CHAPTER13OtherTopicsinCapitalBudgeting EvaluatingprojectswithunequallivesEvaluatingprojectswithembeddedoptionsValuingrealoptionsinprojects SandLaremutuallyexclusiveandwillberepeated k 10 Whichisbetter ExpectedNetCFs Year ProjectS ProjectL 0 100 000 100 000 1 59 000 33 500 2 59 000 33 500 3 33 500 4 33 500 S L CF0 100 000 100 000 CF1 59 000 33 500 Nj 2 4 I 10 10 NPV 2 397 6 190 Q NPVL NPVS IsLbetter A Can tsay Needreplacementchainanalysis NotethatProjectScouldberepeatedafter2yearstogenerateadditionalprofits UsereplacementchaintocalculateextendedNPVStoacommonlife SinceShasa2 yearlifeandLhasa4 yearlife thecommonlifeis4years L S 0 1 2 3 10 33 500 4 0 1 2 3 10 59 000 4 33 500 33 500 33 500 100 000 59 000 59 000 59 000 100 000 NPVL 6 190 alreadytoYear4 NPVS 4 377 onextendedbasis 100 000 41 000 Whatisrealoptionanalysis Realoptionsexistwhenmanagerscaninfluencethesizeandriskinessofaproject scashflowsbytakingdifferentactionsduringtheproject slife RealoptionanalysisincorporatestypicalNPVbudgetinganalysiswithananalysisforopportunitiesresultingfrommanagers decisions Whataresomeexamplesofrealoptions InvestmenttimingoptionsAbandonment shutdownoptionsGrowth expansionoptionsFlexibilityoptions AnIllustrationofInvestmentTimingOptions IfweproceedwithProjectL itsNPVis 6 190 Recalltheup frontcostwas 100 000andthesubsequentCFswere 33 500ayearforfouryears However ifwewaitoneyear wewillfindoutsomeadditionalinformationregardingoutputpricesandthecashflowsfromProjectL InvestmentTiming Continued Ifwewait thereisa50 chancethesubsequentCFswillbe 43 500ayear anda50 chancethesubsequentCFswillbe 23 500ayear Ifwewait theup frontcostwillremainat 100 000 InvestmentTimingDecisionTree 50 prob 50 prob 012345 Years 100 00043 50043 50043 50043 500 100 00023 50023 50023 50023 500 Atk 10 theNPVatt 1is 37 889 ifCF sare 43 500peryear or 25 508 ifCF sare 23 500peryear inwhichcasethefirmwouldnotproceedwiththeproject Shouldwewaitorproceed Ifweproceedtoday NPV 6 190 Ifwewaitoneyear ExpectedNPVatt 1is0 5 37 889 0 5 0 18 944 58 whichisworth 18 944 58 1 10 17 222 34intoday sdollars assuminga10 discountrate Therefore itmakessensetowait IssuestoConsider What stheappropriatediscountrate Notethatincreasedvolatilitymakestheoptiontodelaymoreattractive Ifinstead therewasa50 chancethesubsequentCFswillbe 53 500ayear anda50 chancethesubse quentCFswillbe 13 500ayear expectedNPVnextyear ifwedelay wouldbe 0 5 69 588 0 5 0 34 794 18 944 57 FactorstoConsiderWhenDecidingWhentoInvest Delayingtheprojectmeansthatcashflowscomelaterratherthansooner Itmightmakesensetoproceedtodayifthereareimportantadvantagestobeingthefirstcompetitortoenteramarket Waitingmayallowyoutotakeadvantageofchangingconditions Abandonment ShutdownOption ProjectYhasaninitial up frontcostof 200 000 att 0 Theprojectisexpectedtoproduceafter taxnetcashflowsof 80 000forthenextthreeyears Ata10 discountrate whatisProjectY sNPV More 0123 200 00080 00080 00080 000 k 10 NPV 1 051 84 Abandonment Shutdown continued ProjectY sA Tnetcashflowsdependcriticallyuponcustomeracceptanceoftheproduct Thereisa60 probabilitythattheproductwillbewildlysuccessfulandproduceA Tnetcashflowsof 150 000 anda40 chanceitwillproduceannualA Tcashflowof 25 000 200 000 Abandonment ShutdownDecisionTree 60 prob 40 prob 123 Years 0 150 000150 000150 000 25 000 25 000 25 000 k 10 Ifthecustomerusestheproduct NPVis 173 027 80 Ifthecustomerdoesnotusetheproduct NPVis 262 171 30 E NPV 0 6 173 027 0 4 262 171 1 051 84 Abandonment Shutdown continued Companydoesnothavetheoptiontodelaytheproject Companymayabandontheprojectafterayear ifthecustomerhasnotadoptedtheproduct Iftheprojectisabandoned therewillbenooperatingcostsincurrednorcashinflowsreceivedafterthefirstyear NPVwiththeAbandonmentOption Ifthecustomerusestheproduct NPVis 173 027 80 Ifthecustomerdoesnotusetheproduct NPVis 222 727 27 E NPV 0 6 173 027 0 4 222 727 14 725 77 200 000 60 prob 40 prob 123 Years 150 000150 000150 000 25 000 k 10 0 Isitreasonabletoassumethattheabandonmentoptiondoesnotaffectthecostofcapital No itisnotreasonabletoassumethattheabandonmentoptionhasnoeffectonthecostofcapital Theabandonmentoptionreducesrisk andthereforereducesthecostofcapital GrowthOption ProjectZhasaninitialup frontcostof 500 000 TheprojectisexpectedtoproduceA Tcashinflowsof 100 000attheendofeachofthenextfiveyears Sincetheprojectcarriesa12 costofcapital itclearlyhasanegativeNPV Thereisa10 chancetheprojectwillleadtosubsequentopportunitiesthathaveanNPVof 3 000 000att 5 anda90 chanceofanNPVof 1 000 000att 5 100 000100 000100 000100 000100 000 NPVwiththeGrowthOption 500 000 10 prob 90 prob 12345 Years 0 100 000100 000100 000100 000100 000 1 000 000 3 000 000 Atk 12 NPVoftopbranch w 10 prob 1 562 758 19 NPVofbottombranch w 90 prob 139 522 38 NPVwiththeGrowthOption cont d IfitturnsoutthattheprojecthasfutureopportunitieswithanegativeNPV thecompanywouldchoosenottopursuethem Therefore theNPVofthebottombranchshouldincludeonlythe 500 000initialoutlayandthe 100 000annualcashflows whichleadtoanNPVof 139 522 38 NPVwiththeGrowthOpti