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1、 2003 The McGraw-Hill Companies,Inc.All rights reserved.公司理财第六章(B)2003 The McGraw-Hill Companies,Inc.All rights reserved.Discounted Cash Flow Valuation(Formulas)ChapterSixMcGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.All rights reserved.Key Concepts and SkillsBe able to compute the future val
2、ue of multiple cash flowsBe able to compute the present value of multiple cash flowsBe able to compute loan paymentsBe able to find the interest rate on a loanUnderstand how loans are amortized or paid offUnderstand how interest rates are quotedMcGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.Al
3、l rights reserved.Chapter OutlineFuture and Present Values of Multiple Cash FlowsValuing Level Cash Flows:Annuities and PerpetuitiesComparing Rates:The Effect of Compounding PeriodsLoan Types and Loan AmortizationMcGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.All rights reserved.Multiple Cash
4、Flows Future Value Example 6.1Find the value at year 3 of each cash flow and add them together.Today(year 0):FV=7000(1.08)3=8,817.98Year 1:FV=4,000(1.08)2=4,665.60Year 2:FV=4,000(1.08)=4,320Year 3:value=4,000Total value in 3 years=8817.98+4665.60+4320+4000=21,803.58Value at year 4=21,803.58(1.08)=23
5、,547.87McGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.All rights reserved.Multiple Cash Flows FV Example 2Suppose 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?FV=500(1.09)2+600(1.09)=1248.05McGraw-Hill/Irwin 2003 The
6、McGraw-Hill Companies,Inc.All rights reserved.Multiple Cash Flows Example 2 ContinuedHow much will you have in 5 years if you make no further deposits?First way:FV=500(1.09)5+600(1.09)4=1616.26Second way use value at year 2:FV=1248.05(1.09)3=1616.26McGraw-Hill/Irwin 2003 The McGraw-Hill Companies,In
7、c.All rights reserved.Multiple Cash Flows FV Example 3Suppose 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%?FV=100(1.08)4+300(1.08)2=136.05+349.92=485.97McGraw-Hill/Irwin 2003 The M
8、cGraw-Hill Companies,Inc.All rights reserved.Multiple Cash Flows Present Value Example 6.3Find the PV of each cash flows and add themYear 1 CF:200/(1.12)1=178.57Year 2 CF:400/(1.12)2=318.88Year 3 CF:600/(1.12)3=427.07Year 4 CF:800/(1.12)4=508.41Total PV=178.57+318.88+427.07+508.41=1432.93McGraw-Hill
9、/Irwin 2003 The McGraw-Hill Companies,Inc.All rights reserved.Example 6.3 Timeline01234200400600800178.57318.88427.07508.411432.93McGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.All rights reserved.Multiple Cash Flows Using a SpreadsheetYou can use the PV or FV functions in Excel to find the pr
10、esent value or future value of a set of cash flowsSetting the data up is half the battle if it is set up properly,then you can just copy the formulasClick on the Excel icon for an exampleMcGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.All rights reserved.Multiple Cash Flows PV Another ExampleYo
11、u 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 be willing to pay?PV=1000/(1.1)1=909.09PV=2000/(1.1)2=1652.89PV=3000/(1.1)3=2253.94PV=909.09+1652.89+2253.94=4815.93McGraw-Hill/Irwin
12、2003 The McGraw-Hill Companies,Inc.All rights reserved.Multiple Uneven Cash Flows Usingthe CalculatorAnother way to use the financial calculator for uneven cash flows is to use the cash flow keysTexas Instruments BA-II PlusPress CF and enter the cash flows beginning with year 0.You have to press the
13、“Enter”key for each cash flowUse the down arrow key to move to the next cash flowThe“F”is the number of times a given cash flow occurs in consecutive yearsUse the NPV key to compute the present value by entering the interest rate for I,pressing the down arrow and then computeClear the cash flow keys
14、 by pressing CF and then CLR WorkMcGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.All rights reserved.Decisions,DecisionsYour 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、15%return on investments of this risk,should you take the investment?Use the CF keys to compute the value of the investmentCF;CF0=0;C01=40;F01=1;C02=75;F02=1NPV;I=15;CPT NPV=91.49No the broker is charging more than you would be willing to pay.McGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.All
16、rights reserved.Saving For RetirementYou are offered the opportunity to 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%?Use cash flow keys:CF;CF0=0;C01=0;F01=39;C02=25000;F02=5;NPV;I=12;CPT NPV=1084.71McGraw-Hill/Irwin 2003 The McGraw-Hill Companies,Inc.All rights reserved.Saving For Retirement Timeline0 1 2 39 40 41 42 43 44 0 0 0 0 25K 25K 25K 25K 25
