公司理财-未来现金流量的价值评估.ppt

1,公 司 理 财,2,斯蒂芬 A.罗斯,史蒂芬罗斯先生目前是麻省理工学院斯隆管理学院财务经济学教授。作为在财务和经济领域著述最为丰富的作者之一，罗斯教授以他在发展套利价格理论上所做的工作，以及通过研究信息折射理论、代理理论、利率期限结构理论和其他诸多领域所做出的大量贡献，成为备受称道的著名学者。罗斯曾任美国金融协会主席，现在担任数家学术型和实战型杂志的副主编。他还是CalTech的受托人，大学退休股权基金和GenRe公司的董事。此外，他还兼任劳尔&罗斯资产管理公司的联席主席。,3,伦道夫 W.韦斯特菲尔德,伦道夫韦斯特菲尔德先生是南加州大学马歇尔商学院的院长。 从1988到1993年，韦斯特菲尔德教授担任马歇尔商学院财务和商业经济系主任和查尔斯桑顿财务教授。在来到南加州大学之前，他曾是宾夕法尼亚大学沃顿商学院财务系主任，并在那里执教20年。他还曾是沃顿商学院罗德尼怀特财务研究中心的高级研究员。他所擅长的领域包括：公司财务政策、投资管理和分析、兼并和收购以及股票市场价格行为。 韦斯特菲尔德教授是大陆银行信托委员会的成员，负责指导信托部门的所有决策。他还担任着许多公司和机构的顾问，包括：美国电报电话公司、莫比尔石油和太平洋公司以及联合国、美国司法和劳工部以及加利福尼亚州州政府。,4,布拉德福德 D.乔丹,布拉德福德乔丹先生是肯塔基大学财务教授和加藤研究员。长期以来，他对公司理财的理论和实务一直保持着浓厚兴趣，而且在公司理财和财务管理政策的各个层面上拥有丰富的经验。乔丹教授在诸如资本成本、资本结构和证券价格行为等领域发表了大量的论文。,5,作者写作该教材的基本理念,快速而广泛的变化，给财务课程的教学者设置了重重障碍。保持资料的及时性，变得越来越困难。况且，还必须将持久性的内容与临时的东西区别开来,以避免追随那些仅是昙花一现的时尚。我们的方法是：强调财务的现代基础，并使所探讨的主题与当代实践紧密结合。 当时光流逝，细节将湮没，留下来的，将是对基本原理的深刻把握，如果我们的努力能够成功的话。这就是为什么我们能自始至终，从本书第一页到最后一页，一直专注于财务决策的基本逻辑,6,未来现金流量的价值评估,财务管理的核心问题： 未来的现金流量在今天价值多少 ？,7,货币的时间价值 & 现金流量的折现,8,对于 今天的$1000 和 5 年后的 $1000,你选择哪一个呢 ？,货币的时间价值,显然是, 今天的 $1000. 你已经承认了 货币的时间价值 !,9,为什么： 在决策中必须考虑 货币的时间价值 ?,Why TIME ?,因为： 如果眼前就能取得 $1000，那么我们 至少有一个 用这笔钱去 获取 利息收益 的 投资机会.,10,实例 -货币的时间价值,1982年12月2日,通用汽车的子公司 Acceptance 公司(GMAC)，公开发行了一些债券。在此债券的条款中，GMAC 承诺将在2012年12月1日按照每张 $10,000 的价格向该债券的所有者进行偿付，但是投资者们在此日期之前不会有任何收入。投资者购入每一张债券支付给 GMAC $500，因此，他们在1982年12月2日放弃 $500,是为了在30年后获得$10,000。这样的债券让你在今天付出一笔钱，从而得到在将来的某日收到一大笔钱的承诺，它是所有可能性中最简单的形式.,11,续实例 -货币的时间价值,今天放弃 $500 以在30年后获得 $10,000 是不是一项好交易呢? 从正面来看，每$1投入都能得到 $20 的回报,它听起来很不错；但是从负面来看，你必须等待30年才能得到这笔钱。如何来分析这种此消彼涨的关系 ？ 这堂课的目标是介绍财务中最重要的一个原理：货币的时间价值。如何确定未来的现金流入在今日的价值，是一项非常基础的商业技能，并且是对各种不同类型的投资和融资计划进行分析的理论基础。 几乎所有的商业活动，都要将今天的耗费与将来的预计收益相比较。,12,Outline,Future Value and Compounding Present Value and Discounting Discount Rate The Number of Periods Multiple Cash Flows Annuities and Perpetuities APR and EAR Loan Types & Loan Amortization,13,Part 1,Future Value and Compounding,14,主要内容,单利 复利,15,利息,复利 (Compounding = Interest on Interest) 不仅借贷的本金要求支付利息，而且前期的利息在下一期也要求支付利息.,单利 (Simple Interest) 只对借贷的原始金额或本金支付利息。,16,公式 SI = P0 *(r)*(n) SI: 单利利息(Simple Interest) P0: 原始金额 (时间下标 t = 0) r: 利率 n: 期数,单利公式,17,单利 Example,假设投资者按 7% 的单利把 $1,000 存入银行 2年. 第 2 年年末的利息额是多少 ? SI = P0 * (r) * (n) = $1,000(.07)(2) = $140,18,单利 Future Value (SIFV) 是多少? SIFV = P0 + SI = $1,000 + $140 = $1,140 终值FV 现在或将来的一笔钱或一系列支付款按给定的利率计算，所得到的 在某个更远的未来时点的 价值.,单利终值 SIFV,19,上页例子中，两年后的$1,140的 单利现值 (SIPV) 是多少? 现值PV 未来的一笔钱或一系列支付款按给定的利率折算，所得到的在先前时点的价值. 这种折算称为折现。 在上页例子中，你先前存的 $1,000 原始金额，就是两年后的$1,140 的 单利现值PV ,即在先前时点的价值 !,单利现值 SIPV,20,假设投资者按 7% 的 复利 把$1,000 存入银行 2 年，那么它的复利终值 是多少？,复利终值,0 1 2,$1,000,FV2,7%,21,Basic Definitions,Present Value - earlier money on a time line（相对于其后的 money 而言） Future Value - later money on a time line（相对于其前的 money 而言） PV 与 FV 是 相对而言的 ！ Interest rate - “exchange rate” between earlier money and later money,22,FV1 = P0 (1+r)1 = $1,000 (1.07) = $1,070 复利 在第一年年末你得了$70的利息. 这与单利利息相等.,复利终值公式1/2,23,FV1 = P0 (1+r)1 = $1,000 (1.07) = $1,070 FV2 = FV1 (1+r)1 = P0 (1+r)(1+r) = $1,000(1.07)(1.07) = P0 (1+r)2 = $1,000(1.07)2 = $1,144 . 90 第 2 年，你比单利利息多得 $4 . 90 = $70 (0.07),复利终值公式2/2,24,Future Values: General Formula,FV = PV (1 + r)t FV = Future Value PV = Present Value r = period interest rate, expressed as a decimal t = number of periods Future Value Interest Factor = (1 + r)t,25,FV1 = P0(1+r)1 FV2 = P0(1+r)2 , etc. F V 公式: FV n = P0 (1+r)n or FV n = P0 (FVIF r,n) 可查表 (FVIF r,n)可直观地记为(FV/PV, r , n),一般复利终值公式,26,FVIF r,n 可以查表如下所示：,复利终值因子表： FVIF r,n,27,FV2 = $1,000 (FVIF7%,2) = $1,000 (1.145) = $1,145 四舍五入,查表FVIF r,n计算,28,按 10% 的复利把$1000存入银行， 5年后的终值是多少？,Example 复利终值,0 1 2 3 4 5,$1000,FV5,10%,29,查表 : FV5 = $1,000 (FVIF10%, 5) = $1,000 (1.611) = $1,611 四舍五入,解：,用一般公式: FV n = P0 (1+r)n FV5 = $1,000 (1+ 0.10)5 = $1,610. 51,30,Effects of Compounding - 1,Consider the previous example FV with simple interest = 1000 + 70 + 70 = 1140 FV with compound interest = 1144.90 The extra 4.90 comes from the interest of .07(70) = 4.90 earned on the first interest payment,31,Effects of Compounding - 2,Suppose you invest the $1000 from the previous example for 5 years. How much would you have? FV = 1000 (1.07)5 = 1402.55 Simple interest would have a future value of $1350, for a difference of $52.55 The effect of compounding is small for a small number of periods, but increases as the number of periods increases.,32,Figure 4.1: 终值、单利 vs. 复利,33,Effects of Compounding - 3,Suppose you had a deposit $1k at 7% interest 30 years ago. How much would the investment be worth today ? FV = 1k (1.07)30 7,612 What is the effect of compounding ? Simple interest = 1k + 30(1k)(.07) = 3100 Compounding added $ 4,512 to the value of the investment,34,单利 v.s. 复利 ?,Future Value (U.S. Dollars),35,Effects of Compounding - 4,Suppose you had a deposit $1 at 7% interest 200 years ago. How much would the investment be worth today ? FV = 1 (1.07)200 752,932 What is the effect of compounding ? Simple interest = 1 + 200(1)(.07) = 15 Compounding added $ 752,917 to the value of the investment,36,美国曼哈顿岛值多少钱 ？-1/4,为了阐述复利在长时期中的作用，不妨看看彼得麦纽因特和印第安人买卖曼哈顿岛的交易。 1626年，麦纽因特以价值仅仅$24的商品和小饰品，购买了整个曼哈顿岛。这个价格听起来很便宜，但是印第安人也能从这个交易中获得很不错的结果。 为了弄明白其中原由，假设印第安人将卖岛所得 $24 以10的利率进行投资。 这项投资到今天 会值 多少钱呢 ? 请同学们猜一猜 ！,37,美国曼哈顿岛值多少钱 ？ -2/4,这项投资到今天大约过了377年。 当利率为10时，$24能够在这段时期内大幅增长。到底增长到多少呢? 该复利终值因子为：(1+ r)377 = 1.1377 4 000 000 000 000 000 那也就是4后面跟15个零。终值因子带来的结果是 $24x4 后面再加15个零，也就是 $96 后面加15个零（9.6亿亿）。 这么多钱可以买下整个美国,乃至整个世界.对此同学们有何感想 ？,38,美国曼哈顿岛值多少钱 ？ -3/4,这当然是一个夸张的例子。在1626年，要想进行一笔利率为10且377年都不减息的投资可不是件容易的事。 假设印第安人将卖岛所得$24 以5的利率进行投资。 这项投资到今天 会值 多少钱呢 ? 该复利终值因子为：(1+ r)377 = 1.05377 1 00 000 000 那也就是1后面跟 8个零。终值因子带来的结果是 $24x1 后面再加 8个零，也就是$24亿。,39,美国曼哈顿岛值多少钱 ？ -4/4,假设印第安人将卖岛所得$24 以2.5的利率进行投资。 这项投资到今天 会值 多少钱呢 ? 该复利终值因子为：(1+ r)377 = 1.025377 11,038,40,Effects of Compounding 小结,The effect of compounding is small for a low interest rate, and for a small number of periods. For a given interest rate the longer the time period, the bigger the future value. For a given time period the higher the interest rate, the bigger the future value.,41,Figure 4.2: $1于不同利率、多期后的复利终值,42,$1,000 按 12% 复利，需要多久成为$2,000 (近似) ?,想使自己的财富倍增吗 !,快捷计算方法: 72 法则,43,近似. N = 72 / i% 72 / 12% = 6 年 精确计算是 6.12 年,快捷计算方法：72法则,$1,000 按 12% 复利，需要多久成为$2,000 (近似) ?,44,Quick Quiz: Part 1,What is the difference between simple interest and compound interest ? Suppose you have $500 to invest and you believe that you can earn 6% per year over the next 12 years. How much would you have at the end of 12 years using simple interest ? How much would you have at the end of 12 years with compound interest ?,45,Part 2,Present Value and Discounting,46,Present Values,How much do I have to invest today to have some amount in the future? FV = PV(1 + r)t Rearrange to solve for PV = FV / (1 + r)t When we talk about discounting, we mean finding the present value of some future amount. When we talk about the “value” of someth., we are talking about the present value unless we specifically indicate that we want the future value.,47,假设 2 年后你需要$1,000. 那么按 7%复利，你现在要存多少钱 ？,0 1 2,$1,000,7%,PV1,PV0,复利现值,48,PV0 = FV2 / (1+r)2 = $1,000 / (1.07)2 = FV2 / (1+r)2 = $873.44,复利现值公式,0 1 2,$1,000,7%,PV0,49,PV0 = FV1 / (1+r)1 = FV1(1+r)-1 PV0 = FV2 / (1+r)2 = FV2(1+r)-2 P V 公式: PV0 = FV n / (1+r)n = FV n (1+r)-n or PV0 = FV n (PVIF r,n) - 见下页表格 (PVIF r,n) 可直观地记为 (PV/FV, r , n),一般复利现值公式,etc.,50,PVIF r,n表如下所示：,复利现值因子表：PVIF r,n,51,PV2 = $1,000 (PVIF7%,2) = $1,000 (.873) = $873 四舍五入,查复利现值因子表,52,按10% 的复利折算，5 年后的 $1,000 的现值是多少？,Example -复利现值,0 1 2 3 4 5,$1,000,PV0,10%,53,用公式: PV0 = FV n / (1+r)n PV0 = $1,000 / (1+ 0.10)5 = $620. 92 查表: PV0 = $1,000 (PVIF10%, 5) = $1,000 (.621) = $621. 00 四舍五入,解：,54,欺骗性广告 1/2,最近，一些商家都这样宣称 “来试一下我们的产品。如果你试了，我们将为你的光顾支付 $100 ！” 你会发现他们给你的是一个在25年之后支付给你 $100 的存款证书。 如果该存款的年利率是 10的话，今天他们真正给你多少钱呢 ?,55,欺骗性广告 2/2,你真正得到的是在25年后才能得到的$100 在今日的现值。 假如折现率是每年10，那么折现因子应是：1/1.125 = 1/10.8347 = 0.0923 这告诉你在折现率为10时，25年后的 $1在今天仅值9美分多一点。 由此可见，该促销仅能给你0.0923x$l00 = $9.23。可能这$9.23 已经足以吸引顾客，但它的确不是 $l00 。,56,PV One Period Example,Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today ? PV = 10,000 / (1.07)1 = 9345.79,57,Present Values Example 2,You want to begin saving for your daughters college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 7% per year, how much do you need to invest today? PV = 150,000 / (1.07)17 = 47,486.16,58,Present Values Example 3,Your 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 = 10,000,59,PV Important Relationship I,For a given interest rate the longer the time period, the lower the present value What is the present value of $100 to be received in 5 years ? 10 years ? The discount rate is 10% 5 years: PV = 100 / (1.1)5 = 62.09 10 years: PV = 100 / (1.1)10 = 38.55,60,PV Important Relationship II,For a given time period the higher the interest rate, the smaller the present value. What is the present value of $100 received in 5 years if the interest rate is 10%? Or 20%? Rate = 10%: PV = 100 / (1.1)5 = 62.09 Rate = 20%: PV = 100 / (1.2)5 = 40.19,61,Figure 4.3 : $1于不同利率、折现期的现值,62,Quick Quiz: Part 2,What is the relationship between present value and future value? Suppose you need $7,000 in 12 years. If you can earn 6% annually, how much do you need to invest today ? If you could invest the money at 12%, would you have to invest more or less than at 6% ?,63,Part 3,Discount Rate,64,The Basic PV Equation - Refresher,PV = FV / (1 + r)t There are four parts to this equation PV, FV, r and t If we know any three, we can solve for the fourth,65,Discount Rate,Often we will want to know what the implied interest rate is in an investment Rearrange the basic PV equation and solve for r FV = PV (1 + r)t r = (FV / PV)1/t 1,66,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 ? r = (1200 / 1000)1/5 1 = .03714 = 3.714%,67,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 rate of interest ? r = (20,000 / 10,000)1/6 1 = .122462 = 12.25%,68,Discount Rate Example 3,Suppose you have a 1-year old son and you want to provide $75,000 in 17 years towards his college education. You currently have $5000 to invest. What interest rate must you earn to have the $75,000 when you need it ? r = (75,000 / 5,000)1/17 1 = .172688 = 17.27%,69,Quick Quiz : Part 3,What are some situations where you might want to compute the implied interest rate ? Suppose you are offered the following two choices of investment. Which is better ? You can invest $1000 today with low risk and receive $2000 in 12 years. Or you can invest the $1000 in a bank account paying 6% for 12 years. What is the implied interest rate for the first choice and which investment should you choose?,70,Part 4,Finding the Number of Periods,71,Finding the Number of Periods,Start with basic equation and solve for t (remember your logs) FV = PV (1 + r)t t = l n (FV / PV) / l n (1 + r),72,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 ? t = l n (20,000 / 15,000) / l n (1.1) = 3.02 years,73,Number of Periods Example 2,Suppose you want to buy a new house. You currently have $18,000 and you figure you need to have a 10% down payment plus an additional 5% of the loan value in closing costs. If the type of house you want costs about $150,000 and you can earn 7.5% per year, how long will it be before you have enough money for the down payment and closing costs ?,74,Example 2 Continued,How much do you need to have in the future? Down payment = .1(150,000) = 15,000 Bank Loan = 150,000 15,000 = 135,000 Closing costs = .05 (135,000) = 6,750 Total needed = 15,000 + 6,750 = 21,750 t = l n (21,750 / 18,000) / l n (1.075) = 2.62 years,75,Work the Web Example,financial calculators are available online such as /consumer/tools/present_value.html You may go to Cignas web site and work the following example: You need $40,000 in 15 years. If you can earn 9.8% interest, how much do you need to invest today ? You should get $9,841,76,Quick Quiz: Part 4,When might you want to compute the number of periods? Suppose you want to buy some new furniture for your family room. You currently have $500 and the furniture you want costs $1000. If you can earn 12%, how long will you have to wait if you dont add any additional money ?,77,Part 5,Multiple Cash Flows,78,Multiple Cash Flows FV Example 1,Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%? FV = 100(1.08)4 + 300(1.08)2 = 136.05 + 349.92 = 485.97,79,Example 1 - Timeline,5,80,Multiple Cash Flows PV Example 5.3,You are offered an investment that will pay you $200 in one year, $400 in two years, $600 in three years, and $800 in four years. You can earn 12% on very similar investments. What is the most you should pay for this one ?,81,Multiple Cash Flows PV Example 5.3,Find the PV of each cash flow and add them PV1 of Year 1 CF1: 200 / (1.12)1 = 178.57 PV2 of Year 2 CF2: 400 / (1.12)2 = 318.88 PV3 of Year 3 CF3: 600 / (1.12)3 = 427.07 PV4 of Year 4 CF4: 800 / (1.12)4 = 508.41 Total PV+ = 178.57 + 318.88 + 427.07 + 508.41 = 1432.93 If you can earn 12% on your money, this is the most you should be willing to pay.,82,Example 5.3 Timeline,83,Decisions I,Your broker calls you and tells you that he has this great investment opportunity. If you invest $100 today, you will receive $40 in one year and $75 in two years. If you require a 15% return on investments of this risk, should you take the investment ? PV = 91.49, No - the broker is charging more than you would be willing to pay.,84,Saving For Retirement,You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you be willing to invest today if you desire an interest rate of 12% ? PV = 1084 .71,85,Saving For Retirement - Timeline,0 1 2 39 40 41 42 43 44,0 0 0 0 25K 25K 25K 25K 25K,Notice the year 0 cash flow = 0 (CF0 = 0) The cash flows years 1 39 are 0 The cash flows years 40 44 are 25,000,86,Quick Quiz: Part 5,Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7% What is the value of the cash flows at year 5? What is the value of the cash flows today? What is the value of the cash flows at year 3 ?,87,Part 6,Annuities and Perpetuities,88,Annuities and Perpetuities,Annuity finite series of equal payments that occur at regular intervals If each payment occurs at the end of each period, it is called an ordinary annuity If each payment occurs at the beginning of each period, it is called an annuity due Perpetuity infinite series of equal payments,89,年金,年金：相等间隔期（通常为年，但 是也可为其他间隔期，如： 季 、月、每两年，等）的 一系列 相同 金额的 收款 或 付款.,90,年金实例,学生贷款偿还 汽车贷款偿还 保险金 抵押贷款偿还 养老储蓄,91,年金例 解答见后,某人现年51岁，希望在60岁退休后从61岁初开始的9年内每年年初能从银行得到10,000元，那么他在从52岁初开始到60岁初的9年内必须每年年初存入银行多少钱才行 ？ 年利率6% 某人从银行贷款100万买房，年利率为6%，若在5年内还清，那么他每个月必须还多少钱才行？,92,普通年金: 若所求终值的时刻为最后一笔年金所在的时刻，or 所求现值的时刻为第一笔年金所在的时刻的前1期，则称该年金为普通年金 - 求该年金的现值or终值可查普通年金现值or终值因子表。 先付年金: 若所求现值的时刻为第一笔年金所在的时刻，or 所求终值的时刻为最后一笔年金所在的时刻的后1期，则称该年金为先付年金 。,年金分类,93,0 1 2 3年末,假定现值：,Parts of an Annuity,年末,普通年金： $100 $100 $100,(第1年年末 的普通年金）,(第1年年初 的先付年金),相等现金流,(第2年年初 的先付年金),(第3年年初 的先付年金),(第2年年末 的普通年金）,(第3年年末 的普通年金）,若视第1年末为现值时刻，则红年金为先付年金; 若视第2年末为终值时刻，则青年金为后付年金 !,假定终值：,94,对于任何年金，都可以 直接 查普通年金因子表 or 套普通年金公式，求其现值或终值，但须注意：求到的现值或终值 在时间轴上的位置，即，所在的时刻 求到的终值在最后一笔年金所在的时刻，求到的现值在第一笔年金所在时刻的前1时刻。,年金计算之要点,95,FVA n = R(1+r)n-1 + R(1+r)n-2 + . . . + R(1+r)1 + R(1+r)0 = R(1+r)n 1/r = RFVIFA r,n = RFVIF r,n 1/r,普通年金 于第 n年末的 终值 FVA(n),0 1 2 n,r,FVA n,R：每年现金流,年末,. . .,年末,?,96,FVA3 = $1,000 (1.07)2 + $1k (1.07)1 + $1k (1.07)0 = $1,145 + $1,070 + $1,000 = $3,215,普通年金终值 - FVA例,$1,000 $1,000 $1,000,0 1 2 3,$3,215 = FVA3,年末,7%,$1,070,$1,145,年末,97,FVA n = R (FVIFA r,n) FVA3 = $1,000 (FVIFA7%,3) = $1,000 (3.215) = $3,215,查普通年金终值表计算,98,FVAD n = R(1+r)n + R(1+r)n-1 + . + R(1+r)2 + R(1+r)1 = FVA n (1+r) = FVA n+1 - R,先付年金 FVAD（Due）,R R R,1 2 n,FVAD n,R: 每年现金流,年初,r,. . .,年初,年末,0 1 n-1 n,年末,年末,年初,年末,现在：,99,FVAD3 = $1,000 (1.07)3 + $1k (1.07)2 + $1k (1.07)1 = $1,225 + $1,145 + $1,070 = $3,440,先付年金 - FVAD例,$1,000 $1,000 $1,000 $1,070,0 1 2 3,FVAD3 = $3,440,年末,7%,$1,225,$1,145,1 2 3,年初,年初,年初,年末,年末,年末,现在：,100,FVAD n = R (FVIFA