ChapterOutline7.1IncrementalCashFlows7.2TheBaldwinCompany:AnExample7.3InflationandCapitalBudgeting7.4InvestmentsofUnequalLives:TheEquivalentAnnualCostMethod7.5SummaryandConclusionsChapterOutline7.1Incremental7.1IncrementalCashFlowsCashflowsmatter—notaccountingearnings.Sunkcostsdon’tmatter.Incrementalcashflowsmatter.Opportunitycostsmatter.Sideeffectslikecannibalismanderosionmatter.Taxesmatter:wewantincrementalafter-taxcashflows.Inflationmatters.7.1IncrementalCashFlowsCashCashFlows—NotAccountingEarnings.Considerdepreciationexpense.Youneverwriteacheckmadeoutto“depreciation”.Muchoftheworkinevaluatingaprojectliesintakingaccountingnumbersandgeneratingcashflows.CashFlows—NotAccountingEarnIncrementalCashFlowsSunkcostsarenotrelevantJustbecause“wehavecomethisfar”doesnotmeanthatweshouldcontinuetothrowgoodmoneyafterbad.Opportunitycostsdomatter.JustbecauseaprojecthasapositiveNPVthatdoesnotmeanthatitshouldalsohaveautomaticacceptance.SpecificallyifanotherprojectwithahigherNPVwouldhavetobepassedupweshouldnotproceed.Sideeffectsmatter.Erosionandcannibalismarebothbadthings.Ifournewproductcausesexistingcustomerstodemandlessofcurrentproducts,weneedtorecognizethat.IncrementalCashFlowsSunkcosEstimatingCashFlowsCashFlowsfromOperationsRecallthat:OperatingCashFlow=EBIT–Taxes+DepreciationNetCapitalSpendingDon’tforgetsalvagevalue(aftertax,ofcourse).ChangesinNetWorkingCapitalRecallthatwhentheprojectwindsdown,weenjoyareturnofnetworkingcapital.EstimatingCashFlowsCashFlowInterestExpenseLaterchapterswilldealwiththeimpactthattheamountofdebtthatafirmhasinitscapitalstructurehasonfirmvalue.Fornow,it’senoughtoassumethatthefirm’slevelofdebt(henceinterestexpense)isindependentoftheprojectathand.InterestExpenseLaterchapters7.2TheBaldwinCompany:AnExample

Costsoftestmarketing(alreadyspent):$250,000. Currentmarketvalueofproposedfactorysite(whichweown):$150,000. Costofbowlingballmachine:$100,000(depreciatedaccordingtoACRS5-yearlife). Increaseinnetworkingcapital:$10,000. Production(inunits)byyearduring5-yearlifeofthemachine:5,000,8,000,12,000,10,000,6,000. Priceduringfirstyearis$20;priceincreases2%peryearthereafter. Productioncostsduringfirstyearare$10perunitandincrease10%peryearthereafter. Annualinflationrate:5% WorkingCapital:initially$10,000changeswithsales.7.2TheBaldwinCompany:AnExTheWorksheetforCashFlowsoftheBaldwinCompany

Year0 Year1 Year2 Year3 Year4Year5Investments:(1) Bowlingballmachine –100.00 21.76*(2) Accumulated 20.00 52.00 71.20 82.7294.24depreciation(3) Adjustedbasisof 80.00 48.00 28.80 17.285.76machineafter

depreciation(endofyear)(4) Opportunitycost –150.00 150.00

(warehouse)(5) Networkingcapital 10.00 10.00 16.32 24.97 21.22 0(endofyear)(6) Changeinnet –10.00 –6.32 –8.65 3.7521.22workingcapital(7) Totalcashflowof –260.00 –6.32 –8.65 3.75192.98investment

[(1)+(4)+(6)]*Weassumethattheendingmarketvalueofthecapitalinvestmentatyear5is$30,000.Capitalgainisthedifferencebetweenendingmarketvalueandadjustedbasisofthemachine.Theadjustedbasisistheoriginalpurchasepriceofthemachinelessdepreciation.Thecapitalgainis$24,240(=$30,000–$5,760).WewillassumetheincrementalcorporatetaxforBaldwinonthisprojectis34percent.Capitalgainsarenowtaxedattheordinaryincomerate,sothecapitalgainstaxdueis$8,240[0.34($30,000–$5,760)].Theafter-taxsalvagevalueis$30,000–[0.34($30,000–$5,760)]=21,760.($thousands)(Allcashflowsoccurattheendoftheyear.)TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompanyAttheendoftheproject,thewarehouseisunencumbered,sowecansellitifwewantto.($thousands)(Allcashflowsoccurattheendoftheyear.)

Year0 Year1 Year2 Year3 Year4Year5Investments:(1) Bowlingballmachine –100.00 21.76*(2) Accumulated 20.00 52.00 71.20 82.7294.24depreciation(3) Adjustedbasisof 80.00 48.00 28.80 17.285.76machineafter

depreciation(endofyear)(4) Opportunitycost –150.00 150.00

(warehouse)(5) Networkingcapital 10.00 10.00 16.32 24.97 21.22 0(endofyear)(6) Changeinnet –10.00 –6.32 –8.65 3.7521.22workingcapital(7) Totalcashflowof –260.00 –6.32 –8.65 3.75192.98investment

[(1)+(4)+(6)]TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompany(continued)

Year0 Year1 Year2 Year3 Year4Year5Income:(8)SalesRevenues 100.00 163.00 249.72 212.20129.90

($thousands)(Allcashflowsoccurattheendoftheyear.)Recallthatproduction(inunits)byyearduring5-yearlifeofthemachineisgivenby:(5,000,8,000,12,000,10,000,6,000).Priceduringfirstyearis$20andincreases2%peryearthereafter.Salesrevenueinyear3=12,000×[$20×(1.02)2]=12,000×$20.81=$249,720.TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompany(continued)

Year0 Year1 Year2 Year3 Year4Year5Income:(8)SalesRevenues 100.00 163.00 249.72 212.20129.90(9) Operatingcosts 50.00 88.00 145.20133.1087.84

($thousands)(Allcashflowsoccurattheendoftheyear.)Again,production(inunits)byyearduring5-yearlifeofthemachineisgivenby:(5,000,8,000,12,000,10,000,6,000).Productioncostsduringfirstyear(perunit)are$10and(increase10%peryearthereafter).Productioncostsinyear2=8,000×[$10×(1.10)1]=$88,000TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompany(continued)

Year0 Year1 Year2 Year3 Year4Year5Income:(8)SalesRevenues 100.00 163.00 249.72 212.20129.90(9) Operatingcosts 50.00 88.00 145.20133.1087.84(10) Depreciation 20.00 32.00 19.20 11.5211.52($thousands)(Allcashflowsoccurattheendoftheyear.)DepreciationiscalculatedusingtheAcceleratedCostRecoverySystem(shownatright)Ourcostbasisis$100,000Depreciationchargeinyear4=$100,000×(.1152)=$11,520.Year ACRS% 1 20.00% 2 32.00% 3 19.20% 4 11.52% 5 11.52% 6 5.76% Total 100.00% TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompany(continued)

Year0 Year1 Year2 Year3 Year4Year5Income:(8)SalesRevenues 100.00 163.00 249.72 212.20129.90(9) Operatingcosts 50.00 88.00 145.20133.1087.84(10) Depreciation 20.00 32.00 19.20 11.5211.52(11) Incomebeforetaxes 30.00 43.20 85.32 67.5830.54

[(8)–(9)-(10)](12) Taxat34percent 10.20 14.69 29.01 22.9810.38(13)NetIncome 19.80 28.51 56.31 44.6020.16

($thousands)(Allcashflowsoccurattheendoftheyear.)TheWorksheetforCashFlowsoIncrementalAfterTaxCashFlows

oftheBaldwinCompany

Year0Year1Year2Year3Year4Year5(1)SalesRevenues

$100.00$163.00$249.72$212.20$129.90(2)Operatingcosts

-50.00-88.00-145.20133.10-87.84(3)Taxes

-10.20-14.69-29.01-22.98-10.38(4)OCF(1)–(2)-(3)

39.8060.5175.5156.1231.68(5)TotalCFofInvestment–260.

–6.32–8.653.75192.98(6)IATCF[(4)+(5)]–260.39.8054.1966.8659.87224.66IncrementalAfterTaxCashFlo7.3InflationandCapitalBudgetingInflationisanimportantfactofeconomiclifeandmustbeconsideredincapitalbudgeting.Considertherelationshipbetweeninterestratesandinflation,oftenreferredtoastheFisherrelationship:(1+NominalRate)=(1+RealRate)×(1+InflationRate)Forlowratesofinflation,thisisoftenapproximatedasRealRateNominalRate–InflationRateWhilethenominalrateintheU.S.hasfluctuatedwithinflation,mostofthetimetherealratehasexhibitedfarlessvariancethanthenominalrate.Whenaccountingforinflationincapitalbudgeting,onemustcomparerealcashflowsdiscountedatrealratesornominalcashflowsdiscountedatnominalrates.7.3InflationandCapitalBudgExampleofCapitalBudgetingunderInflation

SonyInternationalhasaninvestmentopportunitytoproduceanewstereocolorTV.TherequiredinvestmentonJanuary1ofthisyearis$32million.Thefirmwilldepreciatetheinvestmenttozerousingthestraight-linemethod.Thefirmisinthe34%taxbracket.ThepriceoftheproductonJanuary1willbe$400perunit.Thepricewillstayconstantinrealterms.Laborcostswillbe$15perhouronJanuary1.Thewillincreaseat2%peryearinrealterms.Energycostswillbe$5perTV;theywillincrease3%peryearinrealterms.Theinflationrateis5%Revenuesarereceivedandcostsarepaidatyear-end.ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflationTherisklessnominaldiscountrateis4%.Therealdiscountrateforcostsandrevenuesis8%.CalculatetheNPV.

Year1Year2Year3Year4PhysicalProduction(units)100,000200,000200,000150,000LaborInput(hours)2,000,0002,000,0002,000,0002,000,000Energyinput,physicalunits200,000200,000200,000200,000ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflationThedepreciationtaxshieldisarisk-freenominalcashflow,andisthereforediscountedatthenominalrisklessrate.Costofinvestmenttoday=$32,000,000Projectlife=4yearsAnnualdepreciationexpense:Depreciationtaxshield=$8,000,000×.34=$2,720,000ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflationRiskyRealCashFlowsPrice:$400perunitwithzerorealpriceincreaseLabor:$15perhourwith2%realwageincreaseEnergy:$5perunitwith3%realenergycostincreaseYear1After-taxRealRiskyCashFlows:After-taxrevenues=$400×100,000×(1-.34)=$26,400,000After-taxlaborcosts=$15×2,000,000×1.02×(1-.34)=$20,196,000After-taxenergycosts=$5×2,00,000×1.03×(1-.34)=$679,800After-taxnetoperatingCF=$26,400,000-$20,196,000-$679,800=$5,524,200ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflation$5,524,200

$31,499,886 $31,066,882 $17,425,007-$32,000,0000 1 2 3 4YearOneAfter-taxrevenues=$400×100,000×(1-.34)=$26,400,000YearOneAfter-taxlaborcosts=$15×2,000,000×1.02×(1-.34)=$20,196,000YearOneAfter-taxenergycosts=$5×2,00,000×1.03×(1-.34)=$679,800YearOneAfter-taxnetoperatingCF=$5,524,200ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflation

TheprojectNPVcannowbecomputedasthesumofthePVofthecost,thePVoftheriskycashflowsdiscountedattheriskyrateandthePVoftherisk-freecashflowsdiscountedattherisk-freediscountrate.NPV=-$32,000,000+$69,590,868+$9,873,315=$47,464,183ExampleofCapitalBudgetinguInvestmentsofUnequalLivesTheEquivalentAnnualCostMethodReplacementChainRepeattheprojectsforever,findthePVofthatperpetuity.Assumption:Bothprojectscanandwillberepeated.MatchingCycleRepeatprojectsuntiltheybeginandendatthesametime—likewejustdidwiththeaircleaners.ComputeNPVforthe“repeatedprojects”.InvestmentsofUnequalLivesTh7.4InvestmentsofUnequalLives:TheEquivalentAnnualCostMethodTherearetimeswhenapplicationoftheNPVrulecanleadtothewrongdecision.Considerafactorywhichmusthaveanaircleaner.Theequipmentismandatedbylaw,sothereisno“doingwithout”.Therearetwochoices:The“Cadillaccleaner”costs$4,000today,hasannualoperatingcostsof$100andlastsfor10years.The“cheapercleaner”costs$1,000today,hasannualoperatingcostsof$500andlastsfor5years.Whichoneshouldwechoose?7.4InvestmentsofUnequalLiv7.4InvestmentsofUnequalLives:TheEquivalentAnnualCostMethodAtfirstglance,thecheapcleanerhasthelowerNPV(r=10%):ThisoverlooksthefactthattheCadillaccleanerlaststwiceaslong.Whenweincorporatethat,theCadillaccleanerisactuallycheaper.7.4InvestmentsofUnequalLiv7.4InvestmentsofUnequalLives:TheEquivalentAnnualCostMethodTheCadillaccleanertimelineofcashflows:-$4,000–100-100-100-100-100-100-100-100-100-100012345678910-$1,000–500-500-500-500-1,500-500-500-500-500-500012345678910The“cheapercleaner”timelineofcashflowsovertenyears:7.4InvestmentsofUnequalLivInvestmentsofUnequalLives:EACTheEquivalentAnnualCostMethodApplicabletoamuchmorerobustsetofcircumstancesthanreplacementchainormatchingcycle.TheEquivalentAnnualCostisthevalueofthelevelpaymentannuitythathasthesamePVasouroriginalsetofcashflows.NPV=EAC×ArTForexample,theEACfortheCadillacaircleaneris$750.98

TheEACforthecheaperaircleaneris$763.80whichconfirmsourearlierdecisiontorejectit.InvestmentsofUnequalLives:ExampleofReplacementProjectsConsideraBelgianDentist’soffice;heneedsanautoclavetosterilizehisinstruments.Hehasanoldonethatisinuse,butthemaintenancecostsarerisingandsoisconsideringreplacingthisindispensablepieceofequipment.NewAutoclaveCost=$3,000today,Maintenancecost=$20peryearResalevalueafter6years=$1,200NPVofnewautoclave(atr=10%):

EACofnewautoclave=-$553.29ExampleofReplacementProjectExampleofReplacementProjectsExistingAutoclaveYear 0 1 2 3 4 5Maintenance 0 200 275 325 450 500Resale 900 850 775 700 600 500TotalAnnualCost TotalCostforyear1=(900×1.10–850)+200=$340340435TotalCostforyear2=(850×1.10–775)+275=$435478TotalCostforyear3=(775×1.10–700)+325=$478620TotalCostforyear4=(700×1.10–600)+450=$620TotalCostforyear5=(600×1.10–500)+500=$660660Notethatthetotalcostofkeepinganautoclaveforthefirstyearincludesthe$200maintenancecostaswellastheopportunitycostoftheforegonefuturevalueofthe$900wedidn’tgetfromsellingitinyear0lessthe$850wehaveifwestillownitatyear1.ExampleofReplacementProjectExampleofReplacementProjects340435478620660NewAutoclaveEACofnewautoclave=-$553.29ExistingAutoclaveYear 0 1 2 3 4 5Maintenance 0 200 275 325 450 500Resale 900 850 775 700 600 500TotalAnnualCost Weshouldkeeptheoldautoclaveuntilit’scheapertobuyanewone.Replacetheautoclaveafteryear3:atthatpointthenewonewillcost$553.29forthenextyear’sautoclavingandtheoldonewillcost$620foronemoreyear.ExampleofReplacementProject7.5SummaryandConclusionsCapitalbudgetingmustbeplacedonanincrementalbasis.SunkcostsareignoredOpportunitycostsandsideeffectsmatterInflationmustbehandledconsistentlyDiscountrealflowsatrealratesDiscountnominalflowsatnominalrates.Whenafirmmustchoosebetweentwomachinesofunequallives:thefirmcanapplyeitherthematchingcycleapproachortheequivalentannualcostapproach.7.5SummaryandConclusionsCapChapterOutline7.1IncrementalCashFlows7.2TheBaldwinCompany:AnExample7.3InflationandCapitalBudgeting7.4InvestmentsofUnequalLives:TheEquivalentAnnualCostMethod7.5SummaryandConclusionsChapterOutline7.1Incremental7.1IncrementalCashFlowsCashflowsmatter—notaccountingearnings.Sunkcostsdon’tmatter.Incrementalcashflowsmatter.Opportunitycostsmatter.Sideeffectslikecannibalismanderosionmatter.Taxesmatter:wewantincrementalafter-taxcashflows.Inflationmatters.7.1IncrementalCashFlowsCashCashFlows—NotAccountingEarnings.Considerdepreciationexpense.Youneverwriteacheckmadeoutto“depreciation”.Muchoftheworkinevaluatingaprojectliesintakingaccountingnumbersandgeneratingcashflows.CashFlows—NotAccountingEarnIncrementalCashFlowsSunkcostsarenotrelevantJustbecause“wehavecomethisfar”doesnotmeanthatweshouldcontinuetothrowgoodmoneyafterbad.Opportunitycostsdomatter.JustbecauseaprojecthasapositiveNPVthatdoesnotmeanthatitshouldalsohaveautomaticacceptance.SpecificallyifanotherprojectwithahigherNPVwouldhavetobepassedupweshouldnotproceed.Sideeffectsmatter.Erosionandcannibalismarebothbadthings.Ifournewproductcausesexistingcustomerstodemandlessofcurrentproducts,weneedtorecognizethat.IncrementalCashFlowsSunkcosEstimatingCashFlowsCashFlowsfromOperationsRecallthat:OperatingCashFlow=EBIT–Taxes+DepreciationNetCapitalSpendingDon’tforgetsalvagevalue(aftertax,ofcourse).ChangesinNetWorkingCapitalRecallthatwhentheprojectwindsdown,weenjoyareturnofnetworkingcapital.EstimatingCashFlowsCashFlowInterestExpenseLaterchapterswilldealwiththeimpactthattheamountofdebtthatafirmhasinitscapitalstructurehasonfirmvalue.Fornow,it’senoughtoassumethatthefirm’slevelofdebt(henceinterestexpense)isindependentoftheprojectathand.InterestExpenseLaterchapters7.2TheBaldwinCompany:AnExample

Costsoftestmarketing(alreadyspent):$250,000. Currentmarketvalueofproposedfactorysite(whichweown):$150,000. Costofbowlingballmachine:$100,000(depreciatedaccordingtoACRS5-yearlife). Increaseinnetworkingcapital:$10,000. Production(inunits)byyearduring5-yearlifeofthemachine:5,000,8,000,12,000,10,000,6,000. Priceduringfirstyearis$20;priceincreases2%peryearthereafter. Productioncostsduringfirstyearare$10perunitandincrease10%peryearthereafter. Annualinflationrate:5% WorkingCapital:initially$10,000changeswithsales.7.2TheBaldwinCompany:AnExTheWorksheetforCashFlowsoftheBaldwinCompany

Year0 Year1 Year2 Year3 Year4Year5Investments:(1) Bowlingballmachine –100.00 21.76*(2) Accumulated 20.00 52.00 71.20 82.7294.24depreciation(3) Adjustedbasisof 80.00 48.00 28.80 17.285.76machineafter

depreciation(endofyear)(4) Opportunitycost –150.00 150.00

(warehouse)(5) Networkingcapital 10.00 10.00 16.32 24.97 21.22 0(endofyear)(6) Changeinnet –10.00 –6.32 –8.65 3.7521.22workingcapital(7) Totalcashflowof –260.00 –6.32 –8.65 3.75192.98investment

[(1)+(4)+(6)]*Weassumethattheendingmarketvalueofthecapitalinvestmentatyear5is$30,000.Capitalgainisthedifferencebetweenendingmarketvalueandadjustedbasisofthemachine.Theadjustedbasisistheoriginalpurchasepriceofthemachinelessdepreciation.Thecapitalgainis$24,240(=$30,000–$5,760).WewillassumetheincrementalcorporatetaxforBaldwinonthisprojectis34percent.Capitalgainsarenowtaxedattheordinaryincomerate,sothecapitalgainstaxdueis$8,240[0.34($30,000–$5,760)].Theafter-taxsalvagevalueis$30,000–[0.34($30,000–$5,760)]=21,760.($thousands)(Allcashflowsoccurattheendoftheyear.)TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompanyAttheendoftheproject,thewarehouseisunencumbered,sowecansellitifwewantto.($thousands)(Allcashflowsoccurattheendoftheyear.)

Year0 Year1 Year2 Year3 Year4Year5Investments:(1) Bowlingballmachine –100.00 21.76*(2) Accumulated 20.00 52.00 71.20 82.7294.24depreciation(3) Adjustedbasisof 80.00 48.00 28.80 17.285.76machineafter

depreciation(endofyear)(4) Opportunitycost –150.00 150.00

(warehouse)(5) Networkingcapital 10.00 10.00 16.32 24.97 21.22 0(endofyear)(6) Changeinnet –10.00 –6.32 –8.65 3.7521.22workingcapital(7) Totalcashflowof –260.00 –6.32 –8.65 3.75192.98investment

[(1)+(4)+(6)]TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompany(continued)

Year0 Year1 Year2 Year3 Year4Year5Income:(8)SalesRevenues 100.00 163.00 249.72 212.20129.90

($thousands)(Allcashflowsoccurattheendoftheyear.)Recallthatproduction(inunits)byyearduring5-yearlifeofthemachineisgivenby:(5,000,8,000,12,000,10,000,6,000).Priceduringfirstyearis$20andincreases2%peryearthereafter.Salesrevenueinyear3=12,000×[$20×(1.02)2]=12,000×$20.81=$249,720.TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompany(continued)

Year0 Year1 Year2 Year3 Year4Year5Income:(8)SalesRevenues 100.00 163.00 249.72 212.20129.90(9) Operatingcosts 50.00 88.00 145.20133.1087.84

($thousands)(Allcashflowsoccurattheendoftheyear.)Again,production(inunits)byyearduring5-yearlifeofthemachineisgivenby:(5,000,8,000,12,000,10,000,6,000).Productioncostsduringfirstyear(perunit)are$10and(increase10%peryearthereafter).Productioncostsinyear2=8,000×[$10×(1.10)1]=$88,000TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompany(continued)

Year0 Year1 Year2 Year3 Year4Year5Income:(8)SalesRevenues 100.00 163.00 249.72 212.20129.90(9) Operatingcosts 50.00 88.00 145.20133.1087.84(10) Depreciation 20.00 32.00 19.20 11.5211.52($thousands)(Allcashflowsoccurattheendoftheyear.)DepreciationiscalculatedusingtheAcceleratedCostRecoverySystem(shownatright)Ourcostbasisis$100,000Depreciationchargeinyear4=$100,000×(.1152)=$11,520.Year ACRS% 1 20.00% 2 32.00% 3 19.20% 4 11.52% 5 11.52% 6 5.76% Total 100.00% TheWorksheetforCashFlowsoTheWorksheetforCashFlowsoftheBaldwinCompany(continued)

Year0 Year1 Year2 Year3 Year4Year5Income:(8)SalesRevenues 100.00 163.00 249.72 212.20129.90(9) Operatingcosts 50.00 88.00 145.20133.1087.84(10) Depreciation 20.00 32.00 19.20 11.5211.52(11) Incomebeforetaxes 30.00 43.20 85.32 67.5830.54

[(8)–(9)-(10)](12) Taxat34percent 10.20 14.69 29.01 22.9810.38(13)NetIncome 19.80 28.51 56.31 44.6020.16

($thousands)(Allcashflowsoccurattheendoftheyear.)TheWorksheetforCashFlowsoIncrementalAfterTaxCashFlows

oftheBaldwinCompany

Year0Year1Year2Year3Year4Year5(1)SalesRevenues

$100.00$163.00$249.72$212.20$129.90(2)Operatingcosts

-50.00-88.00-145.20133.10-87.84(3)Taxes

-10.20-14.69-29.01-22.98-10.38(4)OCF(1)–(2)-(3)

39.8060.5175.5156.1231.68(5)TotalCFofInvestment–260.

–6.32–8.653.75192.98(6)IATCF[(4)+(5)]–260.39.8054.1966.8659.87224.66IncrementalAfterTaxCashFlo7.3InflationandCapitalBudgetingInflationisanimportantfactofeconomiclifeandmustbeconsideredincapitalbudgeting.Considertherelationshipbetweeninterestratesandinflation,oftenreferredtoastheFisherrelationship:(1+NominalRate)=(1+RealRate)×(1+InflationRate)Forlowratesofinflation,thisisoftenapproximatedasRealRateNominalRate–InflationRateWhilethenominalrateintheU.S.hasfluctuatedwithinflation,mostofthetimetherealratehasexhibitedfarlessvariancethanthenominalrate.Whenaccountingforinflationincapitalbudgeting,onemustcomparerealcashflowsdiscountedatrealratesornominalcashflowsdiscountedatnominalrates.7.3InflationandCapitalBudgExampleofCapitalBudgetingunderInflation

SonyInternationalhasaninvestmentopportunitytoproduceanewstereocolorTV.TherequiredinvestmentonJanuary1ofthisyearis$32million.Thefirmwilldepreciatetheinvestmenttozerousingthestraight-linemethod.Thefirmisinthe34%taxbracket.ThepriceoftheproductonJanuary1willbe$400perunit.Thepricewillstayconstantinrealterms.Laborcostswillbe$15perhouronJanuary1.Thewillincreaseat2%peryearinrealterms.Energycostswillbe$5perTV;theywillincrease3%peryearinrealterms.Theinflationrateis5%Revenuesarereceivedandcostsarepaidatyear-end.ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflationTherisklessnominaldiscountrateis4%.Therealdiscountrateforcostsandrevenuesis8%.CalculatetheNPV.

Year1Year2Year3Year4PhysicalProduction(units)100,000200,000200,000150,000LaborInput(hours)2,000,0002,000,0002,000,0002,000,000Energyinput,physicalunits200,000200,000200,000200,000ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflationThedepreciationtaxshieldisarisk-freenominalcashflow,andisthereforediscountedatthenominalrisklessrate.Costofinvestmenttoday=$32,000,000Projectlife=4yearsAnnualdepreciationexpense:Depreciationtaxshield=$8,000,000×.34=$2,720,000ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflationRiskyRealCashFlowsPrice:$400perunitwithzerorealpriceincreaseLabor:$15perhourwith2%realwageincreaseEnergy:$5perunitwith3%realenergycostincreaseYear1After-taxRealRiskyCashFlows:After-taxrevenues=$400×100,000×(1-.34)=$26,400,000After-taxlaborcosts=$15×2,000,000×1.02×(1-.34)=$20,196,000After-taxenergycosts=$5×2,00,000×1.03×(1-.34)=$679,800After-taxnetoperatingCF=$26,400,000-$20,196,000-$679,800=$5,524,200ExampleofCapitalBudgetinguExampleofCapitalBudgetingunderInflation$5,524,200

$31,499,886 $31,066,882 $17,425,007-$32,000,0000 1 2 3 4YearOneAfter-taxrevenues=$400×100,000×(