公司理财精要chap005课件

Discounted

Cash

Flow

ValuationChapter51McGraw-Hill/Irwin©2004The

McGraw-HillCompanies,Inc.

Allrights

res•

Beabletocomputethefuturevalueofmulti

cashflows•

Beabletocomputethepresentvalueofmult

cashflows•

Beabletocompute

loan

payments•

Beabletofindtheinterestrateonaloan•Understandhowloansareamortized

orpaid

o•

Understandhow

interestratesarequotedKeyConceptsand

Skills2McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•FutureandPresentValuesofMultipleCash

Flows•Valuing

Level

Cash

Flows:Annuities

and

Perpetuities•Comparing

Rates:The

Effect

of

Compounding

Periods•

LoanTypesand

Loan

AmortizationChapterOutline3McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

Find

the

value

at

year3of

each

cash

floandadd

them

together.•

Today

(year0)

:FV=7000(1.08)3

=8,817.98•Year

1:FV=4,000(1.08)2

=4,665.60•Year2:FV=4,000(1.08)=4,320•Year3:value=4,000•Totalvaluein3years=8817.98+4665.60+4320+4000=21,803.58•Value

at

year4=21,803.58(1.08)=23,547.8MultipleCashFlows–FVExample5.14McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Supposeyouinvest$500inamutualfundtodand$600inoneyear.Ifthefundpays9%annually,howmuchwillyouhaveintwoyear•FV=500(1.09)2+600(1.09)=1248.05Multiple

CashFlows–FVExample

25McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

Howmuch

willyouhavein

5years

ifyoumake

nofurtherdeposits?•First

way:•

FV=500(1.09)5

+

600(1.09)4

=1616.26•

Second

way–use

value

at

year2:•

FV=

1248.05(1.09)3

=

1616.26Example2Continued6McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Supposeyouplantodeposit$100intoanaccountinoneyearand$300intotheaccounthreeyears.Howmuchwillbeintheaccountfiveyearsiftheinterestrateis8%?•FV=100(1.08)4+300(1.08)2=136.05+349.92=485.97Multiple

CashFlows–FVExample

37McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresExample3Timeline136.05349.92485.97©2004TheMcGraw-HillCompanies,Inc.Allrightsres/IrwinMcGraw-Hill100/Irwin3040023518•FindthePVofeachcashflowandaddthem•Year1CF:200/(1.12)1=178.57•Year2CF:400/(1.12)2=318.88•Year3CF:600/(1.12)3=427.07•Year4CF:800/(1.12)4=508.41•TotalPV=178.57+318.88+427.07+508.41=1432.93Multiple

CashFlows–Present

ValueExample5.39McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresExample5.3Timeline178.57318.88427.07508.41©2004TheMcGraw-HillCompanies,Inc.Allrightsres1432.93/IrwinMcGraw-Hill400800600200/Irwin4023110/IrwinMcGraw-HillMultipleCashFlows–PVAnotherExample•Youareconsideringaninvestmentthatwillyou$1000inoneyear,$2000intwoyearsand$3000inthreeyears.Ifyouwanttoearn10onyourmoney,howmuchwouldyoubewillingtopay?•PV=1000/(1.1)1=909.09•PV=2000/(1.1)2=1652.89•PV=3000/(1.1)3=2253.94•PV=909.09+1652.89+2253.94=4815.9311/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres/IrwinMcGraw-HillMultiple

UnevenCashFlows–

UsingtheCalculator•

Anotherwaytousethefinancialcalculatorfor

une

cashflowsisyouusethecashflowkeys•

TexasInstruments

BA-II

Plus•

PressCFandenterthecashflowsbeginningwithyear•

Youhavetopressthe

“Enter

”

keyforeachcashflo•

Use

the

down

arrow

key

to

move

to

the

next

cash

flow•

The

“F

”is

the

number

of

times

a

given

cash

flow

occursinconsecutiveyears•

Use

the

NPV

key

to

compute

the

present

value

by

enter

theinterestrateforI,pressingthedownarrowandthencom•Clear

the

cash

flow

keys

by

pressing

CF

and

then

CLRWork12/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

You

canuse

thePV

orFV

functionsinExceltfindthepresentvalueorfuturevalueofas

cashflows•Settingthedataupishalfthebattle

–ifupproperly,thenyoucanjustcopythe

form•ClickontheExcel

iconforan

exampleExample:Spreadsheet

Strategies13McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Yourbrokercallsyouandtellsyouthathehasthisgreatinvestmentopportunity.Ifyouinvest$100toyouwillreceive$40inoneyearand$75intwoyearsIfyourequirea15%returnoninvestmentsofthisrshouldyoutaketheinvestment?•UsetheCFkeystocomputethevalueoftheinvestment•CF;CF0=0;C01=40;F01=1;C02=75;F02=1•NPV;I=15;CPTNPV=91.49•No–thebrokerischargingmorethanyouwouldbwillingtopay.14McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresDecisions,Decisions•Youareofferedtheopportunitytoputsomemoneyawayforretirement.Youwillreceivefiveannualpaymentsof$25,000eachbeginnin40years.Howmuchwouldyoubewillingtoinvesttodayifyoudesireaninterestrate•Usecashflowkeys:•CF;CF0=0;C01=0;F01=39;C02=25000;F02=5;NPV;I=12;CPTNPV=1084.71Saving

For

Retirement15McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

Supposeyouarelookingatthefollowingpossible

cash

flows:Year

1CF=$100;Yearsand3CFs=

$200;

Years

4

and

5

CFs

=

$300.Therequireddiscountrateis7%•

What

isthevalueofthecashflowsat

year

5•

What

isthevalueofthecashflows

today?•

What

isthevalueofthecashflowsat

year

3QuickQuiz

:Part

117McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Annuity

–finiteseriesofequalpayments

t

occuratregularintervals•

If

the

first

paymentoccursattheendofthep

itiscalledanordinary

annuity•

If

the

first

paymentoccursatthebeginningo

period,itiscalledanannuitydue•Perpetuity

–infiniteseriesofequalpaymAnnuitiesandPerpetuitiesDefin18McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

YouborrowmoneyTODAY

soyou

need

tocomputethepresentvalue.•

48N;

1I/Y;-632PMT;CPTPV=23,999.54($24,000)Annuity–Example5.521McGraw-Hill/Irwin•

Formula:©2004TheMcGraw-HillCompanies,Inc.Allrightsres•SupposeyouwinthePublishersClearinghou$10millionsweepstakes.Themoneyispaidequalannualinstallmentsof$333,333.33ov30years.Iftheappropriatediscountratehowmuchisthesweepstakesactuallyworthtoday?•PV=333,333.33[1–1/1.0530]/.05=5,124,150.29Annuity–SweepstakesExample22McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Youarereadytobuyahouseandyouhave$20,000foradownpaymentandclosingcosts.Closingcostsareestimatedtobe4%oftheloanvalue.Youhaveanannualsalaryof$36,000andthebankiswillingtoallowyourmonthlymortgagepaymenttobeequalto28%ofyourmonthlyincome.Theinterestrateontheloanis6%peryearwithmonthlycompounding(.5%permonth)fora30-yearfixedrateloan.Howmuchmoneywillthebankloanyou?Howmuchcanyouofferforthehouse?BuyingaHouse23McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

Bank

loan•Monthly

income=36,000/

12=3,000•

Maximumpayment=.28(3,000)=840•

PV=840[1

–

1/1.005360]/.005=140,

105•TotalPrice•Closing

costs=.04(140,

105)=5,604•

Downpayment=20,000–5604=

14,396•TotalPrice=140,

105+14,396=

154,501BuyingaHouse-Continued24McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresExample:SpreadsheetStrategies

AnnuityPV•

Thepresentvalueandfuturevalueformulas

spreadsheetincludeaplaceforannuitypay•ClickontheExcel

icon

to

seean

example©2004TheMcGraw-HillCompanies,Inc.Allrightsres/IrwinMcGraw-Hill/Irwin25•Youknowthepaymentamountforaloanandyouwanttoknowhowmuchwasborrowed.Doyoucomputeapresentvalueorafuturevalu•Youwanttoreceive5000permonthinretirement.Ifyoucanearn.75%permonthayouexpecttoneedtheincomefor25years,hmuchdoyouneedtohaveinyouraccountatretirement?Quick

Quiz

:

Part226McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Supposeyouwanttoborrow$20,000foranewcar.Youcanborrowat8%peryear,compoundedmonthly(8/12=.66667%permonth).Ifyoutakea4yearloan,whatisyomonthlypayment?•20,000=C[1–1/1.006666748]/.0066667•C=488.26FindingthePayment27McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresExample:SpreadsheetStrategies

AnnuityPayment•

AnotherTVMformulathat

canbe

found

ina

spreadsheet

isthepaymentformula•

PMT(rate,nper,pv,fv)•

ThesamesignconventionholdsasforthePVan

FVformulas•ClickontheExcel

iconforan

example©2004TheMcGraw-HillCompanies,Inc.Allrightsres/IrwinMcGraw-Hill/Irwin28FindingtheNumberofPayments–Example5.6•Startwiththeequationandrememberyourlo•1000=20(1–1/1.015t)/.015•.75=1–1/1.015t•1/1.015t=.25•1/.25=1.015t•t=ln(1/.25)/ln(1.015)=93.111months=7.7years•Andthisisonlyifyoudon’tchargeanythimoreonthecard!/IrwinMcGraw-Hill29/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Supposeyouborrow$2000at5%andyouaregoingtomakeannualpaymentsof$734.42.Howlongbeforeyoupayofftheloan?•2000=734.42(1–1/1.05t)/.05•.136161869=1–1/1.05t•1/1.05t=.863838131•1.157624287=1.05t•t=ln(1.157624287)/ln(1.05)=3yearsFindingtheNumberofPayments–

AnotherExample

30McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresSignconventionmatters!!!60N10,000PV-207.58PMTCPTI/Y=.75%31©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Supposeyouborrow$10,000fromyourparenttobuyacar.Youagreetopay$207.58permonthfor60months.Whatisthemonthlyinterestrate?FindingtheRate••

•

•

•McGraw-Hill/Irwin•Youwanttoreceive$5000permonthforthenext5years.Howmuchwouldyouneedtodeposittodayifyoucanearn.75%permonth?•Whatmonthlyratewouldyouneedtoearnifyouonlyhave$200,000todeposit?•Supposeyouhave$200,000todepositandcanearn.permonth.•Howmanymonthscouldyoureceivethe$5000payment?•

How

much

could

you

receive

every

month

for

5yearQuick

Quiz

:Part333McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresAnnuityDueTimeline©2004TheMcGraw-HillCompanies,Inc.Allrightsres35,016.1232,464100001000010000/IrwinMcGraw-Hill/Irwin023136/IrwinMcGraw-Hill•AnotheronlinefinancialcalculatorcanbeatMoneyChimp•Clickonthewebsurferandworkthefollowiexample•Choosecalculatorandthenannuity•Youjustinherited$5million.Ifyoucanearnonyourmoney,howmuchcanyouwithdraweachyearforthenext40years?•Datachimpassumesannuitydue!!!•Payment=$313,497.81/IrwinExample:WorktheWeb©2004TheMcGraw-HillCompanies,Inc.Allrightsres37•Perpetuity

formula:PV=C/r•Currentrequiredreturn:•

40=

1

/

r•r=.025or2.5%perquarter•Dividendfornewpreferred

:•100=C/.025•

C=2.50perquarterPerpetuity

–

Example5.738McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres39McGraw-Hill/IrwinTable5.2©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Youwanttohave$1milliontouseforretirementinyears.Ifyoucanearn1%permonth,howmuchdoyouneedtodepositonamonthlybasisifthefirstpaymismadeinonemonth?•Whatifthefirstpaymentismadetoday?•Youareconsideringpreferredstockthatpaysaquarterlydividendof$1.50.Ifyourdesiredreturnperquarter,howmuchwouldyoubewillingtopay?Quick

Quiz

:Part440McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

Thisistheactual

rate

paid

(or

received)afteraccounting

for

compounding

that

occurs

during

the

y•Ifyouwanttocomparetwoalternativeinvestments

withdifferent

compoundingperiodsyouneedtocomputetheEARandusethatforcomparison.Effective

Annual

Rate

(EAR)41McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Thisistheannualratethat

isquotedby

law•

Bydefinition

APR=period

rate

times

the

numberofperiodsperyear•Consequently,to

get

the

period

rate

we

rearrangetheAPRequation:•Periodrate=APR/numberofperiodsperyear•

You

shouldNEVER

dividetheeffectiverateb

thenumberofperiodsperyear–it

will

NOT

giveyoutheperiodrateAnnualPercentageRate42McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

What

istheAPR

if

the

monthly

rate

is.5%?•

.5(12)=6%•

What

istheAPR

if

the

semiannual

rate

is.5%?•

.5(2)=

1%•

WhatisthemonthlyrateiftheAPRis12%

withmonthlycompounding?•

12

/

12

=

1%•

Can

you

divide

the

above

APR

by

2

to

get

thesemiannualrate?NO!!!YouneedanAPRbasedonsemiannualcompoundingtofindthe

semiannualrateComputingAPRs43McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

YouALWAYSneedtomakesurethatthe

interest

rateandthetimeperiodmatch.•Ifyouarelookingatannualperiods,youneedan

annualrate.•Ifyouarelookingatmonthlyperiods,youneeda

monthlyrate.•

IfyouhaveanAPRbasedonmonthlycompounding,youhavetousemonthlyperiodsforlumpsums,oradjusttheinterest

rateappropriatelyifyou

have

paymentsotherthanmonthlyThingstoRemember44McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Supposeyoucanearn1%permonthon$1investedtoday.•WhatistheAPR?1(12)=12%•Howmuchareyoueffectivelyearning?•FV=1(1.01)12=1.1268•Rate=(1.1268–1)/1=.1268=12.68%•Supposeifyouputitinanotheraccount,youearn3perquarter.•WhatistheAPR?3(4)=12%•Howmuchareyoueffectivelyearning?•FV=1(1.03)4=1.1255•Rate=(1.1255–1)/1=.1255=12.55%45McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresComputingEARs-ExampleEAR-Formula46McGraw-Hill/IrwinRememberthattheAPR

isthequotedrate©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Youarelookingattwosavingsaccounts.Onepays5.25%,withdailycompounding.Theothpays5.3%withsemiannualcompounding.Whichaccountshouldyouuse?•Firstaccount:•EAR=(1+.0525/365)365–1=5.39%•Secondaccount:•EAR=(1+.053/2)2–1=5.37%•Whichaccountshouldyouchooseandwhy?Decisions,DecisionsII47McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Let’sverifythechoice.Supposeyouinves$100ineachaccount.Howmuchwillyouhaveineachaccountinoneyear?•FirstAccount:•Dailyrate=.0525/365=.00014383562•FV=100(1.00014383562)365=105.39•SecondAccount:•Semiannualrate=.0539/2=.0265•FV=100(1.0265)2=105.37•Youhavemoremoneyinthefirstaccount.Decisions,DecisionsII

Continue48McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

Ifyouhaveaneffectiverate,howcanyoucomputetheAPR?RearrangetheEAR

equation

andyou

get

:ComputingAPRsfromEARs49McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Supposeyouwanttoearnaneffectiverateoandyouarelookingatanaccountthatcompoundsonamonthlybasis.WhatAPRmusttheypay?APR-

Example50McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Supposeyouwanttobuyanewcomputersystemandthestoreiswillingtosellittoallowyoutomakemonthlypayments.Theentirecomputersystemcosts$3500.Theloanperiodisfor2yearsandtheintererateis16.9%withmonthlycompounding.Whatisyoumonthlypayment?•Monthlyrate=.169/12=.01408333333•Numberofmonths=2(12)=24•3500=C[1–1/1.01408333333)24]/.0140833333•C=172.8851McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresComputingPaymentswithAPRs•Supposeyoudeposit$50amonthintoanaccountthathasanAPRof9%,basedonmonthlycompounding.Howmuchwillyouhaveintheaccountin35years?•Monthlyrate=.09/12=.0075•Numberofmonths=35(12)=420•FV=50[1.0075420–1]/.0075=147,089.22FutureValueswithMonthly

Compounding

52McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.AllrightsresPresentValuewithDailyCompounding•Youneed$15,000in3yearsforanewcar.IfyoucandepositmoneyintoanaccountthatpanAPRof5.5%basedondailycompounding,howmuchwouldyouneedtodeposit?•Dailyrate=.055/365=.00015068493•Numberofdays=3(365)=1095•FV=15,000/(1.00015068493)1095=12,718.56/IrwinMcGraw-Hill53/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•

What

is

the

definitionofan

APR?•

Whatistheeffectiveannualrate?•

Whichrateshouldyouuse

to

comparealternativeinvestmentsorloans?•

Whichratedoyouneedtouse

inthe

timeval

ofmoneycalculations?Quick

Quiz

:Part554McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Treasurybillsareexcellentexamplesofpudiscountloans.Theprincipalamountisrepatsomefuturedate,withoutanyperiodicinpayments.•IfaT-billpromisestorepay$10,000in12monthsandthemarketinterestrateis7perhowmuchwillthebillsellforinthemarket•PV=10,000/1.07=9345.79PureDiscountLoans–Example5.1155McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Considera5-year,interestonlyloanwithainterestrate.Theprincipalamountis$10,Interestispaidannually.•Whatwouldthestreamofcashflowsbe?•Years1–4:Interestpaymentsof.07(10,000)=•Year5:Interest+principal=10,700•Thiscashflowstreamissimilartothecashflowsoncorporatebondsandwewilltalkabthemingreaterdetaillater.Interest

Only

Loan-Example56McGraw-Hill/Irwin©2004TheMcGraw-HillCompanies,Inc.Allrightsres•Eachpaymentcoverstheinterestexpenseplreducespri