课堂练习Word文件下载.docx

课堂练习Word文件下载.docx

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ANNUITIES:

EXAMPLE

Ø

Salaryof$60,000peryearfor4yearswitha9%discountrate.

WHATISTHEINTERESTRATE?

Youwillsoonbeborrowingalargesumtostartyourownbusiness.Youneedtogetthelowestpossiblerate.

Yourbankeroffersthefollowing5choices:

7.75%compoundeddaily

7.75%compoundedweekly

7.75%compoundedmonthly

7.75%compoundedquarterly

8%compoundedannually

Answer：

7.75%compoundeddaily=

7.75%compoundedweekly=

7.75%compoundedmonthly=

7.75%compoundedquarterly=

8%compoundedannually=

Example2

Atthelocalloanshark,youpay$1perweekcompoundedweeklyforevery$100thatyouborrow.Actuallysoundsverylenientdoesn’tit?

WhatistheEAR?

●Mortgagesarequotedinannualratesbutareusuallycompoundedsemi-annually.WhatistheEARfora9%mortgage?

●Sincemortgagesareusuallypaidmonthly,giventhisEAR,whatisthestatedmonthlyrate?

EXAMPLE3

AcreditcardrequiringmonthlypaymentscarriesanAPRof14.4%andinterestiscalculatedandcompoundedmonthly.WhatistheEAR?

AMORTIZEDLOANS

✧SIMPLEAMORTIZATION

▪7%interestcompoundedannually;

▪$8,000loan

▪4-yearterm

Year

Startofperiod

Interestpaid

Principalpaid

Totalpaid

Endingbalance

1

8,000

560

2,000

2,560

6,000

2

434

2,420

4,000

3

299

2,280

4

154

2,140

1,447

9,400

Note:

thereisslightlymoreinterestpaidastheearlypaymentsarelower.Hence,overallpaymentsareabithigher.Notbetterorworse,justdifferent.

✧FIXEDPAYMENTAMORTIZATION

▪7%interestcompoundedannually

Thisisa4-yearannuitywithapresentvalueof$8,000.

PVA（7%,4）=C*PVIFA（7%,4）

∴C=$2,361.82

Theannualpaymentattheendofeachyearwouldbe$2,361.82.

Let’scallit$2,362.

AMORTIZATIONSCHEDULE

1,802

2,362

6,198

1,928

4,270

2,063

2,207

2,208

9,448

Note:

Example:

A$150,000mortgagewitha25-yearamortization,a5-yeartermanda7.25%interestrate.Whenpresentedinthismanner,the7.25%rateisanAPR,andmightbecalledastatedorquotedannualrate.

（Rememberthatmortgagesalmostalwayscompoundevery6months.）

Twoquestions:

（i）Whatisthemonthlymortgagepaymentwiththe5-yearterm?

（ii）Whatlump-sumpayment（balloonpayment）wouldberequiredtopayoffthemortgageafter5years?

BONDSANDBONDEVALUATION

Whatarethefeaturesofabond?

Howdowefindbondpricesandtheyieldtomaturity?

Whydobondpricesandyieldsmoveinoppositedirections?

Whatdomeantbytheterms“discount”and“premium”bonds?

Whatdowemeanbyinterestrateriskanddefaultrisk?

Howdowedeterminetherateofreturnonabond?

Whatisthedifferencebetweenarealandanominalinterestrate?

HOMEWORK

1.YourjobattheSouthPoledoesn’tworkout,sonowyouhavedecidedtobuyanewsportscartoreplaceyourbelovedbeetle.Thepriceis$37,450andyourbankerwillfinancetheentirecostwitha60-monthloanwithanAPRof16.5%（whatdoyouexpectwithnodownpayment?

）.Whatwillyourmonthlypaymentsbe?

WhatistheEARonthisloan?

2.Gloria,agrandmother,wantstohelphersoon-to-arrivegrandchildbyestablishinganeducationtrusteffectivethedateofbirthofthechild.Shewantstoprovidethegrandchildwith$10,000atage18,$12,000atage19,$14,000atage20,and$16,000atage21.Gloriamakesasinglepaymentintotheeducationtrustonthedaythechildisborn.Byinvestinginstripbonds,sheisabletolockinanEARof7%sothattheexactamountrequiredwillbeavailableoneachofthegrandchild’sfourbirthdays.Whatwasthevalueofthesinglepayment?

Example:

A$1,000bondwitha6%couponmaturingin10years.

∙Thisbondwillpay$60ininterestattheendofeachyearfor10yearsandwillthenrepaythe$1,000facevalueattheendofthe10thyear.

（Note:

mostbondspayinterestsemi-annually.Thisisasimplecomplicationthatwewilldealwithafterunderstandingthebasicvaluationtechniques）

BONDVALUES

Howmuchwouldyoupayforthe$1,000bond,maturingin10yearswitha6%annualcoupon,ifthecurrentmarketrateofinterestwere6%?

Inotherwords,whatisthePresentValueofthisbond?

BUT:

Whatifthemarketrateofinterestforthattypeofbondwasreally7%?

Whywouldyoupay$1,000andearnonly6%?

Ifthemarketrateofinterestforasimilarbondwereonly3.75%,whatwouldyoubepreparedtopayforthebondinquestion?

SEMIANNUALCOUPONS

Whatisthevalueofa$1,000bondwitha6%couponrateandsemiannualpayments,ifthecurrentmarketrateofinterestwere6%?

ANNUALvsSEMIANNUALCOUPONS

ANNUAL

PVbond=

+

=（60*7.3601）+（1,000*0.55839）

PVbond=441.61+558.39=$1,000

SEMIANNUAL

=（30*14.87747）+（1,000*.55368）

PVbond=446.32+553.68=1,000

WHY?

INTERESTRATERISK

∙Example:

Long-termBond

Youowna30-yearbondwitha10%couponpaidannually.

Ifthecurrentmarketinterestrateforsuchabondis10%,itsvalueis:

Ifthecurrentmarketinterestraterosedramaticallyto15%.What’sthevalueofthebondnow?

ThePVofthebondhasfallenby32.8%.

Short-termBond

Youowna1-yearbondwitha10%couponpaidannually.

Supposethecurrentmarketinterestrateforasimilarbondrosedramaticallyto15%.What’sthevalueofthebondnow?

ThePVoftheshort-termbondhasfallenby4.5%.

That’samuchlowerlevelofinterestrateriskthanwiththelonger-termbond.

LowCouponBond

Youowna20-yearbondwitha6%couponpaidannually.

Supposethecurrentmarketinterestrateforasimilarbondrosedramaticallyto15%.Thevalueofthebondhasfallenbyover33.8%.

HighCouponBond

Youowna20-yearbondwitha12%couponpaidannually.

Supposethecurrentmarketinterestrateforasimilarbondrosedramaticallyto15%.Thevalueofthebondhasfallenby30.6%.

Alowerlevelofinterestrateriskthanwiththelowcouponbond.

Example

BUY:

a10-year,7%couponbondfor$1,000.

（Sincethebondsellsatpar,weknowtheyieldtomaturityis7%）.

SELL:

1-yearlater,whentheyieldtomaturityis6%.

Whatisthepricethatyoucouldgetinthebondmarketandwhatwasyournominal（asopposedtoreal）returnonthebond?

REALVSNOMINALRATESOFINTEREST

▪Witha7%interestrate.A$1,000bondwillhaveavalueof$1,070after1year（ifinterestratesdonotchange）.

▪7%inthiscaseisthe:

NOMINALINTERESTRATE:

▪Iftherewere5%inflationoverthesameyear,the$1,070nominalcashflowwouldnotbuy7%moregoodsandservices,sincethepriceofthosegoodsandserviceswouldbe5%higher.

▪Afterweadjustforinflation,wecouldbuyonly1.905%more.

STOCK

Let’staketheexamplesofCIBCandTelus

CIBC

P/E=9.245.70/EPS=9.2

Earningspershare=$4.97

Telus

P/E=14.21.15/EPS=14.2

Earningspershare=$2.90

IstheCIBCnecessarilyabetterstocktoownthanTelusbecausetheP/Eratioisconsiderablylowerandtheearningspersharearehigher?

HowcanthepriceofTelusbesoclosetothepriceofCIBCwhentheearningsaresomuchlowerpershare?

P0=$18.86vs.$45.70

g=9.11%

P0$20vs.$41.15

g=8.60%

Exercise1

TheonlyorebodybeingoperatedbytheTarnishedGoldMineisbeingdepletedandtheDirectorshavedecidedtoslowlydistributetheassetsofthecompanyinaseriesofdividendpayments.Thecompanyjustpaida$30dividendandwillreducethedividendby8%peryear,indefinitely.Ifa20%returnwererequired,whatwouldyoupayforthestocktoday?

（$98.57）

PROJECTEVALUATION

Objectives:

♦LearntouseNetPresentValuemethodologytoevaluateinvestmentsinassets.

♦Considerthestrengthsandweaknessesofseveralotherapproachestoevaluatingacapitalinvestmentopportunity,specifically:

▪Paybackperiod

▪Internalrateofreturn

▪Profitabilityindex

NETPRESENTVALUE:

Example1:

Thereisanopportunitytobuildasmallofficebuildingfor$700,000.Youhaveaninterestedpartywhowishestorentthebuildingfor3years,atanetannualcostof$33,000.Attheendofthethirdyear,thebuildingwillbesoldfor$800,000.Isthisanacceptableinvestment?

Continuetheexample:

Yourcompanyisdrillingawelltoprovidenaturallycarbonatedwatertoabottlingcompany.Thewellwillcost$9milliontobringintoproduction.Annualcashflowfromtheproductionwillbe$1.3millionforthenext15ye