ENGINEERING ECONOMIC ANALYSIS
NEWNAN JONES
WHITTAKER
ESCHENBACH
LAVELLE
OXFORD UNIVERSITY PRESS
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EngineeringeconomicanalysisI DonaldG. Newnan,JohnJones,John Whittaker,TedG.Eschenbach,JeromeP.Lavelle. - Fourth Canadianedition. Includesbibliographicalreferencesandindex. Issuedinprintandelectronicformats.
ISBN 978-0-19-902511-4(hardcover).-ISBN 978-0-19-902522-0(PDF) 1.Engineeringeconomy-Textbooks. 2.Textbooks. I.Jones,John(John Dewey),author II.Whittaker,J. D.,author III.Eschenbach,Ted,author IV.Lavelle,JeromeP.,author V.Title.
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Preface and Acknowledgements ix
1 Economic Decisions, EngineeringCosts, and Cost Estimating 2
ASea of Problems 4
Simple Problems 4
IntermediateProblems 4
Complex Problems 4
The Role of EngineeringEconomicAnalysis 5
Examplesof Engineering Economic Analysis 5
The Decision-MakingProcess 6
Rational Decision Making 6
Ethics 12
Ethical Dimensionsin EngineeringDecision Making 12
Importanceof Ethicsin Engineeringand Engineering Economy 14
EngineeringDecisionMakingforCurrentCosts 14
EngineeringCosts 17
Fixed,Variable,Marginal,and Average Costs 17
Sunk Costs 19
Opportunity Costs 20
Recurringand Non-RecurringCosts 21
Incremental Costs 21
CashCostsversus BookCosts 22
Life-Cycle Costs 22
CostEstimating 23
Typesof Estimate 23
Difficultiesin Estimation 24
EstimatingModels 25
Per-Unit Model 25
Segmenting Model 25
Cost Indexes 25
Power-SizingModel 27
Triangulation 28
Improvementandthe Learning Curve 28
EstimatingBenefits 31
Cash Flow Diagrams 31
Categoriesof Cash Flow 32
Drawinga Cash Flow Diagram 32
Summary 32 Problems 34
2 Accountingand Engineering Economy 50
The Role ofAccounting 52
Accountingfor BusinessTransactions 52
TheBalanceSheet 53
Assets 53
Liabilities 54
Equity 54
FinancialRatiosDerivedfromBalanceSheetData 55
The Income Statement 55
FinancialRatiosDerivedfromIncomeStatementData 57
LinkingtheBalanceSheet.IncomeStatement.andCapitalTransactions 57
Traditional CostAccounting 59
Directand IndirectCosts 59
IndirectCostAllocation 59
ProblemswithTraditionalCostAccounting 59
OtherProblemstoWatchFor 61
Summary 61
Problems 62
3 Interest and Equivalence 66
Computing Cash Flows 67
TimeValueofMoney 69
SimpleInterest 70
CompoundInterest 70
RepayingaDebt 71
Equivalence 73
Single-PaymentCompoundInterest Formulas 75
Nominaland EffectiveInterest 79
ContinuousCompounding 83
SinglePaymentInterestFactors:ContinuousCompounding 83
EquivalenceandSustainability 86
Summary 86
Problems 87
4 Equivalence for Repeated Cash Flows 94
UniformSeriesCompound Interest Formulas 96
CashFlowsThatDoNotMatchBasicPatterns 102
RelationshipsbetweenCompound Interest Factors 106
The Interest RateViewedasFog 107
ArithmeticGradient 108
DerivationofArithmeticGradientFactors 108
RealityandtheAssumed Uniformityofa, G, andg 114
Geometric Gradient 115
WhenCompounding Periodand Payment Period Differ 118
UniformPaymentSeries:ContinuousCompoundingat
NormalRaterperPeriod 120
Summary 122
Problems 125
5 Present Worth Analysis 140
AssumptionsinSolvingEconomicAnalysisProblems 142
End-of-YearConvention 142
ViewpointofEconomicAnalysisStudies 142
BorrowedMoneyViewpoint 143
IncomeTaxes 143
EffectofInflationandDeflation 143
EconomicCriteria 143
PresentWorthTechniques 143
1.UsefulLivesEqualtotheAnalysisPeriod 144
2.UsefulLivesDifferentfromtheAnalysisPeriod 145
3.InfiniteAnalysisPeriod:CapitalizedCost 148
MultipleAlternatives 151
BondPricing 153
FutureWorthAnalysis 154
Summary 156
Problems 156
6 Annual Cash Flow Analysis 176
AnnualCashFlowCalculations 178
ConvertingaPresentCosttoanAnnualCost 178
TreatmentofSalvageValue 179
AnnualCashFlowAnalysis 182
Analysis Period 182
AnalysisPeriodforaCommonMultipleofAlternativeLives 183
AnalysisPeriodforaContinuingRequirement 183
InfiniteAnalysisPeriod 184
SomeOtherAnalysisPeriod 185
MortgagesinCanada 186
BuildinganAmortizationSchedule 187
TypesofMortgageAvailable 188 Equity 188
MortgageInterestRate 188
Summary 189
Problems 189
7 Rate of Return Analysis 200
MinimumAttractiveRateofReturn 202
InternalRateofReturn 203
CalculatingRateofReturn 204
PlotofNPWversusInterestRatei 207
InterestRatesWhenThereAreFeesorDiscounts 209
IncrementalAnalysis 212
AnalysisPeriod 216
SensitivityAnalysis 217
ASecondPitfall 220
Summary 223
Problems 224
8 Benefit-Cost Ratio and Other AnalysisTechniques 242
PublicSectorInvestmentObjectives 244
ViewpointforAnalysis 245
SelectinganInterestRate 247
NoTime-Value-of-MoneyConcept 247
Cost-of-CapitalConcept 247
Opportunity-CostConcept 247
RecommendedConcept 248
TheBenefit-CostRatio 248
IncrementalBenefit-CostAnalysis 249
ElementsoftheIncrementalBenefit-CostRatioMethod 249
OtherEffectsof Public Projects 252
ProjectFinancing 252
DurationofProject 253
QuantifyingandValuingBenefitsandCosts 254
ProjectPolitics 255
PaybackPeriod 257
Summary 262
Problems 262
9 Selection of a Minimum Attractive Rate of Return 272
SourcesofCapital 275
MoneyGeneratedfromtheFirm'sOperations 275
ExternalSourcesofMoney 275
ChoiceofSourcesofFunds 275
CostofFunds 276
CostofBorrowedMoney 276
CostofCapital 276
InvestmentOpportunities 277
OpportunityCost 277
ChoosingaMinimumAttractiveRateofReturn 280
Adjusting MARRtoAccountforRiskandUncertainty 281
RepresentativeValuesofMARR UsedinIndustry 281
CapitalBudgeting.orSelectingtheBestProjects 282
Summary 284
Problems 285
10 Uncertainty in Future Events 292
Break-EvenAnalysis 295
OptimisticandPessimisticEstimates 296
Probability 298
JointProbabilityDistributions 301
ExpectedValue 303
Economic DecisionTrees 305
Risk 311
RiskversusReturn 313
Simulation 315 Summary 318
Problems 319
11 Income, Depreciation, and Cash Flow 330
Taxation 332
BasicAspectsof Depreciation 333
DeteriorationandObsolescence 333
DepreciationandExpenses 334
TypesofProperty 335
CostBasis 336
CalculatingDepreciation 336
DepreciationMethods 337
Straight-LineDepreciation 337
Sum-of-Years'-DigitsDepreciation 339
Declining-BalanceDepreciation 341
Unit-of-ProductionDepreciation 342
DepreciationforTax Purposes-CapitalCostAllowance 343
The50%Rule,orHalf-YearConvention 344
AcceleratedCCA-50%Straight-Line 344
CalculatingtheCCA-Schedule8 347
CalculatingtheCCAandtheUCC(withoutUsingSchedule8) 351
DepreciationandAssetDisposal 351
NaturalResourceAllowances 353
PercentageDepletion 353
CostDepletion 355
Summary 355
Problems 356
12 After-TaxCash Flows 366
A PartnerintheBusiness 369
CalculationofTaxableIncome 369
TaxableIncomeofIndividuals 369
CorporateIncomeTaxes 373
UsingCCAtoCalculateNetProfit 375
AccountingandEngineeringEconomy 376
CalculatingNetCashFlow 379
AcquiringandDisposingofAssets 381
NetSalvageofLand-CapitalGain 381
NetSalvage-Books-ClosedAssumption 382
CapitalTax FactorsandBooksOpen 383
CalculatingAfter Tax PresentWorth 385
WorkingCapitalRequirements 388
InitialWorkingCapital 389
IncreasingWorkingCapitalRequirement 389
LoanFinancing 390
LoanwithEqualPrincipalRepayment 391
LoanwithEqualAnnualRepayment 392
EstimatingtheAfter-TaxRateofReturn 393
Summary 394
Problems 395
13 ReplacementAnalysis 408
TheReplacementProblem 410
ReplacementAnalysisFlow Chart 411
Minimum-CostLifeofaNewAsset TheChallenger 412
Defender'sMarginalCostData 414
ReplacementAnalysisTechnique 1: DefenderMarginalCostsCanBeComputedandAre Increasing 416
ReplacementRepeatabilityAssumptions 417
ReplacementAnalysisTechnique 2: DefenderMarginalCostsCanBeComputedandAre NotIncreasing 418
ReplacementAnalysisTechnique 3: WhenDefenderMarginalCostDataAre Not Available 422
ComplicationsinReplacementAnalysis 422
Defining DefenderandChallenger FirstCosts 422
RepeatabilityAssumptions NotAcceptable 424
ACloser Lookat Future Challengers 425
After-TaxReplacementAnalysis 426
Marginal CostsonanAfter-Tax Basis 426
Minimum-CostLife Problems 428
SpreadsheetsandReplacementAnalysis 430
Summary 432
Problems 433
14 Inflationand Price Change 444
MeaningandEffectofInflation 446
HowDoesInflation Happen? 446
Hyperinflation 447
DefinitionsforConsideringInflationinEngineeringEconomy 447
AnalysisinReal DollarsversusActualDollars 454
PriceChangewithIndexes 456
WhatIsaPriceIndex? 456
CompositeversusCommodityIndexes 458
Howto UsePriceIndexesinEngineeringEconomicAnalysis 459
Cash FlowsThat InflateatDifferentRates 461
DifferentInflationRatesper Period 463
EffectofInflationonAfter-TaxCalculations 464
InflationandtheBuy/Lease Decision 467
InflationandtheCostofBorrowedMoney 470
Summary 471
Problems 472
15 Introductionto Project Management 482
ScientificManagement 483
TheGanttChart 484
CriticalPathMethod(CPM) 487
CPMandPERT 491
The MethodsofOperationsResearch 498
LinearProgrammingandtheSimplex Method 498
Queuing Theory 499
Summary 499
Problems 500
Glossary 504
References 508
Index 510
Preface and Acknowledgements
Engineeringistheapplicationofknowledgetodeveloppracticalandeconomicalsolutions to the problems that confront ourcivilization.Canada,withanareaof 9,984,670 km2 , isthe second-largest countryin the world. But withapopulation ofabout35,300,000, Canadahas less than0.5% ofthe world's people. In populationdensitywe rankabout 230th,with3.9peoplepersquarekilometreoflandarea.Becausemuchofthecountryis acoldandunforgivingplace,Canadianshaveneededalltheengineeringskillstheycould musterinordertoexistinthisformidableenvironmentand,indoingso,toconsistently achieveapositioninthetopfiveontheUnitedNationslistofthebestcountriestolivein.
Thehistoryofthiscountryisahistoryofengineeringinnovationandadaptability.The ingeniousdesignofthebirchbarkcanoeenabledFirstNationspeopletotravelthousands ofkilometresanddeveloptradingroutesthatspannedthecountry.Inthe1800s,engineersfromBritaintaughtushowtoconstructcanalstocircumventrapids;webuiltonthat knowledge,andwiththeopeningoftheStLawrenceSeawayin1959,ocean-goingshipsof commercewereabletobypassevensogreatanobstacleasNiagaraFallsandpenetratethe heartofthecontinent.
ThepromiseofatranscontinentalrailwaywaswhatbroughtBritishColumbiaintothe CanadianConfederation, andagaintheengineersresponded,completing the projectin 1885andopeningthewesternprovincestosettlementanddevelopment.
Canoesworkwellinthesummer,butwintertravelposesspecialchallenges.JosephArmandBombardierattachedaFordenginetoasleigh,which,withcontinuingengineeringrefinements,evolvedintotheirsnowmobile,theSkidoo,anditsinventor'scompany becametheaircraftandlight-rail-transitmanufacturerBombardier,Inc.
TheneedtocommunicatewithnorthernsettlementsledCanadianengineerstodevelop theAnikcommunicationssatellite.And our need tocommunicate,wherever we happentobe,ledaUniversityofWaterlooengineeringstudent,MikeLazaridis,todevelop theBlackBerryandcreatethecompanyResearchInMotion(RIM).
Engineeringhasalwaysbeenamixtureofneed,practicality,andeconomics.Theconceptsofethics,sustainability,andenvironmentalstewardshiparenowbeingaddedtothat mix.This book introduces theeconomicdecisionsthataccompanyengineeringdesign, butitalsoincludesquestionsthatexplorethoseotheraspects.Eachchapterbeginswith avignettedescribingaCanadianengineeringchallengeandinvitingthereadertothink aboutthebroaderimplicationsofengineeringdecisions.
Changes to the Fourth Edition
This edition hassignificantimprovements in organization andcoverage.Before going chapterbychapter,we'dliketopointoutafewglobalchangesmadetokeepthistextthe mostcurrentandmostusefulintoday'scourses:
• Anewdiscussionontheenvironmentalimpactsofengineeringprojectshasbeen added.
• AdditionalCanadianexamplesareincludedthroughout.
• AllunitsarenowinSI.
• Wehaveexpandedcoverageofmoney,inflation,andtheBankofCanada.
• The majority ofin-chapter Excel explanationshave been removed and placed online.
x PrefaceandAcknowledgements
Numerousimprovementstothecontentandwordinghavebeenmadethroughoutthe text.Thetexthasbeencondensedandsomeprintmaterial,suchasthecompoundinterest tables,hasbeenplacedonline.
Changesfromthethirdeditionincludethefollowing:
• Chapters1and2havebeencombinedandcondensedintoonechapter.
• Chapter8hasbeeneliminated,andsomematerialhasbeendistributedinother chapters(informationonincrementalanalysistoChapter7,futureworthcontent toChapter5,benefit-costratiotoChapter8,sensitivityandbreak-evencontent toChapter10).
• Chapter17hasbeenmoveduptobecomeChapter2.
• Chapter16hasbeenmoveduptobecomeChapter8.
• Anewchapteronprojectmanagementhasbeenadded.
• InChapter 12,theexplanationforcalculationoftaxesforindividualshasbeen revisedforclarity,andthecalculationofafter-taxcashflowshasbeenrevised.
Icons
Thesemarginaliconsappearthroughoutthetexttohighlightimportant keyconcepts.
TheseiconsappearintheProblemssectionattheendofeachchaptertosignifythat theanswertotheproblemcanbefoundonthecompanionwebsite:www.oupcanada .com/Newnan4Ce
A Special Word on Spreadsheets
Inthisedition,theauthorshavedeliberatelyomittedanydiscussionofhowtouseanyform ofspreadsheetsoftware.Sincetherearemanyspreadsheetprogramsavailable,andsince theirdetailschangefrequently,thesedetailsare better obtainedfromonline documentation.Studentswillnoticeratherquicklythattheuseofasuitablespreadsheetprogram cangreatlyreducethelabourinvolvedinsolvingeconomicproblems,andtheyshouldbe encouragedtodothis.
Acknowledgements
Thistextbookistheresultofthehardworkofalotofpeopleforover35years.I,along withOxfordUniversityPressCanada,wouldliketogratefullyacknowledgethefollowing reviewers,aswellasthosewhowishedtoremainanonymous:
SohaEidMoussa,UniversityofGuelph
TiffanyBayley,UniversityofWaterloo
ScottFlemming,DalhousieUniversity
MichaelBennett,UOIT
JuanPernia,LakeheadUniversity
MichaelH.Wang,UniversityofWindsor
NadineIbrahim,UniversityofToronto
Theirthoughtfulcommentsandsuggestionshavehelpedtoshapethefourthedition ofthistext.
For the fourth Canadian edition, I would like to thank all the people at OUP Canada-includingMegPatterson,LaurenWing,SuzanneClark,andLianaSpada-and DougLinzeyofAgricolaCommunications.Finally,Iwanttothankmywife,Joan,andmy daughterandeditorialcriticAli.
JohnJones
SimonFraserUniversity,2017
Alternative Futures
Economic Decisions, Engineering Costs, and Cost Estimating
There is no better place to start an engineering economics text than with a discussion of the future of the car, for that question embodies many of the technology and economic factors involved. Hybrids, plug-in electrics, turbocharged diesels, and advanced gasoline engines all compete for the buyer's (and driver's) attention. In 2016 the lineup included the following sedans:
sjo/iStock Photo
Choosing the rightvehicle is a complex problem, and evaluating the choices requires much more information than the price and fuel mileage. Willyou bedriving in the country or city, or a mix? How far doyou drive in ayear? What will the future price of energy (gas. diesel. electricity) be? Howlongwillyou keepthecarbeforeyou sellit? Whatwilltheresalevalue be? Whatfinancing termsdothesellersoffer?
Electricvehicletechnologyhas beenslowlyimproving. Since2012. the UniversityofWaterloo has been challenging teams of high-school students to design and build all-electric vehicles to compete in a 12-volt and a 24-volt endurance race. In the first yearof the competition. Bluevale Secondary School won the 12-volt and 24-volt races. with 41 and 61 laps, respectively. In 2013, theywerenarrowlyedgedoutoffirstplace in the12-voltrace byResurrection Catholic Secondary School, who completed 51.9 laps, but retained first place in the 24-volt race with an impressive 95 laps.
Butthegasoline and dieselengineershavenotbeenstanding still. Futuredriverswillcontinue to beoffered an arrayoftechnologies and will haveto useengineering economicanalysistofind thecorrectchoices.
QUESTIONS TO CONSIDER
1. What marketplace dynamics stimulate or suppress the development of alternative-fuel vehicles? What role. ifany,doesgovernmenthaveinthesedynamics? What additional responsibilitiesshould government have?
2. Developalistofconcernsand questionsthatconsumersmighthaveabouttheconversiontoalternative-fuel vehicles. Which areeconomicfactors. andwhich are non-economic?
3. Some environmentalists have proposed producing bio-fuels from crops as an alternative to fossil fuels. What ethical questions might this involve?
4. Power companies have a lot of extra capacity at night, and so there is a possibility of their offering off-peak power at a reduced cost. This could be used by people with plug-in hybrids. How much investment would a power company have to make in smart circuits for a time-variable pricing policyto be possible?
LEARNING OBJECTIVES
Thischapterwillhelpyou
• describetheeconomicdecision-makingprocess
• chooseappropriate economiccriteria fordifferentproblems
• describe common ethical issues in engineering economic decisions
• definevariouscostconcepts
• providespecificexamplesofhowandwhythese engineeringcostconceptsare important
• defineengineeringcostestimating
• explain thethreetypesofengineering estimates.aswellas common difficultiesencountered in making them
• useseveralcommon mathematicalestimating models incostestimating
• discuss theeffectofthelearningcurveoncostestimates
• drawcash flowdiagramstoshowprojectcostsand benefits
KEYTERMS
averagecost bookcost cashcost cashflowdiagram estimating byanalogy fixedcost forgoneopportunity incremental cost learningcurve
A Sea of Problems
learning curvepercentage learningcurverate life-cyclecosting marginalcost model building non-recurringcost opportunitycost out-of-pocketcost overhead
per unit model power-sizing model recurringcost segmenting model shadow price sunkcost triangulation variablecost
Thisbookisaboutmakingdecisions.Itdevelopsthetoolsforanalyzingandsolvingeconomicproblemscommonlyfacedbyengineers. Our emphasis is on solving problems that confrontfirms in the marketplace, but manyexamplesareproblemsstudentsfaceindailylife.Letusstartbylookingatsomeof theseproblems.
Simple Problems
Manyproblemsaresimple,andgoodsolutionsdonotrequiremuchtimeoreffort.
• ShouldIpaybycashorcreditcard?
• DoIbuyasemesterparkingpassorusetheparkingmeters?
• Shouldwereplaceaburned-outmotor?
• Ifweusethreecratesofanitemaweek,howmanycratesshouldwebuyatatime?
Intermediate Problems
Atthemiddlelevelofcomplexity,wefindproblemsthatareprimarilyeconomic.
• ShouldIbuyorleasemynextcar?
• Whichpiecesofequipmentshouldbechosenforanewassemblyline?
• Shouldourofficeupgradetothenewestversionofourprojectmanagementsoftware?
• ShouldIbuyaone-ortwo-semesterparkingpass?
• Shouldwebuyalow-costpressrequiringthreeoperators,oramoreexpensiveone requiringonlytwooperators?
Complex Problems
Complexproblemsrepresentamixtureofeconomic,political,andsocialandethicalelements.
• ThequestionofbuildingpipelinestoexportAlbertanoiloverseasisanexample ofacomplexproblem.Pipelinessuchas theproposedNorthernGatewayfrom AlbertatoKitimat,BC,willbenefittheAlbertaneconomyandcreatejobsinthe Albertanoilindustry.Ontheotherhand,someenvironmentalistsbelievethatthe riskofoilspillswillendangerFirstNationslandsandtheBCcoastline.Globally,
burningAlberta'soilwillincreaseglobalwarming,withpossibleadverseconsequencesworldwide.
• Thechoiceofagirlfriendoraboyfriend(whomaylaterbecomeaspouse)isobviouslycomplex.Economicanalysiscanbeoflittleornohelp.
• Theannualbudgetof acorporationisanallocation of resources,andall projectsareevaluatedeconomically.Thebudgetprocessisalsoheavilyinfluencedby non-economicforcessuchaspowerstruggles,geographicalbalancing,andeffects onindividuals,programs,andprofits.
The Role of Engineering Economic Analysis
Engineeringeconomicanalysisismostsuitableforintermediateproblemsandtheeconomicaspectsofcomplexproblems.Suchproblemshavethefollowingcharacteristics:
1. Theproblemisimportantenoughtojustifyseriousthoughtandeffort.
2. Theproblemcan'tbeworkedoutinone'shead-thatis,acarefulanalysisrequires thatweorganizetheproblemandallthevariousconsequences.
3. Theproblemhaseconomicaspectsthatareimportantinreachingadecision.
Vastnumbersofproblemshavingthese threecharacteristicsareencounteredinthe businessworldandinpeople'spersonallives,soengineeringeconomicanalysisisoften required.
Examplesof Engineering EconomicAnalysis
Engineeringeconomicanalysisfocusesoncosts,revenues,andbenefitsthatoccuratdifferenttimes.Forexample,whenanuclearengineerdesignsareactor,theconstructioncosts occurinthenearfuture;benefitstotheusersbeginonlywhenconstructionisfinished,but continueforalongtime.
Engineeringeconomicanalysisisusedtoanswermanydifferentquestions.
• Whichengineeringprojectsareworthwhile?Hastheminingorpetroleumengineershownthatthemineraloroildepositisworthdeveloping?
• Whichengineeringprojectsshouldhaveahigherpriority?Hastheelectricalengineershownthatreplacingtheplant'sstep-downtransformerismore urgentthan upgradingthepowersupplytothemachineshop?
• Howshouldtheengineeringprojectbedesigned?Has the mechanical engineer chosenthemosteconomicalsizeofmotor?Hasthesoftwareengineercalculated thedevelopmenttimeforwritingthenextreleaseofthesoftware?Hastheaeronauticalengineermadethebesttrade-offsbetween(1)lightermaterialsthatare expensivetobuybutresultinaplanethatischeapertoflyand{2)heaviermaterialsthatarecheaptobuybutresultinaplanethatismoreexpensivetofly?
Engineeringeconomicanalysiscanalsobeusedtoanswerquestionsthatarepersonallyimportant.
• Howtoachievelong-termfinancialgoals:Howmuchshouldyousaveeachmonth tobuyahouse,retire,orfundatriparoundtheworld?Isgoingtograduateschool agoodinvestment?
• Howtocomparedifferentwaystofinancepurchases:Isitbettertofinanceyour carpurchasebyusingthedealer'slow-interestloanorbytakingtherebateand borrowingmoneyfromyourbankorcreditunion?
• Howtomakeshort-andlong-terminvestmentdecisions:Shouldyoubuyaone-or two-semesterparkingpass?Isahighersalarybetterthanstockoptions?
The Decision-Making Process
Decisionmakingrequiresthattherebeatleasttwoalternatives.Ifonlyonecourseofaction isavailable,thereisnodecisiontomake.Doesdecisionmaking,then,consistofchoosing fromamongalternativecoursesofaction?Considerthefollowingsituation:
Ataracetrack,abettorwasuncertainwhichhorsetobetoninthenextrace.He closedhiseyesandpointedhisfingeratthelistofhorsesprintedintheracing program.Uponopeninghiseyes,hesawthathewaspointingtohorsenumber4. Hehurriedofftoplacehisbetonthathorse.
Doestheracehorseselectionrepresentaprocessofdecisionmaking?Clearly,itwasa processofchoosingamongalternatives.Butthisprocessseemsinadequateandirrational. Wewanttodealwithrationaldecisionmaking.
Rational Decision Making
Rational decisionmakingcanbeacomplexprocess.Onepossiblesystematicapproach to this processisshowninFigure 1-1. Although the steps areshownsequentially, itis commonforadecisionmakertorepeatsteps,takethemoutoforder,anddosomesteps simultaneously.Forexample,whenanewalternativeisidentified,moredatawillberequired.Or when theoutcomesaresummarized,it maybecomeclearthat theproblem needstoberedefinedornewgoalsestablished.ThefollowingsectionsdescribetheelementslistedinFigure1-1.
1.RecognizetheProblem
Thestartingpointinrationaldecisionmakingisrecognizingthataproblemexists.
Someyearsago,forexample,itwasdiscoveredthatseveralspeciesofoceanfishcontainedsubstantial concentrations of mercury.The decision-making processbeganwith thisdiscovery,andtherushwasontodeterminewhatshouldbedone.Researchrevealed thatfish takenfrom the ocean decades beforeandpreservedinlaboratoriescontained similarconcentrationsofmercury.Thustheproblemhadexistedforalongtimebuthad notbeenrecognized.
Inmanysituations,recognitionisobviousandimmediate.Acaraccident,acheque thatbounces,aburned-outmotor,anexhaustedsupplyofpartsallproducetherecognitionofaproblem.Onceweareawareoftheproblem,wesolveitasbestwecan.
2.DefinetheGoalorObjective
Thegoalcanbeagrand,overallgoalofapersonorafirm.Forexample,apersonalgoalcould betoleadapleasantandmeaningfullife,whereasafirm'sgoalisusuallytooperateprofitably. Butanobjectiveneednotbethegrand,overallgoalofabusinessoranindividual.It maybenarrowandspecific:"IwanttopayofftheloanonmycarbyMay"and"Theplant mustproduce300golfcartsinthenexttwoweeks"aremorelimitedobjectives.
2. Definethegoalorobjective
3. Assemblerelevantdata
4 Identifyfeasiblealternatives
5.Selectthecriteriatodeterminethebestalternative
6. Constructamodel
7.Predicttheoutcomesorconsequencesforeachalternative
8. Choosethebestalternative
9. Audittheresults
FIGURE1·1 One possibleflowchartofthedecision-making process.
3.AssembleRelevantData
To makeagood decision, youmustassemblegoodinformation.Inadditionto all the publishedinformation,avastquantityofinformationisnotwrittendownanywherebut is stored as individuals'knowledge and experience. There is also information thatremainsungathered.Aquestionlike"Howmanypeopleinyourtownwouldbeinterestedin buyingapairofleft-handedscissors?"cannotbeansweredbyexaminingpublisheddata orbyaskinganyoneperson.Marketresearchorotherdatagatheringwouldberequiredto obtainthedesiredinformation.
Onepartofthedatathatmustbeassembledisthetimehorizonoftheproblem.How longwillthebuildingorequipmentlast?Howlongwillitbeneeded?Willitbescrapped, sold,orshiftedtoanotheruse?Insomecases,suchasaroadoratunnel,thelifemaybe centurieswithregularmaintenanceandoccasionalrebuilding.However,ashorterperiod, suchas50years,maybechosenasthetimehorizonsothatdecisionscanbebasedonmore reliabledata.
Inengineeringdecisions,animportantsourceof dataisafirm's own accountingsystem.Thesedatamustbeexaminedcarefully.Thatisbecauseaccountingdata focus on pastinformation,whereas engineeringjudgment must oftenbeapplied to estimate current and futurevalues. For example, accounting records canshow the pastcostofbuyingcomputers,butengineeringjudgmentisrequiredtoestimatetheir futurecost.
Financialandcostaccountingaredesignedtoshow theflowofmoney-specifically costsandbenefits-inacompany'soperations.Whencostsaredirectlyrelatedtospecific operations,thereisnodifficulty;butthereareothercostsunrelatedtospecificoperations. Theseindirectcosts. oroverhead.areusuallyallocated to acompany's operationsand
productsbysomesemi-arbitrarymethod.Theresultsaregenerallysatisfactoryforcostaccountingpurposesbutmaybeunreliableforuseineconomicanalysis.
Tocreateameaningfuleconomicanalysis,wemustdeterminethetruedifferencesbetweenalternatives,andthatmightrequiresomeadjustmentofcost-accountingdata.The followingexampleillustratesthissituation.
EXAMPLE 1-1
Thecost-accountingrecordsofalargecompanyshowtheaveragemonthlycostsforthethree-person printingdepartment.Thewagesandbenefitsof thedepartmentmakeup thefirstcategoryofdirect labour.Thecompany'sindirectoroverheadcosts-suchasheat,electricity,andemployeeinsurancemustbedistributedtoitsvariousdepartmentsinsomemannerand,likemanyotherfirms, thisone usesfloorspaceasthebasisforitsallocations.
Directlabour(includingemployeebenefits)
Materialsandsuppliesconsumed
Allocatedoverheadcosts:
Theprintingdepartmentchargestheotherdepartmentsforitsservicestorecoverits$18,000monthly cost.Forexample,thechargetorun1,000copiesofanannouncementis
Theshippingdepartmentcheckswithacommercialprinterthatwouldprintthesame1,000copiesfor $22.95.Althoughtheshippingdepartmentneedsonlyabout30,000copiesprintedamonth,itsforeman decidestostopusingtheprintingdepartmentandhavetheworkdonebytheoutsideprinter.Theinhouseprintingdepartmentobjectstothis.Asaresult,thegeneralmanagerhasaskedyoutostudythe situationandrecommendwhatshouldbedone.
SOLUTION
Muchoftheprintingdepartment'soutputrevealsthecompany'scosts,prices,andotherfinancialinformation.Thecompanypresidentconsiderstheprintingdepartmentnecessaryinorderto prevent disclosingsuchinformationtopeopleoutsidethecompany.
Areviewofthecost-accountingchargesrevealsnothingunusual.Thechargesmadebytheprinting departmentcoverdirectlabour,materialsandsupplies,andoverhead.Theallocationofindirectcosts isacustomaryprocedureincost-accountingsystems,butitmaybemisleadingfordecisionmaking,as thefollowingdiscussionindicates.
Theshippingdepartmentwouldreduceitscostfrom$793to$688byusingtheoutsideprinter.Inthat case,byhowmuchwouldtheprintingdepartment'scostsdecline?Wewillexamineeachofthecost components:
1. DirectLabour.Iftheprintingdepartmenthadbeenworkingovertime,thentheovertimecould bereducedoreliminated.But,assumingtherewasnoovertime,howmuchwouldthesaving be?Itseemsunlikelythataprintercouldbefiredorevenputonlessthana40-hourwork week.Thus,althoughtheremightbea$228saving,itismuchmorelikelythattherewillbeno reductionindirectlabour.
2. MaterialsandSupplies.Therewouldbea$294savinginmaterialsandsupplies.
3. AllocatedOverheadCosts.Therewillbenoreductionintheprintingdepartment'smonthly $5,000overhead,becausetherewillbenoreductionindepartmentfloorspace.(Thoughthere maybeaslightreductioninthefirm'spowercostsiftheprintingdepartmentdoeslesswork.) Furthermore,thefirmwillincuradditionalexpensesinpurchasingandaccountingtodeal withtheoutsidefirm.
Thefirmwillsave$294inmaterialsandsuppliesandmayormaynotsave$228indirectlabourif theprintingdepartmentnolongerdoestheshippingdepartment'swork.Themaximumsavingwould be$294+228 = $522.Butiftheshippingdepartmentobtainsitsprintingfromtheoutsideprinter, thefirmmustpay$688.50amonth.Thesavingfromnotdoingtheshippingdepartmentworkinthe printingdepartmentwouldnotexceed$522,anditwouldprobablybeonly$294.Theresultwouldbea netincreaseincosttothefirm.Forthisreason,theshippingdepartmentshouldbediscouragedfrom sendingitsprintingtotheoutsideprinter.
Gathering cost data presents other difficulties. One way to look at the financial consequences-costsandbenefits-ofvariousalternativesisasfollows:
• Market Consequences. These consequences have an established price in the marketplace.We can quickly determineraw material prices,machinerycosts, labourcosts,andsoforth.
• Extra-MarketConsequences.Thereareotheritemsthatarenotdirectlypricedin themarketplace.Butbyindirectmeans,apricemaybeassignedtotheseitems. (Economists callthesepricesshadowprices.)Examplesmightbethecostofan employee'sinjuryorthevaluetoemployeesofgoingfromafive-daytoafour-day 40-hourweek.
• IntangibleConsequences.Numericaleconomicanalysisneverfullydescribesthe differencesbetweenalternatives.Wearetemptedtoleaveoutconsequencesthat donothaveasignificanteffectontheanalysisitselforontheconversionofthe finaldecisionintoitscashequivalent.Howdoesoneevaluatethepotentiallossof workers'jobsbecauseofautomation?Whatisthevalueoflandscapingarounda factory?Theseandsimilarfactorsmaybeleftoutofthenumericalcalculations, buttheyshouldbeconsideredinconjunctionwiththenumericalresultsinreachingadecision.
4. IdentifyFeasibleAlternatives
It should bekept in mind thatunlessthebestalternativeisconsidered, the resultwill alwaysbelessthanideal.Twotypesofalternativesaresometimesignored.First,inmany situationsa"do-nothing"alternativeisfeasible.Second,thereareoftenfeasible(butunglamorous)alternatives,suchas"Patchitupandkeepitrunningforanotheryearbefore replacingit."
Thereisnofoolproofwaytoensurethatthebestalternativeisamongtheonesbeing considered.Youshouldensurethatallconventionalalternativeshavebeenlistedandthen strivetosuggestinnovativesolutions.Sometimesitcanbeusefulforagrouptoconsider alternativesinaninnovativeatmosphere, thatis,bybrainstorming.Evenimpracticalalternativesmayleadtoabetterpossibility.
5.SelecttheCriteriaforDeterminingtheBestAlternative
Tochoosethebestalternative,wemustdefinewhatwemeanbybest.Theremustbeatleast onecriterion,orasetofcriteria,toevaluatewhichalternativeisbest-or,insomeunfortunatecases,theleastbad.Hereareseveralpossiblecriteria:
• Createminimaldisturbancetotheenvironment.
• Improvethedistributionofwealthamongpeople.
• Minimizetheexpenditureofmoney.
• Ensurethatthebenefitstothosewhogainfromthedecisionaregreaterthanthe lossesofthosewhoareharmedbythedecision.1
• Minimizethetimeneededtoaccomplishthegoalorobjective.
• Minimizeunemployment.
• Maximizeprofit.
Selectingthecriteriabywhichtochoosethebestalternativewillnotbeeasyifdifferentgroupssupportdifferentcriteriaandhencedesiredifferentalternatives.Orthecriteria mayconflict.Forexample,minimizingunemploymentmayincreasetheexpenditureof money. Minimizingenvironmental disturbancemayincreasethe timeto complete the project.Disagreementsbetweenmanagementandlabourmayreflectdisagreementsover thecriteriaforchoosingthebestalternative.
Thelastcriterion-maximizeprofit-istheonenormallyselectedinengineeringdecisionmaking.
6. ConstructaModel
Atsomepointinthedecisionmaking,thevariouselementsmustbebroughttogether. The objective, relevant data,feasible alternatives, and selection standards must be merged.
Constructingtherelationshipsbetween thedecision-makingelementsisfrequently calledmodelbuilding.Toanengineer,amodelmaybeaphysicalrepresentationofthe realthingorasetofequationsdescribingthedesiredrelationships.Ineconomicdecision making,themodelisusuallymathematical.
Itishelpfultomodelonlythatpartofthesystemimportanttotheproblemathand. Thusthemathematicalmodelofthestudentcapacityofaclassroommightbe
1 ThisistheKaldorcriterion.
where
l = lengthofclassroom,inmetres
w=widthofclassroom,inmetres
k = classroomarrangementfactor
Theequationforstudentcapacityofaclassroomisaverysimplemodel,yetitmaybeadequatefortheproblembeingsolved.
7. PredicttheOutcomesforEachAlternative
Amodeland thedataare usedto predict theoutcomesforeachfeasiblealternative.As suggestedearlier,eachalternativemightproduceavarietyofoutcomes.Choosingamotorcycleratherthanabicycle,forexample,maymakethefuelsupplierhappy,theneighbours unhappy,theenvironmentmorepolluted,andtheowner'ssavingsaccountsmaller.But,to avoidunnecessarycomplications,weassumethatdecisionsarebasedonasinglecriterion formeasuringtherelativeattractivenessofthevariousalternatives.Ifnecessary,onecould deviseasinglecompositecriterionthatistheweightedaverageofseveraldifferentcriteria.
Tochoose thebestalternative,theoutcomesforeachalternativemustbestatedina comparableway.Usuallytheconsequencesofeachalternativearestatedintermsofmoney. Theconsequencescanbecategorizedasfollows:
• Marketconsequences-whereestablishedmarketpricesareavailable
• Extra-marketconsequences-nodirectmarketprices,sopricedindirectly
• Intangibleconsequences-valuedbyjudgment,notmonetaryprices
Inthefirstproblemsthatwewillexamine,thecostsandbenefitsoccuroverashort periodandcanbeconsideredtooccuratthesametime.Morecommonly,thevariouscosts andbenefitstakeplaceoveralongerperiod.Wewillrepresenttheseasacashflowdiagram toshowthetimingofthevariouscostsandbenefits.
For these longer-term problems, acommon mistake is to assume thatthe current situationwillbeunchangedifthedo-nothingalternativeischosen.Forexample,current profitsmayshrinkorvanishasaresultoftheactionsofcompetitorsandtheexpectations of customers.Asanotherexample,trafficjams normallyincreaseover theyearsasthe numberofvehiclesincreases.
8.ChoosetheBestAlternative
Earlierwesaidthatchoosingthebestalternativemaybesimplyamatterofdeterminingwhich bestmeetstheselectioncriterion.Butthesolutionstomostproblemsineconomicshavemarket consequences,extra-marketconsequences,andintangibleconsequences.Sincetheintangible consequencesofpossiblealternativesareleftoutofthenumericalcalculations,theyshouldbe introducedintothedecisionmakingatthispoint.Therightchoiceistheonethatbestmeets thecriteriaafterwehaveconsideredboththenumericalandintangibleconsequences.
Duringthedecisionmaking,certainfeasiblealternativesareeliminatedbecausethey aredominatedbyother,betteralternatives.Forexample,shoppingforacomputeronline mayallowyoutobuyacustom-configuredcomputerforlessmoneythanastockcomputer inalocalstore.Buyingatthelocalstoreisfeasible,butdominated.
Havingexaminedthestructureofthedecision-makingprocess,wecanask:When isthedecisionmade,andwhomakesit?Ifonepersonperformsallthestepsindecision making, thensheisthedecisionmaker. Whenshemakesthedecisionisless clear.The selectionofthefeasiblealternativesmaybethecrucialstep,withtherestoftheanalysisa methodicalprocessleadingtotheinevitabledecision.
9.AudittheResults
Anauditoftheresultsisacomparisonofwhathappenedagainstthepredictions.Dothe resultsofadecisionanalysisreasonablyagreewithitsprojections?Ifanewmachinetool waspurchasedto save labourandimprovequality, didit?Ifthesavingsarenotbeing obtained,whatwasoverlooked?Theauditmayhelpensurethattheprojectedoperating advantagesareultimatelyobtained.Ontheotherhand,theeconomicanalysisprojections mayhavebeenundulyoptimistic.Wewanttoknow this,too,sothatthemistakes that led to the inaccurate projectionarenot repeated. An effectiveway topromoterealistic economicanalysiscalculationsisforallpeopleinvolvedtoknowthattherewillbeanaudit oftheresults.
Ethics
Youmustbemindfuloftheethicaldimensionsofengineeringeconomicanalysisandof yourengineeringandpersonaldecisions.Thistextcanonlyintroducethetopic,whichwe hopeyouwillexploreingreaterdepth.
Ethicscanbedescribedasdistinguishingrightandwrongwhenmakingdecisions. Thismayinclude establishingsystemsof beliefs and moral obligations, definingvalues andfairness,anddeterminingdutiesandguidelinesforconduct.Ethicaldecisionmaking requiresan understanding ofthecontextoftheproblem, thepossiblechoices,and the outcomesofeachchoice.
Ethical Dimensions in Engineering Decision Making
Ethicalissuescanariseateverystageofthedecision-makingprocess.Ethicsissuchan importantpartofprofessionalandbusinessdecisionsthatethicalcodesorstandardsof conductexistforprofessionalengineeringsocietiesandsmallandlargeorganizations,to guideindividualandcorporatebehaviour.Writtenprofessionalcodesarecommoninthe engineeringprofession,wheretheyserveasareferencefornewengineersandabasisfor legalactionagainstengineerswhoviolatethecode.
In Canada, provincial and territorial associations of professional engineers are responsiblefor the regulation of the practice of engineering.Thefederationof theseorganizationsiscalledEngineersCanada.ThisistheEngineersCanadacode ofethics:
Registrants shall conduct themselves withintegrityandin anhonourableand ethicalmanner.Registrantsshallupholdthevaluesoftruth,honesty,andtrustworthinessandsafeguardhumanlifeandwelfareandtheenvironment.Inkeepingwiththesebasictenets,registrantsshall
1. holdparamountthesafety,health,andwelfareofthepublicandtheprotectionof theenvironment,andpromotehealthandsafetywithintheworkplace;
2. offerservices,adviseonorundertakeengineeringassignmentsonlyinareasof theircompetence,andpractiseinacarefulanddiligentmannerandincompliancewithapplicablelegislation;
3. act as faithful agents of their clients or employers, maintain confidentiality, andavoidconflictsofinterest,but,wheresuchconflictarises,fullydisclosethe circumstanceswithoutdelaytotheemployerorclient;
4. keepthemselvesinformedinordertomaintaintheircompetence,andadvance theirknowledgeinthefieldwithinwhichtheypractise;
5. conduct themselves with integrity, equity, fairness, courtesy, and good faith towardclients,colleagues,andothers,givecreditwhereitisdue,andaccept,as wellasgive,honestandfairprofessionalcriticism;
6. presentclearlytoemployersandclientsthepossibleconsequencesifengineering decisionsorjudgmentsareoverruledordisregarded;
7. reporttotheirassociationorotherappropriateagenciesanyillegalorunethical engineeringdecisionsorpracticesbyengineersorothers;
8. beawareofandensurethatclientsandemployersaremadeawareofsocietaland environmentalconsequencesofactionsor projects,andendeavour tointerpret engineeringissuestothepublicinanobjectiveandtruthfulmanner;
9. treatequitablyandpromotetheequitabletreatmentofpeopleandinaccordance withhumanrightslegislation;
10. upholdandenhancethehonouranddignityoftheprofession.(CCPE2012)
In addition, each provincial and territorial associationhasa code of ethicsforits members.Mostengineeringorganizationshavesimilarwrittenstandards.Forallengineers,difficultiesarisewhentheiractionsarecontrarytothesewrittenorinternalcodes.
The Environment We Live In
Thedecisionmakermustaskwhoincursthecostsfortheprojectandwhoreceivesthe benefits.Ethicalissuescanbe particularly difficultbecausethereareoftenstakeholders withopposingviewpoints,andsomeofthedatamaybeuncertainandhardtoquantify.
Thefollowingareexamplesofdifficultchoices:
• Protectingthehabitatofanendangeredspeciesversusflood-controlprojectsthat protectpeople,animals,andstructures
• Meeting the needfor electrical power when every means of generation causes someenvironmentaldamage:
• Hydroelectric-lossoflandandhabitattoreservoir
• Coal-dangertoworkersfromundergroundmining,damagetohabitatfrom open-pitmining,airpollutionfromburningthecoal,andanincreasedrate ofglobalwarmingbecauseofthereleaseofcarbondioxidetotheatmosphere.
• Nuclear-disposalofradioactivewaste
• Fueloil-airpollutionandeconomicdependenceonforeignsources
• Wind-visualpollutionofwindfarms, killingofbirdsandbatsbywhirling blades
• Determiningstandardsforpollutants:Is1partpermillionacceptable,oris1part perbillionnecessary?
Safety and Cost
Someofthemostcommonandmostdifficultethicaldilemmasinvolvetrade-offsbetween safetyandcost.Ifaproductis"toosafe,"itwillbetooexpensiveanditwillnotbeused. Andsometimesthecostisbornebyonepartyandtheriskbyanother.
• Should the oil platform be designed for the 100-year, SOO-year, or 1,000-year hurricane?
• Shouldtheautomanufactureraddrun-flat tires,stabilitycontrol, side-cushion airbags,andrear-seatairbagstoeverycar?
• Arestainlesssteelvalvesrequired,orisiteconomicallybettertouseless-corrosionresistantvalvesandreplacethemmoreoften?
EmergingIssuesand"Solutions"
BreachesofthelawbythecorporateleadersofEnron,Tyco,andotherfirmsledtoattempts bygovernmentstoprevent,limit,andexposefinancialwrongdoingwithincorporations. OnepartoftheAmericanresponsehasbeentheSarbanes-OxleyActof2002,whichimposedrequirementsonexecutivesandauditingfirms,andpenaltiesforviolations. Globalizationisanotherareaofincreasingimportanceforethicalconsiderations.One reasonisthatdifferentcountriesandregionshavedifferentethicalexpectations.Asecond reasonisthatjobsmaybemovedtoanothercountrybecauseofdifferencesincost,productivity,environmentalstandards,andsoon.WhatmayfromaCanadianperspective beasweatshopmayfromtheperspectiveofalessdevelopednationbeanopportunityto supportmanyfamilies.
Importanceof Ethics In Engineering and Engineering Economy
Frequently,thoughengineersandfirms trytoactethically,mistakesaremade-thedata werewrong, the designwaschanged, or the operatingenvironmentwasdifferent than expected.Butinothercases,suchastheChallengerlaunchdecision,achoicewasmadeto placeexpediencyaboveethics.Undersuchcircumstances,itistheengineers'dutytospeak out,withinandifnecessarybeyondtheircompany,toprotectthesafetyofthepublic. Often,recentengineeringgraduatesareasked,"Whatisthemostimportantthingyou wantfromyoursupervisor?"Themostcommonresponseismentoringandopportunities tolearnandprogress.When employeeswith5, 15,25, ormoreyearsofexperienceare askedthesamequestion,themostcommon responseisintegrity.Thisiswhatyoursubordinates,peers,andsuperiorswillexpectandvaluethemostfromyou.Integrityisthe foundationforlong-termcareersuccess.
Engineering Decision Making for Current Costs
Someoftheeasiestkindsofengineeringdecisionsdealwithproblemsofalternativedesigns, methods,or materials.If theresultsofthedecisionappearinaveryshorttime,onecan quicklyaddupthecostsandbenefitsforeachalternative.Then,byusingsuitableeconomic standards,onecanidentifythebestalternative.Threeexamplesillustratethesesituations.
EXAMPLE 1-2
Aconcreteaggregatemixmustcontainatleast31%sandbyvolumeforproperbatching.Onesourceof material,whichhas25%sandand75%coarseaggregate,sellsfor$3.00percubicmetre(m3). Another source,whichhas40%sandand60%coarseaggregate,sellsfor$4.40/m3 • Determinetheleastcostper cubicmetreofblendedaggregates.
SOLUTION
Theleastcostofblendedaggregateswillresultfrommaximumuseofthelower-costmaterial.Thehighercostmaterialwillbeusedtoincreasetheproportionofsanduptotheminimumlevel(31%)specified.
Letx=Portionofblendedaggregatesfrom$3.00/m3 source
1-x=Portionofblendedaggregatesfrom$4.40/m3 source
SandBalance
x (0.25) + (1 + x)(0.40) = 0.31
0.25x + 0.40 - 0.40x = 0.31
0.31 - 0.40 -0.09 x= 0.25 - 0.40 -0.15 =0.60
Thustheblendedaggregateswillcontain
60%of$3.00/m3material
40%of$4.40/m3 material
Theleastcostpercubicmetreofblendedaggregatesis 0.60($3.00) + 0.40($4.40) = 1.80 + 1.76 = $3.56/m3
EXAMPLE 1·3
Amachinepartismanufacturedataunitcostof404formaterialand15<1:fordirectlabour.Aninvestmentof$500,000intoolingisrequired.Theordercallsfor3millionpieces.Halfwaythroughtheorder, anewmethodofmanufacturecanbeputintoeffectthatwillreducetheunitcoststo344formaterial and10<1:fordirectlabour-butitwillrequire$100,000foradditionaltooling.Thistoolingwillnotbe usefulforfutureorders.Othercostsareallocatedat2.5timesthedirectlabourcost.What,ifanything, shouldbedone?
SOLUTION
Sincethereisonlyonewaytohandlethefirst1.5millionpieces,ourproblemconcernsonlythesecond halfoftheorder.
AlternativeA:ContinuewithPresentMethod
