精品课程PPT公司金融导论第六章.ppt

贴现现金流量估价,第六章,关键的概念和技巧,能计算一系列现金流量的终值能计算一系列现金流量的现值能计算出贷款付款额能够找出一项贷款的利息率理解如何偿还或还清贷款理解如何进行利息率报价,本章概要,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与分期偿还贷款,多期现金流量 终值例子 6.1,计算每一笔现金流量在3年的价值并把它们加起来.今天(第0年 CF):3 N;8 I/Y;-7000 PV;CPT FV=8817.98第一年 CF:2 N;8 I/Y;-4000 PV;CPT FV=4665.60第二年 CF:1 N;8 I/Y;-4000 PV;CPT FV=4320第三年 CF:value=4,000三年的总价值=8817.98+4665.60+4320+4000=21,803.58第四年的价值:1 N;8 I/Y;-21803.58 PV;CPT FV=23,547.87,多期现金流量 终值例子 2,假设你投资一项共同基金,今天投入$500 一年后投入$600。如果这项基金每年支付9%的利息，那么两年以后你将拥有多少？第0年 CF:2 N;-500 PV;9 I/Y;CPT FV=594.05第1年 CF:1 N;-600 PV;9 I/Y;CPT FV=654.00终值和=594.05+654.00=1248.05,多期现金流量 终值例子2 续,如果你不再存款，那么5年后你将拥有多少?第一种方法:第0年 CF:5 N;-500 PV;9 I/Y;CPT FV=769.31第一年 CF:4 N;-600 PV;9 I/Y;CPT FV=846.95终值和=769.31+846.95=1616.26第二种方法：用第二年的价值:3 N;-1248.05 PV;9 I/Y;CPT FV=1616.26,多期现金流量 终值例子 3,假设你计划在一个帐户中存款，一年后存入$100，三年后存入$300。如果利率为8%，那么五年后你将拥有多少？第一年 CF:4 N;-100 PV;8 I/Y;CPT FV=136.05第三年 CF:2 N;-300 PV;8 I/Y;CPT FV=349.92终值和=136.05+349.92=485.97,多期现金流量 现值例子 6.3,计算每一笔现金流量的现值，然后把它们相加第一年 CF:N=1;I/Y=12;FV=200;CPT PV=-178.57第二年 CF:N=2;I/Y=12;FV=400;CPT PV=-318.88第三年 CF:N=3;I/Y=12;FV=600;CPT PV=-427.07第四年 CF:N=4;I/Y=12;FV=800;CPT PV=-508.41现值和=178.57+318.88+427.07+508.41=1432.93,例子6.3 的时间线,用电子表格计算多期现金流量,你可以使用Excel中的计算现值或终值功能找出一系列现金流量的现值或终值。建立数据是成功的一半如果建立正确，然后只需要复制公式就可以了单击Excel图标看下面的例子：,多期现金流量 PV 另一个例子,你正在考虑一项投资，它将在第一年末付给你$1000,在第二年末付给你$2000和第三年末$3000。假如你想挣到你的钱的10%，那么你被希望要付多少呢？N=1;I/Y=10;FV=1000;CPT PV=-909.09N=2;I/Y=10;FV=2000;CPT PV=-1652.89N=3;I/Y=10;FV=3000;CPT PV=-2253.94PV=909.09+1652.89+2253.94=4815.93,使用计算机计算多期不均等现金流量,另一种方法是使用财务计算器来计算不均等现金流量Texas Instruments BA-II Plus按下CF然后进入现金流量以0年开始按下“Enter”键写入每期现金流量。使用向下键移动到另一期现金流量“F”是一个给定的现金流量发生在连续年份的时间的数字。使用净现值键（NPV）计算现值：输入利率1%，按住向下键然后计算。按下CF，出现清晰的现金流量解答然后语音记录工作,结果,你的经纪人打电话给你告诉你一个他有一个很棒的投资机会。假如你今天存$100，你将在一年后收到$40，在两年后收到$75,假如你想要在这种风险产品上得到15%的资本回报率，那么你是否应该投资呢？使用CF计算这笔投资的价值CF;CF0=0;C01=40;F01=1;C02=75;F02=1NPV;I=15;CPT NPV=91.49不 因为净现值小于你的投资,退休储蓄,你被提供机会到存一些钱为了退休，你将在从开始算起的40年后收到每5年$25000的付款，在你期望以12%的利率下，你将被希望存入多少？使用公式CF;CF0=0;C01=0;F01=39;C02=25000;F02=5;NPV;I=12;CPT NPV=1084.71,退休储蓄时间线,0 1 2 39 40 41 42 43 44,0 0 0 0 25K 25K 25K 25K 25K,注意 第0年现金流量为0(CF0=0)现金流量第139年为0(C01=0;F01=39)现金流量第4044为 25,000(C02=25,000;F02=5),快速抢答 第一部分,假设你正在寻找以下可能的现金流量:第一年 CF=$100;第二,三年 CFs=$200;第四,五年 CFs=$300.所需要的贴现利率是 7%.第五年的现金流量的价值是多少?今天的现金流量的价值是多少?第三年的现金流量的价值是多少?,年金和永续年金的定义,年金 在某段固定期间内,发生的一系列固定现金流量如果第一笔现金流量发生在期末,叫做普通年金如果第一笔现金流量发生在期初,叫做期初年金永续年金每年都有相同的现金流量，一直持续到永远,年金和永续年金的基本公式,永续年金:PV=C/r年金:,年金的计算,在计算等额支付的时候你可以使用计算器上的PMT 函数保持 sign状态不变普通年金与期初年金的转换你可以通过使用第二次按住“BGN”并且第二次设置“TI BA-II Plus”来实现这两种年金之间计算的转换.如果你在计算器上看到“BGN”或者是“Begin”,你可以设置成期初年金 大部分问题属于普通年金,年金-例6.5,你现在借钱因此需要计算现值48 N;1 I/Y;-632 PMT;CPT PV=23,999.54($24,000)公式:,年金 赌金例子,假如你赢得了出版社票据交易所的$10，000，000 赌金。每年付给你$333,333.33，30 年付完。如果合适的贴现率是5%。这些赌金在今天实际上值多少钱？30 N;5 I/Y;333,333.33 PMT;CPT PV=5,124,150.29,买套房子,准备买套房子，你有$20,000 支付定金和借款手续费.借款手续费估计是贷款额的4%。你每年薪水是$36,000，银行愿意你每月支付的抵押贷款额为你每月收入的28%。贷款利率为每年6%按照每月复利计息（0.5%每月）期限为30年.银行将贷给你多少钱？你将为这套房子支付多少钱？,购买房子 解题思路,银行贷款月收入=36,000/12=3,000每期付款额=.28(3,000)=84030*12=360 N.5 报酬率840 每期付款额年金现值即贷款额=140,105总的价格成交费=.04(140,105)=5,604头期款=20,000 5604=14,396总的价格=140,105+14,396=154,501,举例:债券发行分析表中的年金,债券发行分析表中会用到年金现值和终值公式.让我们用 Excel 来看一个例子.,小测验,假如你知道你要为贷款付多少钱或者你知道你要借多少钱.你是计算现值还是终值?你想在退休后每月有5000元收入.如果你能赚每月收入的75%,并且会持续25年.那么到退休的时候你的帐户会有多少存款?,找出各期应付款,假如你想要借20000美元来买一辆车.你以8%的年息借入,按月计算利息(8/12=.66667%).如果四年还清,每月应还多少?4(12)=48 N;20,000 PV;.66667 I/Y;CPT PMT=488.26,求解总投资期 例题6.6,相关数据如下:1.5 I/Y1000 现值-20 各期付款额 则总投资期=93.111 月=7.75年而这只是你不索要任何东西时求得的值.,利用表格来求出各期付款额,债券发行分析表中的另一个TVM公式是求付款额的公式.PMT(报酬率,总投资期,现值,终值)其中的标记与现值和终值公式中的相同让我们用 Excel 来看一个例子.,求解总投资期的另一个例子,假如你要借钱2000美元,利率为5%,并且每期支付734.42美元,你会多久付清这笔款项?相关数据如下:5 I/Y2000 现值-734.42 每期付款额则总投资期=3 years,计算利率,假设你从父母那里借了$10,000 买小汽车。你同意每个月付$207.58，一共付 60 个月。那么月利率是多少?签署协议事项!60 N10,000 PV-207.58 PMTCPT I/Y=.75%,年金 不用财务计算器找出利率,反复实验,选择一个利率并且根据这个利率来计算现值把计算出来的现值和实际的贷款总额相比较如果计算出来的现值贷款总额，那么说明利率太低如果计算出来的现值贷款总额,那么说明利率太高了调整利率并且重复这个过程直到计算出来的现值和贷款总额相等,Quick Quiz Part III,You want to receive$5000 per month for the next 5 years.How much would you need to deposit today if you can earn.75%per month?What monthly rate would you need to earn if you only have$200,000 to deposit?Suppose you have$200,000 to deposit and can earn.75%per month.How many months could you receive the$5000 payment?How much could you receive every month for 5 years?,Future Values for Annuities,Suppose you begin saving for your retirement by depositing$2000 per year in an IRA.If the interest rate is 7.5%,how much will you have in 40 years?Remember the sign convention!40 N7.5 I/Y-2000 PMTCPT FV=454,513.04,Annuity Due,You are saving for a new house and you put$10,000 per year in an account paying 8%.The first payment is made today.How much will you have at the end of 3 years?2nd BGN 2nd Set(you should see BGN in the display)3 N-10,000 PMT8 I/YCPT FV=35,061.122nd BGN 2nd Set(be sure to change it back to an ordinary annuity),Annuity Due Timeline,35,016.12,Perpetuity Example 6.7,Perpetuity formula:PV=C/rCurrent required return:40=1/rr=.025 or 2.5%per quarterDividend for new preferred:100=C/.025C=2.50 per quarter,Quick Quiz Part 4,You want to have$1 million to use for retirement in 35 years.If you can earn 1%per month,how much do you need to deposit on a monthly basis if the first payment is made in one month?What if the first payment is made today?You are considering preferred stock that pays a quarterly dividend of$1.50.If your desired return is 3%per quarter,how much would you be willing to pay?,Work the Web Example,Another online financial calculator can be found at MoneyChimpClick on the web surfer and work the following exampleChoose calculator and then annuity You just inherited$5 million.If you can earn 6%on your money,how much can you withdraw each year for the next 40 years?Datachimp assumes annuity due!Payment=$313,497.81,Table 6.2,Effective Annual Rate(EAR),This is the actual rate paid(or received)after accounting for compounding that occurs during the yearIf you want to compare two alternative investments with different compounding periods you need to compute the EAR and use that for comparison.,Annual Percentage Rate,This is the annual rate that is quoted by lawBy definition APR=period rate times the number of periods per yearConsequently,to get the period rate we rearrange the APR equation:Period rate=APR/number of periods per yearYou should NEVER divide the effective rate by the number of periods per year it will NOT give you the period rate,Computing APRs,What is the APR if the monthly rate is.5%?.5(12)=6%What is the APR if the semiannual rate is.5%?.5(2)=1%What is the monthly rate if the APR is 12%with monthly compounding?12/12=1%Can you divide the above APR by 2 to get the semiannual rate?NO!You need an APR based on semiannual compounding to find the semiannual rate.,Things to Remember,You ALWAYS need to make sure that the interest rate and the time period match.If you are looking at annual periods,you need an annual rate.If you are looking at monthly periods,you need a monthly rate.If you have an APR based on monthly compounding,you have to use monthly periods for lump sums,or adjust the interest rate appropriately if you have payments other than monthly,Computing EARs-Example,Suppose you can earn 1%per month on$1 invested today.What is the APR?1(12)=12%How much are you effectively earning?FV=1(1.01)12=1.1268Rate=(1.1268 1)/1=.1268=12.68%Suppose if you put it in another account,you earn 3%per quarter.What is the APR?3(4)=12%How much are you effectively earning?FV=1(1.03)4=1.1255Rate=(1.1255 1)/1=.1255=12.55%,EAR-Formula,Remember that the APR is the quoted rate,Decisions,Decisions II,You are looking at two savings accounts.One pays 5.25%,with daily compounding.The other pays 5.3%with semiannual compounding.Which account should you use?First account:EAR=(1+.0525/365)365 1=5.39%Second account:EAR=(1+.053/2)2 1=5.37%Which account should you choose and why?,Decisions,Decisions II Continued,Lets verify the choice.Suppose you invest$100 in each account.How much will you have in each account in one year?First Account:365 N;5.25/365=.014383562 I/Y;100 PV;CPT FV=105.39Second Account:2 N;5.3/2=2.65 I/Y;100 PV;CPT FV=105.37You have more money in the first account.,Computing APRs from EARs,If you have an effective rate,how can you compute the APR?Rearrange the EAR equation and you get:,APR-Example,Suppose you want to earn an effective rate of 12%and you are looking at an account that compounds on a monthly basis.What APR must they pay?,Computing Payments with APRs,Suppose you want to buy a new computer system and the store is willing to sell it to allow you to make monthly payments.The entire computer system costs$3500.The loan period is for 2 years and the interest rate is 16.9%with monthly compounding.What is your monthly payment?2(12)=24 N;16.9/12=1.408333333 I/Y;3500 PV;CPT PMT=-172.88,Future Values with Monthly Compounding,Suppose you deposit$50 a month into an account that has an APR of 9%,based on monthly compounding.How much will you have in the account in 35 years?35(12)=420 N9/12=.75 I/Y50 PMTCPT FV=147,089.22,Present Value with Daily Compounding,You need$15,000 in 3 years for a new car.If you can deposit money into an account that pays an APR of 5.5%based on daily compounding,how much would you need to deposit?3(365)=1095 N5.5/365=.015068493 I/Y15,000 FVCPT PV=-12,718.56,Continuous Compounding,Sometimes investments or loans are figured based on continuous compoundingEAR=eq 1The e is a special function on the calculator normally denoted by exExample:What is the effective annual rate of 7%compounded continuously?EAR=e.07 1=.0725 or 7.25%,Quick Quiz Part V,What is the definition of an APR?What is the effective annual rate?Which rate should you use to compare alternative investments or loans?Which rate do you need to use in the time value of money calculations?,Pure Discount Loans Example 6.12,Treasury bills are excellent examples of pure discount loans.The principal amount is repaid at some future date,without any periodic interest payments.If a T-bill promises to repay$10,000 in 12 months and the market interest rate is 7 percent,how much will the bill sell for in the market?1 N;10,000 FV;7 I/Y;CPT PV=-9345.79,Interest Only Loan-Example,Consider a 5-year,interest only loan with a 7%interest rate.The principal amount is$10,000.Interest is paid annually.What would the stream of cash flows be?Years 1 4:Interest payments of.07(10,000)=700Year 5:Interest+principal=10,700This cash flow stream is similar to the cash flows on corporate bonds and we will talk about them in greater detail later.,Amortized Loan with Fixed Principal Payment-Example,Consider a$50,000,10 year loan at 8%interest.The loan agreement requires the firm to pay$5,000 in principal each year plus interest for that year.Click on the Excel icon to see the amortization table,Amortized Loan with Fixed Payment-Example,Each payment covers the interest expense plus reduces principalConsider a 4 year loan with annual payments.The interest rate is 8%and the principal amount is$5000.What is the annual payment?4 N8 I/Y5000 PVCPT PMT=-1509.60Click on the Excel icon to see the amortization table,Work the Web Example,There are web sites available that can easily prepare amortization tablesClick on the web surfer to check out the CMB Mortgage site and work the following exampleYou have a loan of$25,000 and will repay the loan over 5 years at 8%interest.What is your loan payment?What does the amortization schedule look like?,Quick Quiz Part VI,What is a pure discount loan?What is a good example of a pure discount loan?What is an interest only loan?What is a good example of an interest only loan?What is an amortized loan?What is a good example of an amortized loan?,