羅斯公司理財Chpt07

CorporateFinance

Ross

Westerfield

JaffeSixthEditionSixthEdition7ChapterSevenNetPresentValueandCapitalBudgetingChapterOutline7.1IncrementalCashFlows7.2TheBaldwinCompany:AnExample7.3InflationandCapitalBudgeting7.4InvestmentsofUnequalLives:TheEquivalentAnnualCostMethod7.5SummaryandConclusions7.1IncrementalCashFlowsCashflowsmatter—notaccountingearnings.Sunkcostsdon’tmatter.Incrementalcashflowsmatter.Opportunitycostsmatter.Sideeffectslikecannibalismanderosionmatter.Taxesmatter:wewantincrementalafter-taxcashflows.Inflationmatters.CashFlows—NotAccountingEarnings.Considerdepreciationexpense.Youneverwriteacheckmadeoutto“depreciation”.Muchoftheworkinevaluatingaprojectliesintakingaccountingnumbersandgeneratingcashflows.IncrementalCashFlowsSunkcostsarenotrelevantJustbecause“wehavecomethisfar”doesnotmeanthatweshouldcontinuetothrowgoodmoneyafterbad.Opportunitycostsdomatter.JustbecauseaprojecthasapositiveNPVthatdoesnotmeanthatitshouldalsohaveautomaticacceptance.SpecificallyifanotherprojectwithahigherNPVwouldhavetobepassedupweshouldnotproceed.Sideeffectsmatter.Erosionandcannibalismarebothbadthings.Ifournewproductcausesexistingcustomerstodemandlessofcurrentproducts,weneedtorecognizethat.EstimatingCashFlowsCashFlowsfromOperationsRecallthat:OperatingCashFlow=NetIncome+DepreciationNetCapitalSpendingDon’tforgetsalvagevalue(aftertax,ofcourse).ChangesinNetWorkingCapitalRecallthatwhentheprojectwindsdown,weenjoyareturnofnetworkingcapital.InterestExpenseLaterchapterswilldealwiththeimpactthattheamountofdebtthatafirmhasinitscapitalstructurehasonfirmvalue.Fornow,it’senoughtoassumethatthefirm’slevelofdebt(henceinterestexpense)isindependentoftheprojectathand.7.2TheBaldwinCompany: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.TheWorksheetforCashFlowsoftheBaldwinCompany

Year0 Year1 Year2 Year3 Year4Year5Investments:(1) Bowlingballmachine –100.00 21.76*(2) Accumulated 20.00 52.00 71.20 82.7294.24depreciation(3) Adjustedbasisof 80.0048.00 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.)TheWorksheetforCashFlowsoftheBaldwinCompanyAttheendoftheproject,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)]TheWorksheetforCashFlowsoftheBaldwinCompany(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.TheWorksheetforCashFlowsoftheBaldwinCompany(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]=$88,000TheWorksheetforCashFlowsoftheBaldwinCompany(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% 5.76% Total 100.00% TheWorksheetforCashFlowsoftheBaldwinCompany(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.)IncrementalAfterTaxCashFlows

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)TotalCFOfproject[(4)+(5)]–260.39.8054.1966.8659.87224.667.3InflationandCapitalBudgetingInflationisanimportantfactofeconomiclifeandmustbeconsideredincapitalbudgeting.Considertherelationshipbetweeninterestratesandinflation,oftenreferredtoastherelationship:(1+NominalRate)=(1+RealRate)×(1+InflationRate)Forlowratesofinflation,thisisoftenapproximatedasRealRateNominalRate–InflationRateWhilethenominalrateintheU.S.hasfluctuatedwithinflation,mostofthetimetherealratehasexhibitedfarlessvariancethanthenominalrate.Whenaccountingforinflationincapitalbudgeting,onemustcomparerealcashflowsdiscountedatrealratesornominalcashflowsdiscountedatnominalrates.ExampleofCapitalBudgetingunderInflation

SonyInternationalhasaninvestmentopportunitytoproduceanewstereocolorTV.TherequiredinvestmentonJanuary1ofthisyearis$32million.Thefirmwilldepreciatetheinvestmenttozerousingthestraight-linemethod.Thefirmisinthe34%taxbracket.ThepriceoftheproductonJanuary1willbe$400perunit.Thepricewillstayconstantinrealterms.Laborcostswillbe$15perhouronJanuary1.Thewillincreaseat2%peryearinrealterms.Energycostswillbe$5perunit;theywillincrease3%peryearinrealterms.Theinflationrateis5%Revenuesarereceivedandcostsarepaidatyear-end.ExampleofCapitalBudgetingunderInflationTherisklessnominaldiscountrateis4%.Therealdiscountrateforcostsandrevenuesis8%.CalculatetheNPV.

Year1Year2Year3Year4PhysicalProduction(units)100,000200,000200,000150,000LaborInput(hours)2,000,0002,000,0002,000,0002,000,000Energyinput,physicalunits200,000200,000200,000200,000ExampleofCapitalBudgetingunderInflationThedepreciationtaxshieldisarisk-freenominalcashflow,andisthereforediscountedatthenominalrisklessrate.Costofinvestmenttoday=$32,000,000Projectlife=4yearsAnnualdepreciationexpense:Depreciationtaxshield=$8,000,000×.34=$2,720,000ExampleofCapitalBudgetingunderInflationRiskyRealCashFlowsPrice:$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=$5,524,200ExampleofCapitalBudgetingunderInflation$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=$5,524,200ExampleofCapitalBudgetingunderInflation

TheprojectNPVcannowbecomputedasthesumofthePVofthecost,thePVoftheriskycashflowsdiscountedattheriskyrateandthePVoftherisk-freecashflowsdiscountedattherisk-freediscountrate.NPV=-$32,000,000+$69,590,868+$9,873,315=$47,464,1837.4InvestmentsofUnequalLives:TheEquivalentAnnualCostMethodTherearetimeswhenapplicationoftheNPVrulecanleadtothewrongdecision.Considerafactorywhichmusthaveanaircleaner.Theequipmentismandatedbylaw,sothereisno“doingwithout”.Therearetwochoices:The“Cadillaccleaner”costs$4,000today,hasannualoperatingcostsof$100andlastsfor10years.The“cheapercleaner”costs$1,000today,hasannualoperatingcostsof$500andlastsfor5years.Whichoneshouldwechoose?7.4InvestmentsofUnequalLives:TheEquivalentAnnualCostMethodAtfirstglance,thecheapcleanerhasthelowerNPV(r=10%):ThisoverlooksthefactthattheCadillaccleanerlaststwiceaslong.Whenweincorporatethat,theCadillaccleanerisactuallycheaper.7.4InvestmentsofUnequalLives: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:InvestmentsofUnequalLivesReplacementChainAssumption:Bothprojectscanandwillberepeated.MatchingCycleRepeatprojectsuntiltheybeginandendatthesametime—likewejustdidwiththeaircleaners.ComputeNPVforthe“repeatedprojects”.TheEquivalentAnnualCostMethodInvestmentsofUnequalLives:EACTheEquivalentAnnualCostMethodTheEquivalentAnnualCostisthevalueofthelevelpaymentannuitythathasthesameNPVasouroriginalsetofcashflows.NPV=EAC×ArTForexample,theEACfortheCadillacaircleaneris$750.98

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

EACofnewautoclave=-$553.29ExampleofReplacementProjectsExistingAutoclaveYear 0 1 2 3 4 5Maintenance 0 200 275 325 450 500Resale 900 850