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1、Introduction to Valuation:The Time Value of MoneyChapter 44.1Key Concepts and SkillsnBe able to compute the future value of an investment made todaynBe able to compute the present value of cash to be received at some future datenBe able to compute the return on an investment4.2Chapter OutlinenFuture
2、 Value and CompoundingnPresent Value and DiscountingnMore on Present and Future Values4.3Basic DefinitionsnPresent Value earlier money on a time linenFuture Value later money on a time linenInterest rate “exchange rate”between earlier money and later moneynDiscount ratenCost of capitalnOpportunity c
3、ost of capitalnRequired return4.4Future ValuesnSuppose you invest$1000 for one year at 5%per year.What is the future value in one year?nInterest=1000(.05)=50nValue in one year=principal+interest=1000+50=1050nFuture Value(FV)=1000(1+.05)=1050nSuppose you leave the money in for another year.How much w
4、ill you have two years from now?nFV=1000(1.05)(1.05)=1000(1.05)2=1102.504.5Future Values:General FormulanFV=PV(1+r)tnFV=future valuenPV=present valuenr=period interest rate,expressed as a decimalnT=number of periodsnFuture value interest factor=(1+r)t4.6Effects of CompoundingnSimple interest nCompou
5、nd interestnConsider the previous examplenFV with simple interest=1000+50+50=1100nFV with compound interest=1102.50nThe extra 2.50 comes from the interest of.05(50)=2.50 earned on the first interest payment4.7Figure 4.14.8Figure 4.24.9Calculator KeysnTexas Instruments BA-II PlusnFV=future valuenPV=p
6、resent valuenI/Y=period interest ratenP/Y must equal 1 for the I/Y to be the period ratenInterest is entered as a percent,not a decimalnN=number of periodsnRemember to clear the registers(CLR TVM)after each problemnOther calculators are similar in format4.10Future Values Example 2nSuppose you invest
7、 the$1000 from the previous example for 5 years.How much would you have?nFV=1000(1.05)5=1276.28nThe effect of compounding is small for a small number of periods,but increases as the number of periods increases.(Simple interest would have a future value of$1250,for a difference of$26.28.)4.11Future V
8、alues Example 3nSuppose you had a relative deposit$10 at 5.5%interest 200 years ago.How much would the investment be worth today?nFV=10(1.055)200=447,189.84nWhat is the effect of compounding?nSimple interest=10+200(10)(.055)=210.55nCompounding added$446,979.29 to the value of the investment4.12Futur
9、e Value as a General Growth FormulanSuppose your company expects to increase unit sales of widgets by 15%per year for the next 5 years.If you currently sell 3 million widgets in one year,how many widgets do you expect to sell in 5 years?nFV=3,000,000(1.15)5=6,034,0724.13Quick Quiz:Part 1nWhat is the
10、 difference between simple interest and compound interest?nSuppose you have$500 to invest and you believe that you can earn 8%per year over the next 15 years.nHow much would you have at the end of 15 years using compound interest?nHow much would you have using simple interest?4.14Present ValuesnHow
11、much do I have to invest today to have some amount in the future?nFV=PV(1+r)tnRearrange to solve for PV=FV/(1+r)tnWhen we talk about discounting,we mean finding the present value of some future amount.nWhen we talk about the“value”of something,we are talking about the present value unless we specifi
12、cally indicate that we want the future value.4.15PV One Period ExamplenSuppose you need$10,000 in one year for the down payment on a new car.If you can earn 7%annually,how much do you need to invest today?nPV=10,000/(1.07)1=9345.79nCalculatorn1 Nn7 I/Yn10,000 FVnCPT PV=-9345.794.16Present Values Exa
13、mple 2nYou want to begin saving for you daughters college education and you estimate that she will need$150,000 in 17 years.If you feel confident that you can earn 8%per year,how much do you need to invest today?nPV=150,000/(1.08)17=40,540.344.17Present Values Example 3nYour parents set up a trust f
14、und for you 10 years ago that is now worth$19,671.51.If the fund earned 7%per year,how much did your parents invest?nPV=19,671.51/(1.07)10=10,0004.18PV Important Relationship InFor a given interest rate the longer the time period,the lower the present valuenWhat is the present value of$500 to be rec
15、eived in 5 years?10 years?The discount rate is 10%n5 years:PV=500/(1.1)5=310.46n10 years:PV=500/(1.1)10=192.774.19PV Important Relationship IInFor a given time period the higher the interest rate,the smaller the present valuenWhat is the present value of$500 received in 5 years if the interest rate
16、is 10%?15%?nRate=10%:PV=500/(1.1)5=310.46nRate=15%;PV=500/(1.15)5=248.584.20Quick Quiz:Part 2nWhat is the relationship between present value and future value?nSuppose you need$15,000 in 3 years.If you can earn 6%annually,how much do you need to invest today?nIf you could invest the money at 8%,would you have to invest more or less than at 6%?How much?4.21Figure 4.34.22The Basic PV Equation-RefreshernPV=FV/(1+r)tnThere are four parts to this equationnPV,FV,r and tnIf we know any three,we can solv
