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1、Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,1,Chapter 4:Allocating Resources Over Time,ObjectiveExplain the concept of compounding and discounting and to provide examples of real lifeapplications,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,2,第四章：跨期配置资源,Copyr
2、ight,2000 Prentice Hall Author Nick Bagley,bdellaSoft,Inc.,学习目的通过现实生活的例子掌握复利和折现的概念,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,3,Introduction:Time Value of Money(TVM)引言：货币的时间价值,$1 today is worth more than the expectation of$1 tomorrow because:今天1美元的价值超过明天1美元的预期值，原因：a bank would
3、pay interest on the$1 银行支付利息inflation makes tomorrows$1 less valuable than todays 通货膨胀使明天的1美元不如今天值钱uncertainty of receiving tomorrows$1 明天获取1美元的不确定性,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,4,4.1 Compounding 复利,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,
4、5,4.1 Compounding 复利,Assume that the interest rate is 10%p.a.假设年利率是10What this means is that if you invest$1000 for one year,you have been promised$1000*(1+10%)or$1100 next year 这意味着如果你一年投资1000美元，明年就有 1000*(1+10%)=1100 美元Investing$1000 for yet another year promises to produce 1100*(1+10%)or$1210 in
5、2 years 投资1000美元再多一年，2年产生 1100*(1+10%)=1210 美元,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,6,Value of Investing$1 投资1美元的价值,Continuing in this manner you will find that the following amounts will be earned:持续以这种方式进行投资，你会发现下面的账户将赚取：,Copyright 2009 Pearson Education,Inc.Publishing
6、as Prentice Hall,7,Value of$5 Invested 投资5美元的价值,More generally,with an investment of$5 at 10%interest rate,we obtain 按10年利率投资5美元的收益：,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,8,$5 投资的价值,$5 的投资，收益率为10%,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,9,Definitio
7、ns 定义,Generalizing the method requires some definitions.对术语进行定义：i be the interest rate i=利率n be the number of years n=年数PV be the present value PV=现值FV be the future value FV=终值（未来价值）,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,10,Definitions 定义,Generalizing the method requires
8、some definitions.对术语进行定义：Principal 本金Simple interest 单利Compound interest 复利单利：本金所得到的利息称为单利复利：在已经支付的利息上所得到的利息称为复利全部利息=单利+复利,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,11,单利&复利,PV=$1000,i=10%,n=2,FV=?FV=$1000*(1+10%)2=$1210本金=$1000单利=$200(=$1000*10%*2)复利=$10(=$1000*10%*10%)全部利息=单
9、利+复利本息=本金+全部利息=本金+单利+复利,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,12,Future Value and Compound Interest 未来价值和复利 P121,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,13,练习,快速测查4-1(P120)如果在前面的例子中，利率仅为每年5，那么终值是多少？单利和复利各是多少？,复利=终值 本金 单利,Copyright 2009 Pearson Educ
10、ation,Inc.Publishing as Prentice Hall,14,Future Value&Present Value终值和现值的关系,(P123),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,15,Example:Future Value Calculation例题：终值计算,Your bank offers a deposit with an interest rate of 3%for a 5 year investment.5年银行定期存款，年利率3You wish to invest
11、$1,500 for 5 years,how much will your investment be worth?$1500投资5年，价值几何？,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,16,RULE OF 72 72法则(P123),This rule says that the number of years it takes for a sum of money to double in value(“the doubling time”)is approximately equal to the
12、 number 72 divided by the interest rate expressed in percent per year“72法则”：是指一笔金钱在价值上翻番需要的时间（“翻番时间”），大约等于72除以百分比形式的年利率Doubling Time=72/Interest Rate 翻番时间=,72利率,注 意：分母指前的数字,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,17,Present Value Calculation 现值计算,(现值公式 P129),(终值公式 P123),Copy
13、right 2009 Pearson Education,Inc.Publishing as Prentice Hall,18,4.1.2 储蓄防老,例题：P123你现在20岁，正在考虑为养老储蓄如果现在存入100美元，年利率为8在你65岁时，账户余额是多少？方法一：复利计算年数 n=65 20=45 年终值 FV=100(1+8%)45=3192.04 美元方法二：72法则翻番时间 t=72/8=9 年翻番次数 N=45/9=5 次终值 FV=10025=3200 美元,Copyright 2009 Pearson Education,Inc.Publishing as Prentice H
14、all,19,annual percentage rate(APR)年利率effective rate(EFF)有效年利率,4.2 The Frequency of Compounding 复利的频率,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,20,4.2 The Frequency of Compounding 复利的频率,You have a credit card that carries a rate of interest of 6%per year compounded monthly.What
15、 is the interest rate compounded annually?That is,if you borrowed$1 with the card,what would you owe at the end of a year?你的信用卡按照6的年利率（APR），以月计息年度复利（有效年利率 EFF）是多少？如果你用卡借了1美元，年底欠多少钱？,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,21,年利率6%，以月计息，相当于每月利息为：6%/12=0.5%1美元在年末的价值为：FV=1(1+0.
16、5%)12=1.0616778 有效年利率为这个数减去1：EFF=(1+0.005)12-1=0.0616778=6.16778%,The Frequency of Compounding 复利的频率,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,22,The Frequency of Compounding 复利的频率,有效年利率：,EFF=有效年利率APR=年利率m=复利时间的数量,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hal
17、l,23,The Frequency of Compounding 复利的频率,All calculation must be expressed in terms of consistent units 所有的计算单位必须统一A raw rate of interest expressed in terms of years and months may never be used in a calculation 原始的年/月利率可能根本不会被用于计算中The two equal APR with different frequency of compounding have differ
18、ent effective annual rates 年收益率相同时，有效收益率可不同,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,24,年收益率APR=6%时的有效收益率EFF,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,25,练习,快速测查4-2(P126)你在月复利的条件下按照12的APR获得一笔贷款。这笔贷款的有效年利率EFF是多少？,EFF(12%,12)=(1+12%/12)12-1=(1+1%)12-1=12.
19、68%,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,26,4.5 Multiple Cash Flows 复合现金流,Time Lines 时间线Future Value of a Stream of Cash Flows 一项现金流的未来价值Present Value of a Stream of Cash Flows 一系列现金流的现值Investing with Multiple Cash Flows 在复合现金流的条件下进行投资,Copyright 2009 Pearson Education,Inc
20、.Publishing as Prentice Hall,27,4.5.1 Time Line 时间线,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,28,4.5.2 一项现金流的未来价值,PV=$1000,i=10%,n=2,FV=?方法一：FV=10001.12+10001.1=2310方法二：FV=(10001.1+1000)1.1=2310,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,29,练习,快速测查4-7(P13
21、7)假设你现在储蓄1000美元，然后1年后储蓄2000美元。如果利率为每年10，2年后你将拥有多少？,方法一:10001.12+20001.1=1210+2200=3410方法二:(10001.1+2000)1.1=31001.1=3410,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,30,4.5.3 一系列现金流的现值,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,31,4.6 Annuities 年金,年金：相同现金流或相
22、同支付流称为年金(annuity)Immediate annuity 即期年金，现金流开始于本期初（先付年金）Ordinary annuity 普通年金，现金流开始于本期末（后付年金）,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,32,Cash Flow Diagram of Annuities图4-5 年金的现金流框架,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,33,Future Value for an Ordinar
23、y Annuity of$1 per year is普通年金的未来价值,(P139),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,34,Present Value for an Ordinary Annuity of$1 per year is 普通年金的现值,(P139),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,35,4.7 Perpetual Annuities 永续年金,回忆下普通年金的现值：,当 n-with i
24、 0:,(P139),(P141),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,36,Present Value of a Perpetual Annuity永续年金的现值,(P141),相同支付永续年金的现值=,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,37,4.8 Loan Amortization:Mortgage 贷款的分期偿还：抵押,Many loans,such as home mortgage loans a
25、nd car loans,are repaid in equal periodic installments.许多贷款以等额定期分期还款的形式进行偿还，例如住房按揭贷款和汽车消费贷款Part of each payment is interest on the outstanding balance of the loan and part is repayment of principal.每笔还款的一部分是该贷款尚未偿还余额的利息，另一部分则是本金的偿还,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,38,
26、Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,39,4.9 Exchange Rates and Time Value of Money汇率以及货币的时间价值,如果美元和英镑之间的汇率是1英镑兑2美元美元的利率是每年6英镑的利率是每年41年后美元兑英镑未来汇率的“盈亏相抵”(收支平衡)值是多少？（快速测查48,P145）,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,40,4.9 Exchange Rates and Time
27、Value of Money汇率以及货币的时间价值,如果美元和英镑之间的汇率是1英镑兑2美元美元的利率是每年6英镑的利率是每年41年后美元兑英镑未来汇率的“盈亏相抵”值是多少？$2=1=$1=0.5投资美元1年:$1(1+6%)=$1.06投资英镑1年:0.5(1+4%)=0.52盈亏相抵的汇率:1.06/0.52=2.0385 或 1=$2.0385,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,41,4.9.1 Computing NPV in Different Currencies在不同货币条件下计算净
28、现值,In any time-value-of-money calculation,the cash flows and interest rates must be denominated in the same currency在任何货币时间价值的计算中，现金流和利率必须以相同的货币进行计价(P145),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,42,4.10 Inflation and Discounted Cash Flow Analysis通货膨胀和折现现金流分析,用以下符号表示名义利率：in t
29、he nominal interest rate实际利率：ir the real interest rate通货膨胀率：r the inflation rate,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,43,4.10 Inflation and Discounted Cash Flow Analysis通货膨胀和折现现金流分析,名义利率、实际利率和通货膨胀率之间的关系：,通过连续复利，简化后得到：实际利率 名义利率 通货膨胀率,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,44,4.11 Taxes and Investment Decisions税收与投资决策,投资规则 Rule:(P153)Invest so as to maximize your after-tax rate of return为了最大化税后现金流的净现值而进行投资This is not at all the same thing as Minimize the tax you pay(False)并非等同于为了最小化税收支付而进行投资,
