【正文】 直觀地記為 (PV/FV, r , n) 一般復(fù)利現(xiàn)值公式 etc. 52 PVIF r,n表如下所示： 復(fù)利現(xiàn)值因子表： PVIF r,n 期限 6% 7% 8% 1 .943 .935 .926 2 .890 .873 .857 3 .840 .816 .794 4 .792 .763 .735 5 .747 .713 .681 53 PV2 = $1,000 (PVIF7%,2) = $1,000 (.873) = $873 [四舍五入 ] 查復(fù)利現(xiàn)值因子表 期限 6% 7% 8% 1 .943 .935 .926 2 .890 .873 .857 3 .840 .816 .794 4 .792 .763 .735 5 .747 .713 .681 54 按 10% 的復(fù)利折算， 5 年 后的 $1,000 的現(xiàn)值是多少？ Example 復(fù)利現(xiàn)值 0 1 2 3 4 5 $1,000 PV0 10% 55 ? 用公式 : PV0 = FV n / (1+r)n PV0 = $1,000 / (1+ )5 = $620. 92 ? 查表 : PV0 = $1,000 (PVIF10%, 5) = $1,000 (.621) = $621. 00 [四舍五入 ] 解： 56 欺騙性廣告 —1/2 ?最近，一些商家都這樣宣稱 “ 來試一下我們的產(chǎn)品。 ?如果該存款的年利率是 10％ 的話，今天他們真正給你多少錢呢 ? 57 欺騙性廣告 —2/2 ?你真正得到的是在 25年后才能得到的 $100 在今日的現(xiàn)值。 ?由此可見，該促銷僅能給你 $l00 = $。 58 PV – One Period Example ?Suppose 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 = 59 Present Values – Example 2 ?You want to begin saving for your daughter’s college education and you estimate that she will need $150,000 in 17 years. ?If you feel confident that you can earn 7% per year, how much do you need to invest today? ?PV = 150,000 / ()17 = 47, 60 Present Values – Example 3 ?Your parents set up a trust fund for you 10 years ago that is now worth $19,. If the fund earned 7% per year, how much did your parents invest ? ?PV = 19, / ()10 = 10,000 61 PV – Important Relationship I ?For a given interest rate – the longer the time period, the lower the present value ?What is the present value of $100 to be received in 5 years ? 10 years ? The discount rate is 10% ? 5 years: PV = 100 / ()5 = ?10 years: PV = 100 / ()10 = 62 PV – Important Relationship II ? For a given time period – the higher the interest rate, the smaller the present value. ?What is the present value of $100 received in 5 years if the interest rate is 10%? Or 20%? ?Rate = 10%: PV = 100 / ()5 = ?Rate = 20%: PV = 100 / ()5 = 63 Figure : $1于不同利率、折現(xiàn)期的現(xiàn)值 64 Quick Quiz: Part 2 ?What is the relationship between present value and future value? ?Suppose you need $7,000 in 12 years. If you can earn 6% annually, how much do you need to invest today ? ?If you could invest the money at 12%, would you have to invest more or less than at 6% ? 65 Part 3 Discount Rate 66 The Basic PV Equation Refresher ?PV = FV / (1 + r)t ?There are four parts to this equation ?PV, FV, r and t ?If we know any three, we can solve for the fourth 67 Discount Rate ?Often we will want to know what the implied interest rate is in an investment ?Rearrange the basic PV equation and solve for r ? FV = PV (1 + r)t ? r = (FV / PV)1/t – 1 68 Discount Rate – Example 1 ?You are looking at an investment 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 = % 69 Discount Rate – Example 2 ?Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest ? ? r = (20,000 / 10,000)1/6 – 1 = .122462 = % 70 Discount Rate – Example 3 ?Suppose you have a 1year old son and you want to provide $75,000 in 17 years towards his college education. ?You currently have $5000 to invest. What interest rate must you earn to have the $75,000 when you need it ? ? r = (75,000 / 5,000)1/17 – 1 = .172688 = % 71 Quick Quiz : Part 3 ?What are some situations where you might want to pute the implied interest rate ? ?Suppose you are offered the following two choices of investment. Which is better ? ?You can invest $1000 today with low risk and receive $2021 in 12 years. ?Or you can invest the $1000 in a bank account paying 6% for 12 years. ?What is the implied interest rate for the first choice and which investment should you choose? 72 Part 4 Finding the Number of Periods 73 Finding the Number of Periods ?Start with basic equation and solve for t (remember your logs) ?FV = PV (1 + r)t ? t = l n (FV / PV) / l n (1 + r) 74 Number of Periods – Example 1 ?You want to purchase a new car and you are willing 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 = l n (20,000 / 15,000) / l n () = years 75 Number of Periods – Example 2 ?Suppose you want to buy a new house. You currently have $18,000 and you figure you need to have a 10% down payment plus an additional 5% of the loan value in closing costs. ?If the type of house you want costs about $150,000 and you can earn % per year, how long will it be before you have enough money for the down payment and closing costs ? 76 Example 2 Continued ? How much do you need to have in the future? ?Down payment = .1(150,000) = 15,000 ?Bank Loan = 150,000 – 15,000 = 135,000 ?Closing costs = .05 (135,000) = 6,750 ?Total needed = 15,000 + 6,750 = 21,750 ? t = l n (21,750 / 18,000) / l n () = years 77 Work the Web Example ?financial calculators are available online such as ?You may go to Cigna’s web site and work the following example: ?You need $40,000 in 15 years. If you can earn % interest, how much do you need to invest today ? ?You should get $9,841 78 Quick Quiz: Part 4 ?When might you want to pute the number o