財(cái)務(wù)管理專業(yè)英語TheTimeValueofMoney課件

1、The Time Value of MoneyChapter 3The Time Value of MoneyChapter2Chapter OutlineFuture Value and CompoundingPresent Value and DiscountingMore on Present and Future ValuesFuture and Present Values of Multiple Cash FlowsValuing Level Cash Flows: Annuities and PerpetuitiesLoan Types and Loan Amortization

2、2Chapter OutlineFuture Value a3Basic DefinitionsPresent Value earlier money on a time lineFuture Value later money on a time lineInterest rate “exchange rate” between earlier money and later moneyDiscount rateCost of capitalOpportunity cost of capitalRequired return3Basic DefinitionsPresent Valu4Fut

3、ure ValuesSuppose you invest $1000 for one year at 5% per year. What is the future value in one year?Interest = 1000(.05) = 50Value in one year = principal + interest = 1000 + 50 = 1050Future Value (FV) = 1000(1 + .05) = 1050Suppose you leave the money in for another year. How much will you have two

4、 years from now?FV = 1000(1.05)(1.05) = 1000(1.05)2 = 1102.504Future ValuesSuppose you inve5Future Values: General FormulaFV = PV(1 + r)tFV = future valuePV = present valuer = period interest rate, expressed as a decimalT = number of periodsFuture value interest factor = (1 + r)t5Future Values: Gene

5、ral Formul6Effects of CompoundingSimple interest Compound interestConsider the previous exampleFV with simple interest = 1000 + 50 + 50 = 1100FV with compound interest = 1102.50The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment6Effects of CompoundingSimple

6、7Figure 3.17Figure 3.18Figure 3.28Figure 3.29Future Values Example 2Suppose you invest the $1000 from the previous example for 5 years. How much would you have?FV = 1000(1.05)5 = 1276.28The effect of compounding is small for a small number of periods, but increases as the number of periods increases

7、. (Simple interest would have a future value of $1250, for a difference of $26.28.)9Future Values Example 2Supp10Future Values Example 3Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today?FV = 10(1.055)200 = 447,189.84What is the effect

8、 of compounding?Simple interest = 10 + 200(10)(.055) = 210.55Compounding added $446,979.29 to the value of the investment10Future Values Example 3Sup11Future Value as a General Growth FormulaSuppose your company expects to increase unit sales of widgets by 15% per year for the next 5 years. If you c

9、urrently sell 3 million widgets in one year, how many widgets do you expect to sell in 5 years?FV = 3,000,000(1.15)5 = 6,034,07211Future Value as a General Gr12Quick Quiz: Part 1What is the difference between simple interest and compound interest?Suppose you have $500 to invest and you believe that

10、you can earn 8% per year over the next 15 years.How much would you have at the end of 15 years using compound interest?How much would you have using simple interest?12Quick Quiz: Part 1What is t13Present ValuesHow much do I have to invest today to have some amount in the future?FV = PV(1 + r)tRearra

11、nge to solve for PV = FV / (1 + r)tWhen we talk about discounting, we mean finding the present value of some future amount.When we talk about the “value” of something, we are talking about the present value unless we specifically indicate that we want the future value.13Present ValuesHow much do I 1

12、4PV One Period ExampleSuppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?PV = 10,000 / (1.07)1 = 9345.79Calculator1 N7 I/Y10,000 FVCPT PV = -9345.7914PV One Period ExampleSuppo15Present Values Example 2You want to

13、 begin saving for you daughters college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today?PV = 150,000 / (1.08)17 = 40,540.3415Present Values Example 2Yo16Present Values Example 3Your parents

14、set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest?PV = 19,671.51 / (1.07)10 = 10,00016Present Values Example 3Yo17PV Important Relationship IFor a given interest rate the longer the time period, the lower the prese

15、nt valueWhat is the present value of $500 to be received in 5 years? 10 years? The discount rate is 10%5 years: PV = 500 / (1.1)5 = 310.4610 years: PV = 500 / (1.1)10 = 192.7717PV Important Relationship 18PV Important Relationship IIFor a given time period the higher the interest rate, the smaller t

16、he present valueWhat is the present value of $500 received in 5 years if the interest rate is 10%? 15%?Rate = 10%: PV = 500 / (1.1)5 = 310.46Rate = 15%; PV = 500 / (1.15)5 = 248.5818PV Important Relationship 19Quick Quiz: Part 2What is the relationship between present value and future value?Suppose

17、you need $15,000 in 3 years. If you can earn 6% annually, how much do you need to invest today?If you could invest the money at 8%, would you have to invest more or less than at 6%? How much?19Quick Quiz: Part 2What is th20Figure 3.320Figure 3.321The Basic PV Equation - RefresherPV = FV / (1 + r)tTh

18、ere are four parts to this equationPV, FV, r and tIf we know any three, we can solve for the fourthIf you are using a financial calculator, be sure and remember the sign convention or you will receive an error when solving for r or t21The Basic PV Equation - Refr22Discount RateOften we will want to

19、know what the implied interest rate is in an investmentRearrange the basic PV equation and solve for rFV = PV(1 + r)tr = (FV / PV)1/t 1If you are using formulas, you will want to make use of both the yx and the 1/x keys22Discount RateOften we will w23Discount Rate Example 1You are looking at an inve

20、stment that will pay $1200 in 5 years if you invest $1000 today. What is the implied rate of interest?r = (1200 / 1000)1/5 1 = .03714 = 3.714%23Discount Rate Example 1You24Discount Rate Example 2Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,0

21、00 to invest. What is the implied rate of interest?r = (20,000 / 10,000)1/6 1 = .122462 = 12.25%24Discount Rate Example 2Sup25Discount Rate Example 3Suppose you have a 1-year old son and you want to provide $75,000 in 17 years towards his college education. You currently have $5000 to invest. What i

22、nterest rate must you earn to have the $75,000 when you need it?r = (75,000 / 5,000)1/17 1 = .172688 = 17.27%25Discount Rate Example 3Sup26Quick Quiz: Part 3What are some situations where you might want to compute the implied interest rate?Suppose you are offered the following investment choices:You

23、 can invest $500 today and receive $600 in 5 years. The investment is considered low risk.You can invest the $500 in a bank account paying 4%.What is the implied interest rate for the first choice and which investment should you choose?26Quick Quiz: Part 3What are s27Finding the Number of PeriodsSta

24、rt with basic equation and solve for t (remember your logs)FV = PV(1 + r)tt = ln(FV / PV) / ln(1 + r)You can use the financial keys on the calculator as well, just remember the sign convention.27Finding the Number of Period28Number of Periods Example 1You want to purchase a new car and you are willi

25、ng to pay $20,000. If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?t = ln(20,000 / 15,000) / ln(1.1) = 3.02 years28Number of Periods Example 29Number of Periods Example 2Suppose you want to buy a new house. Yo

26、u currently have $15,000 and you figure you need to have a 10% down payment plus an additional 5% in closing costs. If the type of house you want costs about $150,000 and you can earn 7.5% per year, how long will it be before you have enough money for the down payment and closing costs?29Number of P

27、eriods Example 30Example 2 ContinuedHow much do you need to have in the future?Down payment = .1(150,000) = 15,000Closing costs = .05(150,000 15,000) = 6,750Total needed = 15,000 + 6,750 = 21,750Using the formulat = ln(21,750 / 15,000) / ln(1.075) = 5.14 years30Example 2 ContinuedHow much 31Table 3.

28、431Table 3.432Quick Quiz: Part 4When might you want to compute the number of periods?Suppose you want to buy some new furniture for your family room. You currently have $500 and the furniture you want costs $600. If you can earn 6%, how long will you have to wait if you dont add any additional money

29、?32Quick Quiz: Part 4When might33Multiple Cash Flows FV Example Suppose 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) = 1248.0533Multiple Cash Flows FV Exa34Example ContinuedHow much will you

30、 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 = 1616.2634Example ContinuedHow much w35Multiple Cash Flows FV Example Suppose you plan to deposit $100 into an account in one year and $300 into the ac

31、count 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 = 485.9735Multiple Cash Flows FV Exa36Example Timeline100012345300136.05349.92485.9736Example Timeline1000123453037Multiple Cash Flows PV ExampleYou are consi

32、dering 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

33、.9337Multiple Cash Flows PV Ex38Timeline01234100020003000909.091652.92253.94815.938Timeline0123410002000300090939Decisions, 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

34、you require a 15% return on investments of this risk, should you take the investment?No the broker is charging more than you would be willing to pay.39Decisions, DecisionsYour bro40Saving For RetirementYou are offered the opportunity to put some money away for retirement. You will receive five annua

35、l 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%?40Saving For RetirementYou are41Saving For Retirement Timeline0 1 2 39 40 41 42 43 44 0 0 0 0 25K 25K 25K 25K 25KNotice that the year 0 cash flow = 0 The cash flows y

36、ears 1 39 are The cash flows years 40 44 are 25,00041Saving For Retirement Timeli42Quick Quiz: Part 5Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7%What is the value of the cash flows

37、 at year 5?What is the value of the cash flows today?42Quick Quiz: Part 5Suppose yo43Annuities and Perpetuities DefinedAnnuity finite series of equal payments that occur at regular intervals If the first payment occurs at the end of the period, it is called an ordinary annuityIf the first payment oc

38、curs at the beginning of the period, it is called an annuity duePerpetuity infinite series of equal payments43Annuities and Perpetuities D44Annuities and Perpetuities Basic FormulasPerpetuity: PV = C / rAnnuities:Lump sum paymentinstallment44Annuities and Perpetuities 45Annuity Sweepstakes ExampleSu

39、ppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today?PV = 333,333.331 1/1.0530 / .05 = 5,124,150.2945Annuity Sweepstake

40、s Exampl46Buying a HouseYou are ready to buy a house and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your month

41、ly income. The interest rate on the loan is 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan. How much money will the bank loan you? How much can you offer for the house?46Buying a HouseYou are ready 47Buying a House - ContinuedBank loanMonthly income = 36,000 / 12

42、= 3,000Maximum payment = .28(3,000) = 840PV = 8401 1/1.005360 / .005 = 140,105Total PriceClosing costs = .04(140,105) = 5,604Down payment = 20,000 5604 = 14,396Total Price = 140,105 + 14,396 = 154,50147Buying a House - ContinuedBa48Quick Quiz: Part 6You know the payment amount for a loan and you wan

43、t to know how much was borrowed. Do you compute a present value or a future value?(You want to receive 5000 per month in retirement. If you can earn .75% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement?)48Quick Quiz: Part 6You know

44、 49Finding the PaymentSuppose you want to borrow $20,000 for a new car. You can borrow at 8% per year, compounded monthly (8/12 = .66667% per month). If you take a 4 year loan, what is your monthly payment?20,000 = C1 1 / 1.006666748 / .0066667C = 488.2649Finding the PaymentSuppose y50Finding the Nu

45、mber of Payments ExampleSuppose you borrow $2000 at 5% and you are going to make annual payments of $734.42. How long before you pay off the loan?2000 = 734.42(1 1/1.05t) / .05.136161869 = 1 1/1.05t1/1.05t = .8638381311.157624287 = 1.05tt = ln(1.157624287) / ln(1.05) = 3 years50Finding the Number of

46、 Paymen51Annuity Finding the Rate Trial and Error ProcessChoose an interest rate and compute the PV of the payments based on this rateCompare the computed PV with the actual loan amountIf the computed PV loan amount, then the interest rate is too lowIf the computed PV loan amount, then the interest

47、rate is too highAdjust the rate and repeat the process until the computed PV and the loan amount are equal51Annuity Finding the Rate T52Quick Quiz: Part 7You want to receive $5000 per month for the next 5 years. How much would you need to deposit today if you can earn .75% per month?What monthly rat

48、e would you need to earn if you only have $200,000 to deposit?Suppose you have $200,000 to deposit and can earn .75% per month.How many months could you receive the $5000 payment?How much could you receive every month for 5 years?52Quick Quiz: Part 7You want t53Future Values for AnnuitiesSuppose you

49、 begin saving for your retirement by depositing $2000 per year in an IRA. If the interest rate is 7.5%, how much will you have in 40 years?FV = 2000(1.07540 1)/.075 = 454,513.0453Future Values for AnnuitiesS54Example: Work the Web Online financial calculator can be found at MoneyChimpClick on the we

50、b surfer and work the following exampleChoose calculator and then annuity You just inherited $5 million. If you can earn 6% on your money, how much can you withdraw each year for the next 40 years?Datachimp assumes annuity due!Payment = $313,497.8154Example: Work the Web Online55 Perpetuity Preferre

51、d stock is an important example of perpetuity. When a corporation sells preferred stock, the buyer is promised a fixed cash dividend every period(usually every quarter) forever. This dividend must be paid before any dividend can be paid to regular stockholders, hence the term preferred.55 Perpetuit5

52、6 Preferred stock- ExampleSuppose a firm wants to sell preferred stock. P=$100, to be competitive, r=2.5% per quarter, what should the dividend per quarter be?Perpetuity formula: PV = C / rr = .025 or 2.5% per quarterDividend for new preferred:100 = C / .025C = 2.50 per quarter56 Preferred stock- Ex

53、ampleSu57Table 3.557Table 3.558Quick Quiz: Part 8You want to have $1 million to use for retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made in one month?You are considering preferred stock that pays a quarterly dividend of $1.50. If your desired retur