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1、Discounted Cash Flow ValuationChapter 55.1Key Concepts and SkillsnBe able to compute the future value of multiple cash flowsnBe able to compute the present value of multiple cash flowsnBe able to compute loan paymentsnBe able to find the interest rate on a loannUnderstand how loans are amortized or
2、paid offnUnderstand how interest rates are quoted5.2Chapter OutlinenFuture and Present Values of Multiple Cash FlowsnValuing Level Cash Flows:Annuities and PerpetuitiesnComparing Rates:The Effect of Compounding PeriodsnLoan Types and Loan Amortization5.3Multiple Cash Flows FV Example 5.1nFind the va
3、lue at year 3 of each cash flow and add them together.nToday(year 0):FV=7000(1.08)3=8,817.98nYear 1:FV=4,000(1.08)2=4,665.60nYear 2:FV=4,000(1.08)=4,320nYear 3:value=4,000nTotal value in 3 years=8817.98+4665.60+4320+4000=21,803.58nValue at year 4=21,803.58(1.08)=23,547.875.4Multiple Cash Flows FV Ex
4、ample 2nSuppose you invest$500 in a mutual fund today and$600 in one year.If the fund pays 9%annually,how much will you have in two years?nFV=500(1.09)2+600(1.09)=1248.055.5Example 2 ContinuednHow much will you have in 5 years if you make no further deposits?nFirst way:nFV=500(1.09)5+600(1.09)4=1616
5、.26nSecond way use value at year 2:nFV=1248.05(1.09)3=1616.265.6Multiple Cash Flows FV Example 3nSuppose you plan to deposit$100 into an account in one year and$300 into the account in three years.How much will be in the account in five years if the interest rate is 8%?nFV=100(1.08)4+300(1.08)2=136.
6、05+349.92=485.975.7Example 3 Timeline100012345300136.05349.92485.975.8Multiple Cash Flows Present Value Example 5.3nFind the PV of each cash flow and add themnYear 1 CF:200/(1.12)1=178.57nYear 2 CF:400/(1.12)2=318.88nYear 3 CF:600/(1.12)3=427.07nYear 4 CF:800/(1.12)4=508.41nTotal PV=178.57+318.88+42
7、7.07+508.41=1432.935.9Example 5.3 Timeline01234200400600800178.57318.88427.07508.411432.935.10Multiple Cash Flows PV Another ExamplenYou are considering an investment that will pay you$1000 in one year,$2000 in two years and$3000 in three years.If you want to earn 10%on your money,how much would you
8、 be willing to pay?nPV=1000/(1.1)1=909.09nPV=2000/(1.1)2=1652.89nPV=3000/(1.1)3=2253.94nPV=909.09+1652.89+2253.94=4815.935.11Multiple Uneven Cash Flows Using the CalculatornAnother way to use the financial calculator for uneven cash flows is you use the cash flow keysnTexas Instruments BA-II PlusnPr
9、ess CF and enter the cash flows beginning with year 0.nYou have to press the“Enter”key for each cash flownUse the down arrow key to move to the next cash flownThe“F”is the number of times a given cash flow occurs in consecutive yearsnUse the NPV key to compute the present value by entering the inter
10、est rate for I,pressing the down arrow and then computenClear the cash flow keys by pressing CF and then CLR Work5.12Example:Spreadsheet StrategiesnYou can use the PV or FV functions in Excel to find the present value or future value of a set of cash flowsnSetting the data up is half the battle if i
11、t is set up properly,then you can just copy the formulasnClick on the Excel icon for an example5.13Decisions,DecisionsnYour broker calls you and tells you that he has this great investment opportunity.If you invest$100 today,you will receive$40 in one year and$75 in two years.If you require a 15%ret
12、urn on investments of this risk,should you take the investment?nUse the CF keys to compute the value of the investmentnCF;CF0=0;C01=40;F01=1;C02=75;F02=1nNPV;I=15;CPT NPV=91.49nNo the broker is charging more than you would be willing to pay.5.14Saving For RetirementnYou are offered the opportunity t
13、o put some money away for retirement.You will receive five annual payments of$25,000 each beginning in 40 years.How much would you be willing to invest today if you desire an interest rate of 12%?nUse cash flow keys:nCF;CF0=0;C01=0;F01=39;C02=25000;F02=5;NPV;I=12;CPT NPV=1084.715.15Saving For Retire
14、ment Timeline0 1 2 39 40 41 42 43 44 0 0 0 0 25K 25K 25K 25K 25KNotice that the year 0 cash flow=0(CF0=0)The cash flows years 1 39 are 0(C01=0;F01=39The cash flows years 40 44 are 25,000(C02=25,000;F02=5)5.16Quick Quiz:Part 1nSuppose you are looking at the following possible cash flows:Year 1 CF=$10
15、0;Years 2 and 3 CFs=$200;Years 4 and 5 CFs=$300.The required discount rate is 7%nWhat is the value of the cash flows at year 5?nWhat is the value of the cash flows today?nWhat is the value of the cash flows at year 3?5.17Annuities and Perpetuities DefinednAnnuity finite series of equal payments that
16、 occur at regular intervalsnIf the first payment occurs at the end of the period,it is called an ordinary annuitynIf the first payment occurs at the beginning of the period,it is called an annuity duenPerpetuity infinite series of equal payments5.18Annuities and Perpetuities Basic FormulasnPerpetuity:PV=C/rnAnnuities:rrCFVrrCPVtt1)1()1(115.19Annuities and the CalculatornYou can use the PMT key on the calculator for the equal paymentnThe sign convention still holdsnOrdinary annuity versus annuity
