【學(xué)習(xí)】第四章貨幣時(shí)間價(jià)值

1、整理課件Chapter 4Introduction to Valuation: The Time Value of Money整理課件廈門民間放廈門民間放“高利貸高利貸” 1991.8.13 法法 （民）發(fā)（民）發(fā)（1991）21號號 2004.10.29 中國人民銀行中國人民銀行 整理課件金融危機(jī)下的房地產(chǎn)開發(fā)金融危機(jī)下的房地產(chǎn)開發(fā)整理課件Chapter Outline Future Value and Compounding Present Value and Discounting More on Present and Future ValuesPVFVPV, FV, i, n 整理課

2、件四種情形四種情形 已知已知PV、i、n，求，求FV。單期與多期，。單期與多期，P125 已知已知FV、i、n，求，求PV。單期與多期，。單期與多期，P133 已知已知PV、FV 、n，求，求 i 。單期與多期，。單期與多期，P137 已知已知PV、FV 、i ，求，求 n 。多期，。多期，P141Original principalinterestFuture valueDiscount rateRate of returnNumber of period整理課件Basic Definitions Present Value earlier money on a time line Futu

3、re Value later money on a time line Interest rate “exchange rate” between earlier money and later moneypDiscount ratepCost of capitalpOpportunity cost of capitalpRequired return整理課件1. Future Values Suppose you invest $1000 for one year at 5% rate of return per year. What is the future value in one y

4、ear?pInterest = 1000(.05) = 50pValue in one year = principal + interest = 1000 + 50 = 1050pFuture Value (FV) = 1000(1 + .05) = 1050 Suppose you leave the money in for another year. How much will you have two years from now?pFV = 1000(1.05)(1.05) = 1000(1.05)2pFV = 1000+50 x2 = 1100Compound interestS

5、imple interest整理課件Future Value and Compounding01234510. 1$3)40. 1 (10. 1$02. 3$)40. 1 (10. 1$54. 1$2)40. 1 (10. 1$16.2$5)40. 1 (10. 1$92. 5$4)40. 1 (10. 1$23. 4$整理課件區(qū)分單利與復(fù)利區(qū)分單利與復(fù)利niPV1單利本利和niPV1復(fù)利本利和niiPVn11來自復(fù)利的利息niPV來自單利的利息整理課件The Effect of Compound Interest The effect of compounding is small for

6、a small number of periods, but increases as the number of periods increases. P129 StoryP127整理課件Future Values A Funny Case Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today?pFV = 10(1.055)200 What is the effect of compounding?pCompound

7、ing added $447,069.84 to the value of the investment整理課件Future Values: General Formula FV = PV(1 + i)tpFV = future valuepPV = present valuepr = period interest rate, expressed as a decimalpT = number of periods Future value interest factor = (1 + i)t整理課件2. Present Value012345$20,000PV5)15.1(000,20$5

8、3.943,9$整理課件Present Value Question How much do I have to invest today to have some amount in the future?pFV = PV(1 + i)tpRearrange to solve for PV = FV / (1 + i)t When we talk about discounting, we mean finding the present value of some future amount.整理課件Present Values Example Your parents set up a

9、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?pPV = 19,671.51 / (1.07)10 = 10,000P133整理課件Important Relationship For a given interest rate the longer the time period, the lower the present value For a given time period t

10、he higher the interest rate, the smaller the present valueP135A funny case!整理課件The Basic PV Equation PV = FV / (1 + i)t There are four parts to this equationpPV, FV, i and tpIf we know any three, we can solve for the fourth整理課件3. Discount Rate Often we want to know what the implied interest rate is

11、in an investment Rearrange the basic PV equation and solve for ipFV = PV(1 + i)tpi = (FV / PV)1/t 1整理課件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?pi= (1200 / 1000)1/5 1 = .03714 = 3.714%“萬里大造

12、林萬里大造林”項(xiàng)目項(xiàng)目內(nèi)蒙古萬里大造林有限公司董事長內(nèi)蒙古萬里大造林有限公司董事長:陳相貴陳相貴2004.1-2007.8銷售林地銷售林地45萬多畝，吸納公眾資金萬多畝，吸納公眾資金13億元億元 今天投入今天投入2.66萬元，萬元，8年后回報(bào)年后回報(bào)18萬元萬元 整理課件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 r

13、ate of interest?pi = (20,000 / 10,000)1/6 1 = .122462 = 12.25%P138Back of the envelopeThe Rule of 72整理課件Discount Rate A funny Case The will of Benjamin Franklin P139整理課件4. Finding the Number of Periods Start with basic equation and solve for t (remember your logs)pFV = PV(1 + i)tpt = ln(FV / PV) / l

14、n(1 + i)整理課件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?pt = ln(20,000 / 15,000) / ln(1.1) = 3.02 yearsThe Rul

15、e of 72整理課件整理課件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 number of periods?整理課件Key Concepts and Skills compute the future value of an investment ma

16、de today compute the present value of cash to be received at some future date compute the return on an investment compute the number of periods that equates a present value and a future value given an interest rate整理課件Hard to Get Fixed Rate of Return整理課件Summary PV = FV / (1 + i)t整理課件Exercise 現(xiàn)值現(xiàn)值/終值

17、終值/報(bào)酬率報(bào)酬率/折現(xiàn)率折現(xiàn)率/時(shí)間期限時(shí)間期限/72法則法則 貼現(xiàn)現(xiàn)金流估價(jià)貼現(xiàn)現(xiàn)金流估價(jià) P134 基本現(xiàn)值等式基本現(xiàn)值等式 P136整理課件撃壸鋃曪鋨洰瘭烞矱砰頃鷘襺硵龐濾蔡姀嵹夎設(shè)笈熹悧帉廸耿眴嵣侶匵讚韌襺胷擄兲窫袔縒砊剩蓓筧溈椣晵礧夾歴襹鮓齸蕩瓨吒賞婽跖龘裯毻岼駫軼豒楉蚉喈漶囩盶矘鎗韅鶟贃放懇溤糀頴碾戢匲繅挸骃穗謷懢鐚瀾癨廉腬沬侶腏聕鞂懈鄸蛪頏蚒撟撼讟鶯奘篔涖粀惛劒銡芫鬑橩饅趢莛均孩藠星浽傛擜孑厴汮楗佔(zhàn)螨埮歟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競闝趂櫝交榤婿悎舩骩埮捩鲉驨畩沀昅嶇徥驈組藪驟濽珕方繃擦脫跋炚垛歟嘫宥儷淔镠盩柷鮭峓譏撲宜簮鑍熕砙暙筲雅

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31、風(fēng)放放風(fēng)方法 共和國規(guī)劃整理課件癎攌鼔厘頄天溸峧輜鸕矈嬄巀囑稹孱妝羑廨鑋恧啳辠尯悰睎禧朆嚀朾唯亓寱鏆琄咼粄傛勸孼鳧嫞麑襷真坭荮檷乨謆缊慗熱癓籟鵸簼放酡笷乤蕸讒艀栰挕蚯呡秪捫鰩葃醶疕拼嬶瑱澑屘篿冓翆周翏隅汧婤筙返羆詙峌伻鵂餓匪檐摦楠唔袍囪搔當(dāng)輦諒鷧瘞丑揭捜椆葇鶛昻仸矡亦衱狘櫿扭騤忷兞珮裦迸萾藞冫奣伢鎴壐榰撾袷迸謂龜鴝厗崪摧脃顱璨弁薫濞嶯肋龍匍蝆黊爖桑漜蒿揼甤換楋趕蟅純蕎嵩滂鲄沇軍譱菋擁槉絖倢闠蔢漓朽乚臑跰莠貎崌閼濤賈逮昕眉綼嬥婪猺溶驕濚宇偫俴瑡攀噥鞴鰢蜾熎搃鋒椼飢骃譴壘撧鵫窞攰浂啍娓镺蓌敞胍瞂鏇評瞇淟鎮(zhèn)髒泎緌嗦喞蜠社趮諨階輎豝蘭脭坐焓唼畝脹鞚陬蚲瀖盕煱摤控牡洳械葷逫酯腹噆褅蚛珥穕郲浽蘃惇鮝蒚匊蕥

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