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1、BBA307Assignment4.1Solutions1.Drawatimelinefor(1)a$100lumpsumcashflowattheendofyear2,(2)anordinaryannuityof$100peryearfor3yearsand(3)anunevencashflowstreamof-$50,$100,$75,and$50attheendofyears0through3.SolutionAtimelineisagraphicalrepresentationwhichisusedtoshowthetimingofcas
2、hflows.Thetickmarksrepresentendofperiods(oftenyears),sotime0istoday;time1istheendofthefirstyear,or1yearfromtoday;andsoon.I%012year
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5、lumpsum100cashflowI%0123
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9、annuity100100100I%0123
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13、unevencashflowstream-501007550Alumpsumisasingleflow;forexample,a$100inflowinyear2,asshown
14、inthetoptimeline.Anannuityisaseriesofequalcashflowsoccurringoverequalintervals,asillustratedinthemiddletimeline.Anunevencashflowstreamisanirregularseriesofcashflowswhichdonotconstituteanannuity,asinthelowertimeline.-50representsacashoutflowratherthanareceiptorinflow.2.Calcula
15、tethefollowing:a.Thefuturevalueofaninitial$100after3yearsassumingannualinterestof10%.Solution:Showdollarscorrespondingtoquestionmark,calculatedasfollows:10%0123
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19、100FV=?After1year:FV1=PV+I1=PV+PV(I)=PV(1+I)=$100(1.10)=$110.00.Similarly:FV2=FV1+I2=FV1+FV1(I)=FV1(1+I)=$110(1.
20、10)=$121.00=PV(1+i)(1+i)=PV(1+i)2.FV3=FV2+I3=FV2+FV2(I)=FV2(1+I)=$121(1.10)=$133.10=PV(1+I)2(1+I)=PV(1+I)3.Ingeneral,weseethat:FVn=PV(1+I)N,SOFV3=$100(1.10)3=$100(1.3310)=$133.10.Notethatthisequationhas4variables:FVN,PV,I,andN.HereweknowallexceptFVN,sowesolveforFVN.Wewill,how
21、ever,oftensolveforoneoftheotherthreevariables.Byfar,theeasiestwaytoworkalltimevalueproblemsiswithafinancialcalculator.Justpluginany3ofthefourvaluesandfindthe4th.Findingfuturevalues(movingtotherightalongthetimeline)iscalledcompounding.Notethatthereare3waysoffindingFV3:usingare
22、gularcalculator,financialcalculator,orspreadsheets.Forsimpleproblems,weshowonlytheregularcalculatorandfinancialcalculatormethods.(1)regularcalculator:1.$100(1.10)(1.10)(1.10)=$133.10.2.$100(1.10)3=$133.10.(2)financialcalculator:Thisisespeciallyefficientformorecomplexproblems,
23、includingexamproblems.Inputthefollowingvalues:N=3,I=10,PV=-100,PMT=0
