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1CHAPTER2PresentValues,TheObjectivesoftheFirm,andCorporateGovernanceAnswerstoPracticeQuestions1.Thefacevalueofthetreasurysecurityis$1,000.Ifthissecurityearns5%,theninoneyearwewillreceive$1,050.Thus:NPV=C0+[C1/(1+r)]=−$1000+($1050/1.05)=0Thisisnotasurprisingresultbecause5percentistheopportunitycostofcapital,i.e.,5percentisthereturnavailableinthecapitalmarket.Ifanyinvestmentearnsarateofreturnequaltotheopportunitycostofcapital,theNPVofthatinvestmentiszero.2.NPV=−$1,300,000+($1,500,000/1.10)=+$63,636SincetheNPVispositive,youwouldconstructthemotel.Alternatively,wecancomputerasfollows:r=($1,500,000/$1,300,000)–1=0.1539=15.39%Sincetherateofreturnisgreaterthanthecostofcapital,youwouldconstructthemotel.3.InvestmentNPVReturn(1)$5,0001.2018,00010,000=+−80.0%0.8010,00010,00018,000==−(2)$2,5001.209,0005,000=+−80.0%0.805,0005,0009,000==−(3)$2501.205,7005,000−=+−14.0%0.145,0005,0005,700==−(4)$1,333.331.204,0002,000=+−100.0%1.002,0002,0004,000==−a.Investment1,becauseithasthehighestNPV.b.Investment1,becauseitmaximizesshareholders’wealth.24.a.NPV=(−$50,000+$20,000)+($38,000/1.05)=$6,190.48b.NPV=(−$50,000+$20,000)+($38,000/1.10)=$4,545.45InPart(a),theNPVishigherthantheNPVoftheofficebuilding($5,000);therefore,weshouldacceptE.Coli’soffer.InPart(b),theNPVislessthantheNPVoftheofficebuilding,soweshouldnotaccepttheoffer.Youcanalsothinkofthisinanotherway.Thetrueopportunitycostofthelandiswhatyoucouldsellitfor,i.e.,$56,190(or$54,545).At$56,190,theofficebuildinghasanegativeNPV.At$54,545,theofficebuildinghasapositiveNPV.5.a.NPV=−$2,000,000+[($2,000,000×1.05)/1.05]=$0b.NPV=−$900,000+[($900,000×1.07)/1.10]=−$24,545.45Thecorrectdiscountrateis10%becausethisistheappropriaterateforaninvestmentwiththelevelofriskinherentinNorman’snephew’srestaurant.TheNPVisnegativebecauseNormanwillnotearnenoughtocompensatefortherisk.c.NPV=−$2,000,000+[($2,000,000×1.12)/1.12]=$0d.NPV=−$1,000,000+($1,100,000/1.12)=−$17,857.14Normanshouldinvestineithertherisk-freegovernmentsecuritiesortheriskystockmarket,dependingonhistoleranceforrisk.CorrectlypricedsecuritiesalwayshaveanNPV=0.6.a.Expectedrateofreturnonproject=Thisisequaltothereturnonthegovernmentsecurities.b.Expectedrateofreturnonproject=Thisislessthanthecorrect10%rateofreturnforrestaurantswithsimilarrisk.c.Expectedrateofreturnonproject=Thisisequaltotherateofreturninthestockmarket.5.0%0.05$2,000,0002,000,000$$2,100,000==−7.0%0.07$900,000900,000$$963,000==−12.0%0.12$2,000,000$2,000,000$2,240,000==−3d.Expectedrateofreturnonproject=Thisislessthanthereturnintheequallyriskystockmarket.7.$17,857.141.121.12)0($1,600,00$1,100,000$2,600,000NPV−=⎥⎦⎤⎢⎣⎡×++−=TherateatwhichNormancanborrowdoesnotreflecttheopportunitycostoftheinvestments.Normanisstillinvesting$1,000,000at10%whiletheopportunitycostofcapitalis12%.8.Theinvestment’spositiveNPVwillbereflectedinthepriceofScaledCompositesstock.Inordertoderiveacashflowfromherinvestmentthatwillallowhertospendmoretoday,Ms.Espinozacansellsomeofhersharesatthehigherpriceorshecanborrowagainsttheincreasedvalueofherholdings.9.a.Letx=theamountthatCaspershouldinvestnow.Then($200,000–x)istheamounthewillconsumenow,and(1.08x)istheamounthewillconsumenextyear.SinceCasperwantstoconsumeexactlythesameamounteachperiod:200,000–x=1.08x10.0%0.10$1,000,000$1,000,000$1,100,000==−203,704200,000220,000216,000DollarsNextYearDollarsNow4Solving,wefindthatx=$96,153.85sothatCaspershouldinvest$96,153.85now,heshouldspend($200,000-$96,153.85)=$103,846.15now,andheshouldspend(1.08×$96,153.85)=$103,846.15nextyear.b.SinceCaspercaninvest$200,000at10%risk-free,hecanconsumeasmuchas($200,000×1.10)=$220,000nextyear.Thepresentvalueofthis$220,000is:($220,000/1.08)=$203,703.70ThereforeCaspercanconsumeasmuchas$203,703.70nowbyfirstinvesting$200,000at10%andthenborrowing,atthe8%rate,againstthe$220,000availablenextyear.Ifweusethe$203,703.70astheavailableconsumptionnow,andagainletx=theamountthatCaspershouldinvestnow,wecanthensolvethefollowingforx:$203,703.70–x=1.08xx=$97,934.47Therefore,Caspershouldinvest$97,934.47nowat8%,heshouldspend($203,703.70–$97,934.47)=$105,769.23now,andheshouldspend($97,934.47×1.08)=$105,769.23nextyear.[NotethatthisapproachleadstotheresultthatCasperborrows$203,703.70at8%andtheninvests$97,934.47at8%.Wecouldsimplysaythatheshouldborrow($203,703.70-$97,934.47)=$105,769.23at8%againstthe$220,000availablenextyear.Thisistheamountthathewillconsumenow.]c.TheNPVoftheopportunityin(b)is:($203,703.70-$200,000)=$3,703.705ChallengeQuestions1.a.Expectedcashflow=($8million+$12million+$16million)/3=$12millionb.Expectedrateofreturn=($12million/$8million)–1=0.50=50%c.Expectedcashflow=($8+$12+$16)/3=$12Expectedrateofreturn=($12/$10)–1=0.20=20%ThenetcashflowfromsellingthetankerloadisthesameasthepayofffromonemillionsharesofStockZineachstateoftheworldeconomy.Therefore,theriskofeachofthesecashflowsisthesame.d.NPV=−$8,000,000+($12,000,000/1.20)=+$2,000,000TheprojectisagoodinvestmentbecausetheNPVispositive.Investorswouldbepreparedtopayasmuchas$10,000,000fortheproject,whichcosts$8,000,000.2.a.Expectedcashflow(ProjectB)=($4million+$6million+