《金融学》答案第四章 货币的时间价值与现金流贴现分析Word文档下载推荐.docx

《金融学》答案第四章 货币的时间价值与现金流贴现分析Word文档下载推荐.docx

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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

-100

3

50

4

60

5

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:

47.63

34%

SolutionstoProblemsatEndofChapter

1.Ifyouinvest$1000todayataninterestrateof10%peryear,howmuchwillyouhave20yearsfromnow,assumingnowithdrawalsintheinterim?

SOLUTION:

n

i

PV

FV

PMT

Result

20

10

1000

?

FV=6,727.50

2.a.Ifyouinvest$100everyyearforthenext20years,startingoneyearfromtodayandyouearninterestof10%peryear,howmuchwillyouhaveattheendofthe20years?

b.Howmuchmustyouinvesteachyearifyouwanttohave$50,000attheendofthe20years?

a.20

100

FV=5,727.50

b.20

50,000

PMT=872.98

3.Whatisthepresentvalueofthefollowingcashflowsataninterestrateof10%peryear?

a.$100receivedfiveyearsfromnow.

b.$100received60yearsfromnow.

c.$100receivedeachyearbeginningoneyearfromnowandending10yearsfromnow.

d.$100receivedeachyearfor10yearsbeginningnow.

e.$100eachyearbeginningoneyearfromnowandcontinuingforever.

a.5

PV=$62.09

b.60

PV=$.3284

c.10

100ordinary

PV=$614.46

d.10

100immediate

PV=$675.90

e.Perpetuity

Seebelow

e.PV=$100=$1,000

.10

4.Youwanttoestablisha“wasting”fundwhichwillprovideyouwith$1000peryearforfouryears,atwhichtimethefundwillbeexhausted.Howmuchmustyouputinthefundnowifyoucanearn10%interestperyear?

1,000

PV=$3,169.87

5.Youtakeaone-yearinstallmentloanof$1000ataninterestrateof12%peryear（1%permonth）toberepaidin12equalmonthlypayments.

a.Whatisthemonthlypayment?

b.Whatisthetotalamountofinterestpaidoverthe12-monthtermoftheloan?

12

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?

a.300

16/12

100,000

PMT=$1358.89

b.300

PV=$73,590

c.?

1,500

n=166

d.300

i=1.482%permonth

a.Note:

Donotroundofftheinterestratewhencomputingthemonthlyrateoryouwillnotgetthesameanswerreportedhere.Divide16by12andthenpresstheikey.

b.Note:

YoumustinputPMTandPVwithoppositesigns.

c.Note:

7.In1626PeterMinuitpurchasedManhattanIslandfromtheNativeAmericansforabout$24worthoftrinkets.Ifthetribehadtakencashinsteadandinvestedittoearn6%peryearcompoundedannually,howmuchwouldtheIndianshavehadin1986,360yearslater?

360

24

FV=3.091010

FV=30,925,930,000

8.Youwina$1millionlotterywhichpaysyou$50,000peryearfor20years,beginningoneyearfromnow.Howmuchisyourprizereallyworthassuminganinterestrateof8%peryear?

8

PV=$490,907

9.Yourgreat-auntleftyou$20,000whenshedied.Youcaninvestthemoneytoearn12%peryear.Ifyouspend$3,540peryearoutofthisinheritance,howlongwillthemoneylast?

20,000

3,540

n=10years

10.Youborrow$100,000fromabankfor30yearsatanAPRof10.5%.Whatisthemonthlypayment?

Ifyoumustpaytwopointsupfront,meaningthatyouonlyget$98,000fromthebank,whatisthetrueAPRonthemortgageloan?

.875

PMT=$914.74

Ifyoumustpay2pointsupfront,thebankisineffectlendingyouonly$98,000.Keyingin98000asPVandcomputingi,weget:

98,000

914.74

i=.89575

i=.89575%permonth;

APR=12.8957510.75%

11.Supposethatthemortgageloandescribedinquestion10isaone-yearadjustableratemortgage（ARM）,whichmeansthatthe10.5%interestappliesforonlythefirstyear.Iftheinterestrategoesupto12%inthesecondyearoftheloan,whatwillyournewmonthlypaymentbe?

Step1istocomputetheremainingbalanceafterthefirst12payments:

348

PV=$99499.57

Step2istocomputethenewmonthlypaymentataninterestrateof1%permonth:

99499.57

PMT=$1,027.19

12.Youjustreceivedagiftof$500fromyourgrandmotherandyouarethinkingaboutsavingthismoneyforgraduationwhichisfouryearsaway.YouhaveyourchoicebetweenBankAwhichispaying7%forone-yeardepositsandBankBwhichispaying6%onone-yeardeposits.Eachbankcompoundsinterestannually.WhatisthefuturevalueofyoursavingsoneyearfromtodayifyousaveyourmoneyinBankA?

BankB?

Whichisthebetterdecision?

Whatsavingsdecisionwillmostindividualsmake?

WhatlikelyreactionwillBankBhave?

FutureValueinBankA:

-$500

Solve

$535

Formula:

$500x（1.07）=$535

FutureValueinBankB:

$530

$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