su" analysis is sometimes referre# to as 6hat if analysis )e"ause it e0amines what !ill a$$en if a $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 te $ro#u"ts a "om$any sells are similar .e'%' &arious fla&ors of i"e "ream( &arious mo#els of similar )oats/( te !ei%te# a&era%e "ontri)ution mar%in $er unit "an )e use# in CVP analysis' Te !ei%te# a&era%e "ontri)ution mar%in $er unit is "al"ulate# e0a"tly te same as "ontri)ution mar%in $er unit for a sin%le $ro#u"t e0"e$t tat o&erall fi%ures are use#' Contribution &ar'in +atio pproach @ If te $ro#u"ts tat a "om$any sells are su)stantially #ifferent( CVP analysis soul# )e $erforme# usin% te "ontri)ution mar%in ratio' en a "om$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" sales must )e ma#e to )rea+ e&en or %enerate a $rofit' To "al"ulate o! mu" sales #ollars are nee#e#( te "ontri)ution mar%in ratio( rater tan te "ontri)ution mar%in $er unit( soul# )e use#' Te "ontri)ution mar%in ratio "an also )e use# to analy3e te effe"t on net in"ome of a "an%e in total "om$any sales'

ASSUMPTIONS IN CVP ANALYSIS ene&er CVP analysis is $erforme#( a num)er of assum$tions are ma#e tat affe"t te &ali#ity of te analysis> Costs "an )e a""urately se$arate# into teir fi0e# an# &aria)le "om$onents' • Fi0e# "osts remain fi0e#' • Varia)le "osts $er unit #o not "an%e o&er te a"ti&ity le&els of interest' • en $erformin% multi$ro#u"t CVP analysis( it is assume# tat te mi0 remains "onstant' • Sellin% $ri"e $er unit #oes not "an%e' •

78

LO5


Discuss the effect of operating leverage.

OPERATIN LEVERAE Operatin' levera'e relates to te le&el of fi0e# &ersus &aria)le "osts in a firm4s "ost stru"ture' Firms tat a&e relati&ely i% le&els of fi0e# "ost are sai# to a&e i% o$eratin% le&era%e' Te le&el of o$eratin% le&era%e is im$ortant )e"ause it affe"ts te "an%e in $rofit !en sales "an%e' Firms tat a&e i% o$eratin% le&era%es are %enerally tou%t to )e more ris+y )e"ause tey ten# to a&e lar%e flu"tuations in $rofit !en sales flu"tuate' ,e"ause of fi0e# "osts in te "ost stru"ture( !en sales in"rease )y say 12 $er"ent( $rofit !ill in"rease )y more tan 12 $er"ent' Te only time $rofit !ill in"rease )y te 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/( ten $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 tere 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 sorta%es of s$a"e( e*ui$ment( or la)or' In su" "ases( te fo"us sifts from te contribution mar'in per unit to te contribution mar'in per unit of the constraint3 For e0am$le( su$$ose a "om$any "an $ro#u"e eiter Pro#u"t A or Pro#u"t , usin% te same e*ui$ment' Te "ontri)ution mar%in of A is 5922' Te "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 $er unit' Te "om$any !oul# only $ro#u"e Pro#u"t ,' Altou% 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' PP9":;

Using Regression in Ecel ! to Estimate "ied and #ariable $osts.

Te a$$en#i0 uses #ata for Co#eConne"t $resente# in Illustration 7-: in te te0t)oo+ to illustrate te Re%ression fun"tion in E0"el' Te s$rea#seet $ro%ram ma+es performing re%ression analysis &ery easy' o!e&er( it #oes not ma+e understanding re%ression analysis easy On"e you a&e installe# te #ata analysis $ro%rams( o$en a s$rea#seet an# enter te $ro#u"tion an# "ost #ata from Illustration 7-:' No! %o un#er Data ta) an# s"roll #o!n to Data Analysis' Ten s"roll #o!n to Regression an# "li"+ O' Un#er Input Y ( s"roll #o!n from ,1 to ,1H .note tat tis in"lu#es te ea#in% Cost)' Un#er Input X, s"roll #o!n from A1 to A1H .tis in"lu#es te ea#in% Pro!uction/' Cli"+ on La)els !i" in#i"ates tat you a&e la)els in Pro#u"tion an# Cost #ata "olumns' Un#er output options ( "li"+ on ew wor!"oo! ' Un#er residuals ( "li"+ on #ine fit plot ' Tis in#i"ates tat you !ant a $lot of #ata an# te re%ression line' Inter$retation of "riti"al elements .te $lot( R S*uare( Inter"e$t an# Slo$e of te Re%ression Line( an# P-Value/ of te re%ression out$ut is im$ortant' ,he plot of te #ata an# te $lot of te re%ression line in#i"ate tat te #ata line u$ *uite "lose to te re%ression line' Tis su%%ests tat a strai%t line fit to te #ata !ill )e *uite su""essful' + $.uare is a statisti"al measure of o! !ell te re%ression line fits te #ata' R S*uare ran%es from a lo! of 2( in#i"atin% tat tere is no linear relation )et!een "ost an# $ro#u"tion( to a i% of 1( in#i"atin% tat tere is a $erfe"t linear relation )et!een


77

"ost an# $ro#u"tion' Te intercept of the re'ression line is inter$rete# as te estimate of fi0e# "ost !ile te slope of the re'ression line is inter$rete# as te &aria)le "ost $er unit' Te p-values "orres$on#in% to te inter"e$t an# te slo$e measure te $ro)a)ility of o)ser&in% &alues as lar%e as te estimate# "oeffi"ients !en te true &alues are 3ero'

7<


Review o !e" Terms ccount analysis= A meto# of estimatin% "ost )ea&ior !i" re*uires $rofessional ?u#%ment to "lassify "osts as eiter fi0e# or &aria)le' Te total of te "osts "lassifie# as &aria)le are #i&i#e# )y a measure of a"ti&ity to "al"ulate te &aria)le "ost $er unit of a"ti&ity' Te total of te "osts "lassifie# as fi0e# $ro&i#es te estimate of fi0e# "ost' .19H/ rea2-even point= Te num)er of units a "om$any must sell to earn a 3ero $rofit' .1H2/ Committe! fie! costs= Tose fi0e# "osts tat "annot )e easily "an%e# in te sort-run' .199/ Contribution mar'in= Te #ifferen"e )et!een sales an# &aria)le "osts' .1H9/ Contribution mar'in ratio= Te "ontri)ution mar%in #i&i#e# )y sales or te "ontri)ution mar%in $er unit #i&i#e# )y te sellin% $ri"e' .1HH/ Cost-volume-profit (CVP)= Te analysis of o! "osts an# $rofit "an%e !en &olume "an%es' .116/ "iscretionary fie! costs= Tose fi0e# "osts tat mana%ement "an easily "an%e in te sort-run' .191/ Fie! cost= Costs tat #o not "an%e !en tere is a "an%e in )usiness a"ti&ity' .192/ >i'h-lo metho!= A meto# of estimatin% fi0e# an# &aria)le "ost "om$onents in !i" a strai%t line is fitte# to te #ata $oints re$resentin% te i%est an# lo!est le&els of a"ti&ity' .19/ &ar'in of safety= Te #ifferen"e )et!een te e0$e"te# le&el of sales an# )rea+-e&en sales' .1H1/

&ie! cost= Costs tat "ontain )ot &aria)le an# fi0e# "ost elements' .199/ Operatin' levera'e= Le&el of fi0e# &ersus &aria)le "osts in a firm4s "ost stru"ture' Firms tat 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 tat states tat $rofit is e*ual to re&enue .sellin% $ri"e times *uantity/ minus &aria)le "ost .&aria)le "ost $er unit times *uantity/ minus total fi0e# "ost' .1H2/ +e'ression analysis= A statisti"al te"ni*ue use# to estimate te inter"e$t .an estimate of fi0e# "ost/ an# te slo$e .an estimate of &aria)le "ost/ of a "ost e*uation' .19

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'

Te a""ount analysis meto# is su)?e"ti&e in tat #ifferent mana%ers usin% te same set of fa"ts may rea" #ifferent "on"lusions re%ar#in% te "lassifi"ation of "osts into fi0e# an# &aria)le "om$onents'

 J'

Usin% te i%-lo! meto# to "lassify "osts as fi0e# or &aria)le( te slo$e of te line is te estimate of &aria)le "ost'

 '

Te le&el of o$eratin% le&era%e is im$ortant )e"ause it affe"ts te "an%e in $rofit !en sales "an%e'

 :'

To "al"ulate te )rea+-e&en $oint( te $rofit e*uation is set to 51( an# ten te a$$ro$riate sellin% $ri"e( &aria)le "ost( an# fi0e# "ost information are inserte# into te e*uation'

 <'

Te "ontri)ution mar%in is e*ual to te #ifferen"e in te sellin% $ri"e $er unit an# fi0e# "ost $er unit'

 6'

Firms tat a&e relati&ely i% le&els of fi0e# "ost are sai# to a&e i% o$eratin% le&era%e'

 12'

Te "ontri)ution mar%in $er unit measures te amount of in"remental $rofit %enerate# )y sellin% an a##itional unit'

 11'

One of te $rimary uses of CVP analysis is to "al"ulate te )rea+-e&en $oint'

 19'

Fi0e# "osts #o not affe"t te in"remental $rofit asso"iate# !it sellin% an a##itional unit )e"ause fi0e# "osts are not affe"te# )y "an%es in &olume'


C#a$ter 4 % !e" Terms )atc#in* Mat" te terms foun# in Ca$ter 7 !it te follo!in% #efinitions> a' )' "' #' e' f'

A""ount analysis ,rea+-e&en $oint Contri)ution mar%in i%-lo! meto# Mi0e# "ost Mar%in of safety

%' O$eratin% le&era%e ' Profit e*uation i' Re%ression analysis ?' S"atter%ra$ +' Ste$ "osts l' at if analysis

 1'

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

 9'

E*uation tat states tat $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 te results of &arious "ourses of a"tion'

 7'

Te num)er of units a "om$any must sell to earn a 3ero $rofit'

 J'

Costs tat "ontain )ot &aria)le an# fi0e# elements'

 '

A meto# of estimatin% "ost )ea&ior !i" re*uires $rofessional ?u#%ment to "lassify "osts as eiter fi0e# or &aria)le'

 :'

Te #ifferen"e )et!een sales an# &aria)le "osts'

 <'

A statisti"al te"ni*ue use# to estimate te inter"e$t .an estimate of fi0e# "ost/ an# te slo$e .an estimate of &aria)le "ost/ of a "ost e*uation'

 6'

Te #ifferen"e )et!een te e0$e"te# le&el of sales an# )rea+-e&en sales'

 12' Tose "osts tat are fi0e# for a ran%e of &alue )ut in"rease to a i%er le&el !en te u$$er )oun# of te ran%e is e0"ee#e#'  11' Le&el of fi0e# &ersus &aria)le "osts in a firm4s "ost stru"ture'  19' A meto# of estimatin% fi0e# an# &aria)le "ost "om$onents in !i" a strai%t line is fitte# to te #ata $oints re$resentin% te i%est an# lo!est le&els of a"ti&ity'


<1

C#a$ter 4 % )u(ti$(e C#oice 1'

Mi0e# "osts are also referre# to as> a' #ou)le "osts' )' assorte# "osts' "' sun#ry "osts' #' semi&aria)le "osts'

9'

i" of te follo!in% meto#s uses a statisti"al te"ni*ue to estimate fi0e# an# &aria)le "ostsQ a' S"atter%ra$' )' Re%ression analysis' "' A""ount analysis' #' i%-lo! meto#'

H'

An e0am$le of a #is"retionary fi0e# "ost is> a' a#&ertisin%' )' in#ire"t la)or' "' rent' #' #e$re"iation'

se the folloin' information to anser .uestions 4 throu'h <' Vi"+ Com$any $ro#u"es )oat motors' Te sellin% $ri"e $er motor is 51(922' Te &aria)le "ost $er motor is 5J22 an# te fi0e# "ost $er $erio# is 5<(:22' Vi"+ e0$e"ts to sell 9J motors #urin% te $erio#

7'

Te "ontri)ution mar%in $er unit is> a' 5H7<' )' 5J22' "' 5:22' #' 5
J'

Te )rea+-e&en $oint in units is> a' 12' )' 1H' "' 1<' #' 9J'

'

Te )rea+-e&en $oint in #ollars is> a' 519(222' )' 51J(22' "' 591(22' #' 5H2(222'

:'

Te "ontri)ution mar%in ratio is> a' 96'2' )' 71':' "' J<'H' #' :2'<'

<#


<'

Te mar%in of safety is> a' 5<(:22' )' 517(722' "' 51<(222' #' 5H2(222'

6'

Te tree elements of te $rofit e*uation are> 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'

Te "ontri)ution mar%in ratio $ro&i#es a measure of> a' te "ontri)ution of e&ery sales #ollar to "o&erin% fi0e# "ost an# %eneratin% a $rofit' )' te "ontri)ution of e&ery sales #ollar to "o&erin% &aria)le "ost an# %eneratin% a $rofit' "' te "ontri)ution of e&ery sales #ollar to "o&erin% &aria)le an# fi0e# "osts an# %eneratin% a $rofit' #' none of te a)o&e'

11'

i" of te follo!in% assum$tions ma#e !en usin% CVP analysis mi%t affe"t te &ali#ity of te analysisQ a' Costs "an )e a""urately se$arate# into teir fi0e# an# &aria)le "om$onents' )' Fi0e# "osts remain fi0e# an# &aria)le "osts $er unit #o not "an%e o&er te a"ti&ity le&els of interest' "' ,ot a an# )' #' Neiter a nor )'

19'

=alton Com$any "an $ro#u"e Pro#u"t A an# Pro#u"t , usin% te same e*ui$ment' Te "ontri)ution mar%in for A is 5922 !ile te "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 te follo!in% units soul# =alton $ro#u"eQ a' Pro#u"t A )e"ause te "ontri)ution mar%in of 5922 is %reater tan te "ontri)ution mar%in of 51J2 for Pro#u"t ,' )' Pro#u"t , )e"ause te "ontri)ution mar%in $er "onstraint of 5H22 is %reater tan te "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 teir res$e"ti&e "ontri)ution mar%ins' #' Pro#u"t A an# Pro#u"t , e*ually'


<*

E+ercise 4 % 

=urin% a re"ent si0-mont $erio#( Connie4s olesale Cu$"a+es a# te follo!in% montly &olume of "u$"a+es sol# an# total montly utilities e0$ense> &onth ;anuary Fe)ruary Mar" A$ril May ;une

9umber of Cupca2es H(J22 J(722 7(622 6(222 :(<22 (H22

tilities pense 5 622 1(H92 1(<22 9(112 9(222 9(22

Re*uire#> 1'

Com$ute te estimate# &aria)le "ost $er "u$"a+e for utilities e0$ense' 9umber of Cupca2es

tilities pense

i% le&el of a"ti&ity Lo! le&el of a"ti&ity Can%e

Estimate of Varia)le "ost 9'

B

Can%e in "ost Can%e in a"ti&ity

5

 "u$"a+es

B 5 $er "u$"a+e

Com$ute te total estimate# fi0e# "ost $er mont for utilities e0$ense' Total "ost at te i% le&el of a"ti&ity



Less &aria)le "ost



Fi0e# "ost

H'

Com$ute te total amount of utilities e0$ense tat !oul# )e in"urre# at a le&el of 9(922 "u$"a+es' Varia)le "ost at a le&el of 9(922 "u$"a+es



Fi0e# "ost at a le&el of 9(922 "u$"a+es



Total utility "ost at a le&el of 9(922 "u$"a+es

<4


E+ercise 4 % -

arren( In"' as a sellin% $ri"e of 5<22 $er unit for its $ro#u"ts'' Varia)le "osts $er unit are 522 an# fi0e# "osts total 51J2(222 1'

at is te "ontri)ution mar%in $er unitQ

9'

at is te "ontri)ution mar%in ratioQ

H'

Com$ute te )rea+-e&en $oint in units'

7'

Com$ute te )rea+-e&en $oint in #ollar &olume of re&enue'

J'

Pro&e your ans!ers in $arts H an# 7 )y $re$arin% a "ontri)ution mar%in in"ome statement in %oo# or#er'

Re&enue

?arrenB :nc3 Contribution &ar'in :ncome $tatement une *AB #A1* 

Less &aria)le "osts



Contri)ution mar%in



Less fi0e# "osts



Net in"ome


E+ercise 4./

<5

For se&eral years( ,ella%io4s Restaurant as offere# a lun" s$e"ial for 5:'22' Montly fi0e# e0$enses a&e )een 57(922' Te &aria)le "ost of a meal as )een 59'12' Antony ,ella%io( te o!ner( )elie&es tat )y remo#elin% te restaurant an# u$%ra#in% te foo# ser&i"es( e "an in"rease te $ri"e of te lun" s$e"ial to 5:'72' Montly fi0e# e0$enses !oul# in"rease to 57(<22 an# te &aria)le e0$enses !oul# in"rease to 59'6 $er meal'

1'

Com$ute ,ella%ios montly )rea+-e&en sales in #ollars )efore remo#elin%'

9'

Com$ute ,ella%ios montly )rea+-e&en sales in #ollars after remo#elin%'

H'

at re"ommen#ation !oul# you ma+e to Antony ,ella%io "on"ernin% remo#elin% te restaurantQ

<8


Prob(em 4 % 4

o%an Manufa"turin% Com$any ma+es an# sells a sin%le $ro#u"t' Te "om$anys sales an# e0$enses for te most re"ent mont are %i&en )elo!> ,otal

Sales Less &aria)le e0$enses Contri)ution mar%in Less fi0e# e0$enses Net in"ome

5J22(222 H72(222 512(222 <2(222 5 <2(222

Per nit 5 

9J 1: <

122 < H9

1' at is te montly )rea+-e&en $oint in units an# in sales #ollarsQ

9' itout resortin% to "om$utations( !at is te total "ontri)ution mar%in at te )rea+-e&en $ointQ

H' o! many units !oul# a&e to )e sol# ea" mont to earn a minimum tar%et net in"ome of 5122(222Q Pro&e your ans!er )y $re$arin% a "ontri)ution in"ome statement at te tar%et le&el of sales'

7' Assumin% o%an in"reases sales )y 12( o! mu" !ill net in"ome in"reaseQ

J' Pro&e your ans!er in $art 7 )y $re$arin% a "ontri)ution mar%in in"ome statement at tat le&el of a"ti&ity'


<7

0o(utions % True&'a(se 1' 9' H' 7' J' ' :'

F F T T T F

<' F 6' 12' 11' 19'

F A "ommon fi0e# "ost is rent an# a "ommon &aria)le "ost is sales "ommissions' Varia)le "osts in total "an%e $ro$ortionately !it "an%es in a"ti&ity' Mi0e# "osts "ontain elements of )ot fi0e# "ost an# &aria)le "ost'

To "al"ulate te )rea+-e&en $oint( te $rofit e*uation is set to 3ero( an# ten insert te a$$ro$riate sellin% $ri"e( &aria)le "ost( an# fi0e# "ost information' Te "ontri)ution mar%in is e*ual to te #ifferen"e in te sellin% $ri"e $er unit an# &aria)le "ost $er unit'

T T T T

0o(utions % !e" Terms )atc#in* 1' 9' H' 7' J' '

?' S"atter%ra$ ' Profit e*uation l' at if analysis )' ,rea+-e&en $oint e' Mi0e# "ost a' A""ount analysis

:' <' 6' 12' 11' 19'

"' Contri)ution mar%in i' Re%ression analysis f' Mar%in of safety +' Ste$ "osts %' O$eratin% le&era%e #' i%-lo! meto#

0o(utions % )u(ti$(e C#oice 1' 9' H' 7' J' '

# ) a " ) )

:' <' 6' 12' 11' 19'

" ) " a " )

<<


0o(ution % E+ercise 4 % 

=urin% a re"ent si0-mont $erio#( Connie4s olesale Cu$"a+es a# te follo!in% montly &olume of "u$"a+es sol# an# total montly utilities e0$ense> &onth ;anuary Fe)ruary Mar" A$ril May ;une

9umber of Cupca2es H(J22 J(722 7(622 6(222 :(<22 (H22

tilities pense 5 622 1(H92 1(<22 9(112 9(222 9(22

Re*uire#> a'

Com$ute te estimate# &aria)le "ost $er "u$"a+e for utilities e0$ense'

i% le&el of a"ti&ity Lo! le&el of a"ti&ity Can%e Estimate of Varia)le "ost )'

B

9umber of Cupca2es 6(222 H(J22 J(J22

Can%e in "ost  Can%e in a"ti&ity

51(912 J(J22 "u$"a+es

B 52'99 $er "u$"a+e

Com$ute te total estimate# fi0e# "ost $er mont for utilities e0$ense' Total "ost at te i% le&el of a"ti&ity Less &aria)le "ost .6(222 0 52'99/ Fi0e# "ost

"'

tilities pense 59(112 622 51(912

59(112 1(6<2 5 1H2

Com$ute te total amount of utilities e0$ense tat !oul# )e in"urre# at a le&el of 9(922 "a+es' Varia)le "ost at a le&el of 9(922 "u$"a+es Fi0e# "ost at a le&el of 9(922 "u$"a+es Total utility "ost at a le&el of 9(922 "u$"a+es

57<7 1H2 517


<@

0o(ution % E+ercise 4 % -

arren( In"' as a sellin% $ri"e of 5<22 $er unit for its $ro#u"ts'' Varia)le "osts $er unit are 522 an# fi0e# "osts total 51J2(222 1' at is te "ontri)ution mar%in $er unitQ Re&enue 5<22 Varia)le "ost 22 Contri)ution mar%in 5922 9' at is te "ontri)ution mar%in ratioQ Re&enue Varia)le "osts Contri)ution mar%in

5<22 22 5922

122 :J 9J

H' Com$ute te )rea+-e&en $oint in units' 51J2(222 ÷ 5922 B :J2 units 7' Com$ute te )rea+-e&en $oint in #ollar &olume of re&enue' 51J2(222 ÷ '9J B 522(222 J' Pro&e your ans!ers in $arts H an# 7 )y $re$arin% a "ontri)ution mar%in in"ome statement in %oo# or#er' arren( In"' Contri)ution Mar%in In"ome Statement ;une H2( 921H Re&enue .:J2 units  5<22/ Less &aria)le "osts .:J2 units  522/ Contri)ution mar%in Less fi0e# "osts Net in"ome

522(222 7J2(222 51J2(222 1J2(222 -2-

@A


0o(ution % E+ercise 4 . /

For se&eral years( ,ella%io4s Restaurant as offere# a lun" s$e"ial for 5:'22' Montly fi0e# e0$enses a&e )een 57(922' Te &aria)le "ost of a meal as )een 59'12' Antony ,ella%io( te o!ner( )elie&es tat )y remo#elin% te restaurant an# u$%ra#in% te foo# ser&i"es( e "an in"rease te $ri"e of te lun" s$e"ial to 5:'72' Montly fi0e# e0$enses !oul# in"rease to 57(<22 an# te &aria)le e0$enses !oul# in"rease to 59'6 $er meal'

1' Com$ute ,ella%ios montly )rea+-e&en sales in #ollars )efore remo#elin%' Sales Varia)le "osts ontri)ution mar%in

5:'22 9'12 57'62

122 H2 :2

Fi0e# "osts ÷ CM ratio B ,EP in 5 &olume 57(922 ÷ ':2 B 5(222

9' Com$ute ,ella%ios montly )rea+-e&en sales in #ollars after remo#elin%' Sales Varia)le "osts Contri)ution mar%in

5:'72 9'6 57'77

122 72 2

Fi0e# "osts ÷ CM ratio B ,EP in 5 &olume 57(<22 ÷ '2 B 5<(222 H' at re"ommen#ation !oul# you ma+e to Antony ,ella%io "on"ernin% remo#elin% remo#elin% te restaurantQ Antony soul# not remo#el te restaurant )uil#in%' At te $resent time( e nee#s to a&e montly re&enue of only 5(222 to )rea+ e&en' o!e&er( !it te remo#elin%( e !oul# nee# montly re&enue of 5<(222 to )rea+-e&en'


@1

0o(ution % Prob(em 4 % 4

o%an Manufa"turin% Com$any ma+es an# sells a sin%le $ro#u"t' Te "om$anys sales an# e0$enses for te most re"ent mont are %i&en )elo!> ,otal

Sales Less &aria)le e0$enses Contri)ution mar%in Less fi0e# e0$enses Net in"ome

5J22(222 H72(222 512(222 <2(222 5 <2(222

Per nit 5 

9J 1: <

122 < H9

1' at is te montly )rea+-e&en $oint in units an# in sales #ollarsQ 5<2(222 5< B 12(222 units 5<2(222  'H9 B 59J2(222 9' itout resortin% to "om$utations( !at is te total "ontri)ution mar%in at te )rea+-e&en $ointQ 5<2(222 @ At te )rea+e&en $oint( "ontri)ution mar%in is al!ays e*ual to fi0e# "osts' H' o! many units !oul# a&e to )e sol# ea" mont to earn a minimum tar%et net in"ome of 5122(222Q Pro&e your ans!er )y $re$arin% a "ontri)ution in"ome statement at te tar%et le&el of sales' .5<2(222 D 5122(222/  5< B 99(J22 units Sales .99(J22 0 9J/ Varia)le "osts .99(J22 0 51:/ Contri)ution mar%in Fi0e# "ost Net in"ome

5J9(J22 H<9(J22 1<2(222 <2(222 5122(222

7' Assumin% o%an in"reases sales )y 12( o! mu" !ill net in"ome in"reaseQ 51<2(222 0 '12 B 51<(222 J' Pro&e your ans!er in $art 7J )y $re$arin% a "ontri)ution in"ome statement at tat le&el of a"ti&ity' Sales .99(222 0 59J/ 5JJ2(222 Varia)le "osts .99(222 0 51:/ H:7(222 Contri)ution mar%in 1:(222 Fi0e# "ost <2(222 Net in"ome 5 6(222 5J22(222859J B 92(222 units 92(2220 1'12 B 99(222 units

Ch04 Cost Volume Profit Analysis

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