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Time Value of Money, Bond and Stock Evaluation

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Department
Finance
Course Code
MGFB10H3
Professor
Eileen

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MGTB09H3PrinciplesofFinance
Winter2009
Additionalselfæstudyexercisestopics2,3and4
(answersaregivenattheend)
Firstmaketheseexercisesonyourown,andthencheckthesolutions!
Questions
Question1(TimeValueofMoney)
Khayat&ElkindFinancialPlannersofferedEileenChantwodifferentinvestmentplans.PlanAisa
perpetuitythatpays$4,500peryear.PlanBisa10year,$15,000annualannuity.Bothplanswillmake
theirfirstpaymenttwoyearsfromtoday.AtwhatdiscountratewouldEileenbeindifferentbetween
thesetwoplans?
Question2(TVM)
KatherineHuiwouldliketopurchaseanewToyotafromBai&BeczAutos.Shewillfinancethecar
purchasebyborrowing$20,000.Theloancontractisintheformofa30monthannuitydueat12.685%
EAR.
a) Calculatethemonthlyinterestrate.
b) Whatwillhermonthlypaymentbe?
Question3(TVM)
Consideraninvestmentthatpays$2,000everythirdyearforever.Theannualdiscountrateis10%.
a) Whatisthevalueoftheinvestmentwhenthefirstcashflowoccursoneyearfromnow?
b) Whatwouldthevaluebeifthefirstcashflowoccursintwoyears?
c) Infouryears?
Question4(TVM)
FlorenceLeerecentlyboughtahouseinScarborough.Tofinancethepurchaseshetookamortgageloan
of$250,000fromtheChristidis&RibeiroTrustCompanyforanamortizationperiodof25yearsata
quotedinterestrateof8%peryearcompoundedsemiannually.
a) Whatishermonthlypayment?Florencemakespaymentsattheendofeachmonth.
b) After10yearsofpaymentshowmuchdoesshestillowetotheTrustCompany?
c) Whatisthetotalamountofinterest(in$)thatshehaspaidduringthese10years?
Question5(TVM)
NavpreetSinghisabouttoenteruniversityandhastwooptionstoher.
1. StudyBusiness.Ifshedoesthis,herundergraduatedegreewouldcosther$12,000ayear
for4years.Havingobtainedthis,shewouldneedtogettwoyearsofpracticalexperience:in
thefirstyearshewouldearn$30,000,andinthesecondyearshewouldearn$35,000.She
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thenwouldneedtoobtainherMBAdegree,whichwillcosther$20,000peryearfor2years.
Afterthatshewillbefullyqualifiedandcanearn$80,000peryearfor21years.
2. StudyScience.Ifshedoesthis,herundergraduatedegreewouldcosther$15,000ayearfor
4yearsandthenshewouldearn$50,000ayearfor25years.
Allearningsandcostsarepaidattheendoftheyear.Whatadvicewouldyougiveheriftheapplicable
rateofreturnwere10%peryear?
Question6(TVM)
SheilaSantosisconsideringthefollowingthreeinvestmentsofferedbyAngeloSimoes&NavneetHans
InvestmentsLimited.Theinvestmentswillpay:
1. $60,000everyfouryearsforever,withthefirstpaymentoccurringoneyearfromtoday.
2. $5,000everyquarterfor20years(80paymentsintotal),withthefirstpaymentoccurringtwo
monthsfromtoday.
3. $10,000every6monthsfor25years(50paymentsintotal)starting2yearsfromtoday.
Whichoftheabove3investmentsshouldsheselectifeachinvestmentcosts$140,000andherrequired
rateofreturnis12%peryear?
Question7(TVM)
VivianTsanghasjustboughtahouseinScarborough.Tohelpfinancethepurchaseshetookamortgage
loanof$300,000at8%interestratecompoundedsemiannually.Amortizationperiodforthemortgage
loanis20years.
a) Determinehowmuchshehastopayattheendofeverymonthtopayofftheloanin20years.
b) Howmuchwillsheowetothebankaftermakingpaymentsfor15years?(i.e.,whatisthemortgage
balanceafter15years?)
c) Supposetwoyearsaftertakingthemortgage,shewantstoendthemortgagebypayingoffthe
remainingbalance.However,thebankwillchargeherapenaltyfordoingthis.Thepenaltyequals
theamountofinterestshewouldhavepaidinthenext3months.(Hence,theinterestshewould
havetopayinthefirstthreemonthswhentherearestill18yearsleftofmaturity.)Determinethe
amountofinterestpenaltyshehastopay.

Question8(Bonds)
Valesquez&VinokourManufacturinghastwodifferentbondscurrentlyoutstanding.BondXhasaface
valueof$100,000andmaturesin20years.Thebondmakesnopaymentsforthefirst4years,thenpays
$6,000semiannuallyoverthesubsequent6years,afterthatpays$8,000semiannuallyfor5years,and
finallypays$9,000semiannuallyoverthelast5years.BondYhasafacevalueof$100,000anda
maturityof10years;itmakesnocouponpaymentsoverthelifeofthebond.Iftherequiredrateof
returnonbothbondsis12%compoundedsemiannually,whatisthecurrentpriceofBondX?Andof
BondY?
Question9(Bonds)
Truong&LlewellynEnterprisesissuedanewseriesofbondsonJanuary1,1976.Thebondsweresoldat
par($1,000),hada12%coupon,andhadanoriginalmaturityof30years.Couponpaymentsaremade
annuallyonDecember31ofeachyear.
a) WhatwastheyieldtomaturityofthebondonJanuary1,1976?
b) WhatwasthepriceofthebondonJanuary1,1981(5yearslater),assumingthatthelevelof
interestrateshadfallento10%?
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c) Calculatethebond’scurrentyieldonJanuary1,1996(20yearsafterthebondswereissued),
assumingthattheinterestratewas13%atthattime.
Question10(Stocks)
Jingshu&SerhadManufacturing(JSM)isexperiencingrapidgrowth.JSMhasjustpaidadividendand
thestockpriceiscurrentlyequalto$80pershare.Dividendsareexpectedtogrowby40%peryear
duringthenext2years,20%duringthe3rdyear,10%duringthe4thyear,andthen5%peryear
indefinitely.Therequiredrateofreturnis10%peryear.
a) CalculatethedividendthatJSMhasjustpaidout.
b) Whatistheprojecteddividendforthecomingyear?
Question11(Stock)
YoucanbuyashareoftheMaryMina&VivianLeungTechnologist’s(MLT)stocktodayfor$24.MLT’s
lastdividendwas$1.60.InviewoftheMLT’slowrisk,itsrequiredrateofreturnisonly12%.Dividends
areexpectedtogrowataconstantrate,g,inthefuture.Assumethattherequiredrateofreturnis
expectedtoremainat12%.WhatisMLTsexpectedshareprice5yearsfromnow?
Question12(Stock)
MayurGandhi&DanielTsangComputers(MDC)isexperiencingaperiodofrapidgrowth.Earningsand
dividendsareexpectedtogrowatarateof18%duringthenexttwoyears,at15%inthe3rdyear,andat
aconstantrateof6%thereafter.MDC’slastdividendwas$1.15,andtherequiredrateofreturnonthe
sharesis12%.
a) Calculatethepriceofasharetoday.
b) CalculateP1andP2.
c) Calculatethedividendyield,capitalgainsyield,andtotalreturnforyears1,2,and3.
Question13(Stocks)
Anar&RebeccaWangTechnologies(A&RWT)isayoungstartupcompany.Nodividendswillbepaidon
thestockforthenext2years.Firstdividendwillbepaid3yearsfromtoday.Dividendsareexpectedto
growat25%peryearduringthe4thandthe5thyear,15%duringthe6thyear,10%peryearduringthe7th
and8thyear,andthen5%peryearindefinitely.A&RWTstockiscurrentlysellingfor$107.673pershare,
andtherequiredrateofreturnis10%.
a) Whatdividendwillbepaid3yearsfromtoday?
b) Ifyoupurchasethestock7yearsfromtodayandsellitafterholdingitforoneyear,whatwillbethe
dividendyield,capitalgainyield,andthetotalyield?
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Description
MGTB09H3PrinciplesofFinance Winter2009 Additionalselfstudyexercisestopics2,3and4 (answersaregivenattheend) Firstmaketheseexercisesonyourown,andthencheckthesolutions! Questions Question1(TimeValueofMoney) Khayat & Elkind Financial Planners offered Eileen Chan two different investment plans. Plan A is a perpetuitythatpays$4,500peryear.PlanBisa10year,$15,000annualannuity.Bothplanswillmake theirfirstpaymenttwoyearsfromtoday.AtwhatdiscountratewouldEileenbeindifferentbetween thesetwoplans? Question2(TVM) KatherineHuiwouldliketopurchaseanewToyotafromBai&BeczAutos.Shewillfinancethecar purchasebyborrowing$20,000.Theloancontractisintheformofa30monthannuitydueat12.685% EAR. a) Calculatethemonthlyinterestrate. b) Whatwillhermonthlypaymentbe? Question3(TVM) Consideraninvestmentthatpays$2,000everythirdyearforever.Theannualdiscountrateis10%. a) Whatisthevalueoftheinvestmentwhenthefirstcashflowoccursoneyearfromnow? b) Whatwouldthevaluebeifthefirstcashflowoccursintwoyears? c) Infouryears? Question4(TVM) FlorenceLeerecentlyboughtahouseinScarborough.Tofinancethepurchaseshetookamortgageloan of$250,000fromtheChristidis&RibeiroTrustCompanyforanamortizationperiodof25yearsata quotedinterestrateof8%peryearcompoundedsemiannually. a) Whatishermonthlypayment?Florencemakespaymentsattheendofeachmonth. b) After10yearsofpaymentshowmuchdoesshestillowetotheTrustCompany? c) Whatisthetotalamountofinterest(in$)thatshehaspaidduringthese10years? Question5(TVM) NavpreetSinghisabouttoenteruniversityandhastwooptionstoher. 1. StudyBusiness.Ifshedoesthis,herundergraduatedegreewouldcosther$12,000ayear for4years.Havingobtainedthis,shewouldneedtogettwoyearsofpracticalexperience:in thefirstyearshewouldearn$30,000,andinthesecondyearshewouldearn$35,000.She 1 www.notesolution.com thenwouldneedtoobtainherMBAdegree,whichwillcosther$20,000peryearfor2years. Afterthatshewillbefullyqualifiedandcanearn$80,000peryearfor21years. 2. StudyScience.Ifshedoesthis,herundergraduatedegreewouldcosther$15,000ayearfor 4yearsandthenshewouldearn$50,000ayearfor25years. Allearningsandcostsarepaidattheendoftheyear.Whatadvicewouldyougiveheriftheapplicable rateofreturnwere10%peryear? Question6(TVM) SheilaSantosisconsideringthefollowingthreeinvestmentsofferedbyAngeloSimoes&NavneetHans InvestmentsLimited.Theinvestmentswillpay: 1. $60,000everyfouryearsforever,withthefirstpaymentoccurringoneyearfromtoday. 2. $5,000everyquarterfor20years(80paymentsintotal),withthefirstpaymentoccurringtwo monthsfromtoday. 3. $10,000every6monthsfor25years(50paymentsintotal)starting2yearsfromtoday. Whichoftheabove3investmentsshouldsheselectifeachinvestmentcosts$140,000andherrequired rateofreturnis12%peryear? Question7(TVM) VivianTsanghasjustboughtahouseinScarborough.Tohelpfinancethepurchaseshetookamortgage loanof$300,000at8%interestratecompoundedsemiannually.Amortizationperiodforthemortgage loanis20years. a) Determinehowmuchshehastopayattheendofeverymonthtopayofftheloanin20years. b) Howmuchwillsheowetothebankaftermakingpaymentsfor15years?(i.e.,whatisthemortgage balanceafter15years?) c) Supposetwoyearsaftertakingthemortgage,shewantstoendthemortgagebypayingoffthe remainingbalance.However,thebankwillchargeherapenaltyfordoingthis.Thepenaltyequals theamountofinterestshewouldhavepaidinthenext3months.(Hence,theinterestshewould havetopayinthefirstthreemonthswhentherearestill18yearsleftofmaturity.)Determinethe amountofinterestpenaltyshehastopay. Question8(Bonds) Valesquez&VinokourManufacturinghastwodifferentbondscurrentlyoutstanding.BondXhasaface valueof$100,000andmaturesin20years.Thebondmakesnopaymentsforthefirst4years,thenpays $6,000semiannuallyoverthesubsequent6years,afterthatpays$8,000semiannuallyfor5years,and finally pays $9,000 semiannually over the last 5 years. Bond Y has a face value of $100,000 and a maturityof10years;itmakesnocouponpaymentsoverthelifeofthebond.Iftherequiredrateof returnonbothbondsis12%compoundedsemiannually,whatisthecurrentpriceofBondX?Andof BondY? Question9(Bonds) Truong&LlewellynEnterprisesissuedanewseriesofbondsonJanuary1,1976.Thebondsweresoldat par($1,000),hada12%coupon,andhadanoriginalmaturityof30years.Couponpaymentsaremade annuallyonDecember31ofeachyear. a) WhatwastheyieldtomaturityofthebondonJanuary1,1976? b) What was the price of the bond on January 1, 1981 (5 years later), assuming that the level of interestrateshadfallento10%? 2 www.notesolution.com
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