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45 Pages

Session 6 TVM1

Course: BUS M 301, Fall 2011
School: BYU
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Word Count: 1406

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little BM301IntroductiontoFinance A something for our wonderful Asian students Why?:Mostlongtermprojecthavecashflows thatoccuratdifferentpointsintime.Giventhat thepassageoftimeimpactsthevalueofcash flows,thevalueofaprojectisdependentonhow weassessthesedifferences.Thepurposeofthis chapteristodevelopthetoolsnecessaryto evaluatecashflowsovertimeinordertomake optimaldecisions. Learningobjective: Developanunderstandingofhowtimeimpactsthe valueofcashflows Quantifythetime/valuerelationship Evaluatecomplexfinancialcontracts/projects Keywords/concepts: TVM PV,FV,PVA,FVA Lumpsum,annuity Ordinaryannuityvs.Annuitydue Perpetuity Deferredannuity Mixedstreamcashflow WORKLOTSOFPROBLEMS! SupposethatIofferedtogiveyouadollar (emphasisonsuppose) Wouldyouratherhavethedollartodayorone yearfromtoday?Why? Risk Opportunity Inflation Youwina$100,000,000lottery! Problem:oneyearuntilyougetthe$$$. Whatistheleastyouwouldtaketodayin exchangeforthe$100,000,000nextyear? A. B. C. D. E. $50,000,000? $70,000,000? $87,500,000? $95,000,000? $99,999,999? Translate$1todayintoitsequivalentinthefuture. Future Future Now Compounding Future Value Translate$1inthefutureintoitsequivalenttoday. Future Present Value Discounting Itseasiesttouseyourfinancial functionsonyourcalculatorto solvetimevalueproblems. However,youwillneedalotof practicetoeliminatemistakes. Itwillbehelpfullatertotakeextra timenowlearningtousethe formulasaswellasthefinancial functionsonyourcalculator! FutureValue CompoundingProblems PV = FV = 0 1 Negative indicates you put money in PV = -100 0 FV = 106 106 MathematicalSolution: FV=PV(1+i)n FV=100(1.06)1=$106 Noticethatthereisoneequationandfour variables.Whatdoesthistellyouabout howmuchinformationyouneed? 1 PV = -100 0 FV = 106 106 MathematicalSolution: FutureValue FutureValue InterestFactor FV=PV(1+i)n InterestFactor FV=100(1.06)1=$106 Noticethatthereisoneequationandfour variables.Whatdoesthistellyouabout howmuchinformationyouneed? 1 Thereisoneequationand4variables So,howmanyunknownscanyouhave? I(orrorI/Y),PV,FV,andn ForalmostallTVMproblems,yousimply playa3find4game Threesteps: 1. Setupyourcalculator a) 1payment/year b) ClearalldataoutofTVMregisters 2. Enterthe3knownvariables(anyorder) 3. Solvefortheunknown Twoproblems 1.Pmtsperyear:Wewilldoall calculationsin1P/Yrmode. 2.Clearingyourcalculatorbefore eachproblem HP:2ndCAll;TI:2ndCLRTVM PV = -100 FV = 106 106 0 CalculatorSolution: P/Y=1 I=6 N=1 PV=100 FV=$106 1 Future ValueSingle Sum If you deposit $100 into an account earning 6% interest, how much will you have in the account after 5 years? PV = -100 0 FV = 5 Id guess $100 plus $6 x 5 = $130, OK? Future ValueSingle Sum If you deposit $100 into an account earning 6% interest, how much will you have in the account after 5 years? PV = -100 FV = 133.82 133. 0 MathematicalSolution: FV=PV(1+i)n FV=100(1.06)5=$133.82 Where did the extra $3.82 come from? 5 Future ValueSingle Sum If you deposit $100 into an account earning 6% interest, how much will you have in the account after 5 years? PV = -100 FV = 0 CalculatorSolution: P/Y=1 I=6 N=5 PV=100 FV=$133.82 5 PresentValue DiscountingProblems Present ValueSingle Sum If you will receive $100 one year from now, what is the present value of that $100 if your opportunity cost is 6%? PV = FV = 0 ? Present ValueSingle Sum If you will receive $100 one year from now, what is the present value of that $100 if your opportunity cost is 6%? PV = -94.34 PV -94. 0 MathematicalSolution: PV=FV/(1+i)n PV=100/(1.06)1=$94.34 FV = 100 1 Present ValueSingle Sum If you will receive $100 one year from now, what is the present value of that $100 if your opportunity cost is 6%? PV = -94.34 PV -94. FV = 100 0 MathematicalSolution: PV=FV/(1+i)n PVIF PV=100/(1.06)1=$94.34 1 Present ValueSingle Sum If you will receive $100 one year from now, what is the present value of that $100 if your opportunity cost is 6%? PV = -94.34 PV -94. FV = 100 0 CalculatorSolution: P/Y=1 I=6 N=1 FV=100 PV=94.34 1 Present ValueSingle Sum If you will receive $100 five years now, from what is the present value of that $100 if your opportunity cost is 6%? PV = FV = 0 MathematicalSolution: PV=FV/(1+i)n PV=100/(1.06)5=$74.73 ? Present ValueSingle Sum If you will receive $100 five years from now, what is the present value of that $100 if your opportunity cost is 6%? PV = PV FV = 100 0 Calculator Solution: Calculator P/Y = 1 I=6 P/Y N=5 FV = 100 100 PV = -74.73 -74.73 5 Hint for Single Sum Problems Hint Ineverysinglesumfuturevalueand presentvalueproblem,thereare4 variables: FV,PV,i,andn Whendoingproblems,youwillbe given3ofthesevariablesandaskedto solveforthe4thvariable. KeepingthisinmindmakesTVM problemsmucheasier! Ifanoblerevolutionaryancestorofyourshadput just$1inanaccountforyouin1776(whenour countrywasfounded),howmuchwoulditbe worthtodayifthataccountearned6%peryear?If ithadearned8%/yr? Ifanoblerevolutionaryancestorofyourshadput just$1inanaccountforyouin1776(whenour countrywasfounded),howmuchwoulditbe worthtodayifthataccountearned6%peryear?If ithadearned8%/yr? I = 8% Clear registers! Comp. FV = $61,338,765 N=2009-1776=233 PV = 1 I = 6% Compute FV = $787,529 CardfoundintheTannerBuildingin2006 Earn44%in12days! Ifyouhadputjust$100intothatopportunityand hadactuallyrealizedthatreturnforoneyear (assume360days),howmuchmoneywouldyou haveaccumulated?(Hint:Howmany12day periodsarethereinone360dayyear?) Thereare360/12=3012dayperiodsinoneyear (well,a360dayyear). Assumeyoullreinvesteverything. I=44theinterestrateperperiod N=30thenumberofyearsorcompounding periods PV=100 SolveforFV=$5,634,751 Areyoureadytoinvest? The Time Value of Money The Compoundingand Discounting CashFlowStreams 0 1 2 3 4 Annuities Annuities Annuity:anequallyspaced sequenceofequalcashflows. 0 1 2 3 4 Examples of Annuities: Examples Ifyoubuyabond,youwill receiveequalcouponinterest paymentsoverthelifeofthe bond. Ifyouborrowmoneytobuya houseoracar,youwillpaya streamofequalpayments. Future Value of an Annuity If you invest $1,000 at the END of each of the next three years, how much will you have accumulated at 8%? 1000 0 1000 1000 1 2 3 MathematicalSolution: FV=PMT(1+i)n1 i FV = 1,000 (1.08)3 - 1 .08 = $3246.40 FVIFA Future Value of an Annuity If you invest $1,000 at the END of each of the next three years, how much will you have accumulated at 8%? 1000 1000 0 1 1000 1000 2 CalculatorSolution: P/Y=1 I=8 N=3 PMT=1,000 FV=$3,246.40 3 Present Value of an Annuity What is the present value of $1,000 at the END of each of the next three years if the opportunity cost is 8%? 1000 1000 0 1 1000 1000 2 3 Present Value of an Annuity What is the present value of $1,000 at the END of each of the next three years if the opportunity cost is 8%? MathematicalSolution: 1 PV=PMT1(1+i)n i 1 PV=10001(1.08)3=$2,577.10 .08 1000 1000 0 1 1000 1000 2 CalculatorSolution: P/Y=1 I=8 N=3 PMT=1,000 PV=$2,577.10 3 Interestrateis6%(thats0.5%permonth) Itsa30yearmortgage Price=$200,000(butyouput20%down) Neglectallthoseothercosts Whatwillyourmonthlypaymentbe? N=30x12=360 I=.5 PV=160,000Thats200,000x(1.20) ComputePMT=$959.28 Howmuchdoyoupayintotalforthemortgage overtime? 360x959.28=345,341! Totalhomecost=$345,341+40,000= $385,341 Howmuchwasinterest?($185,341) Howmuchtoinvest?Say$1.00(thatsPV) WhatisI? WhatisFV? SolveforN Answer=12.00years Tryitfor8% Tryitfor12% 8%gives10years 12%gives7years Buyourproductwithonly4easyinstallment paymentsof$100permonth! Oryoucouldpaycashnow$250. Whatistheeffectivemonthlyratetheyare chargingforgoingtoinstallments? Whatannualratewouldthatbe? Whichpaymentmodeisbest? Buyourproductwithonly4easyinstallment paymentsof$100permonth! Oryoucouldpaycashnow$250. Whatistheeffectivemonthlyratetheyare chargingforgoingtoinstallments? Whatannualratewouldthatbe? Whichpaymentmodeisbest? N=4,PV=250,PMT=100,solveforI I=21.86(annuallythats12x21.86=262% Gothroughtheproblemsinthissessionwith yourowncalculatorandmakesureyoucomeup withthesameanswers.Ifnot,getaTAor anotherpersontohelpyou. 2. TrytheproblemsattheendofChapter5. 3. AnswersareonBlackboardsoyoucancheck yourwork. 1.

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