《金融学》答案第四章 货币的时间价值与现金流贴现分析.docx
《《金融学》答案第四章 货币的时间价值与现金流贴现分析.docx》由会员分享，可在线阅读，更多相关《《金融学》答案第四章 货币的时间价值与现金流贴现分析.docx（27页珍藏版）》请在冰豆网上搜索。
《金融学》答案第四章货币的时间价值与现金流贴现分析
CHAPTER4
THETIMEVALUEOFMONEYANDDISCOUNTEDCASHFLOWANALYSIS
Objectives
∙Toexplaintheconceptsofcompoundinganddiscounting,futurevalueandpresentvalue.
∙Toshowhowtheseconceptsareappliedtomakingfinancialdecisions.
Outline
4.1Compounding
4.2TheFrequencyofCompounding
4.3PresentValueandDiscounting
4.4AlternativeDiscountedCashFlowDecisionRules
4.5MultipleCashFlows
4.6Annuities
4.7PerpetualAnnuities
4.8LoanAmortization
4.9ExchangeRatesandTimeValueofMoney
4.10InflationandDiscountedCashFlowAnalysis
4.11TaxesandInvestmentDecisions
Summary
∙Compoundingistheprocessofgoingfrompresentvalue（PV）tofuturevalue（FV）.Thefuturevalueof$1earninginterestatrateiperperiodfornperiodsis（1+i）n.
∙Discountingisfindingthepresentvalueofsomefutureamount.Thepresentvalueof$1discountedatrateiperperiodfornperiodsis1/（1+i）n.
∙Onecanmakefinancialdecisionsbycomparingthepresentvaluesofstreamsofexpectedfuturecashflowsresultingfromalternativecoursesofaction.Thepresentvalueofcashinflowslessthepresentvalueofcashoutflowsiscallednetpresentvalue（NPV）.IfacourseofactionhasapositiveNPV,itisworthundertaking.
∙Inanytimevalueofmoneycalculation,thecashflowsandtheinterestratemustbedenominatedinthesamecurrency.
∙Neveruseanominalinterestratewhendiscountingrealcashflowsorarealinterestratewhendiscountingnominalcashflows.
HowtoDoTVMCalculationsinMSExcel
Assumeyouhavethefollowingcashflowssetupinaspreadsheet:
A
B
1
t
CF
2
0
-100
3
1
50
4
2
60
5
3
70
6
NPV
7
IRR
MovethecursortocellB6inthespreadsheet.Clickthefunctionwizardfxinthetoolbarandwhenamenuappears,selectfinancialandthenNPV.Thenfollowtheinstructionsforinputtingthediscountrateandcashflows.Youcaninputthecolumnofcashflowsbyselectingandmovingitwithyourmouse.UltimatelycellB6shouldcontainthefollowing:
=NPV（0.1,B3:
B5）+B2
Thefirstvariableinparenthesisisthediscountrate.Makesuretoinputthediscountrateasadecimalfraction（i.e.,10%is.1）.NotethattheNPVfunctioninExceltreatsthecashflowsasoccurringattheendofeachperiod,andthereforetheinitialcashflowof100incellB2isaddedaftertheclosingparenthesis.WhenyouhittheENTERkey,theresultshouldbe$47.63.
NowmovethecursortocellB7tocomputeIRR.ThistimeselectIRRfromthelistoffinancialfunctionsappearinginthemenu.UltimatelycellB7shouldcontainthefollowing:
=IRR（B2:
B5）
WhenyouhittheENTERkey,theresultshouldbe34%.
Yourspreadsheetshouldlooklikethiswhenyouhavefinished:
A
B
1
t
CF
2
0
-100
3
1
50
4
2
60
5
3
70
6
NPV
47.63
7
IRR
34%
SolutionstoProblemsatEndofChapter
1.Ifyouinvest$1000todayataninterestrateof10%peryear,howmuchwillyouhave20yearsfromnow,assumingnowithdrawalsintheinterim?
SOLUTION:
n
i
PV
FV
PMT
Result
20
10
1000
?
0
FV=6,727.50
2.a.Ifyouinvest$100everyyearforthenext20years,startingoneyearfromtodayandyouearninterestof10%peryear,howmuchwillyouhaveattheendofthe20years?
b.Howmuchmustyouinvesteachyearifyouwanttohave$50,000attheendofthe20years?
SOLUTION:
n
i
PV
FV
PMT
Result
a.20
10
0
?
100
FV=5,727.50
b.20
10
0
50,000
?
PMT=872.98
3.Whatisthepresentvalueofthefollowingcashflowsataninterestrateof10%peryear?
a.$100receivedfiveyearsfromnow.
b.$100received60yearsfromnow.
c.$100receivedeachyearbeginningoneyearfromnowandending10yearsfromnow.
d.$100receivedeachyearfor10yearsbeginningnow.
e.$100eachyearbeginningoneyearfromnowandcontinuingforever.
SOLUTION:
n
i
PV
FV
PMT
Result
a.5
10
?
100
0
PV=$62.09
b.60
10
?
100
0
PV=$.3284
c.10
10
?
0
100ordinary
PV=$614.46
d.10
10
?
0
100immediate
PV=$675.90
e.Perpetuity
10
?
0
100ordinary
Seebelow
e.PV=$100=$1,000
.10
4.Youwanttoestablisha“wasting”fundwhichwillprovideyouwith$1000peryearforfouryears,atwhichtimethefundwillbeexhausted.Howmuchmustyouputinthefundnowifyoucanearn10%interestperyear?
SOLUTION:
n
i
PV
FV
PMT
Result
4
10
?
0
1,000
PV=$3,169.87
5.Youtakeaone-yearinstallmentloanof$1000ataninterestrateof12%peryear（1%permonth）toberepaidin12equalmonthlypayments.
a.Whatisthemonthlypayment?
b.Whatisthetotalamountofinterestpaidoverthe12-monthtermoftheloan?
SOLUTION:
n
i
PV
FV
PMT
Result
12
1
1,000
0
?
PMT=$88.85
a.PMT=$88.85
b.12x$88.85-$1,000=$66.20
6.Youaretakingouta$100,000mortgageloantoberepaidover25yearsin300monthlypayments.
a.Iftheinterestrateis16%peryearwhatistheamountofthemonthlypayment?
b.Ifyoucanonlyaffordtopay$1000permonth,howlargealoancouldyoutake?
c.Ifyoucanaffordtopay$1500permonthandneedtoborrow$100,000,howmanymonthswouldittaketopayoffthemortgage?
d.Ifyoucanpay$1500permonth,needtoborrow$100,000,andwanta25yearmortgage,whatisthehighestinterestrateyoucanpay?
SOLUTION:
n
i
PV
FV
PMT
Result
a.300
16/12
100,000
0
?
PMT=$1358.89
b.300
16/12
?
0
1,000
PV=$73,590
c.?
16/12
100,000
0
1,500
n=166
d.300
?
100,000
0
1,500
i=1.482%permonth
a.Note:
Donotroundofftheinterestratewhencomputingthemonthlyrateoryouwillnotgetthesameanswerreportedhere.Divide16by12andthenpresstheikey.
b.Note:
YoumustinputPMTandPVwithoppositesigns.
c.Note:
YoumustinputPMTandPVwithoppositesigns.
7.In1626PeterMinuitpurchasedManhattanIslandfromtheNativeAmericansforabout$24worthoftrinkets.Ifthetribehadtakencashinsteadandinvestedittoearn6%peryearcompoundedannually,howmuchwouldtheIndianshavehadin1986,360yearslater?
SOLUTION:
n
i
PV
FV
PMT
Result
360
6
24
?
0
FV=3.091010
FV=30,925,930,000
8.Youwina$1millionlotterywhichpaysyou$50,000peryearfor20years,beginningoneyearfromnow.Howmuchisyourprizereallyworthassuminganinterestrateof8%peryear?
SOLUTION:
n
i
PV
FV
PMT
Result
20
8
?
0
50,000
PV=$490,907
9.Yourgreat-auntleftyou$20,000whenshedied.Youcaninvestthemoneytoearn12%peryear.Ifyouspend$3,540peryearoutofthisinheritance,howlongwillthemoneylast?
SOLUTION:
n
i
PV
FV
PMT
Result
?
12
20,000
0
3,540
n=10years
10.Youborrow$100,000fromabankfor30yearsatanAPRof10.5%.Whatisthemonthlypayment?
Ifyoumustpaytwopointsupfront,meaningthatyouonlyget$98,000fromthebank,whatisthetrueAPRonthemortgageloan?
SOLUTION:
n
i
PV
FV
PMT
Result
360
.875
100,000
0
?
PMT=$914.74
Ifyoumustpay2pointsupfront,thebankisineffectlendingyouonly$98,000.Keyingin98000asPVandcomputingi,weget:
n
i
PV
FV
PMT
Result
360
?
98,000
0
914.74
i=.89575
i=.89575%permonth;APR=12.8957510.75%
11.Supposethatthemortgageloandescribedinquestion10isaone-yearadjustableratemortgage（ARM）,whichmeansthatthe10.5%interestappliesforonlythefirstyear.Iftheinterestrategoesupto12%inthesecondyearoftheloan,whatwillyournewmonthlypaymentbe?
SOLUTION:
Step1istocomputetheremainingbalanceafterthefirst12payments:
n
i
PV
FV
PMT
Result
348
.875
?
0
914.74
PV=$99499.57
Step2istocomputethenewmonthlypaymentataninterestrateof1%permonth:
n
i
PV
FV
PMT
Result
348
1
99499.57
0
?
PMT=$1,027.19
12.Youjustreceivedagiftof$500fromyourgrandmotherandyouarethinkingaboutsavingthismoneyforgraduationwhichisfouryearsaway.YouhaveyourchoicebetweenBankAwhichispaying7%forone-yeardepositsandBankBwhichispaying6%onone-yeardeposits.Eachbankcompoundsinterestannually.WhatisthefuturevalueofyoursavingsoneyearfromtodayifyousaveyourmoneyinBankA?
BankB?
Whichisthebetterdecision?
Whatsavingsdecisionwillmostindividualsmake?
WhatlikelyreactionwillBankBhave?
SOLUTION:
FutureValueinBankA:
n
i
PV
FV
PMT
1
7
-$500
Solve
0
$535
Formula:
$500x（1.07）=$535
FutureValueinBankB:
n
i
PV
FV
PMT
1
6
-$500
Solve
$530
Formula:
$500x（1.06）=$530
a.YouwilldecidetosaveyourmoneyinBankAbecauseyouwillhavemoremoneyattheendoftheyear.Youmadeanextra$5becauseofyoursavingsdecision.Thatisanincreaseinvalueof1%.Becauseinterestcompoundedonlyonceperyearandyourmoneywasleftintheaccountforonlyoneyear,theincreaseinvalueisstrictlyduetothe1%differenceininterestrates.
b.MostindividualswillmakethesamedecisionandeventuallyBankBwillhavetoraiseitsrates.However,itisalsopossiblethatBankAispayingahighratejusttoattractdepositorseventhoughthisrateisnotprofitableforthebank.EventuallyBankAwillhavetoloweritsratetoBankB’srateinordertomakemoney.
13.
SueConsultanthasjustbeengivenabonusof$2,500byheremployer.Sheisthinkingaboutusingthemoneytostartsavingforthefuture.Shecaninvesttoearnanannualrateofinterestof10%.
a.AccordingtotheRuleof72,approximatelyhowlongwillittakeforSuetoincreaseherwealthto$5,000?
b.Exactlyho
升级会员 