1、第6章 现金流量折现估值(计算器)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.怎样决定涉及多期现金流投资的现值和终值 贷款支付额是怎样计算的以及怎样求解贷款的利率 贷款是怎样被分期偿还或偿清的 利率的报价是怎样的（以及误导性报价）学习目标Copyright 2019 McGraw-Hill Education.All rights reserve
2、d.No reproduction or distribution without the prior written consent of McGraw-Hill Education.多期现金流量的现值和终值 评估均衡现金流量：年金和永续年金 比较利率：复利的影响 贷款种类和分期偿还贷款章节纲要Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.你有能
3、力在接下来的3年中每年存4 000美元于一个利率为8%的银行账户内。你目前在这个账户里有7 000美元。你认为3年之后你会有多少钱？4年之后呢？多期现金流-终值FV(例6.1)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.找出每个现金流在第3年的价值，并把它们加在一起。(计算机键入)Todays(year 0)CF:3 N;8 I/Y;-7,000
4、 PV;CPT FV=8817.98 Year 1 CF:2 N;8 I/Y;-4,000 PV;CPT FV=4,665.60 Year 2 CF:1 N;8 I/Y;-4,000 PV;CPT FV=4,320 Year 3 CF:value=4,000 三年内的总价值=8,817.98+4,665.60+4,320+4,000=21,803.58 Value at year 4:1 N;8 I/Y;-21,803.58 PV;CPT FV=23,547.87多期现金流-终值FV(例6.1，ctd.)Copyright 2019 McGraw-Hill Education.All righ
5、ts reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假设你今天投资500美元，一年后投资600美元。如果基金每年支付9%，两年后你会有多少钱？Year 0 CF:2 N;-500 PV;9 I/Y;CPT FV=594.05 Year 1 CF:1 N;-600 PV;9 I/Y;CPT FV=654.00 Total FV=594.05+654.00=1,248.05多期现金流-终值FV(例2)Copyright 2019 McGraw-H
6、ill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.如果你不再存钱，5年后你会有多少钱？第一种方法:Year 0 CF:5 N;-500 PV;9 I/Y;CPT FV=769.31 Year 1 CF:4 N;-600 PV;9 I/Y;CPT FV=846.95 Total FV=769.31+846.95=1,616.26 第二种方法:3 N;-1,248.05 PV;9 I/Y;CPT FV
7、=1,616.26多期现金流-终值FV(例2，ctd.)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假设你计划在一年内存入100美元，在三年内存入300美元。如果利率是8%，五年后你的账户里会有多少存款？Year 1 CF:4 N;-100 PV;8 I/Y;CPT FV=136.05 Year 3 CF:2 N;-300 PV;8 I/Y;CP
8、T FV=349.92 Total FV=136.05+349.92=485.97多期现金流-终值FV(例3)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.你有一项投资，预期第1年会回报你200美元，第2年回报你400美元，第3年600美元，第4年800美元。你对投资要求的报酬率为12%。那么为了该笔投资你最多可以支付多少钱呢？找出每个现金流的PV
9、并将它们相加 Year 1 CF:N=1;I/Y=12;FV=200;CPT PV=-178.57 Year 2 CF:N=2;I/Y=12;FV=400;CPT PV=-318.88 Year 3 CF:N=3;I/Y=12;FV=600;CPT PV=-427.07Year 4 CF:N=4;I/Y=12;FV=800;CPT PV=-508.41 Total PV=178.57+318.88+427.07+508.41=1,432.93多期现金流-现值PV(例6.3)Copyright 2019 McGraw-Hill Education.All rights reserved.No r
10、eproduction or distribution without the prior written consent of McGraw-Hill Education.例6.3的时间轴01234200400600800178.57318.88427.07508.411,432.93Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.你可以使用Exc
11、el中的PV或FV函数来查找一组现金流的现值或终值。设置数据是成功的一半如果设置正确，那么您可以直接复制公式。单击Excel图标查看示例。多期现金流使用电子表格Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.你正在考虑一项投资，它将在一年后给你1000美元，两年后给你2000美元，三年后给你3000美元。如果你想赚10%的钱，你现在愿意付多少？N=1
12、;I/Y=10;FV=1,000;CPT PV=-909.09 N=2;I/Y=10;FV=2,000;CPT PV=-1,652.89 N=3;I/Y=10;FV=3,000;CPT PV=-2,253.94 PV=909.09+1,652.89+2,253.94=4,815.93多期现金流-现值PV另一个示例Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Educa
13、tion.使用财务计算器计算不均衡现金流的另一种方法是使用现金流键-CF。按CF，输入从第0年开始的现金流。你必须为每个现金流按下“Enter”键。使用向下箭头键移动到下一个现金流。“F”是给定的现金流在连续期间发生的次数。使用NPV键通过输入I的利率来计算现值，按下箭头，然后计算答案。按CF键清除现金流工作表，然后按2nd clr键工作。多期不均衡的现金流-使用计算器Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written
14、 consent of McGraw-Hill Education.你的经纪人打电话给你，告诉你他有一个很好的投资机会。如果你今天投资100美元，一年后你将得到40美元，两年后你将得到75美元。如果你要求这个风险的投资有15%的回报，你是否应该投资？使用CF键来计算投资的价值。CF;CF0=0;C01=40;F01=1;C02=75;F02=1 NPV;I=15;CPT NPV=91.49 不经纪人的要价比你愿意支付的要高。决策1Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distrib
15、ution without the prior written consent of McGraw-Hill Education.你有机会存一些钱以备退休之用。四十年后开始，你将得到五笔25,000美元的年度付款。如果你现在想要12%的利率，你愿意投资多少？使用CF键:CF;CF0=0;C01=0;F01=39;C02=25,000;F02=5;NPV;I=12;CPT NPV=1,084.71为退休储蓄Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without
16、 the prior written consent of McGraw-Hill Education.为退休储蓄0 1 2 39 40 41 42 43 44 0 0 0 0 25K 25K 25K 25K 25K注意，0年现金流=0(CF0=0)第1 39年的现金流为0(C01=0;F01=39)40 44年的现金流是25000(C02=25,000;F02=5)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written
17、consent of McGraw-Hill Education.假设你考虑以下可能的现金流 第1年CF=$100;第2年和第3年CFs=$200;第4年和第5年CFs=$300；所需贴现率为7%第5年的现金流价值是多少？今天的现金流价值是多少？第3年的现金流价值是多少？快速测验-第一部分Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.年金：定期发生
18、的有限级数的等额支付 如果第一笔付款发生在期末，就称为普通年金。如果第一笔付款发生在期初，则称为预付年金。永续年金：无穷级数的等额支付年金和永续年金的定义Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.永续年金:PV=C/r 年金:年金和永续年金-基本公式rrCFVrrCPVtt1)1()1(11Copyright 2019 McGraw-Hill
19、Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.你可以使用计算器上的PMT键来计算等额支付。符号惯例仍然有效。普通年金vs预付年金 你可以通过使用TI BA-II Plus上的 the 2nd BGN 2nd来在这两种类型之间切换计算器。如果您看到计算器显示中的BGN或Begin，您就设置了预付年金。大多数问题是普通年金。年金和计算器Copyright 2019 McGraw-Hill Educatio
20、n.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.在仔细检查了你的预算之后，你决定每月支付632美元买一辆新的跑车。在询问了银行后你得知，48个月的贷款利率为每月1%。你可以贷款多少？为了得到你可以承担的贷款数额，我们需要计算48个月，月利率为1%，每个月偿付632美元的贷款现值。年金-例6.5Copyright 2019 McGraw-Hill Education.All rights reserved.No repr
21、oduction or distribution without the prior written consent of McGraw-Hill Education.你今天贷款，所以你需要计算现值。48 N;1 I/Y;-632 PMT;CPT PV=23,999.54($24,000)公式年金-例6.5(ctd.)54.999,2301.)01.1(1163248PVCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior writte
22、n consent of McGraw-Hill Education.假设你赢得了出版商清算所1000万美元的奖金。这笔钱将在30年内分期付款，每年支付333,333.33美元。如果贴现率是5%，那么今天这些奖金的实际价值是多少？30 N;5 I/Y;333,333.33 PMT;CPT PV=5,124,150.29年金-奖金的例子Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw
23、-Hill Education.你准备买一套房子，你有2万美元的首付和交易费用。交易成本估计为贷款价值的4%你的年薪是36,000美元，银行愿意让你每月的按揭还款等于你每月收入的28%。按月复利计算，贷款的利率是每年6%（每月0.5%）。30年期的固定利率贷款。银行会贷款给你多少钱？你能出多少钱买这所房子？买房子Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Educa
24、tion.银行贷款 月收入=36,000/12=3,000 最高额度=0.28(3,000)=840 3012=360 N 0.5 I/Y-840 PMT CPT PV=140,105 总价 交易成本=0.04(140,105)=5,604 首付=20,000 5,604=14,396 总价=140,105+14,396=154,501买房子(ctd.)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent
25、 of McGraw-Hill Education.电子表格中的现值和终值的公式包括年金支付的位置。单击Excel图标查看示例。电子表格计算年金-示例Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.你知道贷款的支付金额，那么你想知道借了多少。你计算的是现值还是终值？你希望退休后每个月能拿到5000美元。如果你每个月能赚0.75%，而且你预计需要25年
26、的收入，你退休时需要在你的账户里存多少钱？快速测验-第二部分Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假设你想借2万美元买一辆新车。你可以以每年8%的利率贷款，每月复利(8/12=0.66667%/月)。如果你贷款4年，你的月供是多少?4(12)=48 N;20,000 PV;.66667 I/Y;CPT PMT=488.26求付款额Copyr
27、ight 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.在电子表格中可以找到的另一个TVM公式是支付公式。PMT(rate,nper,pv,fv)同样的符号惯例适用于PV和FV公式。单击Excel图标查看示例。在电子表格中求付款额Copyright 2019 McGraw-Hill Education.All rights reserved.No reproducti
28、on or distribution without the prior written consent of McGraw-Hill Education.在春假期间你由于手头紧张透支了1 000美元。你每月只能负担最低的20美元还款额。信用卡的利率为每月1.5%。你需要多久才可以还清1 000美元？求支付期数 例6.6Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill E
29、ducation.符号惯例很重要 1.5 I/Y 1,000 PV-20 PMT CPT N=93.111 months=7.75 years 而且这只是在不收取任何费用的情况下!求支付期数 例6.6(ctd.)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假设你以5%的利率借了2000美元，你将每年支付734.42美元。你要多久才能还清贷款？符号
30、惯例问题!5 I/Y 2,000 PV-734.42 PMT CPT N=3 years求支付期数 另一个示例Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假设你从父母那里借了1万美元买了一辆车。你同意在60个月内每月支付207.58美元。每月的利率是多少？符号惯例问题!60 N 10,000 PV-207.58 PMT CPT I/Y=0.75%
31、求贴现率Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.试错法 选择一个利率并根据这个利率计算支付的PV。将计算出的PV与实际贷款金额进行比较。如果计算出PV 贷款金额，则利率太低。如果计算的PV 贷款金额，则利率过高。调整利率并重复这个过程，直到计算出的PV和贷款金额相等。年金不用计算器就能计算出利率Copyright 2019 McGraw-Hi
32、ll Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.你想在接下来的5年里每个月得到5000美元。如果月利率为0.75%，你今天需要存多少钱？如果你只有20万美元存款，每月的利率应为多少？假设你有20万美元存款，每个月能赚0.75%。每月5000美元的付款，你能收到几个月？你在5年内每月能收到多少钱？快速测验-第三部分Copyright 2019 McGraw-Hill Education.All ri
33、ghts reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假设你开始为你的退休生活存钱，每年在IRA（个人退休账户）里存2000美元。如果利率是7.5%，40年后你会有多少?记住符号约定!40 N 7.5 I/Y-2,000 PMT CPT FV=454,513.04年金的终值Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribut
34、ion without the prior written consent of McGraw-Hill Education.你在攒钱买新房子，你每年把1万美元存入一个账户，支付8%的利息。今天第一次付款。3年后你会有多少（付三年）？2nd BGN 2nd Set(你应该在显示屏上看到BGN)3 N-10,000 PMT 8 I/Y CPT FV=35,061.12 2nd BGN 2nd Set(一定要换回普通年金)预付年金Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribut
35、ion without the prior written consent of McGraw-Hill Education.预付年金时间轴 0 1 2 310000 10000 1000032,46435,016.12Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假如Fellini公司计划以每股100美元的价格发售优先股 已经在外流通的类似优先股
36、的每股价格是40美元，每季度支付1美元的股利。对于这种新发售的优先股，Fellini每季度应支付多少股利？永续年金-例6.7Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.永续年金公式:PV=C/r 当前必要报酬率:40=1/r r=.025 or 2.5%per quarter 新优先股股息:100=C/.025 C=2.50 per quarte
37、r永续年金-例6.7(ctd.)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.你想在35年后有100万美元退休金。如果月利率为1%，第一次付款在第一个月，你每月需要存多少钱？如果第一次付款是今天呢？你正在考虑季度股息为1.50美元的优先股。如果你期望的回报率是每季度3%，你愿意支付多少？快速测验-第四部分Copyright 2019 McGraw-
38、Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.另一个在线财务计算器可以在MoneyChimp上找到。访问该网站并学习以下示例。选择计算器，然后是年金 你继承了500万美元。如果年利率6%，那么在接下来的40年里，你每年能从银行取多少钱?MoneyChimp 假定预付年金！Payment=$313,497.81Web示例1Copyright 2019 McGraw-Hill Education
39、.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.表6.2Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.固定期限的不断增长的现金流增长年金ttrgCrgCrCPV)1()1()
40、1()1()1(12trggrCPV)1()1(1Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.一个固定收益退休计划提供40年每年支付2万美元，每年增加3%。如果贴现率是10%，退休后的现值是多少？增长年金:示例57.121,265$10.103.1103.10.000,20$40PVCopyright 2019 McGraw-Hill Educa
41、tion.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.持续不断的现金流增长型永续年金322)1()1()1()1()1(rgCrgCrCPVgrCPVCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hil
42、l Education.预计明年的股息为1.30美元，预计股息将永远以5%的速度增长。如果贴现率是10%，这个承诺的股息流的价值是多少？增长型永续年金:示例00.26$05.10.30.1$PVCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.在一年内进行复利计算的实际收到或支付的利率 如果你想比较两个不同复利期的可选择投资，你需要计算EAR并将其用于
43、比较。有效年利率(EAR)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.这是法律规定的年利率 根据定义，APR=期利率乘以每年的计息次数。因此，为了得到期利率，我们重新排列APR方程:期利率=APR/每年的计息次数 永远不应该用有效利率除以每年的期数它无法求出期利率。贷款的年百分率（APR）Copyright 2019 McGraw-Hill Ed
44、ucation.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.如果月利率是5%，APR是多少？.5(12)=6%如果半年利率是5%，APR是多少？.5(2)=1%如果按月复利计算APR是12%，那么每月利率是多少？12/12=1%计算APRsCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution wi
45、thout the prior written consent of McGraw-Hill Education.你总是需要确保利率和时间段相匹配。如果期数以年为单位，则要关注年利率 如果期数以年为单位，则要关注月利率 如果你的APR是按月计算的 你必须用每月的周期来计算总金额，如果你不是按月还款，也可以适当调整利率。要注意的事项Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-H
46、ill Education.假设你现在投资1美元，每月能赚1%（月利率1%）。APR是多少？1(12)=12%有效年利率是多少？FV=1(1.01)12=1.1268 Rate=(1.1268 1)/1=.1268=12.68%假设你把它存入另一个账户，每个季度赚3%。APR是多少？3(4)=12%有效年利率是多少？FV=1(1.03)4=1.1255 Rate=(1.1255 1)/1=.1255=12.55%计算 EAR 示例Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distrib
47、ution without the prior written consent of McGraw-Hill Education.EAR 公式1 mAPR 1 EARm记住APR是报价利率，m是每年的复利期数Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.您正在查看两个储蓄账户。一个按日复利计算，利息为5.25%。另一种是半年复利5.3%。您应该使用
48、哪个账户？第一个账户:EAR=(1+.0525/365)365 1=5.39%第二个账户:EAR=(1+.053/2)2 1=5.37%你应该选择哪个账户，为什么？决策2Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.我们来验证一下。假设你在每个账户上存入100美元。一年后每个账户里会有多少钱？第一个账户:365 N;5.25/365=.014383
49、562 I/Y;100 PV;CPT FV=105.39 第二个账户:2 N;5.3/2=2.65 I/Y;100 PV;CPT FV=105.37 你在第一个账户里有更多的钱。决策2(ctd)Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.如果你有一个有效利率，如何计算APR？重新排列EAR方程，得到:从EARs计算APRs 1 -EAR)(1 m
50、 APRm1Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假设你想获得12%的有效利率，你正在查看一个按月计算复利的账户。APR必须为多少？APR 示例11.39%or 8655152113.1)12.1(1212/1APRCopyright 2019 McGraw-Hill Education.All rights reserved.No rep
