课堂练习Word文件下载.docx
《课堂练习Word文件下载.docx》由会员分享,可在线阅读,更多相关《课堂练习Word文件下载.docx(26页珍藏版)》请在冰豆网上搜索。
750800700900
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