The Learning Rate and Learning Effect _ F5 Performance Management _ ACCA Qualification _ Students _ ACCA Global _ ACCA Global

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29/08/2015 Thelearningrateandlearningeffect|F5PerformanceManagement|ACCAQualification|Students|ACCAGlobal|ACCAGlobalhttp://www.accaglobal.com/sg/en/student/examsupportresources/fundamentalsexamsstudyresources/f5/technicalarticles/thelearningrateandlearni 1/4Home > Students > Examresources > Fundamentalslevel > F5PerformanceManagement > TechnicalarticlesTHE LEARNING RATE AND LEARNING EFFECTMyACCASearchRELATED LINKSStudentAccountanthubpageUnderthenewexamstructureforPaperF5,learningcurveswillcontinuetobeexamined,theonlychangebeingthatquestionsmayvaryalittlebitmorethantheyhavedoneinthepast.TheDecember2013syllabusreadsestimatethelearningeffectandapplythelearningcurvetoabudgetaryproblem,includingcalculationsonsteadystates.Thusfar,thishasbeeninterpretedtomeanthatthelearningratewillalwaysbegiveninaquestionandquestionswillfocuspurelyon'estimatingthelearningeffect'thatis,calculatingthelabourtimeandusuallycostforagivenprocess.Historically,therequirementsofquestionshavebeensuchithasbeennecessaryforcandidatestousethealgebraicmethod,applyingthelearningcurveformulatoproblems,ratherthanthetabularapproach.Bothmethods,however,haveactuallybeenexaminableunderthesyllabus,andforteachingpurposes,thetabularapproachisalwaysagoodstartingpointtodemonstratehowthelearningcurveeffectactuallyworks.InthesyllabusforDecember2014onwards,thewordslearningrateandlearningeffectwillbeusedratherthansimplylearningeffect.Thiswordinghasbeenchangedinordertomakeitclearthatcandidatescouldnowbeaskedtocalculatelearningratestoo.Thepurposeofthisarticleis,however,twofold:first,itistosummarisethehistoryofthelearningcurveeffectandhelpcandidatesunderstandwhyitisimportant.Second,itistolookatwhatpastlearningcurvequestionshaverequiredofcandidatesandtoclarifyhowfuturequestionsmaygobeyondthis.ABRIEFHISTORYOFTHELEARNINGCURVEInpractice,itisoftenfoundthattheresourcesrequiredtomakeaproductdecreaseasproductionvolumesincrease.Itcostsmoretoproducethefirstunitofaproductthanitdoestoproducetheonehundredthunit.Inpart,thisisduetoeconomiesofscalesincecostsusuallyfallwhenproductsaremadeonalargerscale.Thismaybeduetobulkquantitydiscountsreceivedfromsuppliers,forexample.Thelearningcurve,effect,however,isnotaboutthisitisnotaboutcostreduction.Itisahumanphenomenonthatoccursbecauseofthefactthatpeoplegetquickeratperformingrepetitivetasksoncetheyhavebeendoingthemforawhile.Thefirsttimeanewprocessisperformed,theworkersareunfamiliarwithitsincetheprocessisuntried.Astheprocessisrepeated,however,theworkersbecomemorefamiliarwithitandbetteratperformingit.Thismeansthatittakesthemlesstimetocompleteit.Thefirstreportedobservationofthelearningcurvegoesasfarbackas1925whenaircraftmanufacturersobservedthatthenumberofmanhourstakentoassembleplanesdecreasedasmoreplaneswereproduced.TPWrightsubsequentlyestablishedfromhisresearchoftheaircraftindustryinthe1920sand1930sthattherateatwhichlearningtookplacewasnotrandomatallandthatitwasactuallypossibletoaccuratelypredicthowmuchlabourtimewouldberequiredtobuildplanesinthefuture.DuringWorldWarII,USgovernmentcontractorsthenusedthelearningcurvetopredictcostandtimeforshipandplaneconstruction.Gradually,privatesectorcompaniesalsoadopteditafterthewar.ThespecificlearningcurveeffectidentifiedbyWrightwasthatthecumulativeaveragetimeperunitdecreasedbyafixedpercentageeachtimecumulativeoutputdoubled.Whileintheaircraftindustrythisrateoflearningwasgenerallyseentobearound80%,indifferentindustriesotherratesoccur.Similarly,dependingontheindustryinquestion,itisoftenmoreappropriatefortheunitofmeasurementtobeabatchratherthananindividualunit.Thelearningprocessstartsassoonasthefirstunitorbatchcomesofftheproductionline.Sinceadoublingofcumulativeproductionisrequiredinorderforthecumulativeaveragetimeperunittodecrease,itisclearlythecasethattheeffectofthelearningrateonlabourtimewillbecomemuchlesssignificantasproductionincreases.Eventually,thelearningeffectwillcometoanendaltogether.YoucanseethisinFigure1below.Whenoutputislow,thelearningcurveisreallysteepbutthecurvebecomesflatterascumulativeoutputincreases,withthecurveeventuallybecomingastraightlinewhenthelearningeffectends.TheglobalbodyforprofessionalaccountantsAboutus Contactus Workforus Technicalactivities Help&support Singapore29/08/2015 Thelearningrateandlearningeffect|F5PerformanceManagement|ACCAQualification|Students|ACCAGlobal|ACCAGlobalhttp://www.accaglobal.com/sg/en/student/examsupportresources/fundamentalsexamsstudyresources/f5/technicalarticles/thelearningrateandlearni 2/4Figure1Thelearningcurveeffectwillnotalwaysapply,ofcourse.Itflourisheswherecertainconditionsarepresent.Itisnecessaryfortheprocesstobearepetitiveone,forexample.Also,thereneedstobeacontinuityofworkersandtheymustntbetakingprolongedbreaksduringtheproductionprocess.THEIMPORTANCEOFTHELEARNINGCURVEEFFECTLearningcurvemodelsenableuserstopredicthowlongitwilltaketocompleteafuturetask.Managementaccountantsmustthereforebesuretotakeintoaccountanylearningratewhentheyarecarryingoutplanning,controlanddecisionmaking.Iftheyfailtodothis,seriousconsequenceswillresult.Asregardsitsimportanceindecisionmaking,letuslookattheexampleofacompanythatisintroducinganewproductontothemarket.Thecompanywantstomakeitspriceasattractiveaspossibletocustomersbutstillwantstomakeaprofit,soitpricesitbasedonthefullabsorptioncostplusasmall5%markupforprofit.Thefirstunitofthatproductmaytakeonehourtomake.Ifthelabourcostis$15perhour,thenthepriceoftheproductwillbebasedontheinclusionofthatcostof$15perhour.Othercostsmaytotal$45.Theproductisthereforereleasedontothemarketatapriceof$63.Subsequently,itbecomesapparentthatthelearningeffecthasbeenignoredandthecorrectlabourtimeperunitshouldisactually0.5hours.Withoutcrunchingthroughthenumbersagain,itisobviousthattheproductwillhavebeenlaunchedontothemarketatapricewhichisfartoohigh.Thismaymeanthatinitialsalesaremuchlowerthantheyotherwisewouldhavebeenandtheproductlaunchmayfail.Worsestill,thecompanymayhavedecidednottolaunchitinthefirstplaceasitbelieveditcouldnotofferacompetitiveprice.Letusnowconsideritsimportanceinplanningandcontrol.Ifstandardcostingistobeused,itisimportantthatstandardcostsprovideanaccuratebasisforthecalculationofvariances.Ifstandardcostshavebeencalculatedwithouttakingintoaccountthelearningeffect,thenallthelabourusagevarianceswillbefavourablebecausethestandardlabourhoursthattheyarebasedonwillbetoohigh.Thiswillmaketheiruseforcontrolpurposespointless.Finally,itisworthnotingthattheuseoflearningcurveisnotrestrictedtotheassemblyindustriesitistraditionallyassociatedwith.Itisalsousedinotherlesstraditionalsectorssuchasprofessionalpractice,financialservices,publishingandtravel.Infact,researchhasshownthatjustunderhalfofusersareintheservicesector.HOWLEARNINGCURVESHAVEBEENEXAMINEDINTHEPASTThelearningcurveeffecthasregularlybeenexaminedinPaperF5.Forexample,inDecember2011,itwasexaminedinconjunctionwithlifecyclecosting.Candidateswereaskedtocalculatearevisedlifecyclecostperunitaftertakingintoaccountthelearningeffect.Thisinvolvedworkingouttheincrementallabourtimetakentoproducethefinal100thunitmadebeforethelearningeffectended.Thisisafairlycommonexamrequirementwhichtestscandidatesunderstandingofthedifferencebetweencumulativeandincrementaltimetakentoproduceaproductandtheapplicationofthelearningcurveformula.Itisworthmentioningatthispointthatyoushouldneverroundlearningcurvecalculationstolessthanthreedecimalplaces.Insomequestions,wherethelearningeffectissmall,overroundingwillleadtoacandidatewipingouttheentirelearningeffectandthenthequestionbecomespointless.Thelearningcurveformula,asshownbelow,isalwaysgivenontheformulasheetintheexam.Y=axbWhereY=cumulativeaveragetimeperunittoproducexunitsa=thetimetakenforthefirstunitofoutputx=thecumulativenumberofunitsproducedb=theindexoflearning(logLR/log2)LR=thelearningrateasadecimalWhileavalueforbhasusuallybeengiveninpastexamsthereisnoreasonwhythisshouldalwaysbethecase.Allcandidatesshouldknowhowtouseascientificcalculatorandshouldbesuretotakeoneintotheexamhall.InJune2013,thelearningeffectwasagainexaminedinconjunctionwithlifetimecosting.Again,ashashistoricallybeenthecase,thelearningratewasgiveninthequestion,aswasthevalueforb.BackinJune2009,thelearningcurveeffectwasexaminedinconjunctionwithtargetcosting.Onceagain,thelearningratewasgiven,andavalueforbwasgiven,butthistime,anaveragecostforthefirst128unitsmadewasrequired.Itwasafterthispointthatthelearningeffectended,sothequestionthenwentontoaskcandidatestocalculatethecostforthelastunitmade,sincethiswasgoingtobethecostofmakingoneunitgoingforwardinthebusiness.Itcanbeseen,justfromtheexamplesgivenabove,thatlearningcurvequestionshavetendedtofollowafairlyregularpatterninthepast.Theproblemwiththisisthatcandidatesdontalwaysactuallythinkaboutthecalculationstheyareperforming.Theysimplypractisepastpapers,learnhowtoanswerquestions,29/08/2015 Thelearningrateandlearningeffect|F5PerformanceManagement|ACCAQualification|Students|ACCAGlobal|ACCAGlobalhttp://www.accaglobal.com/sg/en/student/examsupportresources/fundamentalsexamsstudyresources/f5/technicalarticles/thelearningrateandlearni 3/4andneverreallythinkbeyondthis.Intheworkplace,whenfacedwithcalculationsinvolvingthelearningeffect,candidatesmaynotbeabletotacklethem.Intheworkplace,thelearningratewillnotbeknowninadvanceforanewprocessandsecondly,evenifithasbeenestimated,differencesmaywellarisebetweenexpectedlearningratesandactuallearningrateexperienced.Therefore,itseemedonlyrightthatfuturequestionsshouldexaminecandidatesabilitytocalculatethelearningrateitself.Thisleadsusontothenextsectionofthearticle.HOWTHELEARNINGEFFECTANDLEARNINGRATESMAYBEEXAMINEDFROMDECEMBER2014ONWARDSObviously,thelearningeffectcouldbeexaminedexactlyasithasbeeninpastexams,withcandidatesbeingaskedtocalculatethetimetakentoproduceanindividualunitoranumberofunitsofaproducteitherwhenthelearningcurveisstillineffectorwhenithasended.Thisobjectiveofthesyllabushasnotchanged.Asmentionedearlier,historically,questionshaverequiredtheuseofthealgebraicmethodandavalueforbhasusuallybeengivenintheexam.Movingforward,sincecalculationsofthelearningrateitselfmayberequiredinfutureexams,itbecomesevenmoreimportantthatcandidatesarefamiliarwithboththetabularmethodandusingtheirscientificcalculators.Thefollowingquestionisanexampleofthekindofquestionthatmayappearinfutureexams.Here,thetabularmethodisthesimplestwaytoanswerthequestion.Example1PCooperatesastandardcostingsystem.Thestandardlabourtimeperbatchforitsnewestproductwasestimatedtobe200hours,andresourceallocationandcostdatawerepreparedonthisbasis.Theactualnumberofbatchesproducedduringthefirstsixmonthsandtheactualtimetakentoproducethemisshownbelow:Month IncrementalnumberofbatchesproducedeachmonthIncrementallabourhourstakentoproducethebatchesJune 1 200July 1 152August 2 267.52September 4 470.8October 8 1,090.32November 16 2,180.64Required(a)Calculatethemonthlylearningratethataroseduringtheperiod.(b)IdentifywhenthelearningperiodendedandbrieflydiscusstheimplicationsofthisforPCo.Solution(a)MonthlyratesoflearningMonth IncrementalnumberofbatchesIncementaltotalhoursCumulativenumberofbatchesCumulativetotalhoursCumulativeaveragehoursperbatchJune 1 200 1 200 200 July 1 152 2 352 176 August 2 267.52 4 619.52 154.88 September 4 470.8 8 1090.32 136.29 October 8 1090.32 16 2180.64 136.29 November 16 2180.64 32 4361.28 136.29 Learningrate:176/200=88%154.88/176=88%136.29/154.88=88%Thereforethemonthlyrateoflearningwas88%.29/08/2015 Thelearningrateandlearningeffect|F5PerformanceManagement|ACCAQualification|Students|ACCAGlobal|ACCAGlobalhttp://www.accaglobal.com/sg/en/student/examsupportresources/fundamentalsexamsstudyresources/f5/technicalarticles/thelearningrateandlearni 4/4Lastupdated:10Aug2015(b)EndoflearningrateandimplicationsThelearningperiodendedattheendofSeptember.ThismeantthatfromOctoberonwardsthetimetakentoproduceeachbatchoftheproductwasconstant.Therefore,infuture,whenPComakesdecisionsaboutallocatingitsresourcesandcostingtheproduct,itshouldbasethesedecisionsonthetimetakentoproducetheighthbatch,whichwasthelastbatchproducedbeforethelearningperiodcametoanend.Theresourceallocationsandcostdatapreparedforthelastsixmonthswillhavebeeninaccuratesincetheywerebasedonastandardtimeperbatchof200hours.PCocouldtryandimproveitsproductionprocesssothatthelearningperiodcouldbeextended.Itmaybeabletodothisbyincreasingthelevelofstafftrainingprovided.Alternatively,itcouldtrytoincentivisestafftoworkharderthroughpaymentofbonuses,althoughthequalityofproductionwouldneedtobemaintained.Example2Thefirstbatchofanewproducttooksixhourstomakeandthetotaltimeforthefirst16unitswas42.8hours,atwhichpointthelearningeffectcametoanend.Calculatetherateoflearning.SolutionAgain,theeasiestwaytosolvethisproblemandfindtheactuallearningrateistouseacombinationofthetabularapproachplus,inthiscase,alittlebitofmaths.Thereisanalternativemethodthatcanbeusedthatwouldinvolvesomemoredifficultmathsanduseoftheinverselogbuttononthecalculator,butthiscanbequitetrickyandcandidateswouldnotbeexpectedtousethismethod.Shouldtheychoosetodoso,however,fullmarkswouldbeawarded,ofcourse.Usingalgebra:Step1:Writeouttheequation:42.8=16x(6xr4)Step2:Divideeachsideby16inordertogetridofthe16xontherighthandsideoftheequation:2.675=(6xr4)Step3:Divideeachsideby6inordertogetridofthe6xontherighthandsideoftheequation:0.4458333=r4Step4:takethefourthrootofeachsideinordertogetridofther4ontherighthandsideoftheequation.Youshouldhaveabuttononyourcalculatorthatsaysr4orx1/y.Eitherofthesecanbeusedtofindthefourthroot(oranyroot,infact)ofanumber.Thekeyistomakesurethatyoucanuseyourcalculatorproperlybeforeyouentertheexamhallratherthantryingtoworkitoutunderexampressure.Youthengettheanswer:r=0.8171Thismeansthatthelearningrate=81.71%.SUMMARYTheabovetwoexamplesdemonstratethetypeofrequirementsthatyoumayfindinfuturequestionsonlearningcurves,togetherwiththeoldstylerequirementsthathavetraditionallybeenfoundinpastquestionsinPaperF5.Remember:nothingnewisbeingaddedtothesyllabushere.Allthatwearedoingisencouragingyoutothinkalittleand,insomecase,perhapsusealittlebitofthemathsthat,asatraineeaccountant,youshouldbemorethancapableofapplying.WrittenbyamemberofthePaperF5examiningteam

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