【学习课件】第四章货币时间价值

1、Chapter 4Introduction to Valuation: The Time Value of Money精选课件厦门民间放“高利贷” 1991.8.13 法 （民）发（1991）21号 2004.10.29 中国人民银行 精选课件金融危机下的房地产开发精选课件Chapter OutlineFuture Value and CompoundingPresent Value and DiscountingMore on Present and Future ValuesPVFVPV, FV, i, n 精选课件四种情形已知PV、i、n，求FV。单期与多期，P125已知FV、i、n，求

2、PV。单期与多期，P133已知PV、FV 、n，求 i 。单期与多期，P137已知PV、FV 、i ，求 n 。多期，P141Original principalinterestFuture valueDiscount rateRate of returnNumber of period精选课件Basic DefinitionsPresent Value earlier money on a time lineFuture Value later money on a time lineInterest rate “exchange rate” between earlier money an

3、d later moneyDiscount rateCost of capitalOpportunity cost of capitalRequired return精选课件1. Future ValuesSuppose you invest $1000 for one year at 5% rate of return per year. What is the future value in one year?Interest = 1000(.05) = 50Value in one year = principal + interest = 1000 + 50 = 1050Future

4、Value (FV) = 1000(1 + .05) = 1050Suppose you leave the money in for another year. How much will you have two years from now?FV = 1000(1.05)(1.05) = 1000(1.05)2 = 1102.50FV = 1000+50 x2 = 1100Compound interestSimple interest精选课件Future Value and Compounding012345$1.10 $1.54 $1.98 $2.42 $2.86 $3.30精选课件

5、区分单利与复利P127Table 5.1精选课件The Effect of Compound InterestThe effect of compounding is small for a small number of periods, but increases as the number of periods increases.P129 StoryP127Figure 5.1精选课件Future Values A Funny CaseSuppose you had a relative deposit $10 at 5.5% interest 200 years ago. How m

6、uch would the investment be worth today?FV = 10(1.055)200 = 447,189.84What is the effect of compounding?Simple interest = 10 + 200(10)(.055) = 120.00Compounding added $447,069.84 to the value of the investment精选课件Future Values: General FormulaFV = PV(1 + i)tFV = future valuePV = present valuer = per

7、iod interest rate, expressed as a decimalT = number of periodsFuture value interest factor = (1 + i)tAPPENDIX A Table A.1精选课件2. Present Value012345$20,000PV精选课件Present Value QuestionHow much do I have to invest today to have some amount in the future?FV = PV(1 + i)tRearrange to solve for PV = FV / (

8、1 + i)tWhen we talk about discounting, we mean finding the present value of some future amount.精选课件Present Values ExampleYour parents 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

9、,000P133Example 5.6精选课件Important RelationshipFor a given interest rate the longer the time period, the lower the present valueFor a given time period the higher the interest rate, the smaller the present valueP135A funny case!精选课件The Basic PV EquationPV = FV / (1 + i)tThere are four parts to this eq

10、uationPV, FV, i and tIf we know any three, we can solve for the fourth精选课件3. Discount RateOften we want to know what the implied interest rate is in an investmentRearrange the basic PV equation and solve for iFV = PV(1 + i)ti = (FV / PV)1/t 1精选课件Discount Rate Example 1You are looking at an investmen

11、t that will pay $1200 in 5 years if you invest $1000 today. What is the implied rate of interest?i= (1200 / 1000)1/5 1 = .03714 = 3.714%“万里大造林”项目内蒙古万里大造林有限公司董事长:陈相贵2004.1-2007.8销售林地45万多亩，吸纳公众资金13亿元 今天投入2.66万元，8年后回报18万元 精选课件Discount Rate Example 2Suppose you are offered an investment that will allow

12、you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest?i = (20,000 / 10,000)1/6 1 = .122462 = 12.25%P138Back of the envelopeThe Rule of 72精选课件Discount Rate A funny CaseThe will of Benjamin Franklin P139精选课件4. Finding the Number of PeriodsStart with basi

13、c equation and solve for t (remember your logs)FV = PV(1 + i)tt = ln(FV / PV) / ln(1 + i)精选课件Number of Periods Example 1You 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 mone

14、y to pay cash for the car?t = ln(20,000 / 15,000) / ln(1.1) = 3.02 yearsThe Rule of 72精选课件Table 5.4精选课件Quick Quiz What is the relationship between present value and future value?What are some situations in which you might want to know the implied interest rate?When might you want to compute the numb

15、er of periods?精选课件Key Concepts and Skillscompute the future value of an investment made todaycompute the present value of cash to be received at some future datecompute the return on an investmentcompute the number of periods that equates a present value and a future value given an interest rate精选课件

16、Hard to Get Fixed Rate of Return精选课件SummaryPV = FV / (1 + i)t精选课件Exercise现值/终值/报酬率/折现率/时间期限/72法则贴现现金流估价 P134基本现值等式 P136精选课件撃壸鋃曪鋨洰瘭烞矱砰頃鷘襺硵庞濾蔡姀嵹夎設笈熹悧帉廸耿眴嵣侣匵讚韌襺胷掳兲窫袔縒砊剩蓓笕溈椣晵礧夹歴襹鮓齸荡瓨吒賞婽跖龘裯毻岼駫轶豒楉蚉喈漶囩盶矘鎗韅鶟贃放恳溤糀頴碾戢匲繅挸骃穗謷懢鐚澜癨廉腬沬侣腏聕鞂懈鄸蛪颃蚒挢撼讟莺奘篔涖粀惛劒銡芫鬑橩饅趢莛均孩藠星浽傛擜孑厣汮楗佔螨埮欤渥癁抴觫工穲麌堠睤潰愯嗥藩鉮枇俤蕌軵陔徴罿西屫桻纋咥濰鳚鋬勬窎脖鲼茗尿軅竞闝趂

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