公司理财第七版Chap005

1、McGraw-Hill/IrwinCopyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved.Money has a time value. It can be expressed in multiple ways:A dollar today held in savings will grow.A dollar received in a year is not worth as much as a dollar received today.Time Value of MoneyFuture ValuesFut

2、ure Value: Amount to which an investment will grow after earning interest.Let r = annual interest rateLet t = # of years Simple InterestCompound InterestFV = Initial investment(1)tCompoundrFV = Initial investment(1)Simplert Simple Interest: ExampleInterest earned at a rate of 7% for five years on a

3、principal balance of $100.Example - Simple InterestTodayFuture Years 1 2 3 4 5Interest Earned Value100Value at the end of Year 5: $13571077114712171287135Interest earned at a rate of 7% for five years on the previous years balance.Example - Compound InterestTodayFuture Years 1 2 3 4 5Interest Earned

4、Value100Compound Interest: Example71077.49114.498.01122.508.58131.089.18140.26Value at the end of Year 5 = $140.26The Power of CompoundingInterest earned at a rate of 7% for the first forty years on the $100 invested using simple and compound interest.Present ValueWhat is it?Why is it useful?Present

5、 ValuePresent Value:Discount Rate:Discount Factor:1(1)trPVFV1(1)trDFRecall: t = number of yearsrPresent Value: ExampleAlways ahead of the game, Tommy, at 8 years old, believes he will need $100,000 to pay for college. If he can invest at a rate of 7% per year, how much money should he ask his rich U

6、ncle GQ to give him?101(1.07)1$100,000$50,835(1)tPVFVrNote: Ignore inflation/taxes$ 1 0 0 , 0 0 01 07 %F VtyrsrThe PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable. 1(1)trPVFVTime Value of Money(applications)Present Values: Changing Disc

7、ount RatesDiscount RatesThe present value of $100 to be received in 1 to 20 years at varying discount rates:PV of Multiple Cash Flows1212(1)(1)(1).ttCCCrrrPVThe present value of multiple cash flows can be calculated:12: The cash flow in year 1 The cash flow in year 2 The cash flow in year t (with an

8、y number of cash flows in between)tDenoteCCCRecall: r = the discount rateMultiple Cash Flows: ExampleYour auto dealer gives you the choice to pay $15,500 cash now or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money (discount rate) is 8%, which d

9、o you prefer?124,0001(1 .08)4,0002(1 .08)Initial Payment* 8,000.003,703.703,429.36Total PV $15,133.06PV of CPV of C* The initial payment occurs immediately and therefore would not be discounted.PerpetuitiesLet C = Yearly Cash PaymentPV of Perpetuity:CrPV What are they?Recall: r = the discount ratePe

10、rpetuities: ExampleIn order to create an endowment, which pays $185,000 per year forever, how much money must be set aside today if the rate of interest is 8%?What if the first payment wont be received until 3 years from today?185,000.08$2,312,500PV 22,312,500(1 .08)$1,982,596PVAnnuitiesWhat are the

11、y?Annuities are equally-spaced, level streams of cash flows lasting for a limited period of time. Why are they useful?Present Value of an AnnuityLet:C = yearly cash payment r = interest rate t = number of years cash payment is received11(1)trrrPVC The terms within the brackets are collectively calle

12、d the “annuity factor.”Annuities: ExampleYou are purchasing a home and are scheduled to make 30 annual installments of $10,000 per year. Given an interest rate of 5%, what is the price you are paying for the house (i.e. what is the present value)?3011.05.05(1 .05)$10,000$153,724.51PVPVFuture Value o

13、f Annuities: ExampleYou plan to save $4,000 every year for 20 years and then retire. Given a 10% rate of interest, how much will you have saved by the time you retire? 202011.10.10(1 .10)$4,000(1 .10)$229,100FVFVAnnuity DueHow does it differ from an ordinary annuity?What is it?Recall: r = the discou

14、nt rate(1)AnnuityDueAnnuityFVFVrHow does the future value differ from an ordinary annuity?(1)AnnuityDueAnnuityPVPVrAnnuities Due: Example)1 (rFVFVAnnuityADExample: Suppose you invest $429.59 annually at the beginning of each year at 10% interest. After 50 years, how much would your investment be wor

15、th?000,550$)10. 1 ()000,500($)1 (ADADAnnuityADFVFVrFVFVInterest Rates: EAR & APRWhat is EAR?What is APR?How do they differ?*where MR = monthly interest rateEAR & APR Calculations1)1 (12MREAREffective Annual Interest Rate (EAR):Annual Percentage Rate (APR):12 MRAPREAR and APR: ExampleGiven a

16、monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?%00.12)12()01. 0(%68.121)01. 1 (12APREARInflationWhat is it?What determines inflation rates?What is deflation?Inflation and Real Interest1+nominal interest rate1+inflation rate1real interest rate=Exact calculation:Approximation:rateinflation -rateinterest nominalrateinterest RealInflation: ExampleIf the nominal interest rate on your interest-bearing savings account