财务管理ppt英文课件Chapter-3

1、Chapter 3Time Value of0Time Value of Money“A dollar today is worth than a dollar tomorrow.”1Copyright 2001 Prentice-Hall, Inc.Chapter ObjectivesDistinguish between simple and compound interest.Calculate the present value and future value of a single amount for both one period and multiple periods.Ca

2、lculate the present value and future value of multiple cash flows.Calculate the present value and future value of annuities.Compare nominal interest rates (NIR) and effective annual interest rates (EAR).Determine the amortization schedule.2Copyright 2001 Prentice-Hall, Inc.When youre in your 20s, yo

3、ure young . Who thinks about retiring at this age? . Youre just beginning to make some money . Perhaps there are college loans to be paid.If youre in your 30s, youve probably started a family . Youre scraping enough together to buy your first home and make the mortgage payments.Now in your 40s, you

4、may be facing demands on your earnings . You need a larger home . The kids are taking dance and piano lessons . they need braces . You may have some financial responsibility for aging parents.By your 50s, you have children in college . You may be experiencing late-in-career job changes or setbacks.S

5、uddenly youre 60, and for all the best reasons in the world you didnt save along the way . For so long it seemed so far away . Retirement is now upon you, and you arent ready financially.3Copyright 2001 Prentice-Hall, Inc.Cash-Flow Time LineTime periods0Cash flow-in (现金流入)Cash flow-out(现金流出)123454Co

6、pyright 2001 Prentice-Hall, Inc.Time Value TerminologyFuture value (FV) is the amount an investment is worth after one or more periods.Present value (PV) is the current value of future cash flows of an investment.01234PVFV5Copyright 2001 Prentice-Hall, Inc.Time Value TerminologyThe number of time pe

7、riods between the present value and the future value is represented by n or “t”. The rate of interest for discounting or compounding is called i or “r”.All time value questions involve包括 four values: PV, FV, i and n. Given three of them, it is always possible to calculate the fourth.6Copyright 2001

8、Prentice-Hall, Inc.Interest Rate TerminologySimple interest refers to interest earned only on the original capital investment amount.Compound interest复利 refers to interest earned on both the initial capital investment and on the interest reinvested from prior period.“Worlds eighth wonder” the power

9、of compounding.7Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.8Copyright 2001 Prentice-Hall, Inc.Future Values Example - Simple InterestInterest earned at a rate of 6% for five years on a principa

10、l balance of $100.Interest Earned Per Year = 100 x .06 = $ 69Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.TodayFuture Years 1 2 3 4 5Interest EarnedValue10010Copyright 2001 Prentice-Hall, Inc.Fut

11、ure ValuesExample - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.TodayFuture Years 1 2 3 4 5Interest Earned 6Value10010611Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Simple InterestInterest earned at a rate of 6% for five years on a princi

12、pal balance of $100.TodayFuture Years 1 2 3 4 5Interest Earned 6 6Value10010611212Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.TodayFuture Years 1 2 3 4 5Interest Earned 6 6 6Value10010611211813C

13、opyright 2001 Prentice-Hall, Inc.Future ValuesExample - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.TodayFuture Years 1 2 3 4 5Interest Earned 6 6 6 6 Value10010611211812414Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Simple InterestIntere

14、st earned at a rate of 6% for five years on a principal balance of $100.TodayFuture Years 1 2 3 4 5Interest Earned 6 6 6 6 6Value100106112118124130Value at the end of Year 5 = $13015Copyright 2001 Prentice-Hall, Inc.For any simple interest rate, the future value of an account invested today at the e

15、nd of n periods is:FP( 1 + ni )The present value of an account is:P = F(1+ni)-1Simple Interest Formula16Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous years balance.17Copyright 2001 Prentice-Hall, Inc.Future Va

16、luesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous years balance.Interest Earned Per Year =Prior Year Balance x .0618Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous yea

17、rs balance.TodayFuture Years 1 2 3 4 5Interest EarnedValue10019Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous years balance.TodayFuture Years 1 2 3 4 5Interest Earned 6.00Value100106.0020Copyright 2001 Prentice

18、-Hall, Inc.Future ValuesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous years balance.TodayFuture Years 1 2 3 4 5Interest Earned 6.00 6.36Value100106.00112.3621Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Compound InterestInterest earned at a rat

19、e of 6% for five years on the previous years balance.TodayFuture Years 1 2 3 4 5Interest Earned 6.00 6.36 6.74Value100106.00112.36119.1022Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous years balance.TodayFuture

20、 Years 1 2 3 4 5Interest Earned 6.00 6.36 6.74 7.15Value100106.00112.36119.10126.2523Copyright 2001 Prentice-Hall, Inc.Future ValuesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous years balance.TodayFuture Years 1 2 3 4 5Interest Earned 6.00 6.36 6.74 7.15 7

21、.57Value100106.00112.36119.10126.25133.82Value at the end of Year 5 = $133.8224Copyright 2001 Prentice-Hall, Inc.Future Value of a Lump SumThe accumulated value of this investment at the end of five years can be split into two components:original principal$100interest earned$33.82Using simple intere

22、st, the total interest earned would only have been $30. The other $3.82 is from compounding.25Copyright 2001 Prentice-Hall, Inc.Future Value of a Lump SumIn general, the future value, FVn of an account invested today at i % for t periods is: F= P( 1+i ) nThe expression (1 + i)n is the future value i

23、nterest factor (FVIFi,n). Refer to Table I.26Copyright 2001 Prentice-Hall, Inc.Future Values with CompoundingInterest Rates27Copyright 2001 Prentice-Hall, Inc.The Rule of 72The Rule of 72 is a handy rule of thumb that states:If you earn r % per year, your money will double in about 72 / r % years.Fo

24、r example, if you invest at 6%, your money will double in about 12 years.This rule is only an approximate近似的 rule.28Copyright 2001 Prentice-Hall, Inc.Present Value of a Lump Sum汇总The future value, PVn of an account invested today at i % for t periods is: P = F( 1+i ) -nThe expression (1 + i)-n is th

25、e present value interest factor (PVIFi,n). Refer to Table II.29Copyright 2001 Prentice-Hall, Inc.Present Value of $1 for Different Periods and RatesPresentvalueof $1 ($)Time(years)r = 0%r = 5%r = 10%r = 15%r = 20%1 2 3 4 5 6 7 8 9 101.0030Copyright 2001 Prentice-Hall, Inc.

26、PV of Multiple多样的 Cash FlowsPVs can be added together to evaluate multiple cash flows.31Copyright 2001 Prentice-Hall, Inc.PV 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

27、. If your cost of money is 8%, which do you prefer? 32Copyright 2001 Prentice-Hall, Inc.Types of AnnuitiesAn Annuity(年金) represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.Ordinary Annuity（普通年金）: Payments or receipts occur at the end of each

28、period.Annuity Due （先付年金）: Payments or receipts occur at the beginning of each period.A perpetuity （永续年金）is an annuity in which the cash flows continue forever.33Copyright 2001 Prentice-Hall, Inc.Examples of Annuities Student Loan Payments Car Loan Payments Insurance Premiums Mortgage Payments Retir

29、ement Savings34Copyright 2001 Prentice-Hall, Inc.Future Value of An Annuity01234AAAAA（1+i）0A（1+i）1A（1+i）2A（1+i）3F35Copyright 2001 Prentice-Hall, Inc. F = F1 + F2+ F3+ + Fn = A+A( 1+i ) 1 +A ( 1+i ) 2 +A ( 1+i ) n-1 (1+i )n1 =A iFuture Value of An AnnuityThe compounding term is called the future valu

30、e interest factor for annuities (FVIFAi,n). Refer to Table III.36Copyright 2001 Prentice-Hall, Inc.Present Value of An Annuity 01234AAAAA/（1+i）1A/（1+i）2A/（1+i）3A/（1+i）4P37Copyright 2001 Prentice-Hall, Inc.Present Value of An Annuity P = A( 1+i ) -1 +A ( 1+i ) -2 +A ( 1+i ) -n 1(1+i )-n =A iThe disco

31、unting term is called the present value interest factor for annuities (PVIFAi,n). Refer to Table IV.38Copyright 2001 Prentice-Hall, Inc.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 yo

32、u are paying for the car (i.e. what is the PV)? 39Copyright 2001 Prentice-Hall, Inc.Hint on Annuity ValuationThe present value of an ordinary annuity can be viewed as occurring at the beginning of the first cash flow period.The future value of an ordinary annuity can be viewed as occurring at the en

33、d of the last cash flow period.40Copyright 2001 Prentice-Hall, Inc.PerpetuitiesThe future value of a perpetuity cannot be calculated as the cash flows are infinite.The present value of a perpetuity is calculated as follows: P = A( 1+i ) -1 +A ( 1+i ) -2 +A ( 1+i ) -n 1(1+i )-n =A i n, 1/(1+i)n0 P=A/

34、I 41Copyright 2001 Prentice-Hall, Inc. Julie Miller will receive the set of cash flows below. What is the Present Value at a discount rate of 10%? 0 1 2 3 4 5 $600 $600 $400 $400 $100PV0Mixed Flows Example42Copyright 2001 Prentice-Hall, Inc.1.Solve a “piece-at-a-time” by discounting each piece back

35、to t=0.2.Solve a “group-at-a-time” by first breaking problem into groups of annuity streams and any single cash flow group. Then discount each group back to t=0.How to Solve?43Copyright 2001 Prentice-Hall, Inc. 0 1 2 3 4 5 $600 $600 $400 $400 $10010%$545.45$495.87$300.53$273.21$ 62.09$1677.15 = PV0

36、of the Mixed Flow“Piece-At-A-Time”44Copyright 2001 Prentice-Hall, Inc. 0 1 2 3 4 5 $600 $600 $400 $400 $10010%$1,041.60$ 573.57$ 62.10$1,677.27 = PV0 of Mixed Flow Using Tables“Group-At-A-Time” (#1)$600(PVIFA10%,2)= $600(1.736) = $1,041.60$400(PVIFA10%,2)(PVIF10%,2)=$400(1.736)(0.826) = $573.57$100

37、(PVIF10%,5)= $100 (0.621) = $62.1045Copyright 2001 Prentice-Hall, Inc. 0 1 2 3 4 $400 $400 $400 $400 0 1 2 3 4 5 $100 0 1 2 $200 $200$1,268.00$347.20$62.10PV0 equals$1677.30.PlusPlus“Group-At-A-Time” (#2)46Copyright 2001 Prentice-Hall, Inc.1. Read problem thoroughly2. Determine if it is a PV or FV p

38、roblem3. Create a time line4. Put cash flows and arrows on time line5. Determine if solution involves a single CF, annuity stream(s), or mixed flow6. Solve the problem7. Check with financial calculator (optional)Step To Solve Time Value Of Money Problems47Copyright 2001 Prentice-Hall, Inc. General F

39、ormula:FVn= PV0(1 + i/m)mnn: Number of Yearsm: Compounding Periods per Yeari: Annual Interest RateFVn,m: FV at the end of Year nPV0: PV of the Cash Flow todayFrequency of Compounding48Copyright 2001 Prentice-Hall, Inc.Find “m”Annualized quotation basisInterest/periodLength of a periodAnnually compou

40、ndedr1 yearSemi-annually compoundedr/26 monthsQuarterly compoundedr/43 monthsMonthly compoundedr/121 monthWeekly compoundedr/521 week Daily compoundedr/3651 dayContinuously compounded49Copyright 2001 Prentice-Hall, Inc. example Julie Miller has $1,000 to invest for 2 years at an annual interest rate

41、 of 12%. Annual FV2 = 1,000(1+ .12/1)(1)(2) = 1,254.40 Semi FV2 = 1,000(1+ .12/2)(2)(2) = 1,262.48Impact of Frequency50Copyright 2001 Prentice-Hall, Inc.Quarterly FV2= 1,000(1+ .12/4)(4)(2) = 1,266.77Monthly FV2= 1,000(1+ .12/12)(12)(2) = 1,269.73Daily FV2= 1,000(1+.12/365)(365)(2) = 1,271.20Impact

42、of Frequency51Copyright 2001 Prentice-Hall, Inc.Calculation of EAREffective annual interest rate（实际利率）: interest rate that is annualized using compound interest. nominal interest rate（名义利率）: interest rate that is annualized using simple interest. When interest is compounded more frequently than annu

43、ally, the EAR will be greater than the NIR.52Copyright 2001 Prentice-Hall, Inc.Effective Interest Rates exampleGiven a monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)? EAR=(1+.01)12 1=.1268 or 12.68% APR=.01x12=.12 or 12%53Copyright 2001 Prentice-

44、Hall, Inc.Comparing EARSConsider the following interest rates quoted by three banks:Bank A:15%, compounded dailyBank B:15.5%, compounded quarterlyBank C:16%, compounded annually54Copyright 2001 Prentice-Hall, Inc.Comparing EARS55Copyright 2001 Prentice-Hall, Inc.Comparing EARSWhich is the best bank? For a saver, Bank B offers the best (highest) interest rate. For a borrower, Bank C offers the best (lowest) interest rate.The highest NIR is not necessarily the best.Compounding during the year can lead to a significant difference between the NIR a