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1、Chapter4NPVandtheTimeValueofMoneyChapter<4NPVandtheTimeValueofMoney<4.1TheTimelineAseriesofcashflowslastingseveralperiodsisdefinedasastreamofcashflows.Wecanrepresentastreamofcashflowsonatimeline,alinearrepresentationofthetimingoftheexpectedcashflows.ConstructingaTimeline?Date0representsthepr
2、esent.Date1isoneyearlaterDistinguishingCashInflowsfromOutflowsThefirstcashflowatdate0(today)isrepresentedasnegativebecauseitisanoutflowExample<4.1ConstructingaTimelineProblem:Supposeyoumustpaytuitionof$10,000peryearforthenextfouryears.Yourtuitionpaymentsmustbemadeinequalinstallmentsof$9><>5,
3、000eachevery6months.Whatisthetimelineofyourtuitionpayments?Example<4.1ConstructingaTimelineSolution:Assumingtodayisthestartofthefirstsemester,yourfirstpaymentoccursatdate0(today).Theremainingpaymentsoccurat6-monthintervals.Usingone-halfyear(6months)astheperiodlength,wecanconstructatimelineas
4、follows:<4.2ValuingCashFlowsatDifferentPointsinTimeThreeImportantRulesCentraltoFinancialDecisionMakingRule1:ComparingandCombiningValuesRule2:CompoundingRule3:DiscountingRule1:ComparingandCombiningValuesAdollartodayandadollarinoneyeararenotequivalent.Havingmoneynowismorevaluablethanhavingmone
5、yinthefuture;if?youhavethemoneytodayyoucanearninterestonit.Rule2:CompoundingTheprocessofmovingforwardalongthetimelinetodetermineacashflow’svalueinthefuture(itsfuturevalue)isknownascompounding.Oursecondrulestipulatesthattocalculateacashflow’sfuturevalue,youmustcompoundit.Rule2:CompoundingWeca
6、napplythisrulerepeatedly.Supposewewanttoknowhowmuchthe$1,000isworthintwoyears’time.Iftheinterestrateforyear2isalso10%,thenweconvert:Rule2:CompoundingThiseffectofearninginterestonboththeoriginalprincipalplustheaccumulatedinterest,sothatyouareearning“interestoninterest,”isknownascompoundintere
7、st.Compoundingthecashflowathirdtime,assumingthecompetitivemarketinterestrateisfixedat10%,weget:FutureValueofaCashFlow(Eq.<4.1)Figure<4.1TheCompositionofInterestoverTimeRule3:DiscountingTheprocessoffindingtheequivalentvaluetodayofafuturecashflowiskn
