公司金融课后题答案CHAPTER 27

CHAPTER27CASHMANAGEMENTAnswerstoConceptsReviewandCriticalThinkingQuestions1.Yes.Onceafirmhasmorecashthanitneedsforoperationsandplannedexpenditures,theexcesscashhasanopportunitycost.Itcouldbeinvested(byshareholders)inpotentiallymoreprofitableways.Question10discussesanotherreason.2.Ifithastoomuchcashitcansimplypayadividend,or,morelikelyinthecurrentfinancialenvironment,buybackstock.Itcanalsoreducedebt.Ifithasinsufficientcash,thenitmusteitherborrow,sellstock,orimproveprofitability.3.Probablynot.Creditorswouldprobablywantsubstantiallymore.4.Cashmanagementisassociatedmorewiththecollectionanddisbursementofcash.Liquiditymanagementisbroaderandconcernstheoptimallevelofliquidassetsneededbyafirm.Thus,forexample,acompany’sstockpilingofcashisliquiditymanagement;whereas,evaluatingalockboxsystemiscashmanagement.5.Suchinstrumentsgobyavarietyofnames,butthekeyfeatureisthatthedividendadjusts,keepingthepricerelativelystable.Thispricestability,alongwiththedividendtaxexemption,makesso-calledadjustableratepreferredstockveryattractiverelativetointerest-bearinginstruments.6.Netdisbursementfloatismoredesirablebecausethebankthinksthefirmhasmoremoneythanitactuallydoes,andthefirmis,therefore,receivinginterestonfundsithasalreadyspent.7.Thefirmhasanetdisbursementfloatof$500,000.Ifthisisanongoingsituation,thefirmmaybetemptedtowritechecksformorethanitactuallyhasinitsaccount.8.a.AbouttheonlydisadvantagetoholdingT-billsarethegenerallyloweryieldscomparedtoalternativemoneymarketinvestments.b.Someordinarypreferredstockissuesposebothcreditandpricerisksthatarenotconsistentwithmostshort-termcashmanagementplans.c.TheprimarydisadvantageofNCDsisthenormallylargetransactionssizes,whichmaynotbefeasiblefortheshort-terminvestmentplansofmanysmallertomedium-sizedcorporations.d.Theprimarydisadvantagesofthecommercialpapermarketarethehigherdefaultriskcharacteristicsofthesecurityandthelackofanactivesecondarymarketwhichmayexcessivelyrestricttheflexibilityofcorporationstomeettheirliquidityadjustmentneeds.e.TheprimarydisadvantagesofRANsisthatsomepossessnon-triviallevelsofdefaultrisk,andalso,corporationsaresomewhatrestrictedinthetypeandamountofthesetax-exemptsthattheycanholdintheirportfolios.f.Theprimarydisadvantageoftherepomarketisthegenerallyveryshortmaturitiesavailable.9.Theconcernisthatexcesscashonhandcanleadtopoorlythought-outmanagementdecisions.Thethoughtisthatkeepingcashlevelsrelativelylowforcesmanagementtopaycarefulattentiontocashflowandcapitalspending.10.Apotentialadvantageisthatthequickerpaymentoftenmeansabetterprice.Thedisadvantageisthatdoingsoincreasesthefirm’scashcycle.11.Thisisreallyacapitalstructuredecision.Ifthefirmhasanoptimalcapitalstructure,payingoffdebtmovesittoanunder-leveragedposition.However,acombinationofdebtreductionandstockbuy-backscouldbestructuredtoleavecapitalstructureunchanged.12.Itisunethicalbecauseyouhaveessentiallytrickedthegrocerystoreintomakingyouaninterest-freeloan,andthegrocerystoreisharmedbecauseitcouldhaveearnedinterestonthemoneyinsteadofloaningittoyou.SolutionstoQuestionsandProblemsNOTE:Allendofchapterproblemsweresolvedusingaspreadsheet.Manyproblemsrequiremultiplesteps.Duetospaceandreadabilityconstraints,whentheseintermediatestepsareincludedinthissolutionsmanual,roundingmayappeartohaveoccurred.However,thefinalanswerforeachproblemisfoundwithoutroundingduringanystepintheproblem.Basic1.Theaveragedailyfloatistheaverageamountofchecksreceivedperdaytimestheaveragenumberofdaysdelay,dividedbythenumberofdaysinamonth.Assuming30daysinamonth,theaveragedailyfloatis:Averagedailyfloat=4($156,000)/30Averagedailyfloat=$20,8002.a.Thedisbursementfloatistheaveragemonthlycheckswrittentimestheaveragenumberofdaysforthecheckstoclear,so:Disbursementfloat=4($14,000)Disbursementfloat=$56,000Thecollectionfloatistheaveragemonthlychecksreceivedtimestheaveragenumberofdaysforthecheckstoclear,so:Collectionfloat=2(–$26,000)Collectionfloat=–$52,000Thenetfloatisthedisbursementfloatplusthecollectionfloat,so:Netfloat=$56,000–52,000Netfloat=$4,000b.Thenewcollectionfloatwillbe:Collectionfloat=1(–$26,000)Collectionfloat=–$26,000Andthenewnetfloatwillbe:Netfloat=$56,000–26,000Netfloat=$30,0003.a.Thecollectionfloatistheaveragedailychecksreceivedtimestheaveragenumberofdaysforthecheckstoclear,so:Collectionfloat=3($19,000)Collectionfloat=$57,000b.Thefirmshouldpaynomorethantheamountofthefloat,or$57,000,toeliminatethefloat.c.Themaximumdailychargethefirmshouldbewillingtopayisthecollectionfloattimesthedailyinterestrate,so:Maximumdailycharge=$57,000(.00019)Maximumdailycharge=$10.834.a.Totalfloat=4($17,000)+5($6,000)Totalfloat=$98,000b.Theaveragedailyfloatisthetotalfloatdividedbythenumberofdaysinamonth.Assuming30daysinamonth,theaveragedailyfloatis:Averagedailyfloat=$98,000/30Averagedailyfloat=$3,266.67c.Theaveragedailyreceiptsaretheaveragedailychecksreceiveddividedbythenumberofdaysinamonth.Assuminga30daymonth:Averagedailyreceipts=($17,000+6,000)/30Averagedailyreceipts=$766.67Theweightedaveragedelayisthesumofthedaystoclearacheck,timestheamountofthecheckdividedbytheaveragedailyreceipts,so:Weightedaveragedelay=4($17,000/$23,000)+5($6,000/$23,000)Weightedaveragedelay=4.26days5.Theaveragedailycollectionsarethenumberofchecksreceivedtimestheaveragevalueofacheck,so:Averagedailycollections=$108(8,500)Averagedailycollections=$918,000Thepresentvalueofthelockboxserviceistheaveragedailyreceiptstimesthenumberofdaysthecollectionisreduced,so:PV=(2dayreduction)($918,000)PV=$1,836,000Thedailycostisaperpetuity.Thepresentvalueofthecostisthedailycostdividedbythedailyinterestrate.So:PVofcost=$225/.00016PVofcost=$1,406,250Thefirmshouldtakethelockboxservice.TheNPVofthelockboxisthecostplusthepresentvalueofthereductionincollectiontime,so:NPV=–$1,406,250+1,836,000NPV=$429,750Theannualsavingsexcludingthecostwouldbethefuturevalueofthesavingsminusthecosts,so:Annualsavings=$1,836,000(1.00016)365–1,836,000Annualsavings=$110,406.05Andtheannualcostwouldbethefuturevalueofthedailycost,whichisanannuity,so:Annualcost=$225(FVIFA365,.016%)Annualcost=$84,563.46So,theannualnetsavingswouldbe:Annualnetsavings=$110,406.05–84,563.46Annualnetsavings=$25,842.596.a.Theaveragedailyfloatisthesumofthepercentageeachcheckamountisofthetotalchecksreceivedtimesthenumberofchecksreceivedtimestheamountofthechecktimesthenumberofdaysuntilthecheckclears,dividedbythenumberofdaysinamonth.Assuminga30daymonth,weget:Averagedailyfloat=[.60(5,300)($55)(2)+.40(5,300)($80)(3)]/30Averagedailyfloat=$28,620Onaverage,thereis$28,620thatisuncollectedandnotavailabletothefirm.b.Thetotalcollectionsarethesumofthepercentageofeachcheckamountreceivedtimesthetotalchecksreceivedtimestheamountofthecheck,so:Totalcollections=.60(5,300)($55)+.40(5,300)($80)Totalcollections=$344,500Theweightedaveragedelayisthesumoftheaveragenumberofdaysacheckofaspecificamountisdelayed,timesthepercentagethatcheckamountmakesupofthetotalchecksreceived,so:Weightedaveragedelay=2[.60(5,300)($55)/$344,500]+3[.40(5,300)($80)/$344,500]Weightedaveragedelay=2.49daysTheaveragedailyfloatistheweightedaveragedelaytimestheaveragechecksreceivedperday.Assuminga30daymonth,weget:Averagedailyfloat=2.49($344,500/30days)Averagedailyfloat=$28,620c.Themostthefirmshouldpayisthetotalamountoftheaveragefloat,or$28,620.d.Theaveragedailyinterestrateis:1.07=(1+R)365R=.01854%perdayThedailycostoffloatistheaveragedailyfloattimesthedailyinterestrate,so:Dailycostofthefloat=$28,620(.0001854)Dailycostofthefloat=$5.31e.Themostthefirmshouldpayisstilltheaveragedailyfloat.Underthereducedcollectiontimeassumption,weget:Newaveragedailyfloat=1.5($344,500/30)Newaveragedailyfloat=$17,2257.a.Thepresentvalueofadoptingthesystemisthenumberofdayscollectionsarereducedtimestheaveragedailycollections,so:PV=3(385)($1,105)PV=$1,276,275b.TheNPVofadoptingthesystemisthepresentvalueofthesavingsminusthecostofadoptingthesystem.Thecostofadoptingthesystemisthepresentvalueofthefeepertransactiontimesthenumberoftransactions.Thisisaperpetuity,so:NPV=$1,276,275–[$0.50(385)/.0002]NPV=$313,775c.Thenetcashflowsisthepresentvalueoftheaveragedailycollectionstimesthedailyinterestrate,minusthetransactioncostperday,so:Netcashflowperday=$1,276,275(.0002)–$0.50(385)Netcashflowperday=$62.76Thenetcashflowpercheckisthenetcashflowperdaydividedbythenumberofchecksreceivedperday,or:Netcashflowpercheck=$62.76/385Netcashflowpercheck=$0.16Alternatively,wecouldfindthenetcashflowpercheckasthenumberofdaysthesystemreducescollectiontimetimestheaveragecheckamounttimesthedailyinterestrate,minusthetransactioncostpercheck.Doingso,weconfirmourpreviousansweras:Netcashflowpercheck=3($1,105)(.0002)–$0.50Netcashflowpercheck=$0.16percheck8.a.Thereductionincashbalancefromadoptingthelockboxisthenumberofdaysthesystemreducescollectiontimetimestheaveragedailycollections,so:Cashbalancereduction=3($145,000)Cashbalancereduction=$435,000b.Thedollarreturnthatcanbeearnedistheaveragedailyinterestratetimesthecashbalancereduction.Theaveragedailyinterestrateis:Averagedailyrate=1.091/365–1Averagedailyrate=.0236%perdayThedailydollarreturnthatcanbeearnedfromthereductionindaystoclearthechecksis:Dailydollarreturn=$435,000(.000236)Dailydollarreturn=$102.72c.Ifthecompanytakesthelockbox,itwillreceivethreepaymentsearly,withthefirstpaymentoccurringtoday.Wecanusethedailyinterestratefrompartb,sothesavingsare:Savings=$145,000+$145,000(PVIFA.0236%,2)Savings=$434,897.32Ifthelockboxpaymentsoccurattheendofthemonth,weneedtheeffectivemonthlyinterestrate,whichis:Monthlyinterestrate=1.091/12–1Monthlyinterestrate=0.7207%Assumingthelockboxpaymentsoccurattheendofthemonth,thelockboxpayments,whichareaperpetuity,willbe:PV=C/R$434,897.32=C/.007207C=$3,134.35Itcouldalsobeassumedthatthelockboxpaymentsoccuratthebeginningofthemonth.Ifso,wewouldneedtousethePVofaperpetuitydue,whichis:PV=C+C/RSolvingforC:C=(PV×R)/(1+R)C=(434,897.32×.007207)/(1+.007207)C=$3,112.029.Theinterestthatthecompanycouldearnwillbetheamountofthecheckstimesthenumberofdaysitwilldelaypaymenttimesthenumberofweeksthatcheckswillbedisbursedtimesthedailyinterestrate,so:Interest=$93,000(7)(52/2)(.00015)Interest=$2,538.9010.Thebenefitofthenewarrangementisthe$4millioninacceleratedcollectionssincethenewsystemwillspeedupcollectionsbyoneday.Thecostisthenewcompensatingbalance,butthecompanywillrecovertheexistingcompensatingbalance,so:NPV=$4,000,000–($500,000–400,000)NPV=$3,900,000Thecompanyshouldproceedwiththenewsystem.ThesavingsaretheNPVtimestheannualinterestrate,so:Netsavings=$3,900,000(.05)Netsavings=$195,000Intermediate11.TofindtheNPVoftakingthelockbox,wefirstneedtocalculatethepresentvalueofthesavings.Thepresentvalueofthesavingswillbethereductionincollectiontimetimestheaveragedailycollections,so:PV=2(750)($980)PV=$1,470,000Andthedailyinterestrateis:Dailyinterestrate=1.0701/365–1Dailyinterestrate=.00019or.019%perdayThetransactioncostsareaperpetuity.Thecostperdayisthecostpertransactiontimesthenumberoftransactionsperday,sotheNPVoftakingthelockboxis:NPV=$1,470,000–[$0.35(750)/.00019]NPV=$54,015.17Withoutthefee,thelockboxsystemshouldbeaccepted.TocalculatetheNPVofthelockboxwiththeannualfee,wecansimplyusetheNPVofthelockboxwithouttheannualfeeandsubtracttheadditioncost.Theannualfeeisaperpetuity,so,withthefee,theNPVoftakingthelockboxis:NPV=$54,015.17–[$5,000/.07]NPV=–$17,413.40Withthefee,thelockboxsystemshouldnotbeaccepted.12.TheminimumnumberofpaymentsperdayneededtomakethelockboxsystemfeasibleisthenumberofchecksthatmakestheNPVofthedecisionequaltozero.Theaveragedailyinterestrateis:Dailyinterestrate=1.051/365–1Dailyinterestrate=.0134%perdayThepresentvalueofthesavingsistheaveragepaymentamounttimesthedaysthecollectionperiodisreducedtimesthenumberofcustomers.Thecostsarethetransactionfeeandtheannualfee.Bothareperpetuities.Thetotaltransactioncostsarethetransactioncostsperchecktimesthenumberofchecks.TheequationfortheNPVoftheproject,whereNisthenumberofcheckstransactedperday,is:NPV=0=($5,300)(1)N–$0.10(N)/.000134–$20,000/.05$400,000=$5,300N–$748.05N$4,551.95N=$400,000N=87.8788customersperdayAPPENDIX27A1.a.Decrease.Thiswilllowerthetradingcosts,whichwillcauseadecreaseinthetargetcashbalance.b.Decrease.Thiswillincreasetheholdingcost,whichwillcauseadecreaseinthetargetcashbalance.c.Increase.Thiswillincreasetheamountofcashthatthefirmhastoholdinnon-interestbearingaccounts,sotheywillhavetoraisethetargetcashbalancetomeetthisrequirement.d.Decrease.Ifthecreditratingimproves,thenthefirmcanborrowmoreeasily,allowingittolowerthetargetcashbalanceandborrowifacashshortfalloccurs.e.Increase.Ifthecostofborrowingincreases,thefirmwillneedtoholdmorecashtoprotectagainstcashshortfallsasitsborrowingcostsbecomemoreprohibitive.f.Either.Thisdependssomewhatonwhatthefeesapplyto,butifdirectfeesareestablished,thenthecompensatingbalancemaybelowered,thusloweringthetargetcashbalance.If,ontheotherhand,feesarechargedonthenumberoftransactions,thenthefirmmaywishtoholdahighercashbalancesotheyarenottransferringmoneyintotheaccountasoften.2.ThetargetcashbalanceusingtheBATmodelis:C*=[(2T×F)/R]1/2C*=[2($8,500)($25)/.06]1/2C*=$2,661.45Theinitialbalanceshouldbe$2,661.45,andwheneverthebalancedropsto$0,another$2,661.45shouldbetransferredin.3.Theholdingcostistheaveragedailycashbalancetimestheinterestrate,so:Holdingcost=($1,300)(.05)Holdingcost=$65.00Thetradingcostsarethetotalcashneededtimesthereplenishingcosts,dividedbytheaveragedailybalancetimestwo,so:Tradingcost=[($43,000)($8)]/[($1,300)(2)]Tradingcost=$132.31Thetotalcostisthesumoftheholdingcostandthetradingcost,so:Totalcost=$65.00+132.31Totalcost=$197.31ThetargetcashbalanceusingtheBATmodelis:C*=[(2T×F)/R]1/2C*=[2($43,000)($8)/.05]1/2C*=$3,709.45Theyshouldincreasetheiraveragedailycashbalanceto:Newaveragecashbalance=$3,709.45/2Newaveragecashbalance=$1,854.72Thiswouldminimizethecosts.Thenewtotalcostwouldbe:Newtotalcost=($1,845.72)(.05)+[($43,000)($8)]/[2($1,854.72)]Newtotalcost=$185.474.a.Theopportunitycostsaretheamounttransferredtimestheinterestrate,dividedbytwo,so:Opportunitycost=($1,500)(.05)/2Opportunitycost=$37.50Thetradingcostsarethetotalcashbalancetimesthetradingcostpertransaction,dividedbytheamounttransferred,so:Tradingcost=($16,000)($25)/$1,500Tradingcost=$266.67Thefirmkeepstoolittleincashbecausethetradingcostsaremuchhigherthantheopportunitycosts.b.ThetargetcashbalanceusingtheBATmodelis:C*=[(2T×F)/R]1/2C*=[2($16,000)($25)/.05]1/2C*=$4,0005.Thetotalcashneededisthecashshortagepermonthtimestwelvemonths,so:Totalcash=12($140,000)Totalcash=$1,680,000ThetargetcashbalanceusingtheBATmodelis:C*=[(2T×F)/R]1/2C*=[2($1,680,000)($500)/.057]1/2C*=$171,679.02Thecompanyshouldinvest:Invest=$690,000–171,679.02Invest=$518,320.98ofitscurrentcashholdingsinmarketablesecuritiestobringthecashbalancedowntotheoptimallevel.Overtherestoftheyear,sellsecurities:Sellsecurities=$1,680,000/$171,679.02Sellsecurities=9.7910times.6.Thelowerlimitistheminimumbalanceallowedintheaccount,andtheupperlimitisthemaximumbalanceallowedintheaccount.Whentheaccountbalancedropstothelowerlimit:Securitiessold=$80,000–43,000Securitiessold=$37,000inmarketablesecuritieswillbesold,andtheproceedsdepositedintheaccount.Thismovestheaccountbalancebacktothetargetcashlevel.Whentheaccountbalancerisestotheupperlimit,then:Securitiespurchased=$125,000–80,000Securitiespurchased=$45,000ofmarketablesecuritieswillbepurchased.Thisexpenditurebringsthecashlevelbackdowntothetargetbalanceof$80,000.7.ThetargetcashbalanceusingtheMiller-Orrmodelis:C*=L+(3/4×F×2/R]1/3C*=$1,500+[3/4($40)($70)2/.00021]1/3C*=$2,387.90Theupperlimitis:U*=3×C*–2×LU*=3($2,387.90)–2($1,500)U*=$4,163.71Whenthebalanceinthecashaccountdropsto$1,500,thefirmsells:Sell=$2,387.90–1,500Sell=$887.90ofmarketablesecurities.TheproceedsfromthesaleareusedtoreplenishtheaccountbacktotheoptimaltargetlevelofC*.Conversely,whentheupperlimitisreached,thefirmbuys:Buy=$4,163.71–2,387.90Buy=$1,775.81ofmarketablesecurities.Thisexpenditurelowersthecashlevelbackdowntotheoptimallevelof$2,387.90.8.Asvarianceincreases,theupperlimitandthespreadwillincrease,whilethelowerlimitremainsunchanged.Thelowerlimitdoesnotchangebecauseitisanexogenousvariablesetbymanagement.Asthevarianceincreases,however,theamountofuncertaintyincreases.Whenthishappens,thetargetcashbalance,andthereforetheupperlimitandthespread,willneedtobehigher.Ifthevariancedropstozero,thenthelowerlimit,thetargetbalance,andtheupperlimitwillallbethesame.9.Theaveragedailyinterestrateis:Dailyrate=1.071/365–1Dailyrate=.000185or.0185%perdayThetargetcashbalanceusingtheMiller-Orrmodelis:C*=L+(3/4×F×2/R]1/3C*=$160,000+[3/4($300)($890,000)/.000185]1/3C*=$170,260.47Theupperlimitis:U*=3×C*–2×LU*=3($170,260.47)–2($160,000)U*=$190,781.4110.UsingtheBATmodelandsolvingforR,weget:C*=[(2T×F)/R]1/2$2,700=[2($28,000)($10)/R]1/2R=[2($28,000)($10)]/$2,7002R=.0768or7.68%