公司理财第九版-第5章.ppt

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1、Chapter 5 Chapter 5 FormulasFormulasFormulasFormulasIntroduction to Introduction to Valuation:The Time Valuation:The Time Value of MoneyValue of MoneyMcGraw-Hill/IrwinCopyright 2010 by The McGraw-Hill Companies,Inc.All rights reserved.1Key Concepts and SkillsBe able to compute the future value of an

2、 investment made todayBe able to compute the present value of cash to be received at some future dateBe able to compute the return on an investmentBe able to compute the number of periods that equates a present value and a future value given an interest rateBe able to use a financial calculator and/

3、or a spreadsheet to solve time value of money problems5F-22Chapter OutlineFuture Value and CompoundingPresent Value and DiscountingMore about Present and Future Values5F-33什么是货币的时间价值什么是货币的时间价值货币时间价值：是指货币随着时间的货币时间价值：是指货币随着时间的推移而发生的增值，也称为资金时间推移而发生的增值，也称为资金时间价值。价值。是不是货币在任何状态下都可以产生是不是货币在任何状态下都可以产生时间价值呢？

4、时间价值呢？是不是货币作为资本投入到经营活动是不是货币作为资本投入到经营活动中所获得的增值额都是时间价值呢？中所获得的增值额都是时间价值呢？4利率的构成利率的构成利率利率=时间价值时间价值+风险报酬风险报酬+通货膨胀贴水通货膨胀贴水利率在经济生活中的表现形式利率在经济生活中的表现形式银行存款利息率银行存款利息率银行贷款利率银行贷款利率债券利息率债券利息率股息率股息率时间价值是扣除风险报酬和通货膨胀贴水后时间价值是扣除风险报酬和通货膨胀贴水后的真实收益率（社会平均资金收益率）。的真实收益率（社会平均资金收益率）。5Basic DefinitionsPresent Value 现值（PV），是指未

5、来某一时点上的一定量现金折合到现在的价值，又称本金。Future Value 终值（FV），是现在一定量现金在未来某一时点上的价值，即本利和本利和，又称将来值。Interest rate “exchange rate”between earlier money and later moneyDiscount rateCost of capitalOpportunity cost of capitalRequired return5F-66Future ValuesSuppose you invest$1,000 for one year at 5%per year.What is the fu

6、ture value in one year?Interest=1,000(.05)=50Value in one year=principal+interest=1,000+50=1,050Future Value(FV)=1,000(1+.05)=1,050Suppose you leave the money in for another year.How much will you have two years from now?FV=1,000(1.05)(1.05)=1,000(1.05)2=1,102.505F-77Future Values:General FormulaFV=

7、PV(1+r)tFV=future valuePV=present valuer=period interest rate,expressed as a decimalt=number of periodsFuture value interest factor=(1+r)t 复利终值系数，可查表，中文教材表现为（F/P，i,n)5F-88Effects of CompoundingSimple interest Compound interestConsider the previous exampleFV with simple interest=1,000+50+50=1,100 两年期

8、单利FV with compound interest=1,102.50 两年期复利The extra 2.50 comes from the interest of.05(50)=2.50 earned on the first interest payment5F-99Calculator Keys 计算器Texas Instruments BA-II PlusFV=future valuePV=present valueI/Y=period interest rateP/Y must equal 1 for the I/Y to be the period rateInterest is

9、 entered as a percent,not a decimalN=number of periodsRemember to clear the registers(CLR TVM)after each problemOther calculators are similar in format了解即可5F-1010Future Values Example 2Suppose you invest the$1,000 from the previous example for 5 years.How much would you have?FV=1,000(1.05)5=1,276.28

10、The 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$1,250,for a difference of$26.28.)5F-1111Future Values Example 3Suppose you had a relative deposit$10 at 5.5%interest 200 years ago.How much

11、would the investment be worth today?FV=10(1.055)200=447,189.84What is the effect of compounding?Simple interest=10+200(10)(.055)=120.00Compounding added$447,069.84 to the value of the investment5F-1212Future Value as a General Growth FormulaSuppose your company expects to increase unit sales of widg

12、ets（小部件）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?FV=3,000,000(1.15)5=6,034,0725F-1313Quick Quiz Part IWhat is the difference between simple interest and compound interest?Suppose you have$500 to invest a

13、nd you believe that you can earn 8%per year over the next 15 years.How much would you have at the end of 15 years using compound interest?How much would you have using simple interest?5F-1414Present Values 现值How much do I have to invest today to have some amount in the future?FV=PV(1+r)tRearrange to

14、 solve for PV=FV/(1+r)tWhen we talk about discounting,we mean finding the present value of some future amount.When we talk about the“value”of something,we are talking about the present value unless we specifically indicate that we want the future value.5F-1515Present Value One Period ExampleSuppose

15、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?PV=10,000/(1.07)1=9,345.79Calculator 1 N7 I/Y10,000 FVCPT PV=-9,345.795F-1616Present Values Example 2You want to begin saving for your daughters college education and you est

16、imate 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?PV=150,000/(1.08)17=40,540.345F-1717Present Values Example 3Your parents set up a trust fund（托管基金）for you 10 years ago that is now worth$19,671.51.If the fund earned 7

17、%per year,how much did your parents invest?PV=19,671.51/(1.07)10=10,0005F-1818Present Value Important Relationship IFor a given interest rate the longer the time period,the lower the present valueWhat is the present value of$500 to be received in 5 years?10 years?The discount rate is 10%.五年后收到500的现值

18、5 years:PV=500/(1.1)5=310.4610 years:PV=500/(1.1)10=192.775F-1919Present Value Important Relationship IIFor a given time period the higher the interest rate,the smaller the present valueWhat is the present value of$500 received in 5 years if the interest rate is 10%?15%?Rate=10%:PV=500/(1.1)5=310.46

19、Rate=15%;PV=500/(1.15)5=248.595F-2020Quick Quiz Part IIWhat is the relationship between present value and future value?Suppose you need$15,000 in 3 years.If you can earn 6%annually,how much do you need to invest today?If you could invest the money at 8%,would you have to invest more or less than at

20、6%?How much?5F-2121The Basic PV Equation-RefresherPV=FV/(1+r)tThere are four parts to this equationPV,FV,r and tIf we know any three,we can solve for the fourth 三缺一，学会求第四个？If you are using a financial calculator,be sure to remember the sign convention or you will receive an error(or a nonsense answe

21、r)when solving for r or t5F-2222Discount Rate 折现率Often we will want to know what the implied interest rate is in an investmentRearrange the basic PV equation and solve for rFV=PV(1+r)tr=(FV/PV)1/t 1If you are using formulas,you will want to make use of both the yx and the 1/x keys5F-2323Discount Rat

22、e Example 1You are looking at an investment that will pay$1,200 in 5 years if you invest$1,000 today.What is the implied rate of interest?r=(1,200/1,000)1/5 1=.03714=3.714%Calculator the sign convention matters!N=5PV=-1,000(you pay 1,000 today)FV=1,200(you receive 1,200 in 5 years)CPT I/Y=3.714%5F-2

23、424Discount Rate Example 2Suppose you are offered an investment that will allow you to double your money in 6 years.You have$10,000 to invest.What is the implied rate of interest?r=(20,000/10,000)1/6 1=.122462=12.25%用72法则，72/6=12，即12%同样，假设年利率为10%，多少年可以翻一番？72/10=7.2年5F-2525Discount Rate Example 3Supp

24、ose you have a 1-year old son and you want to provide$75,000 in 17 years towards his college education.You currently have$5,000 to invest.What interest rate must you earn to have the$75,000 when you need it?r=(75,000/5,000)1/17 1=.172688=17.27%，可用计算器5F-2626Quick Quiz Part IIIWhat are some situations

25、 in which you might want to know the implied interest rate?You are offered the following investments:You can invest$500 today and receive$600 in 5 years.The investment is considered low risk.You can invest the$500 in a bank account paying 4%.What is the implied interest rate for the first choice and

26、 which investment should you choose?5F-2727Finding the Number of Periods 计算复利期数Start with the basic equation and solve for t(remember your logs)FV=PV(1+r)tt=ln(FV/PV)/ln(1+r)You can use the financial keys on the calculator as well;just remember the sign convention.5F-2828Number of Periods Example 1Y

27、ou want to purchase a new car,and you are willing to pay$20,000.If you can invest at 10%per year and you currently have$15,000,how long will it be before you have enough money to pay cash for the car?t=ln(20,000/15,000)/ln(1.1)=3.02 years5F-2929Number of Periods Example 2Suppose you want to buy a ne

28、w house.You currently have$15,000,and you figure you need to have a 10%down payment（预付定金）plus an additional 5%of the loan amount for closing costs（买卖房子的过户费用）.Assume the type of house you want will cost about$150,000 and you can earn 7.5%per year,how long will it be before you have enough money for t

29、he down payment and closing costs?5F-3030Number of Periods Example 2 ContinuedHow much do you need to have in the future?Down payment=.1(150,000)=15,000Closing costs=.05(150,000 15,000)=6,750Total needed=15,000+6,750=21,750 终值Compute the number of periods目前手里有15000元,7.5%回报Using the formulat=ln(21,75

30、0/15,000)/ln(1.075)=5.14 yearsPer a financial calculator:PV=-15,000,FV=21,750,I/Y=7.5,CPT N=5.14 years5F-3131Quick Quiz Part IVWhen might you want to compute the number of periods?Suppose you want to buy some new furniture for your family room.You currently have$500,and the furniture you want costs$

31、600.If you can earn 6%,how long will you have to wait if you dont add any additional money?5F-3232Spreadsheet ExampleUse the following formulas for TVM calculationsFV(rate,nper,pmt,pv)PV(rate,nper,pmt,fv)RATE(nper,pmt,pv,fv)NPER(rate,pmt,pv,fv)The formula icon is very useful when you cant remember t

32、he exact formulaClick on the Excel icon to open a spreadsheet containing four different examples.5F-3333Work the Web ExampleMany financial calculators are available onlineClick on the web surfer to go to Investopedias web site and work the following example:You need$50,000 in 10 years.If you can ear

33、n 6%interest,how much do you need to invest today?You should get$27,919.745F-3434Table 5.45F-3535Comprehensive ProblemYou have$10,000 to invest for five years.How much additional interest will you earn if the investment provides a 5%annual return,when compared to a 4.5%annual return?How long will it take your$10,000 to double in value if it earns 5%annually?What annual rate has been earned if$1,000 grows into$4,000 in 20 years?5F-3636End of Chapter5F-3737