英文财务管理.ppt

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1、,Fundamentals of Corporate FinanceSixth EditionRichard A.Brealey Stewart C.MyersAlan J.Marcus,Slides byMatthew Will,Chapter 5,McGraw Hill/Irwin,Copyright 2009 by The McGraw-Hill Companies,Inc.All rights reserved,The Time Value of Money,Topics Covered,Future Values and Compound Interest(终值和复利）Present

2、 ValuesMultiple Cash Flows(多期现金流量)Level Cash Flows Perpetuities and AnnuitiesEffective Annual Interest Rates（实际年利率）Inflation&Time Value,Future Values,Future Value-Amount to which an investment will grow after earning interest.(终值)Compound Interest-Interest earned on interest.(复利)Simple Interest-Inte

3、rest earned only on the original investment.(单利),Future Values,Example-Simple InterestInterest earned at a rate of 6%for five years on a principal balance of$100.,Interest Earned Per Year=100 x.06=$6,Example-Simple InterestInterest earned at a rate of 6%for five years on a principal balance of$100.T

4、odayFuture Years 1 2 3 4 5Interest EarnedValue100,Future Values,6106,6112,6118,6124,6130,Value at the end of Year 5=$130,Future Values,Example-Compound InterestInterest earned at a rate of 6%for five years on the previous years balance.Interest Earned Per Year=Prior Year Balance x.06,Example-Compoun

5、d InterestInterest earned at a rate of 6%for five years on the previous years balance.TodayFuture Years 1 2 3 4 5Interest EarnedValue100,Future Values,6106,6.36112.36,6.74119.10,7.15126.25,7.57133.82,Value at the end of Year 5=$133.82,Future Values,Future Value of$100=FV,Solving for FV:,After 1 year

6、:FV1=PV(1+i)=$100(1.10)=$110.00After 2 years:FV2=PV(1+i)2=$100(1.10)2=$121.00After 3 years:FV3=PV(1+i)3=$100(1.10)3=$133.10After n years(general case):FVn=PV(1+i)n,Future Values,Example-FVWhat is the future value of$100 if interest is compounded annually at a rate of 6%for five years?,Future Values

7、with Compounding,Interest Rates,Manhattan Island Sale,Peter Minuit bought Manhattan Island for$24 in 1626.Was this a good deal?,To answer,determine$24 is worth in the year 2008,compounded at 8%.,FYI-The value of Manhattan Island land is well below this figure.,Present Values,Present Value现值Value tod

8、ay 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.,Present Values,Solve the general FV equation for PV:PV=FVn/(1+i)nPV=FV3/(1+i)3=$100/(1.10)3=$75.13,Present Values,ExampleYou just bough

9、t 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?,Present Values,Discount Factor=DF=PV of$1Discount Factors can be used to compute the present value of an

10、y cash flow.,The PV formula has many applications.Given any variables in the equation,you can solve for the remaining variable.,Time Value of Money(applications),Present Values with Compounding,Interest Rates,Value of Free Credit（免费信用的价值）Implied Interest Rates（隐含利率）Internal Rate of Return（内部收益率）Time

11、 necessary to accumulate funds（积累资金而需要的时间）,Time Value of Money(applications),What is the PV of this uneven cash flow stream?,PV of Multiple 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

12、.If your cost of money is 8%,which do you prefer?,Present Values,Present ValueYear 04000/1.084000/1.082Total,=$3,703.70=$3,429.36=$15,133.06,$4,000,$8,000,Year,0 12,$4,000,$8,000,Perpetuities&Annuities,PV of Multiple Cash Flows,PVs can be added together to evaluate multiple cash flows.,Perpetuities&

13、Annuities,Perpetuity（永续年金）A stream of level cash payments that never ends.Annuity（年金）Equally spaced level stream of cash flows for a limited period of time.,Annuity,Annuity（年金）:A series of payments of an equal amount at fixed intervals for a specified number of periods.Ordinary(Deferred)Annuity（普通年金

14、/后付年金）:An annuity whose payments occur at the end of each period.Annuity Due（先付年金）:An annuity whose payments occur at the beginning of each period.Payment(PMT)（定期等额支付）:Designates equal cash flows coming at regular intervals.,What is the difference between an ordinary annuity and an annuity due?,Perp

15、etuities&Annuities,PV of Perpetuity FormulaC=cash payment r=interest rate,Perpetuities&Annuities,Example-PerpetuityIn order to create an endowment,which pays$100,000 per year,forever,how much money must be set aside today in the rate of interest is 10%?,Perpetuities&Annuities,Example-continuedIf the

16、 first perpetuity payment will not be received until three years from today,how much money needs to be set aside today?,1.FV of Annuity 年金终值FV=A(1+i)t-1=A(1+i)n-1/i,2.FV of Annuity 年金现值,3.年偿债基金 A=FV/年金终值系数,复利、年金终值和现值系数的简称,（1i）n;FVi,n;(F/P,i,n);(S/P,i,n)称为复利现值系数1（1i）n;PVIFi,n;(P/F,i,n);(P/S,i,n)称为复利终

17、值系数FVIFi,n,(F/A,i,n),(S/A,i,n)称为年金终值系数PVIFi,n,(P/A,i,n),(P/A,i,n)称为年金现值系数,Perpetuities&Annuities,PV of Annuity FormulaC=cash payment r=interest rate t=Number of years cash payment is received,Perpetuities&Annuities,PV Annuity Factor(PVAF)-The present value of$1 a year for each of t years.,Perpetuiti

18、es&Annuities,Example-AnnuityYou are purchasing a car.You are scheduled to make 3 annual installments of$4,000 per year.Given a rate of interest of 10%,what is the price you are paying for the car(i.e.what is the PV)?,The PV and FV of Annuity Due,先付FVnA（F/A，i，n1）1 或 FA（1+i）即期数加1，系数减1先付PVnA（P/A，i，n1）+

19、1 或 PA（1+i）即期数减1，系数加1,递延年金,PVnA（P/A，i，mn）（P/A，i，m）或 A（P/A，i，n）（P/s，i，m）,2.递延年的计算：后期收付,延期年金指最初的年金现金流不是发生在当前，而是发生在若干期后。递延年金终值与普通年金终计算一样,主要是现值计算上有所差别。递延年金现值分计算两步:先计算m期期末的n期普遍年金现值;再将计算结果贴现到期初。唯一的特点就是将普通年金的现值往前贴现m期。,Perpetuities&Annuities,ApplicationsValue of paymentsImplied interest rate for an annuityC

20、alculation of periodic payments Mortgage payment（按揭付款）Annual income from an investment payoutFuture Value of annual payments（FV=CFVIFAi,n）,Perpetuities&Annuities,Example-Future Value of annual paymentsYou plan to save$4,000 every year for 20 years and then retire.Given a 10%rate of interest,what wil

21、l be the FV of your retirement account?FVIFA10%,20=57.275 400057.275=229 100,Effective Interest Rates,Annual Percentage Rate-Interest rate that is annualized using simple interest.,Effective Annual Interest Rate(实际年利率）-Interest rate that is annualized using compound interest.,Will the FV of a lump s

22、um be larger or smaller if compounded more often,holding the stated I%constant?,LARGER,as the more frequently compounding occurs,interest is earned on interest more often.,Annually:FV3=$100(1.10)3=$133.10,Semiannually:FV6=$100(1.05)6=$134.01,Classifications of interest rates,Nominal rate(iNOM)also c

23、alled the quoted or state rate.An annual rate that ignores compounding effects.iNOM is stated in contracts.Periods must also be given,e.g.8%Quarterly or 8%Daily interest.Periodic rate(iPER)amount of interest charged each period,e.g.monthly or quarterly.iPER=iNOM/m,where m is the number of compoundin

24、g periods per year.m=4 for quarterly and m=12 for monthly compounding.,Classifications of interest rates,Effective(or equivalent)annual rate(EAR or EFF%)is the annual rate of interest actually being earned,taking into account compounding opposed to the quoted rate.EFF%for 10%semiannual investmentEFF

25、%=(1+iNOM/m)m-1=(1+0.10/2)2 1=10.25%An investor would be indifferent between an investment offering a 10.25%annual return and one offering a 10%annual return,compounded semiannually.,Effective Interest Rates,exampleGiven a monthly rate of 1%,what is the Effective Annual Rate(EAR)?,Why is it importan

26、t to consider effective rates of return?,An investment with monthly payments is different from one with quarterly payments.Must put each return on an EFF%basis to compare rates of return.Must use EFF%for comparisons.See following values of EFF%rates at various compounding levels.EARANNUAL10.00%EARQU

27、ARTERLY10.38%EARMONTHLY10.47%EARDAILY(365)10.52%,When is each rate used?,iNOMwritten into contracts,quoted by banks and brokers.Not used in calculations or shown on time lines.iPERUsed in calculations and shown on time lines.If m=1,iNOM=iPER=EAR.EARUsed to compare returns on investments with differe

28、nt payments per year.Used in calculations when annuity payments dont match compounding periods.,What is the FV of$100 after 3 years under 10%semiannual compounding?Quarterly compounding?,Whats the FV of a 3-year$100 annuity,if the quoted interest rate is 10%,compounded semiannually?,Payments occur a

29、nnually,but compounding occurs every 6 months.Cannot use normal annuity valuation techniques.,Method 1:Compound each cash flow,FV3=$100(1.05)4+$100(1.05)2+$100FV3=$331.80,Method 2:Financial calculator,Find the EAR and treat as an annuity.EAR=(1+0.10/2)2 1=10.25%.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10.

30、25,-100,331.80,0,Find the PV of this 3-year ordinary annuity.,Could solve by discounting each cash flow,or Use the EAR and treat as an annuity to solve for PV.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10.25,100,0,-247.59,Loan amortization,Amortization tables are widely used for home mortgages,auto loans,bus

31、iness loans,retirement plans,etc.Financial calculators and spreadsheets are great for setting up amortization tables.EXAMPLE:Construct an amortization schedule for a$1,000,10%annual rate loan with 3 equal payments.,Step 1:Find the required annual payment,All input information is already given,just r

32、emember that the FV=0 because the reason for amortizing the loan and making payments is to retire the loan.PMT or C or A=PV/VIFA10%,3=1000/2.4869=402.11,Step 2:Find the interest paid in Year 1,The borrower will owe interest upon the initial balance at the end of the first year.Interest to be paid in

33、 the first year can be found by multiplying the beginning balance by the interest rate.INTt=Beg balt(i)INT1=$1,000(0.10)=$100,Step 3:Find the principal repaid in Year 1,If a payment of$402.11 was made at the end of the first year and$100 was paid toward interest,the remaining value must represent th

34、e amount of principal repaid.PRIN=PMT INT=$402.11-$100=$302.11,Step 4:Find the ending balance after Year 1,To find the balance at the end of the period,subtract the amount paid toward principal from the beginning balance.END BAL=BEG BAL PRIN=$1,000-$302.11=$697.89,Constructing an amortization table:

35、Repeat steps 1 4 until end of loan,Interest paid declines with each payment as the balance declines.What are the tax implications of this?,Illustrating an amortized payment:Where does the money go?,Constant payments.Declining interest payments.Declining balance.,$,0,1,2,3,402.11,Interest,302.11,Prin

36、cipal Payments,Effective Interest Rates,exampleGiven a monthly rate of 1%,what is the Effective Annual Rate(EAR)?What is the Annual Percentage Rate(APR)?,Inflation,Inflation-Rate at which prices as a whole are increasing.Nominal Interest Rate（名义利率）-Rate at which money invested grows.Real Interest Ra

37、te（实际利率）-Rate at which the purchasing power of an investment increases.,Inflation,Annual Inflation,%,Annual U.S.Inflation Rates from 1900-2007,Inflation,approximation formula,Inflation,ExampleIf the interest rate on one year govt.bonds is 6.0%and the inflation rate is 2.0%,what is the real interest rate?,SavingsBond,Inflation,Remember:Current dollar cash flows must be discounted by the nominal interest rate;real cash flows must be discounted by the real interest rate.,