《成本与管理会计》教师手册costacctg13-im-5

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10

DeterminingHowCostsBehave

TRANSITIONNOTES

Thefive-stepdecisionmodelisappliedinthischaptertoevaluatechangesincostsandhowtheseaffectthechosencostdrivers.Thereisagreaterdiscussionofmanagerialdecision-makingusingquantitativeanalysis.Theappendixonregressionanalysishasbeenexpanded.AdditionalmaterialrelatingtoABC/ABMisincluded.Severalnewproblemsareintroducedintheendofchaptermaterialandmanyhavebeenrevised.

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I.LEARNINGOBJECTIVES

1.Explainthetwoassumptionsfrequentlyusedincost-behaviorestimation

2.Describelinearcostfunctionsandthreecommonwaysinwhichtheybehave

3.Understandvariousmethodsofcostestimation

4.Outlinesixstepsinestimatingacostfunctionusingquantitativeanalysis

5.Describethreecriteriausedtoevaluateandchoosecostdrivers

6.Explainandgiveexamplesofnonlinearcostfunctions

7.Distinguishthecumulativeaverage-timelearningmodelfromtheincrementalunit-timelearningmodel

8.Beawareofdataproblemsencounteredinestimatingcostfunctions

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II.CHAPTERSYNOPSIS

Chapter3discussedcost-volume-profitanalysisandtherelationshipamongcosts,profits,andactivitylevels.Thischapterpresentsconceptsandmethodsthatcanbeutilizedtoanalyzemixedcostsandtobreakthemintoseparatefixedandvariablecomponents.Managersusecostfunctionstogainabetterunderstandingofcostbehavior.Costfunctionsaremathematicalformulasthatdescribehowcostsbehaverelativetochangesinactivitylevels.Twokeyassumptionsoftenmadebymanagersusingcostfunctionsare:

•

•

Changesinactivitylevelsexplainchangesintotalcosts.

Costbehaviorintherelevantrangecanbeestimatedwithalinearfunction.

Thechapteralsopresentsalternativecostfunctionsthatdonotrelyonthesetwoassumptions.RegressionanalysisisdiscussedingreaterdetailintheAppendix.

III.POINTSOFEMPHASIS

1.Makecertainthestudentsunderstandtheassumptionsincostbehaviorlimitations.Thesearelimitingassumptionsandmustbetakenintoaccount.

2.Emphasizethattheequationforacostfunction,y=a+bX,istheuniversal;itappliesforallmethodsofcostestimation.Alsomakesurethestudentsknowthemathematicalnames,aswellasthecostaccountingnamesforeachelementintheequation.

3.Makesurethatthestudentsunderstandthatfixed,variable,andmixedaredescriptionsofcostbehaviorsandthattheyunderstandtheirbehavioronaper-unitbasisaswellastotal.

4.Asaccountants,wenaturallyhaveapreferenceforquantitativemethodsofestimatingacostfunction.Emphasizethathigh-lowissimple,butthatcomputershavemaderegressionaccessibletoeveryone.Theydonotneedtounderstandhowtocomputearegressionequation,buttheyshouldbeabletointerprettheresults.

5.Itisnotsoimportanttogetintothemathematicaldetailsofthelearningcurve,butbesurethestudentsunderstandtherealityandapplicationoflearningcurves.

6.Helpthestudentsrealizethatdatadoesnotalwayscometotheminneatpackagesasshowninthetext,butemphasizedatacollectionproblems.

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IV.CHAPTEROUTLINE

1

Explainthetwoassumptionsfrequentlyusedincost-

behaviorestimation

...costfunctionsarelinearandhaveasinglecostdriver

1.1Understandinghowcostsbehaveisavaluabletechnicalskill.Amanagementaccountantmustbeabletoidentifycostdrivers,estimatecostrelationships,anddeterminethefixedandvariablecomponentsofcosts.Inordertoeffectivelydothis,themanagementaccountantmusthaveanunderstandingoftheoperationsofthebusiness,beavitalmemberofthemanagementteam,andbeabletoconveyhis/herfindings.

1.2Acostfunctionisamathematicaldescriptionofhowacostchangeswithchangesinthelevelofanactivityrelatingtothatcost.

1.3Managersoftenestimatecostfunctionsbasedontwoassumptions:

•Variationsinthelevelofasingleactivity(costdriver)explainthevariationsintherelatedtotalcosts.

•Costsbehaveinalinearmannerwithintherelevantrangeofactivity.Alinearcostfunctionisrepresentedbyastraightline.

TEACHINGPOINT.Theseassumptionsmaynotalwaysbefulfilled.However,inmanyinstances,theymeetthecriteriacloselyenoughtoallowforusefulanalysis.

1.4Theformulaforacostfunctionisy=a+bX.Thesecomponentswillbediscussedasweprogressthroughthechapter.

2

Describelinearcostfunctions

...graphofcostfunctionisastraightline

andthreecommonwaysinwhichtheybehave

...variable,fixed,andmixed

2.1Costsusuallybehaveinoneofthreecommonlyencounteredmanners.Theycanbevariable,fixed,orsemivariable.

2.2Avariablecostfunctionrepresentsacostthatincreasesintotalasthelevelof

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thecostdriverincreases.Theamountbywhichthecostincreasesasthecostdriverincreasesbyoneistheslopecoefficient,representedby“b”intheequationforacostfunction.

2.3Afixedcostfunctionisoneinwhichthecostdoesnotchangeinresponsetochangesinthelevelofactivity.Itisreferredtoastheconstant,andisrepresentedby“a”intheequation.

2.4Amixedcostfunctionrepresentsacostthathasbothvariableandfixedcomponents.Thisisalsoknownasasemivariablecost.

(Exhibit10-1displaysexamplesoflinearcostfunctions.)

TEACHINGPOINT.Itisgoodtoillustratethethreeconceptsatthispoint.Agoodexamplemaybethesituationofrentingacar.Intheory,thecarrentalagencycanpresentthreeoptions:(1)Aflatrateperday,suchas$50.Therentalcostwillbefixedat$50,regardlessofmilesdriven.(2)Apermilerate,suchas$1.00foreachmiledriven.Therentalcostwillbevariablebasedonthenumberofmilesdriven.(3)Amixedrate,suchas$25perdayplus$.50permiledriven.Therentalcostwillbeafixed$25adayplusanincreasingamountforeachmiledriven.

2.5FromChapter2,therearethreecriteriaforclassifyingacostintoitsfixedandvariablecomponents.Itwillbehelpfultoreviewthesethreeconceptsatthispoint.

•ChoiceofCostObject.Dependingonthechoiceofthecostobjectagivencostmaybefixedorvariable.

•TimeHorizon.Whetheracostisfixedorvariableforaparticular

activitymaydependonthetimehorizonbeingconsideredinthedecision.Thelongerthetimeframe,themorecostsbecomevariable.

•RelevantRange.Costbehaviorpatternsarevalidforlinearcostfunctionsonlywithinthegivenrelevantrange.Outsidethisrange,cost

behaviorpatternschangecausingthecoststobecomenonlinear.(Exhibit10-2illustrateslinearitywithinarelevantrange.)

RefertoQuizQuestion1Exercises10-17,10-18and10-19

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3

Understandvariousmethodsofcostestimation

...forexample,theregressionanalysismethod

determinesthelinethatbestfitspastdata

3.1Managersusecostestimationtomeasurearelationshipbasedondatafrompastcostsandtherelatedlevelofanactivity.

3.2Estimatingthesepastcostfunctionscanhelpmanagersmakemoreaccuratecostpredictionsaboutfuturecosts.

3.3Criticaltothisprocessiscorrectlyidentifyingthefactorsthataffectcosts.Managers,then,arelookingforacause-and-effectrelationshipbetweenthecostsincurredandthelevelofactivity.Werefertothisactivitymeasureasacostdriver.

3.4Thecause-and-effectrelationshipmayariseasaresultof:

•Aphysicalrelationshipbetweenthelevelofactivityandcosts.Thereisaphysicalrelationshipbetweendirectmaterialsandthenumberofunitsproduced.

•Acontractualarrangement.Forexample,inacarrentalcontractthatchargesbythemile,milesdrivenisspecifiedinthecontractastheactivitythataffectstherentalcost.

•Knowledgeofoperations.Aproductwithmanypartswillincurhigherorderingcoststhanaproductwithfewparts.Ifthecompanyismeasuringorderingcosts,theactivitydrivercouldbenumberofparts.

3.5Thereareseveraldifferentmethodsforestimatingcosts.Thesemethodsinclude:

•TheIndustrialengineeringmethod,alsocalledthework-measurementmethod,estimatescostfunctionsbyanalyzingtherelationshipbetweeninputsandoutputsinphysicalterms.Thisisathoroughanddetailedmethod,butcanbeverytime-consuming.

•Theconferencemethodestimatescostfunctionsbasedonanalysisandopinionsaboutcostsandtheirdriversgatheredfromvariousdepartmentsofacompany.Sinceitdoesnotrequiredetailedanalysisofdata,itcanbeusedtodevelopcostfunctionsveryquickly.However,theemphasisonopinionsratherthansystematicestimationcanmakethisalessaccuratemethod.

•Theaccountanalysismethodestimatescostfunctionsbyclassifyingvariouscostaccountsasvariable,fixed,ormixedwithrespecttotheidentifiedlevelofactivity.Althoughthismethodreliesmoreonqualitativeanalysis,itisreasonablyaccurate,cost-effective,andeasytouse.

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•

TheQuantitativeanalysismethodusesformalmathematicalmodelstofitcostfunctionstopastdataobservations.Themostcommonquantitativeanalysismethodsarethehigh-lowmethodandregressionanalysis.

RefertoQuizQuestion2

Exercise10-20

4

Outlinesixstepsinestimatingacostfunctionusing

quantitativeanalysis

...theendresult(step6)istoevaluatethecostdriverof

theestimatedcostfunction

4.1Estimatingacostfunctionusingquantitativeanalysisinvolvesasix-stepprocedure:

Step1:Choosethedependentvariable(costbeingestimatedor

predicted).Thedependentvariableisthecostbeingestimated(yintheequation)anddependsonthecostfunctionbeingestimated.

Step2:Identifytheindependentvariable,orcostdriver.The

independentvariableisthefactorusedtopredictthecostfunction.Thisisthecostdriver,otherwisereferredtoasXintheequation,ortheslope.Thecostdrivershouldhaveaneconomicallyplausiblerelationshiptothedependentvariableandbemeasurable.

TEACHINGPOINT.Bewareofspuriousrelationships.Justbecausearelationshipbetweenthedependentandindependentvariableexistsdoesnotmeanthatthereisacause-and-effectrelationshipinplace.Pointoutthatyoucanprove(statistically)thatdrinkingwaterisfatal;i.e.,100%ofpeoplewhodrinkwaterdie.Obviously,thereisnorelationshipbetweenmortalityanddrinkingwater.

Step3:Collectdataonthedependentvariableandthecostdriver.

Thisisusuallythemostdifficultstep,asthedatacomesfromanumberofsources,andmanagersneedtobeconcernedaboutthevalidityofthedata.

Step4:Plotthedata.Byplottingthedataonascattergraphitcanbe

determinedifalinearrelationshipexists.Also,thisalertsthemanagertoanyextremeobservations.

(Exhibit10-4isanexampleofthisstep,withdataplottedonthegraph.)

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Step5:

Step6:

Estimatethecostfunction.Asmentioned,therearetwoprimarymethodsofestimatingacostfunction—thehigh-lowmethodandregressionanalysis.

Evaluatethecostdriveroftheestimatedcostfunction.Howthecostdriverisevaluatedisdiscussedlaterinthechapter.

4.2Thehigh-lowmethodisthesimplestformofquantitativeanalysis.Thismethodtakesthehighlevelofactivityandthecostsatthatlevelandthelowlevelofactivityandthecostsincurredatthatlevel.

TEACHINGPOINT.Atthisjuncturethehigh-lowmethodshouldbeillustratedbyworkingthroughaproblem.Exercise10-24isagoodillustrationofthismethod.Becertainthestudentsunderstandthatyouselectthehighandlowactivitylevelsandnotthehighandlowlevelsofcost.

(Exhibit10-5illustratesanestimatedcostfunctionusingthehigh-lowmethod.)

4.3Thehigh-lowmethodhastheadvantagesofsimplicitytocomputeandunderstand;itcangiveaquickinsightintocost/activityrelationships.However,itdoesnotutilizeallbutonlytwodatapoints,soagreatdealofvaliddataisnotutilizedinthismethod.

4.4Regressionanalysisisastatisticaltechniquethatmeasurestheaverageamountofchangeinthedependentvariableassociatedwithaunitchangeintheindependentvariable.Thismethodrequirestheuseofstatisticalsoftwarebutwillusuallygivethemostaccurateresults.

4.5Multipleregressionallowsthemanagertoincorporatemultiplecostdriversintheanalysistohelpexplainthechangesincostsastheactivitylevelchanges.

4.6Inaregressionanalysis,theresidualtermmeasuresthedistancebetweentheactualandestimatedcostsforeachobservation.Ther2valueisanindicationofhowgoodapredictorofcoststheequationis.Thisisreferredtoasgoodnessoffit.

(Exhibit10-6illustratesaleast-squaresregressionline.)

RefertoQuizQuestions3,4,and5Exercises10-23,10-24and10-28

5

Describethreecriteriausedtoevaluateandchoosecost

drivers

...economicallyplausiblerelationships,goodnessof

fit,andsignificanteffectofthecostdriveroncosts

5.1Oneofthedifficultiesinapplyingamodeltopredictcostsisdetermininghow

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effectivethemodelisinmakingthosepredictions.Underanyofthesemodels,thedatacanbeenteredandapredictionequationderived.Isthisthebestcostdrivertopredictthebehavior?Howgoodisthisdriveratpredictingcostbehavior?

5.2Therearethreecriteriaoftenusedtoevaluatecostdrivers;theyare:

•Economicplausibility.Dothecostdriverandthelevelofcostsseemtoberelated?Doesitmakesensethatanincreaseintheindependentvariablewillcauseanincreaseinthecosts?

•Goodnessoffit.Arethedifferencesbetweentheactualcostsandpredictedcostssmall?Inaregressionanalysis,goodnessoffitismeasuredbyther2statistic.

•Significanceofindependentvariable.Iftheregressionline(ortotalcostline)hasasteepslope,thisindicatesastrongrelationshipbetweenthecostdriverandthecostsincurred.

(Exhibits10-7and10-8illustratetheuseofalternativecostdriversforcostestimationpurposes.)

5.3Ashasbeendiscussedinapreviouschapter,activity-basedcostingfocusesonindividualactivities.ToimplementABCacostdrivermustbeidentifiedforeachactivity.

•Asaresult,ABCsystemshavealargenumberofcostdriversandcostpools,requiringmanycostrelationshipstobeestimated.Asapartofthisprocess,themanagermustpaycarefulattentiontothecosthierarchy.

•Thiswillrequireagreatdealofwork,butthemanagerwillhaveamuchbetterunderstandingofthecoststructureofthecompanyuponcompletionoftheexercise.

RefertoQuizQuestion6

Problem10-34

6

Explainandgiveexamplesofnonlinearcostfunctions

...graphofcostfunctionisnotastraightline,for

example,becauseofquantitydiscountsorcosts

changinginsteps

6.1Costsdonotalwaysbehaveinaneat,orderly,linearfashion.Anonlinearcostfunctionisoneinwhichthegraphofthetotalcostsbasedonthelevelofasingleactivityisnotastraightline.

6.2Economiesofscalemaypreventacostfrombehavinginalinearfashion.Whenalargernumberofitemsisordered,thepriceperunitmaydecline.

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6.3Stepcostfunctionsareanotherexampleofnonlinearcostfunctions.Theseremainthesameovercertainrangesofactivity,butincreasefromonerangetothenext.

6.4Astepvariable-costfunctionhasanarrowrangeinwhichthecostremainsthesame,whereasastepfixed-costfunctionchangesoverawiderrangeofcosts.

TEACHINGPOINT.Illustratestepfunctionswithexamples.Forexample,thecompanyrequiresonesupervisorforeach20workers.Iftheyhave100workers,therewillbefivesupervisors.Newsupervisorswouldonlybehiredas20additionalworkersareemployed.

(Exhibit10-9displaystheeffectofquantitydiscountsandnonlinearcostfunctions.)

7

Distinguishthecumulativeaverage-timelearningmodel

...averagetimeperunitdeclinesbyconstant

percentage,asunitsproduceddoublefromthe

incrementalunit-timelearningmodel

...incrementaltimetoproducefastunitdeclinesby

constantpercentage,asunitsproduceddouble

7.1Nonlinearcostfunctionsresultfromlearningcurves.Alearningcurveisafunctionthatmeasureshowlabor-hoursperunitdeclineasunitsofproductionincrease.Thisisbecauseworkersarelearningandbecomingbetterattheirjobs.Anexperiencecurveisabroaderapplicationofalearningcurveinwhichmeasuresthedeclineincostsperunitinfunctionsofthevaluechainincrease.

TEACHINGPOINT.Itisgoodtobringthisconcepthometothestudents,helpingthemrealizethisisnotjustatheory,butsomethingtheyhaveexperiencedintheirlives.Forexample,apersonwhohasneversetupanewcomputerwillhavetostop,readtheinstructions,figureoutexactlywhatgoeswhere,andthelike.Itwilltakeawhile.Afterbecomingfamiliarwithcomputersanddoingseveralset-ups,theyareabletodoitmuchmorequickly.Thisisalearningcurveinaction.

7.2Inthecumulativeaverage-timelearningmodel,thecumulativeaveragetimeperunitdecreasesbyaconstantpercentageeachtimethecumulativequantityproduceddoubles.Withan80%learningcurve,ifthequantityproduceddoubles,theaveragetimeforallunitsproduceddropsto80%oftheprevioustime.

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(Exhibit10-10illustratesthecumulativeaverage-timelearningmodel.)

7.3Intheincrementalunit-timelearningmodel,theincrementaltimeneededtoproducethelastunitdeclinesbyaconstantpercentageeachtimethequantityofunitsproduceddoubles.An80%learningcurveunderthismodelmeansthatwhenunitproductiondoubles,thetimeneededtoproducethelastunitis80%ofthetimeneededtoproducethelastunitbeforeproductiondoubled.

(Exhibit10-11illustratestheincrementalaverage-timelearningmodel.)

(Exhibit10-12plotscostsusinglearningcurvesatRayburnCorporation.)

7.4Insettingprices,preparingbudgets,anddeterminingstandardsacompanyneedstoconsiderthelearningcurveeffect.Asproductionincreasestomeetdemand,costperunitdecreases.Allofthisneedstobefactoredintotheplanningundertakenbythecompany.

(Exhibit10-13illustratesthelearningcurveeffectoncostsatRayburncompany.)

TEACHINGPOINT.Observethatthisisonereasonwhycustomproductsaremoreexpensive—sinceitisauniqueproduct,thereisnolearningcurveeffect.

RefertoQuizQuestions7-9Exercises10-29and10-30

8

Beawareofdataproblemsencounteredinestimating

costfunctions

...forexample,unreliabledataandpoorrecordkeeping,

extremeobservations,treatingfixedcostsasiftheyare

variable,andachangingrelationshipbetweenacost

driverandcost

8.1Ashasbeenillustrated,estimatingcostfunctionsisadifficulttaskwhendoneproperly.Oneissueisthequalityofthedatabasefromwhichtheobservationsaretaken.Anidealdatabasehastwocharacteristics:

•Thedatabaseshouldcontainnumerous,reliablymeasuredobservations

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ofthecostdriver(theindependentvariable)andtherelatedcosts(thedependentvariable).

•Thedatabaseshouldincludemanyvaluesspanningawiderangeforthecostdriver.

8.2Sincetheidealdatabasedoesnotusuallypresentitself,thecostanalystshouldbeawareofseveralfrequentlyencounteredproblemsandactionsthatcanbetakentoovercometheproblems.

•Thetimeperiodformeasuringthedependentvariablemaynotmatchtheperiodformeasuringthecostdriver.Keepingrecordsontheaccrualbasiswillfacilitatethesecomparisons.

•Fixedcostsareallocatedasiftheyarevariable.Toavoidthisproblem,takecaretodistinguishbetweenfixedandvariablecostsanddonottreatunitizedfixedcostasavariablecost.

•Dataaremissingorarenotuniformlyreliable.Thisisacollectionissue;toovercometheproblemdatashouldbeobtainedonaregularbasiswithfollowupwhendataaremissing.

•Extremevaluesofobservationsoccurfromerrorsinrecordingcosts.Adjustoreliminateunusualvaluesbeforeestimatingarelationship.

•Thereisnohomogeneousrelationshipbetweenthecostdriverandtheindividualcostitemsinthepool.Thiscanbeovercomewithadditionalcostpoolsorwithmultipleregressionanalysis.

•Therelationshipbetweenthecostdriverandthecostisnotstationary.Thiscanoccurwhenthereisachangeinoperations.Splittingthedatainto“beforeandafter”poolsmayfacilitateunderstanding.

•Inflationhasaffectedcosts,thecostdriverorboth.Removingtheinflationaryeffectsthroughtheuseofapriceindexmayassisttheanalyst.

RefertoQuizQuestion10

V.OTHERRESOURCES

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Pleasevisitthetextbookcompanionwebsiteat.Todownloadtheseandotherresources,visittheInstructor’sResourceCenteroraccessthemontheInstructor’sResourceDVD(IR-DVD).

ThefollowingexhibitswerementionedinthischapteroftheInstructor’sManual,andhavebeenincludedinthePowerPointLecturepresentationcreatedspecificallyforthischapter.YoumayusethePowerPointLecturepresentations“asis”,ormodifythemtosuityourindividualneeds.

Exhibit10-1displaysexamplesoflinearcostfunctions.

Exhibit10-2illustrateslinearitywithinarelevantrange.

Exhibit10-4isanexampleofthisstep,withdataplottedonthegraph.Exhibit10-5illustratesanestimatedcostfunctionusingthehigh-lowmethod.Exhibit10-6illustratesaleast-squaresregressionline.

Exhibits10-7and10-8illustratetheuseofalternativecostdriversforcostestimationpurposes.

Exhibit10-9displaystheeffectofquantitydiscountsandnonlinearcostfunctions.Exhibit10-10illustratesthecumulativeaverage-timelearningmodel.

Exhibit10-11illustratestheincrementalaverage-timelearningmodel.

Exhibit10-12plotscostsusinglearningcurvesatRayburnCorporation.Exhibit10-13illustratesthelearningcurveeffectoncostsatRayburncompany.

DownloadpdfimagesoftextbookillustrationsandexhibitsfromtheImageLibraryoraccessthemviayourIR-DVD.

SolutionstoSelectEnd-of-ChapterProblemsmentionedinthischapter,whichhavebeenfullyworkedoutinPowerPoint,areavailablefordownloadandincludedontheIR-

DVD.

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CHAPTER10QUIZ

1.Amixedcostfunctionhasaconstantcomponentof$20,000.Ifthetotalcostis$60,000andtheindependentvariablehasthevalue200,whatisthevalueoftheslopecoefficient?

a.$200

b.$400

c.$600

d.$40,000

2.[CMAAdapted]Ofthefollowingmethods,theonethatwouldnotbeappropriateforanalyzinghowaspecificcostbehavesis

a.thescattergraphmethod.

b.theindustrialengineeringapproach.

c.linearprogramming.

d.statisticalregressionanalysis.

3.Whenthehigh-lowmethodisusedtoestimateacostfunction,thevariablecostperunitisfoundby

a.performingregressionanalysisontheassociatedcostandcostdriverdatabase.

b.subtractingthefixedcostperunitfromthetotalcostperunitbasedoneitherthehighestorlowestobservationofthecostdriver.

c.dividingthedifferencebetweenthehighestandlowestobservationsofthecostdriverbythedifferencebetweencostsassociatedwiththehighestandlowestobservationsofthecostdriver.

d.dividingthedifferencebetweencostsassociatedwiththehighestandlowestobservationsofthecostdriverbythedifferencebetweenthehighestandlowestobservationsofthecostdriver.

Thefollowingdataapplytoquestions4and5.

ToryCompanyderivedthefollowingcostrelationshipfromaregressionanalysisofitsmonthlymanufacturingoverheadcost.

y=$80,000+$12Xwhere:y=monthlymanufacturingoverheadcost

X=machine-hours

Thestandarderrorofestimateoftheregressionis$6,000.

Thestandardtimerequiredtomanufactureonesix-unitcaseofTory’ssingleproductisfourmachine-hours.Toryappliesmanufacturingoverheadtoproductiononthebasisofmachine-hours,anditsnormalannualproductionis50,000cases.

4.[CMAAdapted]Tory’sestimatedvariableman