英文财务管理.ppt

5- 1McGraw Hill/IrwinCopyright 2009 by The McGraw-Hill Companies, Inc. All rights reserved Fundamentals of Corporate FinanceSixth EditionRichard A. Brealey Stewart C. MyersAlan J. MarcusSlides byMatthew WillChapter 5McGraw Hill/IrwinCopyright 2009 by The McGraw-Hill Companies, Inc. All rights reserved The Time Value of Money5- 2Topics Coveredw Future Values and Compound Interest(终值和复利）w Present Valuesw Multiple Cash Flows (多期现金流量)w Level Cash Flows Perpetuities and Annuitiesw Effective Annual Interest Rates（实际年利率）w Inflation & Time Value5- 3Future ValuesFuture Value - Amount to which an investment will grow after earning interest. (终值)Compound Interest - Interest earned on interest.(复利)Simple Interest - Interest earned only on the original investment.(单利)5- 4Future ValuesExample - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.Interest Earned Per Year = 100 x .06 = $ 65- 5Example - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.TodayFuture Years 1 2 3 4 5Interest EarnedValue100Future Values61066112611861246130Value at the end of Year 5 = $1305- 6Future ValuesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous years balance.Interest Earned Per Year =Prior Year Balance x .065- 7Example - Compound InterestInterest earned at a rate of 6% for five years on the previous years balance.TodayFuture Years 1 2 3 4 5Interest EarnedValue100Future Values61066.36112.366.74119.107.15126.257.57133.82Value at the end of Year 5 = $133.825- 8Future ValuesFuture Value of $100 = FVFVrt$100()15- 9Solving for FV:w After 1 year:FV1 = PV ( 1 + i ) = $100 (1.10) = $110.00w After 2 years:FV2 = PV ( 1 + i )2 = $100 (1.10)2 =$121.00w After 3 years:FV3 = PV ( 1 + i )3 = $100 (1.10)3 =$133.10w After n years (general case):FVn = PV ( 1 + i )n5- 10Future ValuesFVrt$100()1Example - FVWhat is the future value of $100 if interest is compounded annually at a rate of 6% for five years?82.133$)06.1 (100$5FV5- 11Future Values with CompoundingInterest Rates5- 12Manhattan Island SalePeter Minuit bought Manhattan Island for $24 in 1626. Was this a good deal? trillionFV 63.140$)08.1 (24$382To answer, determine $24 is worth in the year 2008, compounded at 8%. 5- 13Present ValuesPresent Value现值Value today of a future cash flow.Discount Rate折现率Interest rate used to compute present values of future cash flows.Discount Factor贴现因子Present value of a $1 future payment.5- 14Present ValuesPresent Value = PVPV =Future Value after t periods (1+r)t5- 15w Solve the general FV equation for PV:PV = FVn / ( 1 + i )nPV = FV3 / ( 1 + i )3 = $100 / ( 1.10 )3 = $75.135- 16Present ValuesExampleYou just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?572, 2$2)08. 1(3000PV5- 17Present ValuesDiscount Factor = DF = PV of $1w Discount Factors can be used to compute the present value of any cash flow.DFrt11()5- 18w The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable. PVFVrt11()Time Value of Money(applications)5- 19Present Values with CompoundingInterest Rates5- 20w Value of Free Credit（免费信用的价值）w Implied Interest Rates（隐含利率 ）w Internal Rate of Return（内部收益率）w Time necessary to accumulate funds（积累资金而需要的时间）Time Value of Money(applications)5- 21What is the PV of this uneven cash flow stream?010013002300310%-504 90.91247.93225.39 -34.15530.08 = PV5- 22PV of Multiple Cash FlowsExampleYour 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 is 8%, which do you prefer?$15,133.06 PVTotal36.429, 370.703, 38,000.0021)08.1(000,42)08.1(000,41payment ImmediatePVPV5- 23Present ValuesPresent ValueYear 04000/1.084000/1.082Total= $3,703.70= $3,429.36= $15,133.06$4,000$8,000Year0 12$ 4,000$8,0005- 24Perpetuities & AnnuitiesFinding the present value of multiple cash flows by using a spreadsheetTime until CF Cash flow Present value Formula in Column C08000$8,000.00 =PV($B$11,A4,0,-B4)14000$3,703.70 =PV($B$11,A5,0,-B5)24000$3,429.36 =PV($B$11,A6,0,-B6)SUM:$15,133.06 =SUM(C4:C6)Discount rate:0.085- 25PV of Multiple Cash Flowsw PVs can be added together to evaluate multiple cash flows.PVCrCr112211()().5- 26Perpetuities & AnnuitiesPerpetuity（永续年金）（永续年金） A stream of level cash payments that never ends.Annuity（年金）（年金） Equally spaced level stream of cash flows for a limited period of time.5- 27Annuityw Annuity（年金）（年金）: A series of payments of an equal amount at fixed intervals for a specified number of periods.w Ordinary (Deferred) Annuity（普通年金（普通年金/后付年后付年金）金）: An annuity whose payments occur at the end of each period.w Annuity Due（先付年金）（先付年金）: An annuity whose payments occur at the beginning of each period.w Payment (PMT)（定期等额支付）（定期等额支付）: Designates e