CorporateFinanceSixthEditionChapter3FinancialDecisionMakingandtheLawofOnePriceCopyright?2024,2021,2018PearsonEducation,Inc.AllRightsReservedChapterOutline3.1

ValuingDecisions3.2

InterestRatesandtheTimeValueofMoney3.3

PresentValueandtheNPVDecisionRule3.4

ArbitrageandtheLawofOnePrice3.5

No-ArbitrageandSecurityPricesLearningObjectives(1of3)Assesstherelativemeritsoftwo-periodprojectsusingnetpresentvalue.Definetheterm“competitivemarket,”giveexamplesofmarketsthatarecompetitiveandsomethatarenotanddiscusstheimportanceofacompetitivemarketindeterminingthevalueofagood.LearningObjectives(2of3)ExplainwhymaximizingNPVisalwaysthecorrectdecisionrule.Definearbitrage,anddiscussitsroleinassetpricing.HowdoesitrelatetotheLawofOnePrice?Calculatetheno-arbitragepriceofaninvestmentopportunity.LearningObjectives(3of3)Showhowvalueadditivitycanbeusedtohelpmanagersmaximizethevalueofthefirm.DescribetheSeparationPrinciple.3.1ValuingDecisionsIdentifyCostsandBenefitsMayneedhelpfromotherareasinidentifyingtherelevantcostsandbenefitsMarketingEconomicsOrganizationalBehaviorStrategyOperationsAnalyzingCostsandBenefits(1of4)Supposeajewelrymanufacturerhastheopportunitytotrade400ouncesofsilverandreceive10ouncesofgoldtodayTocomparethecostsandbenefits,wefirstneedtoconvertthemtoacommonunitAnalyzingCostsandBenefits(2of4)Supposesilvercanbeboughtandsoldforacurrentmarketpriceof$25perounceThenthe400ouncesofsilverwegiveuphasacashvalueofAnalyzingCostsandBenefits(3of4)Similarly,ifthecurrentmarketpriceforgoldis$1900perounce,thenthe10ouncesofgoldwereceivehasacashvalueofAnalyzingCostsandBenefits(4of4)Therefore,thejeweler’sopportunityhasabenefitof$12,000todayandacostof$10,000todayInthiscase,thenetvalueoftheprojecttodayisBecauseitispositive,thebenefitsexceedthecosts,andthejewelershouldrejectthetradeUsingMarketPricestoDetermineCashValuesCompetitiveMarketAmarketinwhichgoodscanbeboughtandsoldatthesamepriceInevaluatingthejeweler’sdecision,weusedthecurrentmarketpricetoconvertfromouncesofplatinumorgoldtodollarsWedidnotconcernourselveswithwhetherthejewelerthoughtthatthepricewasfairorwhetherthejewelerwouldusethesilverorgoldTextbookExample3.1(1of2)CompetitiveMarketPricesDetermineValueProblemYouhavejustwonaradiocontestandaredisappointedtofindoutthattheprizeisfourticketstotheDefLeppardreuniontour(facevalue$40each).Notbeingafanof1980spowerrock,youhavenointentionofgoingtotheshow.However,thereisasecondchoice:twoticketstoyourfavoriteband’ssold-outshow(facevalue$45each).YounoticethatoneBay,ticketstotheDefLeppardshowarebeingboughtandsoldfor$30apieceandticketstoyourfavoriteband’sshowarebeingboughtandsoldat$50each.Whichprizeshouldyouchoose?TextbookExample3.1(2of2)SolutionCompetitivemarketprices,notyourpersonalpreferences(northefacevalueofthetickets),arerelevanthere:FourDefLeppardticketsat$30apiece=$120marketvalueTwoofyourfavoriteband’sticketsat$50apiece=$100marketvalueInsteadoftakingtheticketstoyourfavoriteband,youshouldaccepttheDefLeppardtickets,sellthemoneBay,andusetheproceedstobuytwoticketstoyourfavoriteband’sshow.You’llevenhave$20leftovertobuyaT-shirt.AlternativeExample3.1(1of2)ProblemYourcarrecentlybrokedown,anditneeds$2,000inrepairs.Buttodayisyourluckydaybecauseyouhavejustwonacontestwheretheprizeiseitheranewmotorcycle,withaMSRPof$15,000,or$10,000incash.Youdonothaveamotorcyclelicense,nordoyouplanongettingone.Youestimateyoucouldsellthemotorcyclefor$12,000.Whichprizeshouldyouchoose?AlternativeExample3.1(2of2)SolutionCompetitivemarkets,notyourpersonalpreferences(ortheMSRPofthemotorcycle),arerelevanthere:Onemotorcyclewithamarketvalueof$12,000or$10,000cash.Insteadoftakingthecash,youshouldacceptthemotorcycle,sellitfor$12,000,use$2,000topayforyourcarrepairs,andstillhave$10,000leftover.TextbookExample3.2(1of2)ApplyingtheValuationPrincipleProblemYouaretheoperationsmanageratyourfirm.Duetoapre-existingcontract,youhavetheopportunitytoacquire125barrelsofoiland1,500poundsofcopperforatotalof$12,000.Thecurrentcompetitivemarketpriceofoilis$80perbarrelandforcopperis$4perpound.Youarenotsureyouneedalloftheoilandcopper,andareconcernedthatthevalueofbothcommoditiesmayfallinthefuture.Shouldyoutakethisopportunity?TextbookExample3.2(2of2)SolutionToanswerthisquestion,youneedtoconvertthecostsandbenefitstotheircashvaluesusingmarketprices:Thenetvalueoftheopportunityistoday.Becausethenetvalueispositive,youshouldtakeit.Thisvaluedependsonlyonthecurrentmarketpricesforoilandcopper.Evenifyoudonotneedalltheoilorcopper,orexpecttheirvaluestofall,youcansellthematcurrentmarketpricesandobtaintheirvaluesof$16,000.Thustheopportunityisagoodoneforthefirm,andwillincreaseitsvalueby$4,000.AlternativeExample3.2(1of2)ProblemYouareofferedthefollowinginvestmentopportunity:Inexchangefor$50,000today,youwillreceive2,500sharesofstockintheFordMotorCompanyandThecurrentmarketpriceforFordstockis$14pershare,andthecurrentexchangerateisShouldyoutakethisopportunity?Wouldyourdecisionchangeifyoubelievedthevalueoftheeurowouldriseoverthenextmonth?AlternativeExample3.2(2of2)SolutionThecostsandbenefitsmustbeconvertedtotheircashvalues.Assumingcompetitivemarketprices:Thenetvalueoftheopportunityisweshouldnottakeit.ThisvaluedependsonlyonthecurrentmarketpricesforFordandtheeuro.OurpersonalopinionaboutthefutureprospectsoftheeuroandForddoesnotalterthevaluethedecisiontoday.3.2InterestRatesandtheTimeValueofMoneyTimeValueofMoneyConsideraninvestmentopportunitywiththefollowingcertaincashflowsCost:$100,000todayBenefit:$105,000inoneyearThedifferenceinvaluebetweenmoneytodayandmoneyinthefutureisduetothetimevalueofmoneyTheInterestRate:AnExchangeRateAcrossTime(1of8)TherateatwhichwecanexchangemoneytodayformoneyinthefutureisdeterminedbythecurrentinterestrateSupposethecurrentannualinterestrateis7%.Byinvestingorborrowingatthisrate,wecanexchangeinoneyearforeach$1todayRisk-FreeInterestRate(DiscountRate),TheinterestrateatwhichmoneycanbeborrowedorlentwithoutriskInterestRateFactor

TheInterestRate:AnExchangeRateAcrossTime(2of8)ValueofInvestmentinOneYearIftheinterestrateis7%,thenwecanexpressourcostsas:TheInterestRate:AnExchangeRateAcrossTime(3of8)ValueofInvestmentinOneYearBothcostsandbenefitsarenowintermsof“dollarsinoneyear,”sowecancomparethemandcomputetheinvestment’snetvalue:Inotherwords,wecouldearn$2,000moreinoneyearbyputtingour$100,000inthebankratherthanmakingthisinvestmentWeshouldrejecttheinvestmentTheInterestRate:AnExchangeRateAcrossTime(4of8)ValueofInvestmentTodayConsiderthebenefitof$105,000inoneyear.Whatistheequivalentamountintermsofdollarstoday?Thisistheamountthebankwouldlendtoustodayifwepromisedtorepay$105,000inoneyearTheInterestRate:AnExchangeRateAcrossTime(5of8)ValueofInvestmentTodayNowwearereadytocomputethenetvalueoftheinvestment:Onceagain,thenegativeresultindicatesthatweshouldrejecttheinvestmentTheInterestRate:AnExchangeRateAcrossTime(6of8)PresentVersusFutureValueThisdemonstratesthatourdecisionisthesamewhetherweexpressthevalueoftheinvestmentintermsofdollarsinoneyearordollarstodayIfweconvertfromdollarstodaytodollarsinoneyear,ThetworesultsareequivalentbutexpressedasvaluesatdifferentpointsintimeTheInterestRate:AnExchangeRateAcrossTime(7of8)PresentVersusFutureValueWhenweexpressthevalueintermsofdollarstoday,wecallitthepresentvalue(PV)oftheinvestmentIfweexpressitintermsofdollarsinthefuture,wecallitthefuturevalueoftheinvestmentTheInterestRate:AnExchangeRateAcrossTime(8of8)DiscountFactorsandRateWecaninterpretasthepricetodayof$1inoneyear.Theamountiscalledtheone-yeardiscountfactorTherisk-freerateisalsoreferredtoasthediscountrateforarisk-freeinvestmentTextbookExample3.3(1of2)ComparingCostsatDifferentPointsinTimeProblemThecostofrebuildingtheSanFranciscoBayBridgetomakeitearthquake-safewasapproximately$3billionin2004.Atthetime,engineersestimatedthatiftheprojectweredelayedto2005,thecostwouldriseby10%.Iftheinterestratewere2%,whatwouldbethecostofadelayintermsofdollarsin2004?TextbookExample3.3(2of2)SolutionIftheprojectweredelayed,itwouldcostTocomparethisamounttothecostof$3billionin2004,wemustconvertitusingtheinterestrateof2%:Therefore,thecostofadelayofoneyearwasThatis,delayingtheprojectforoneyearwasequivalenttogivingup$235millionincash.AlternativeExample3.3A(1of2)ProblemThecostofreplacingafleetofcompanytrucks

withmoreenergyefficientvehicleswas$100millionin2021.Thecostisestimatedtoriseby8.5%in2022.Iftheinterestrateis4%,whatisthecostofadelayintermsofdollarsin2021?AlternativeExample3.3A(2of2)SolutionIftheprojectweredelayed,itscostin2022willbe

Comparethisamounttothecostof$100millionin2021usingtheinterestrateof4%:

Thecostofadelayofoneyearwouldbe

AlternativeExample3.3B(1of2)ProblemSullyisconsideringpursuingtheirMBA.Theone-timeupfrontcostis$75,000.Highereducationcostsareexpectedtoincreaseby3.5%overthenextyearIftheinterestrateis5%,whatisthecostwaitingoneyeartoentertheMBAprogram?AlternativeExample3.3B(2of2)SolutionIfSullywaitsoneyear,thecostoftheMBAwillbe:

Comparethisamounttothecostof$77,625oneyearfromnowtothecosttodayusinganinterestrateof5%:

Thebenefitofdelayingoneyearwouldbe:

Figure3.1ConvertingBetweenDollarsTodayandGold,Euros,orDollarsintheFuture3.3PresentValueandtheNPVDecisionRuleTheNetPresentValue(NPV)ofaprojectorinvestmentisthedifferencebetweenthepresentvalueofitsbenefitsandthepresentvalueofitscostsNetPresentValueTheNPVDecisionRule(1of3)Whenmakinganinvestmentdecision,takethealternativewiththehighestNPVChoosingthisalternativeisequivalenttoreceivingitsNPVincashtodayTheNPVDecisionRule(2of3)AcceptingorRejectingaProjectAcceptthoseprojectswithpositiveNPVbecauseacceptingthemisequivalenttoreceivingtheirNPVincashtodayRejectthoseprojectswithnegativeNPVbecauseacceptingthemwouldreducethewealthofinvestorsTextbookExample3.4(1of2)TheNPVIsEquivalenttoCashTodayProblemYourfirmneedstobuyanew$9,500copier.Aspartofapromotion,themanufacturerhasofferedtoletyoupay$10,000inoneyear,ratherthanpaycashtoday.Supposetherisk-freeinterestrateis7%peryear.Isthisofferagooddeal?ShowthatitsNPVrepresentscashinyourpocket.TextbookExample3.4(2of2)SolutionIfyoutaketheoffer,thebenefitisthatyouwon’thavetopay$9,500today,whichisalreadyinPVterms.Thecost,however,is$10,000inoneyear.Wethereforeconvertthecosttoapresentvalueattherisk-freeinterestrate:TheNPVofthepromotionalofferisthedifferencebetweenthebenefitsandthecosts:TheNPVispositive,sotheinvestmentisagooddeal.Itisequivalenttogettingacashdiscounttodayof$154.21,andonlypaying$9,345.79todayforthecopier.Toconfirmourcalculation,supposeyoutaketheofferandinvest$9,345.79inabankpaying7%interest.Withinterest,thisamountwillgrowtoinoneyear,whichyoucanusetopayforthecopier.AlternativeExample3.4(1of2)ProblemYouhavesavedup$25,000foranewcar.Acardealerisofferingcaryouwantforapriceof$25,000with0%financingforoneyearoracashpriceof$23,500.Iftheapplicableinterestrateis4%,whichdealisbetter,thecashdealorthe0%financingdeal?AlternativeExample3.4(2of2)SolutionIfyoutakethe0%financingoffer,thebenefitisthatyouwon’thavetopay$25,000forayear.However,ifyoupaycash,youwillsave$1,500today.Wethereforeconvertthecostinoneyeartoapresentvalueatthe4%interestrate:

Thecostintoday’sdollarsis$24,038.46.Thisisgreaterthanthecashpricetoday.Takingthecashdealisequivalenttogetting:TheNPVDecisionRule(3of3)ChoosingAmongAlternativesWecanalsousetheNPVdecisionruletochooseamongprojectsTodoso,wemustcomputetheNPVofeachalternative,andthenselecttheonewiththehighestNPVThisalternativeistheonewhichwillleadtothelargestincreaseinthevalueofthefirmTextbookExample3.5(1of2)ChoosingAmongAlternativePlansProblemSupposeyoustartedaWebsitehostingbusinessandthendecidedtoreturntoschool.Nowthatyouarebackinschool,youareconsideringsellingthebusinesswithinthenextyear.Aninvestorhasofferedtobuythebusinessfor$200,000wheneveryouareready.Iftheinterestrateis10%,whichofthefollowingthreealternativesisthebestchoice?Sellthebusinessnow.Scalebackthebusinessandcontinuerunningitwhileyouareinschoolforonemoreyear,andthensellthebusiness(requiringyoutospend$30,000onexpensesnow,butgenerating$50,000inprofitattheendoftheyear).Hiresomeonetomanagethebusinesswhileyouareinschoolforonemoreyear,andthensellthebusiness(requiringyoutospend$50,000onexpensesnow,butgenerating$100,000inprofitattheendoftheyear).TextbookExample3.5(2of2)SolutionThecashflowsandNPVsforeachalternativearecalculatedinTable3.1facedwiththesethreealternatives,thebestchoiceistheonewithhighestNPV:Hireamanagerandsellinoneyear.Choosingthisalternativeisequivalenttoreceiving$222,727today.Table3.1CashFlowsandNPVsforWebSiteBusinessAlternativesBlankTodayInOneYearNPVSellNow$200,0000$200,000ScaleBackOperationsNegative30,000dollar.$50,000negative30,000dollarplusstartfraction250,000dollarover1.10endfractionequals197,273dollarHireaManagerNegative50,000dollar.$100,000$200,000negative50,000dollarplusstartfraction300,000dollarover1.10endfractionequals222,727dollarAlternativeExample3.5(1of4)ProblemYouhave$10,000toinvestandareconsideringthreeone-yearrisk-freeinvestmentoptions.Investupto$10,000inaT-Billpaying2%.Investinaprojectthatcosts$6,000andreturns$6,100inoneyear.Investinaprojectthatcosts$4,000andreturns$4,100inoneyear.Howshouldthe$10,000investmentbeallocated?AlternativeExample3.5(2of4)SolutionSinceallofinvestmentoptionsareforoneyearandrisk-free,theappropriatediscountrateis2%.ThePVofeachinvestment@2%is:Investing$10,000intheT-Bill

Investing$6,000andreceiving$6,100

Investing$4,000andreceiving$4,100

AlternativeExample3.5(3of4)SolutionGiventhatthe#2investmenthasanegativeNPV,itshouldnotbeconsidered.However,onlyinvestingin#3usesjust$4,000oftheavailablefundstoinvest,yieldingatotalNPVof

Theoptimalstrategyistoinvest$4,000in#3and$6,000intheT-Bill.TheNPVofthisstrategyis

AlternativeExample3.5(4of4)SolutionEventhoughtheNPVoftheT-Billinvestmentis$0,itisabetterinvestmentthannotinvestingthosefundsatall.Thus,thetotalNPVofinvesting$4,000inProject2and$6,000inT-BillsyieldsanNPVof$19.61(NPVofProject2)plusanNPVof$0(NPVofT-Bill),yieldingatotalNPVof$19.61.NPVandCashNeedsRegardlessofourpreferencesforcashtodayversuscashinthefuture,weshouldalwaysmaximizeNPVfirstWecanthenborroworlendtoshiftcashflowsthroughtimeandfindourmostpreferredpatternofcashflowsTable3.2CashFlowsofHiringandBorrowingVersusSellingandInvestingBlankTodayInOneYearHireaManagerBorrow?$50,000$110,000$300,000?$121,000TotalCashFlowVersusSellNowInvest$60,000$200,000?$140,000$179,000$0$154,000TotalCashFlow$60,000$154,0003.4ArbitrageandtheLawofOnePriceArbitrageThepracticeofbuyingandsellingequivalentgoodsindifferentmarketstotakeadvantageofapricedifferenceAnarbitrageopportunityoccurswhenitispossibletomakeaprofitwithouttakinganyriskormakinganyinvestmentNormalMarketAcompetitivemarketinwhichtherearenoarbitrageopportunitiesLawofOnePriceIfequivalentinvestmentopportunitiestradesimultaneouslyindifferentcompetitivemarkets,thentheymusttradeforthesamepriceinbothmarkets3.5No-ArbitrageandSecurityPrices(1of7)ValuingaSecuritywiththeLawofOnePriceAssumeasecuritypromisesarisk-freepaymentof$1,000inoneyear.Iftherisk-freeinterestrateis5%,whatcanweconcludeaboutthepriceofthisbondinanormalmarket?3.5No-ArbitrageandSecurityPrices(2of7)ValuingaSecuritywiththeLawofOnePriceIdentifyingArbitrageOpportunitieswithSecuritiesWhatifthepriceofthebondisnot$952.38?Assumethepriceis$940BlankToday($)InOneYear($)Buythebond?940.00+1,000.00Borrowfromthe

bank+953.38?1,000.00Netcashflow+12.380.00Theopportunityforarbitragewillforcethepriceofthebondtoriseuntilitisequalto$952.383.5No-ArbitrageandSecurityPrices(3of7)ValuingaSecuritywiththeLawofOnePriceIdentifyingArbitrageOpportunitieswithSecuritiesWhatifthepriceofthebondisnot$952.38?Assumethepriceis$960BlankToday($)InOneYear($)Sellthebond+960.00?1,000.00Investatthe

bank?952.38+1,000.00Netcashflow+7.620.00Theopportunityforarbitragewillforcethepriceofthebondtoriseuntilitisequalto$952.383.5No-ArbitrageandSecurityPrices(4of7)ValuingaSecuritywiththeLawofOnePriceDeterminingtheNo-ArbitragePriceUnlessthepriceofthesecurityequalsthepresentvalueofthesecurity’scashflows,anarbitrageopportunitywillappearNoArbitragePriceofaSecurityPrice(security)=PV(Allcashflowspaidbythesecurity)TextbookExample3.6(1of2)ComputingtheNo-ArbitragePriceProblemConsiderasecuritythatpaysitsowner$100todayand$100inoneyear,withoutanyrisk.Supposetherisk-freeinterestrateis10%.Whatistheno-arbitragepriceofthesecuritytoday(beforethefirst$100ispaid)?Ifthesecurityistradingfor$195,whatarbitrageopportunityisavailable?TextbookExample3.6(2of2)SolutionWeneedtocomputethepresentvalueofthesecurity’scashflows.Inthiscasetherearetwocashflows:$100today,whichisalreadyinpresentvalueterms,and$100inoneyear.ThepresentvalueofthesecondcashflowisTherefore,thetotalpresentvalueofthecashflowsistoday,whichistheno-arbitragepriceofthesecurity.Ifthesecurityistradingfor$195,wecanexploititsoverpricingbysellingitfor$195.Wecanthenuse$100ofthesaleproceedstoreplacethe$100wewouldhavereceivedfromthesecuritytodayandinvest$90.91ofthesaleproceedsat10%toreplacethe$100wewouldhavereceivedinoneyear.Theremaininginanarbitrageprofit.Atapriceof$195,weareeffectivelypaying$95toreceive$100inoneyear.So,anarbitrageopportunityexistsunlesstheinterestrateequalsAlternativeExample3.6(1of3)ProblemConsiderasecuritythatpaysitsowner$5,000inoneyear,withoutanyrisk.Supposetherisk-freeinterestrateis6%.Whatistheno-arbitragepriceofthesecuritytoday?Ifthesecurityistradingfor$4,750,whatarbitrageopportunityisavailable?AlternativeExample3.6(2of3)SolutionWeneedtocomputethepresentvalueofthesecurity’scashflow:

Ifthesecurityistradingfor$4,750butonlycosts$4,716.98,aninvestorcanexploititsoverpricingbybuyingthesecurityat$4,716.98andthenimmediatelysellingitat$4,750.Thedifference,inarbitrageprofits.AlternativeExample3.6(3of3)SolutionAnotherwayoflookingatitisthattheinvestorcanpromisetopay$5,000inoneyearinexchangefor$4,750today.Theinvestortakesthe$4,750andimmediatelyinvestsitattherisk-freerateof6%.Inoneyear,the$4,750growsto:

Inoneyear,theinvestorpaysthe$5,000backandkeepsthe$35inarbitrageprofits.OnanNPVbasis,thisisworth:

3.5No-ArbitrageandSecurityPrices(5of7)ValuingaSecuritywiththeLawofOnePriceDeterminingtheInterestRatefromBondPricesIfweknowthepriceofarisk-freebond,wecanusePrice(Security)=PV(Allcashflowspaidbythesecurity)todeterminewhattherisk-freeinterestratemustbeiftherearenoarbitrageopportunities3.5No-ArbitrageandSecurityPrices(6of7)ValuingaSecuritywiththeLawofOnePriceDeterminingtheInterestRatefromBondPricesSupposearisk-freebondthatpays$1,000inoneyeariscurrentlytradingwithacompetitivemarketpriceoftodayThebond’spricemustequalthepresentvalueofthe$1,000cashflowitwillpay3.5No-ArbitrageandSecurityPrices(7of7)ValuingaSecuritywiththeLawofOnePriceDeterminingtheInterestRatefromBondPricesTherisk-freeinterestratemustbe7.55%TheNPVofTradingSecuritiesandFirmDecisionMaking(1of2)Inanormalmarket,theNPVofbuyingorsellingasecurityiszeroTheNPVofTradingSecuritiesandFirmDecisionMaking(2of2)SeparationPrincipleWecanevaluatetheNPVofaninvestmentdecisionseparatelyfromthedecisionthefirmmakesregardinghowtofinancetheinvestmentoranyothersecuritytransactionsthefirmisconsideringTextbookExample3.7(1of3)SeparatingInvestmentandFinancingProblemYourfirmisconsideringaprojectthatwillrequireanupfrontinvestmentof$10milliontodayandwillproduce$12millionincashflowforthefirminoneyearwithoutrisk.Ratherthanpayforthe$10millioninvestmententirelyusingitsowncash,thefirmisconsideringraisingadditionalfundsbyissuingasecuritythatwillpayinvestors$5.5millioninoneyear.Supposetherisk-freeinterestrateis10%.Ispursuingthisprojectagooddecisionwithoutissuingthenewsecurity?Isitagooddecisionwiththenewsecurity?TextbookExample3.7(2of3)Solution

Withoutthenewsecurity,thecostoftheprojectis$10milliontodayandthebenefitis$12millioninoneyear.ConvertingthebenefittoapresentvalueweseethattheprojecthasanNPVofNowsupposethefirmissuesthenewsecurity.Inanormalmarket,thepriceofthissecuritywillbethepresentvalueofitsfuturecashflow:TextbookExample3.7(3of3)Solution

Thus,afteritraises$5millionbyissuingthenewsecurity,thefirmwillonlyneedtoinvestanadditional$5milliontotaketheproject.Tocomputetheproject’sNPVinthiscase,notethatinoneyearthefirmwillreceivethe$12millionpayoutoftheproject,butowe$5.5milliontotheinvestorsinthenewsecurity,leaving$6.5millionforthefirm.ThisamounthasapresentvalueofThus,theprojecthasanNPVoftoday,asbefore.Ineithercase,wegetthesameresultfortheNPV

.Theseparationprincipleindicatesthatwewillgetthesameresultforanychoiceoffinancingforthefirmthatoccursinanormalmarket.Wecanthereforeevaluatetheprojectwithoutexplicitlyconsideringthedifferentfinancingpossibilitiesthefirmmightchoose.AlternativeExample3.7(1of2)ProblemYouareconsideringarisk-freeinvestmentthatcosts$7,000andpays$8,500inoneyear.Youcaneitherpayallcashfortheinvestmentoryoucanborrowhalfandpaycashfortheotherhalf.Ifyouborrow$3,500,youwillberequiredtopayback$3,710inoneyear.Therisk-freerateis6%.Whatistheproject’sNPV?IstheNPVaffectedifyouborrowsomeofthefunds?AlternativeExample3.7(2of2)SolutionIfyoupayallcash,theNPVoftheprojectis

Ifyouborrow$3,500tofinancehalfoftheproject,theNPVoftheprojectis

Themethodoffinancingtheinvestmentdoesnotimpactthevalueoftheinvestment.ValuingaPortfolio(1of2)TheLawofOnePricealsohasimplicationsforpackagesofsecuritiesConsidertwosecurities,AandB.Supposeathirdsecurity,C,hasthesamecashflowsasAandBcombinedInthiscase,securityCisequivalenttoaportfolio,orcombination,ofthesecuritiesAandBValueAdditivityTextbookExample3.8(1of2)ValuinganAssetinaPortfolioProblemHolbrookHoldingsisapubliclytradedcompanywithonlytwoassets:Itowns60%ofHarry’sHotcakesrestaurantchainandanicehockeyteam.SupposethemarketvalueofHolbrookHoldingsis$160million,andthemarketvalueoftheentireHarry’sHotcakeschain(whichisalsopubliclytraded)is$120million.Whatisthemarketvalueofthehockeyteam?TextbookExample3.8(2of2)SolutionWecanthinkofHolbrookasaportfolioconsistingofa60%stakeinHarry’sHotcakesandthehockeyteam.Byvalueadditivity,thesumofthevalueofthestakeinHarry’sHotcakesandthehockeyteammustequalthe$160millionmarketvalueofHolbrook.Becausethe60%stakeinHarry’sHotcakesisworththehockeyteamhasavalueofAlternativeExample3.8(1of2)ProblemMoonHoldingsisapubliclytradedcompanywithonlythreeassets:Itowns50%ofDueBeverageCo.,70%ofMountainIndustries,and100%oftheOxfordBears,afootballteam.ThetotalmarketvalueofMoonHoldingsis$200million,thetotalmarketvalueofDueBeverageCo.is$75