公司理财第四章

Introduction to Valuation:The Time Value of MoneyChapter 41Key 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 investment2Chapter OutlinenFuture Value and CompoundingnPresent Value and DiscountingnMore on Present and Future Values3Basic 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 cost of capitalnRequired return4Future 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 will you have two years from now?nFV=1000(1.05)(1.05)=1000(1.05)2=1102.505Future 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)t6Effects of CompoundingnSimple interest nCompound 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 payment7Figure 4.18Figure 4.29Calculator KeysnTexas Instruments BA-II PlusnFV=future valuenPV=present 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 format10Future Values Example 2nSuppose you invest 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.)11Future Values 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 investment12Future 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=6,034,07213Quick Quiz:Part 1nWhat is the 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?14Present ValuesnHow 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 specifically indicate that we want the future value.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=-9345.7916Present Values Example 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=40,540.3417Present Values Example 3nYour parents set up a trust fund 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=10,00018PV 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 received 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=192.7719PV 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 is 10%?15%?nRate=10%:PV=500/(1.1)5=310.46nRate=15%;PV=500/(1.15)5=248.5820Quick 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?21Figure 4.322The Basic PV Equation-RefreshernPV=FV/(1+r)tnThere are four parts to this equationnPV,FV,r and tnIf we know any three,we can solve for the fourthnIf you are using a financial calculator,be sure and remember the sign convention or you will receive an error when solving for r or t23Discount RatenOften we will want to know what the implied interest rate is in an investmentnRearrange the basic PV equation and solve for rnFV=PV(1+r)tnr=(FV/PV)1/t 1nIf you are using formulas,you will want to make use of both the yx and the 1/x keys24Discount Rate Example 1nYou are looking at an investment that will pay$1200 in 5 years if you invest$1000 today.What is the implied rate of interest?nr=(1200/1000)1/5 1=.03714=3.714%nCalculator the sign convention matters!nN=5nPV=-1000(you pay 1000 today)nFV=1200(you receive 1200 in 5 years)nCPT I/Y=3.714%25Discount Rate Example 2nSuppose 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?nr=(20,000/10,000)1/6 1=.122462=12.25%26Discount Rate Example 3nSuppose you have a 1-year old son and you want to provide$75,000 in 17 years towards his college education.You currently have$5000 to invest.What interest rate must you earn to have the$75,000 when you need it?nr=(75,000/5,000)1/17 1=.172688=17.27%27Quick Quiz:Part 3nWhat are some situations where you might want to compute the implied interest rate?nSuppose you are offered the following investment choices:nYou can invest$500 today and receive$600 in 5 years.The investment is considered low risk.nYou can invest the$500 in a bank account paying 4%.nWhat is the implied interest rate for the first choice and which investment should you choose?28Finding the Number of PeriodsnStart with basic equation and solve for t(remember your logs)nFV=PV(1+r)tnt=ln(FV/PV)/ln(1+r)nYou can use the financial keys on the calculator as well,just remember the sign convention.29Number of Periods Example 1nYou 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?nt=ln(20,000/15,000)/ln(1.1)=3.02 years30Number of Periods Example 2nSuppose you want to buy a new house.You currently have$15,000 and you figure you need to have a 10%down payment plus an additional 5%in closing costs.If the type of house you want costs about$150,000 and you can earn 7.5%per year,how long will it be before you have enough money for the down payment and closing costs?31Example 2 ContinuednHow much do you need to have in the future?nDown payment=.1(150,000)=15,000nClosing costs=.05(150,000 15,000)=6,750nTotal needed=15,000+6,750=21,750nCompute the number of periodsnPV=-15,000nFV=21,750nI/Y=7.5nCPT N=5.14 yearsnUsing the formulant=ln(21,750/15,000)/ln(1.075)=5.14 years32Example:Spreadsheet StrategiesnUse the following formulas for TVM calculationsnFV(rate,nper,pmt,pv)nPV(rate,nper,pmt,fv)nRATE(nper,pmt,pv,fv)nNPER(rate,pmt,pv,fv)nThe formula icon is very useful when you cant remember the exact formulanClick on the Excel icon to open a spreadsheet containing four different examples.33Work the Web ExamplenMany financial calculators are available onlinenClick on the web surfer to go to Cignas web site and work the following example:nYou need$40,000 in 15 years.If you can earn 9.8%interest,how much do you need to invest today?nYou should get$9,84134Table 4.435Quick Quiz:Part 4nWhen might you want to compute the number of periods?nSuppose you want to buy some new furniture for your family room.You currently have$500 and the furniture you want costs$600.If you can earn 6%,how long will you have to wait if you dont add any additional money?36