揭秘著名基金橡树资本(Oaktree Capital)的投资策略：在“垃圾”中淘金(一)
揭秘著名基金橡树资本（Oaktree Capital）的投资策略：在“垃圾”中淘金（一）橡树资本在纽交所上市，再度揭开了受压资产策略基金的神秘面纱。
其上市文件中的描述可为外界解读受压资产策略的本质——“疲弱的经济环境给我们带来最好的投资机会和最好的投资表现。
比如，我们的高收益债券策略在经济低谷时违约率最高，投资表现也最佳；受压债券策略和控制权投资策略从历史数据来看，也是在经济下滑时投资机会最多”。
正是凭借这种投资策略，橡树资本的资产管理规模得以逆势膨胀。
同样身为受压资产策略基金的阿波罗，在其上市文件中也公告了5条投资哲学：别人的砒霜，我们的蜜糖；交易结构复杂，帮助困境公司脱困；经济收缩、金融市场下滑时，别人收缩战线，我们招兵买马；别人是结伴而行，我们是独行侠；我们获得公司的控制权，并理解复杂的法律条款。
进一步分析橡树资本操盘或介入的案例，可以为中国市场提供参照样本。
我们看到，有些申请破产保护的公司通过再次IPO得以重生，回到公众视野，如德尔福和Aleris；有些在其资产被各种层级的债权人瓜分之后以清算告终，如Finova；有些经历了惊心动魄的控制权之争，企业资产的控制权在股东和债权人之间不断摇摆，最终还是摆向债权人，如DYN。
??本刊主笔??文芳/文2012年4月，橡树资本（Oaktree Capital，OAK.NYSE）登陆纽交所，成为继阿波罗（Apollo，APO.NYSE）于2011年4月走入公众视野后，全球第二家上市的受压资产策略基金（distressed strategy）。
这也让我们能够借由公开资料更为深入地研究受压资产策略基金的操作手法。
受压资产策略其实就是如何捡便宜货。
正如橡树资本CEO霍华德·马克斯（Howard Marks）所言，“我们打算用50美分收购1美元的资产。
如果你想拣便宜，只有到垃圾堆去找了”。
马克所言的垃圾堆就是受压的上市公司。
危机发生之际，正是受压资产策略基金大展拳脚之时。
2000年前后的互联网泡沫、2008年全面爆发的美国次贷危机及2011年集中爆发的欧债危机，都将上市公司破产数量和破产申请的资产总额推向新高（图1）。
危机的频频发生，让橡树资本这样的受压资产策略基金得以快速增长（图2）。
而深入分析这些投资案例，可以更清晰地领略受压资产基金在危机中的获利手法。
具体说来，针对上市公司的受压资产策略，在美国已经形成三种子策略：第一种是Long-only ，即买入受压公司的拆分股份或者受压上市公司的债券或债务；第二种是配对交易，做多受压公司债券，同时做空受压公司股票，可以在二级市场上进行操作；第三种是PE 路径，通过收购债权或股权获得公司控制权，进行债务重组和资产重整，再通过重新IPO 、出售或清算的方式退出（表1）。
在这三种策略中，第一种和第二种策略无需获得公司控制权，除上市公司的银行贷款和贸易求偿权，其他品种均可在二级市场上进行操作；而第三种策略则是以获得公司控制权为核心，介乎一级市场和二级市场之间。
第二种策略的投资逻辑在于：如果受压公司前景堪忧，那么其股票价格要比债券跌幅更大，因为债券持有人的受偿层级高于股东，在资不抵债的情况下，股东可能一分钱也收不到；如果受压公司前景好转，债券价格的上涨幅度高于股票，这种策略稳赚股价和债券价格变化之间的差价。
本文中所涉及的案例围绕第三种策略展开。
在大洋彼岸的中国，2012年开始，垃圾债的推出，债券市场的逐步发展，使得受压资产策略在中国的运用渐行渐近。
深入分析海外受压资产策略基金的操作手法，无疑可为中国资本市场提供有价值的借鉴。
DYN的另类破产案：J因素压倒一切母公司DYN是上市公司，子公司DH是主要破产实体。
在DYN陷入困境之际，伊坎通过股权争夺，获得对DYN股权的实际控制权；而橡树资本协同艾威基金，切入DH和DYN 的债券，企图获得DYN旗下资产的控制权。
然而，伊坎通过错综复杂的程序，将占总装机容量27.38%的火电资产，以低于公允价值的价格从破产实体中转移至上市公司DYN，做出有利于伊坎等DYN股东但侵害艾威、橡树等DH债券投资人的安排。
但是，不管伊坎和橡树多么精明，最终都屈服在法官意志之下。
橡树和艾威恰恰利用了法官意志对资产产权归属的决定性影响，也即J因素，发起诉讼保卫自身权益：法院撤销资产转移行为，则重新回到保护破产实体债权人的传统老路，这无疑对橡树资本构成实质性利好。
美国第三大电力供应商Dynegy（Dynegy Inc.，全文简称“DYN”）破产案，集万千瞩目于一身，号称“企业掠夺者”的亿万富翁卡尔·伊坎（Carl C. Icahn）、受压资产策略的对冲基金艾威（Avenue Capital）和橡树资本、PE老大黑石（BlackStone）均身陷其中。
除了资本巨头对其股权的争夺、股东和债权人对其资产的控制权之争外，此案备受关注的原因更是包括J因素对受压资产投资的决定性冲击。
所谓J因素（J factor），即指法官（Judge）判决对受压资产控制人（股东或债权人）的影响。
除了至关重要的流动性风险，J因素是受压资产策略独一无二的风险所在。
法官将在债权人和股东利益中倾向哪一方、法官是否会撤销某笔交易、法官是否会认可并批准债务重组及重整计划等，无不深刻影响着受压资产的投资价值和投资策略。
破产前的安排：火电资产控制权从债权人转移至股东随着经济衰退以及天然气产量增加导致能源价格下调，DYN陷入困境。
因电价低迷以及信贷市场紧缩而受到损害，2009年其收入仅为24.68亿美元，同比下降25.75%，亏损12.47亿美元。
其股价也在2008年6月之后大幅下挫。
2011年3月10日，DYN表示，如果2011年无法达到其债权人的特定盈利要求，可能被迫申请破产保护。
黑石、伊坎争夺控制权2010年8月以来，陷入困境的DYN成了资本大鳄争夺的对象，一开始是黑石和伊坎对决。
2010年8月13日，黑石子公司与DYN签署收购协议，对价为4.5美元/股，全部以现金支付。
同年三季度，伊坎以迅雷不及掩耳之势，通过旗下5只基金（High River、Icahn Partners、Icahn Master、Icahn Master II、Icahn Master III），在公开市场买入DYN的普通股，购入价在2.9-4.87美元/股之间（表1）。
2010年11月16日，黑石不得不将收购对价提高至5美元/股，但其提案在2010年11月23日召开的DYN特别股东大会上，并未获得通过。
双方终止了收购协议，并达成附加条款：自2010年11月23日起的18个月内，如果第三方收购DYN的价格超过4.5美元/股，DYN将向黑石支付1600万美元终止费。
黑石收购协议终止后，DYN不断接触有收购意向的投资者，包括伊坎。
2010年12月15日，DYN董事会通过伊坎旗下基金与DYN的收购协议。
2010年12月22日，伊坎向所有普通股股东发起5.5美元/股的收购要约，但由于当时的二股东Seneca极力反对而未果。
2011年2月18日，该收购协议期限届满自动终止。
伊坎也签署了以下附加条款：自2011年2月18日的18个月内，如果第三方收购DYN的价格超过5.5美元/股，DYN将向伊坎支付500万美元的终止费（图1）。
在如火如荼的股权争夺战中，DYN子公司Dynegy控股（下称“DH”）遭到降级。
截至2011年4月19日，伊坎是DYN的最大单一股东，持股比例为14.8%，第二大股东是Seneca，持股9.2%，Habrok持有5.6%，贝莱德基金（BlackRock）持有4.7%。
2011年4月，在伊坎的主导下，DYN开始着手通过破产前的重组去杠杆化、削减债务。
在重组完成前，原有投资者进行了增持，也引入了新的投资人。
2011年9月30日，富兰克林坦伯顿投资（Franklin Templeton Investments）成为第二大股东，持股10.5%；而其他股东也在增持DYN的普通股，如Seneca于2011年8月22日和23日进行增持，持股比例增至9.9%。
债券投资人入驻DYN2011年3月，DH的标普信用评级降级为CC，穆迪评级降为Caa1和Caa3。
这也是穆迪自2009年以来第四次将其降级。
随着信用评级的下降，不得投资于“投资级别”以下的机构投资者只能抛售DH债券，其债券价格下跌无法避免，外部的债券投资人大举买入DH发行在外的债券。
据后来破产文件披露的数据，2011年9月底，破产实体的总负债为61.81亿美元，其中发行在外的债券为35.7亿美元（表2），这些债券的所有者大部分已经转手给专门投资受压债券的投资者。
据艾威基金和橡树资本等债券投资人2011年9月21日所出具的起诉书，艾威基金通过旗下4只基金，持有2016年、2018年、2019年和2026年到期的DH债券，橡树资本通过旗下高收益债券基金持有2015年到期的DH债券，通过另外5只基金持有2015年、2016年、2018年、2019年和2026年到期的DH债券。
但是，DYN股东和DH债权人的立场是对立的。
精明如艾威基金和橡树资本，如果遇到强盗逻辑的伊坎，胜算概率也会下降。
错综复杂的资产转移没有收购成功的伊坎，没有坐以待毙。
在2011年11月7日DH申请破产保护之前，伊坎做了三件事：于2011年4月着手财务重组，8月将DH旗下的两家火电厂CoalCo转移给母公司DYN，这一转移过程于2011年9月1日全面完成；促使DH及其4家子公司于2011年11月7日申请破产保护（虽然破产保护时由DH自愿申请，但伊坎作为DYN的实际控制人，自然也可以控制DH申请破产保护）；在破产方式上，债权人减记10%的债权，而由股东全力控制公司。
在2011年8月5日的财务重组前，煤电资产部门Dynegy中西部公司为DH的下属公司（图2）。
伊坎随即进行了五步重组，将火电资产从DH转移到DYN。
第一步：创建壳公司新创建的DGI是一个壳公司，无债权人。
在组织架构上，设置了天然气和火电两大部门。
重组前的Dynegy电力公司后改为GasCo（图3）。
第二步：整合天然气资产通过一系列的股权转让，将三处天然气资产（即Sithe天然气发电厂、Kendall天然气发电厂和Ontelauee天然气发电厂）整合在一起。
DH将Sithe转让给Dynegy电力销售公司，Dynegy电力销售公司随后又将Sithe转让给Dynegy电力公司；Dynegy中西部发电厂将Kendall能源公司转让给Dynegy电力公司；Dynegy电力销售公司将Ontelauee发电厂转让给Dynegy电力公司（即GasCo）（图4）。
第三步：剥离Roseton和Danskammer两个电厂Dynegy西北公司下辖Roseton和Danskammer两个电厂，GasCo将Dynegy东北公司转让给Dynegy电力销售公司，后者随后又将东北公司转让给DH（图5）。
谁说站在光里的才算英雄议论文
谁说站在光里的才算英雄议论文“谁说站在光里的才算英雄？从巴菲特超越木头姐说起……”慢就是快，快就是慢。
这句在投资上似乎相悖的话，近期又得到了验证。
慢就是快，快就是慢。
这句在投资上似乎相悖的话，近期又得到了验证。
进入2022年以来，随着全球市场的剧烈调整，很多投资人蓦然发现，前几年如日中天的“科技股女神”木头姐，近期已经被股神巴菲特悄然超越。
从2020年以来的业绩表现看，截至今年2月18日，股神巴菲特掌舵的伯克希尔·哈撒韦(BRK_A)上涨了39.07%，木头姐(Catherine Wood)的旗舰产品Ark Innovation ETF上涨了32.63%。
木头姐何许人也？这个声称“只投资颠覆性创新”的投资人，在2020年因大举押注特拉斯汽车等科技股一战成名，全年收益率超过150%，受到全球投资者的关注。
与之相对应的是，股神巴菲特2020年表现“乏味”，全年收益率仅有两个多百分点。
不过，从2021年以来，木头姐和巴菲特的业绩表现迥异。
木头姐的旗舰基金在短暂冲高后调头向下，同最高点相比，如今已经处于腰斩状态；“股神”巴菲特则稳步向上，2021年以来股价上涨了35%左右。
涨跌的相向而行，让巴菲特超越了木头姐。
在短短两年多时间内，一度豪赚两倍多风头很劲的木头姐，被看似“乏味”的巴菲特超越了，还是让很多投资人为之震惊。
在木头姐创立的ARK Invest公司的官网上，首页就是投资理念：我们只投资颠覆性创新的公司。
对于股神巴菲特来说，他更愿意投资不被世界颠覆的公司，时时不忘护城河。
在《成为沃伦·巴菲特》的那部传奇纪录片里，面对“在投资中最看重哪项指标”的问题，巴菲特脱口而出：我会寻找周围有护城河的公司。
在陈奕迅去年底推出的新歌《孤勇者》里，歌颂了孤身走暗巷的孤勇者。
去吗？去啊！以最卑微的梦战吗？战啊！以最孤高的梦致那黑夜中的呜咽与怒吼谁说站在光里的才算英雄这种激昂的歌声，让人为之振奋。
对于很多投资者来说，更愿意追捧短期业绩，但却缺乏对投资标的的基本理解。
橡树资本：逐利非有效市场
证券投资的经典案例
证券投资的经典案例证券投资的经典案例之一是沃伦·巴菲特的伯克希尔·哈撒韦公司（Berkshire Hathaway）投资案例。
伯克希尔·哈撒韦公司是由美国著名投资家沃伦·巴菲特创立的一家投资管理公司，以其独特的投资理念和卓越的资本配置能力而闻名。
以下是该公司的几个重要投资案例：1. 古德里奇公司（Geico）：这是伯克希尔·哈撒韦公司早期的一次成功投资。
1976年，巴菲特花费了4,600万美元以一股价10美元的价格买入了Geico的大部分股份。
随着时间的推移，Geico公司逐渐成为美国最大的汽车保险公司之一，伯克希尔的投资获得了极高的回报。
2. 可口可乐公司（Coca-Cola）：伯克希尔·哈撒韦公司在1988年开始投资可口可乐公司的股票，并逐渐增加了股份。
随着可口可乐公司的不断发展壮大，伯克希尔·哈撒韦公司的投资回报率也不断增长。
这个案例显示了巴菲特长期稳定持有股票的投资策略的成功。
3. 苹果公司（Apple）：伯克希尔·哈撒韦公司在2016年开始购买苹果公司的股票，并在2018年成为其第三大股东。
这个投资案例表明巴菲特对苹果公司的长期价值和潜力保持了极高的认可，也显示了他对科技公司的看好态度。
4. 美国运通公司（American Express）：伯克希尔公司在1964年首次投资美国运通公司，并成为其最大的股东之一。
巴菲特对美国运通公司的长期持有和信赖帮助了公司度过了几个不利时期，并获得了巨大回报。
这些经典投资案例展示了伯克希尔·哈撒韦公司成功的投资策略和巴菲特对长期投资的坚定信念。
他以价值投资和寻找优质股票为主导，避免了短期市场波动对投资决策的影响。
此外，这些案例也揭示了投资决策背后的深入研究和对公司基本面的分析，以及对市场趋势和行业变化的敏锐洞察。
然而，需要指出的是，以上案例并不是投资中的常态，投资者需要在全面了解市场风险和自身投资能力的基础上，制定适合自己的投资策略。
esg的影响的案例分析
esg的影响的案例分析2月16日，奇点财经曾转述香港《信报》报道，强制性公积金计划管理局(以下简称积金局)建议就道富环球投资管理亚洲有限公司（简称SSGA）是否适合作为盈富基金管理人的适当性进行评估。
这一事件体现积金局对SSGA在ESG决策方面的重视。
近年来，随着ESG理念越来越深入人心，不少国际资产管理公司都提出ESG投资理念。
究竟香港有哪些ESG资管公司？从本期开始，奇点财经ESG研究团队将会就国际上重要的ESG投资机构进行不定期的系列报道和介绍，供对ESG投资有兴趣的读者参考。
富达成立于1969年，是1946年在美国波士顿创立的Fidelity Investments旗下的国际公司。
在1980年，富达脱离美国母公司独立经营。
现时，富达的股权主要由管理层和创始家族成员持有。
截至2020年3月31日富达在全球管理的资产达3,710亿美元，客户遍布亚太区、欧洲、中东和南美洲25个国家，其服务的客户包括中央银行、主权财富基金、大型机构、金融企业、保险公司、财富管理公司及个人投资者。
除资产管理外，富达亦在多个国家为雇主福利计划、投资顾问和个人客户提供投资行政管理及指引服务。
富达的ESG投资富达已在官网开设了独立的ESG板块，并详细阐述了其对ESG 的理解，ESG投资策略和公司自身的ESG状况。
富达对于ESG的理解富达认为：ESG（环境、社会和企业管治）投资是指在做出投资决定的过程中，除了考虑财务因素外，亦同时纳入ESG因素。
可持续投资、社会责任投资、道德投资和影响力投资等不同名称，都是ESG投资的一部份。
富达认为ESG因素涵盖极为广泛的议题，如由避免投资于烟草公司，以至为洁净食水项目提供融资都属于ESG范畴。
具体到ESG的每一项目，富达认为：（1）E包括气候变化、温室气体排放、资源耗尽，包括水资源、废物及污染和伐林等；（2）S包括工作环境（包括奴役及童工）、当地社区（包括原住民社区）、宗教冲突、健康及安全和雇佣关系及多元性等；（3）G包括行政人员薪酬、贿赂及贪腐、政治游说及捐款、董事会多元性及架构和税务策略等。
《大空头》观后感
《大空头》观后感最近看了《大空头》这部电影，感触颇深呐！影片里那一群独具慧眼的投资者，在看似繁荣的金融市场中，愣是看出了即将崩塌的危机，这真不是一般人能做到的。
让我印象特别深刻的是主角们那种敏锐的洞察力和坚定的决心。
在所有人都沉浸在虚假的繁荣里，盲目地相信房价会一直涨涨涨的时候，他们几个却能静下心来，分析那些被大家忽略的细节。
就比如说，有个情节是他们去实地考察那些发放房贷的情况。
他们发现，很多人根本没有稳定的收入，甚至有些连工作都没有，却能轻而易举地拿到高额房贷去买房。
这简直太荒唐了！那些贷款的文件，随便填填就能通过，银行根本就不怎么审查。
还有那些所谓的金融评级机构，也是一塌糊涂。
明明一些垃圾债券，却被评成了优质资产。
这就好像把一堆烂苹果贴上了“特级水果”的标签，然后卖给那些毫不知情的投资者。
电影里有个场景，主角之一去参加一个金融界的派对。
周围的人都在欢呼雀跃，为赚得盆满钵满而举杯庆祝。
可他却在角落里，一脸忧虑。
因为他清楚地看到，这表面的繁荣就像泡沫，一戳就破。
想想咱们现实生活中，也经常会遇到这样的情况。
有时候大家都在追捧某个东西，觉得那是个绝佳的机会，可往往很少有人会真正去深入研究，看看是不是真的那么靠谱。
就像前几年，好多人跟风去投资各种虚拟货币，一开始确实有些人赚了钱，然后消息一传开，越来越多的人涌入。
可最后呢？很多人亏得血本无归。
他们根本就没搞清楚这背后的原理和风险，只是盲目地跟着大流走。
再回到电影里，那些大空头们面对的压力可不小。
周围的人都觉得他们是疯子，放着好好的钱不赚，非要去唱衰市场。
他们不仅要承受巨大的资金压力，还要面对外界的质疑和嘲笑。
但是，他们没有放弃。
他们坚信自己的判断，一直坚持到最后。
当金融危机真的爆发，那些曾经嘲笑他们的人都傻了眼，而他们却成功地赚了大钱。
不过，这部电影也不是单纯地在讲怎么赚钱。
它让我思考了很多关于人性、贪婪和盲目跟风的问题。
在利益面前，很多人都会失去理智，只看到眼前的好处，却忽略了潜在的风险。
《交易思维：价值投资背后的战役》札记
《交易思维：价值投资背后的战役》读书笔记目录一、内容描述 (3)1.1 书籍背景与目的 (4)1.2 价值投资概述 (5)二、交易思维的基础 (5)2.1 交易的本质 (6)2.2 价值投资的理念 (7)2.3 交易思维与价值投资的关联 (8)三、价值投资的关键要素 (9)3.1 企业分析 (11)3.1.1 行业分析 (12)3.1.2 公司分析 (13)3.2 价格评估 (14)3.2.1 市场价格 (15)3.2.2 内在价值 (17)3.3 投资策略 (18)3.3.1 长期投资 (19)3.3.2 短期交易 (21)四、交易思维在价值投资中的应用 (22)4.1 战略性投资 (23)4.1.1 控股收购 (25)4.1.2 资产配置 (26)4.2 战术性交易 (28)4.2.1 价格波动交易 (29)4.2.2 技术分析 (31)五、交易思维的挑战与应对 (32)5.1 市场波动 (33)5.1.1 市场风险 (35)5.1.2 市场机会 (36)5.2 信息不对称 (37)5.2.1 信息收集 (38)5.2.2 信息处理 (40)六、交易思维的培养与提升 (41)6.1 学习与实践 (43)6.2 心理素质 (44)6.3 持续改进 (45)七、结语 (46)7.1 交易思维的价值 (47)7.2 价值投资的发展前景 (48)一、内容描述《交易思维：价值投资背后的战役》是一本深入探讨价值投资理念与实践相结合的书籍。
本书从全新的视角出发，将交易视为一种思维方式，详细阐述了价值投资背后的战略与战术。
书中首先对价值投资进行了定义，指出它不仅仅是一种投资策略，更是一种关于如何发现、评估并利用企业内在价值的方法论。
通过这一定义，作者引导读者进入价值投资的殿堂，了解其核心原则和关键要素。
在内容安排上，本书采用了循序渐进的方式。
介绍了价值投资的基本概念和原理，帮助读者建立起对该投资方法的基本认识；接着，通过丰富的案例分析，展示了众多投资者在实际操作中如何运用价值投资策略取得成功；结合当前的市场环境，对价值投资策略进行了深入的反思与展望，为读者提供了新的思考角度和投资建议。
国际著名工程公司简介
垄项目。 •风力収申 仅 1980 年廹始 COWI 涉足风能颀域，幵丏参不了许多风力収申项目，总裃机容量超迆几 千兆瓦；仅卑独风力収申机系统，到风力柴油収申复合系统，直至大垄风力収申机制造厂， 涉及的项目十分广泌，为私人投资者、政店、以及陆上戒海上风申的供应商和承包商的各 种项目提供了与业的服务。 •石油和天然气 COWI 为石油天然气行业提供与业的和多学科综合的服务，服务范围包括海上和陆上的油 田廹収、设备巟程及平台拆除。关他仸何行业的波劢都丌如石油天然气行业剧烈。丌断波 劢的油价要求操作者、权姕机杴和承包商兴有持续的适应能力。自仅上丧丐纨 60 年代， COWI 就廹始帮劣宠户应对这丧持续发化市场的挅戓。所以，圃石油天然气行业的各丧斱 面都可提供与业的多学科综合的服务。 ★ 水和环境
丹麦 COWI 公司
COWI 是丹麦一家颀兇的国际咨询公叵。创立二 1930 年，至仂工圃全球 175 丧国家迈 作了 50,000 多丧项目。COWI 圃全球有 4500 名雇员，包括巟程帅、生物学家、地质学 家、绉济学家、测量学家、人类学家、社伕学家和廸筑帅。COWI 颀导着一部分全球最大 的基础设斲巟程项目。COWI 公叵设有 9 丧部门，圃 35 丧国家有分公叵和办亊处，所有 国家的项目办公客都是自巤管理的。关丨最大的一家海外子公叵圃挪姕，约有 700 名员巟。 COWI 公叵绉营管理层讣为，国际市场不丹麦本圁同样重要。 COWI 公叵圃巟程、环境及社伕绉济三丧颀域提供多学科的咨询服务，仅对兴体项目的与 业咨询到综合觃划以及对大垄巟程迚行包括监理、迈营维护等典容圃典的整体设计服务。 桥梁巟程是该公叵的一项核心业务，公叵参不了丹麦及丐甸上许多大桥的设计监理巟作， 著名桥梁有：丹麦大贝尔特通道主跨为 1624 米长的悬索桥，厄勒海峡通道的引桥和主跨 为 490 米长的公路铁路两用斜拉桥、香港昂船洲大桥、智利查考海峡大桥、泋国诹曼底大 桥等。 2000 年 5 月公叵确定了新的収屍目标。收贩了徇国铁路咨询公叵 ETC 和丹麦著名的咨询 集团 Kampsax，吐实现公叵的新目标更迈迚了一步。公叵对未来的屍望是：要成为北欧 颀兇的、多学科咨询公叵，幵圃提供某互与业咨询服务斱面成为国际市场的颀导者。 COWI 公叵圃云洲（包括丨国）、欧洲、丨东、非洲和美洲等许多国家拞有帯设分支机杴 和附屎办亊处。2007 年的营业额约达到 4 亿欧元，使关圃北欧继续俅持着颀兇的咨询公 叵之一的地位，幵成为丐甸上这三丧与业颀域的行业颀兇者。这充分证明了 COWI 圃以下 颀域典提供的咨询服务兴有丐甸级水准： ★ 巟业不能源 圃巟业化国家，能源是基础设斲廸设丨的重要部分，征多居民和机杴都依赖二能源供应结 杴，幵丏叐到它的影响。COWI 积杳致力二能源廹収颀域，幵丏满足绉济和环境可持续収 屍的要求。关丨包括气候发化、能敁提高、风力収申、石油和天然气等。 •气候发化 气候发化工绉成为全球人类兯同体最大的环境挅戓。气候发化的挅戓圃丐甸范围典影响着 政店资劣的企亊业以及私营部门。通迆联合国气候发化框架公约理亊伕，气候发化大伕以 及《亪都讧定乢》的签订生敁，国际以及各国均兇后对政答、绉济、金融以及制庙影响做 出应对政答。为了达到《亪都讧定乢》丨所仃终的兰二清洁収屍机制环境挃标的要求， COWI 圃相兰清洁収屍机制项目斱面提供了技术支持不咨询服务。COWI 员巟对《联合国 气候发化框架公约》及《亪都讧定乢》相兰的政答泋觃斱面拞有敂锐的洞察力。为政店部 门实斲国际谈判之后的结果提供了详实的分杵报告。同旪也帮劣他们设计和诂估了相兰政 答和斱泋以及相兰制庙的廸立。 •能敁提高 COWI 圃全球参不了伒多的能源巟程和能源觃划项目，多年为丹麦能源部门提供觃划和収 屍的咨询服务。而丏，由二拞有多与业的咨询团队，可提供对环境产生最小影响的设计斱 案。COWI 的服务包括能源诂估研究、总体觃划和全系统的巟程设计。另外，项目管理、 巟程监理、项目试迈行及关后续巟程咨询均为服务范围。项目既包括小垄项目，也包括大
NetCapitalExpenditures：净资本支出
- Amortization of R&D
= $ 485 mil
+ Acquisitions
= $ 2,516 mil
Adjusted Net Capital Expenditures
= $3,723 mil
(Amortization was included in the depreciation number)
7.04%
8.23%
Aswath Damodaran
120
Dividends and Cash Flows to Equity
In the strictest sense, the only cash flow that an investor will receive from an equity investment in a publicly traded firm is the dividend that will be paid on the stock.
In general, the net capital expenditures will be a function of how fast a firm is growing or expecting to grow. High growth firms will have much higher net capital expenditures than low growth firms.
• managers like to hold on to cash to meet unforeseen future contingencies and
investment opportunities
When actual dividends are less than potential dividends, using a model that focuses only on dividends will under state the true value of the equity in a firm.
华尔街之狼
华尔街之狼J.P.摩根“了不起的金融妖怪”1853年J.P.摩根跟随父亲到伦敦拜会银行家乔治.皮博迪，成为皮博迪合伙人，从此走上世界金融舞台。
1858年J.P.摩根购买了生平第一只股票，并做了咖啡生意。
1861年J.P.摩根买卖武器、操纵黄金1863年25岁的J.P.摩根真正登上世界金融舞台中心。
1869年J.P.摩根与杰伊.古尔德围绕一条铁路爆发了一场震惊美国的争分。
1871年J.P.摩根重挫“白须帝王”杰伊.库克。
1884年美国铁路界发生了一场激烈冲突。
J.P.摩根经谈判使“海盗号”协议获得通过。
1893年十年一遇的金融恐慌如期而至。
J.P.摩根挑起重任，危机缓解。
1901年J.P.摩根将钢铁大王卡内基的公司收入囊中。
1902年J.P.摩根受到来自总统的攻击。
1907年纽约证券交易所一片混乱，人们争先抛售手中股票，J.P.摩根在两周时间里，每天工作19小时，顶住了这股破产狂风。
1913年J.P.摩根在高烧中与世长眠。
杰克.摩根接手管理。
1920年摩根银行发生爆炸事件，摩根财团的过分强大引起了美国社会的惶恐。
1933年律师佩科拉对摩根财团提出指控，将摩根财团拉下神坛。
罗斯福总统签订了《1933年银行法》导致摩根公司正式分家。
本杰明?格雷厄姆“华尔街教父”股市总是非常宣泄，各种小道消息满天飞，一会有人说某某股票涨了，一会有人说某某股票跌了，人们几乎无时不刻地关注股价，频繁抛售、买进、再抛售，如此循环往复。
然而一个稳健、成熟的投资者，是对那些富有成长性的公司长线持股。
格雷厄姆的童年经历让他对股市风云的特质深深扎根心头，他的后半生都将在股市中度过。
格雷厄姆大学毕业后踏入华尔街，他开始的工作并非让他满意，工作一段时间后，他做了证券分析员，小试牛刀取得了成功，渐渐在华尔街小有名声。
然而1916年秋天，华尔街进入“和平恐慌”时期，几乎所有的股票都一路狂跌，格雷厄姆操作的所有证券也随之下跌，他受到了人生中的第一次沉重打击，但两年后随着股市回暖，他因祸得福。
《金融学》答案第四章 货币的时间价值与现金流贴现分析
CHAPTER 4THE TIME VALUE OF MONEY AND DISCOUNTED CASH FLOW ANALYSISObjectives∙To explain the concepts of compounding and discounting, future value and present value.∙To show how these concepts are applied to making financial decisions.Outline4.1Compounding4.2The Frequency of Compounding4.3Present Value and Discounting4.4Alternative Discounted Cash Flow Decision Rules4.5Multiple Cash Flows4.6Annuities4.7Perpetual Annuities4.8Loan Amortization4.9Exchange Rates and Time Value of Money4.10Inflation and Discounted Cash Flow Analysis4.11Taxes and Investment DecisionsSummary∙Compounding is the process of going from present value (PV) to future value (FV). The future value of $1 earning interest at rate i per period for n periods is (1+i)n.∙Discounting is finding the present value of some future amount. The present value of $1 discounted at rate i per period for n periods is 1/(1+i)n.∙One can make financial decisions by comparing the present values of streams of expected future cash flows resulting from alternative courses of action. The present value of cash inflows less the present value of cash outflows is called net present value (NPV). If a course of action has a positive NPV, it is worth undertaking.∙In any time value of money calculation, the cash flows and the interest rate must be denominated in the same currency.∙Never use a nominal interest rate when discounting real cash flows or a real interest rate when discounting nominal cash flows.How to Do TVM Calculations in MS ExcelAssume you have the following cash flows set up in a spreadsheet:A B1t CF20-1003150426053706NPV7IRRMove the cursor to cell B6 in the spreadsheet. Click the function wizard f x in the tool bar and when a menu appears, select financial and then NPV. Then follow the instructions for inputting the discount rate and cash flows. You can input the column of cash flows by selecting and moving it with your mouse. Ultimately cell B6should contain the following:=NPV(0.1,B3:B5)+B2The first variable in parenthesis is the discount rate. Make sure to input the discount rate as a decimal fraction (i.e., 10% is .1). Note that the NPV function in Excel treats the cash flows as occurring at the end of each period, and therefore the initial cash flow of 100 in cell B2 is added after the closing parenthesis. When you hit the ENTER key, the result should be $47.63.Now move the cursor to cell B7to compute IRR. This time select IRR from the list of financial functions appearing in the menu. Ultimately cell B7 should contain the following:=IRR(B2:B5)When you hit the ENTER key, the result should be 34%.Your spreadsheet should look like this when you have finished:A B1t CF20-1003150426053706NPV47.637IRR34%Solutions to Problems at End of Chapter1.If you invest $1000 today at an interest rate of 10% per year, how much will you have 20 years from now,assuming no withdrawals in the interim?2. a. If you invest $100 every year for the next 20 years, starting one year from today and you earninterest of 10% per year, how much will you have at the end of the 20 years?b.How much must you invest each year if you want to have $50,000 at the end of the 20 years?3.What is the present value of the following cash flows at an interest rate of 10% per year?a.$100 received five years from now.b.$100 received 60 years from now.c.$100 received each year beginning one year from now and ending 10 years from now.d.$100 received each year for 10 years beginning now.e.$100 each year beginning one year from now and continuing forever.e.PV = $100 = $1,000.104.You want to establish a “wasting” fund which will provide you with $1000 per year for four years, at which time the fund will be exhausted. How much must you put in the fund now if you can earn 10% interest per year?SOLUTION:5.You take a one-year installment loan of $1000 at an interest rate of 12% per year (1% per month) to be repaid in 12 equal monthly payments.a.What is the monthly payment?b.What is the total amount of interest paid over the 12-month term of the loan?SOLUTION:b. 12 x $88.85 - $1,000 = $66.206.You are taking out a $100,000 mortgage loan to be repaid over 25 years in 300 monthly payments.a.If the interest rate is 16% per year what is the amount of the monthly payment?b.If you can only afford to pay $1000 per month, how large a loan could you take?c.If you can afford to pay $1500 per month and need to borrow $100,000, how many months would it taketo pay off the mortgage?d.If you can pay $1500 per month, need to borrow $100,000, and want a 25 year mortgage, what is thehighest interest rate you can pay?SOLUTION:a.Note: Do not round off the interest rate when computing the monthly rate or you will not get the same answerreported here. Divide 16 by 12 and then press the i key.b.Note: You must input PMT and PV with opposite signs.c.Note: You must input PMT and PV with opposite signs.7.In 1626 Peter Minuit purchased Manhattan Island from the Native Americans for about $24 worth of trinkets. If the tribe had taken cash instead and invested it to earn 6% per year compounded annually, how much would the Indians have had in 1986, 360 years later?SOLUTION:8.You win a $1 million lottery which pays you $50,000 per year for 20 years, beginning one year from now. How much is your prize really worth assuming an interest rate of 8% per year?SOLUTION:9.Your great-aunt left you $20,000 when she died. You can invest the money to earn 12% per year. If you spend $3,540 per year out of this inheritance, how long will the money last?SOLUTION:10.You borrow $100,000 from a bank for 30 years at an APR of 10.5%. What is the monthly payment? If you must pay two points up front, meaning that you only get $98,000 from the bank, what is the true APR on the mortgage loan?SOLUTION:If you must pay 2 points up front, the bank is in effect lending you only $98,000. Keying in 98000 as PV and computing i, we get:11.Suppose that the mortgage loan described in question 10 is a one-year adjustable rate mortgage (ARM), which means that the 10.5% interest applies for only the first year. If the interest rate goes up to 12% in the second year of the loan, what will your new monthly payment be?SOLUTION:Step 2 is to compute the new monthly payment at an interest rate of 1% per month:12.You just received a gift of $500 from your grandmother and you are thinking about saving this money for graduation which is four years away. You have your choice between Bank A which is paying 7% for one-year deposits and Bank B which is paying 6% on one-year deposits. Each bank compounds interest annually. What is the future value of your savings one year from today if you save your money in Bank A? Bank B? Which is the better decision? What savings decision will most individuals make? What likely reaction will Bank B have? SOLUTION:$500 x (1.07) = $535Formula:$500 x (1.06) = $530a.You will decide to save your money in Bank A because you will have more money at the end of the year. Youmade an extra $5 because of your savings decision. That is an increase in value of 1%. Because interestcompounded only once per year and your money was left in the account for only one year, the increase in value is strictly due to the 1% difference in interest rates.b.Most individuals will make the same decision and eventually Bank B will have to raise its rates. However, it isalso possible that Bank A is paying a high rate just to attract depositors even though this rate is not profitable for the bank. Eventually Bank A will have to lower its rate to Bank B’s rate in order to make money.13.Sue Consultant has just been given a bonus of $2,500 by her employer. She is thinking about using the money to start saving for the future. She can invest to earn an annual rate of interest of 10%.a.According to the Rule of 72, approximately how long will it take for Sue to increase her wealth to $5,000?b.Exactly how long does it actually take?SOLUTION:a.According to the Rule of 72: n = 72/10 = 7.2 yearsIt will take approximately 7.2 years for Sue’s $2,500 to double to $5,000 at 10% interest.b.At 10% interestFormula:$2,500 x (1.10)n = $5,000Hence, (1.10)n = 2.0n log 1.10 = log 2.0n = .693147 = 7.27 Years.095310rry’s bank account has a “floating” interest rate on certain deposits. Every year the interest rate is adjusted. Larry deposited $20,000 three years ago, when interest rates were 7% (annual compounding). Last year the rate was only 6%, and this year the rate fell again to 5%. How much will be in his account at the end of this year?SOLUTION:$20,000 x 1.07 x 1.06 x 1.05 = $23,818.2015.You have your choice between investing in a bank savings account which pays 8% compounded annually (BankAnnual) and one which pays 7.5% compounded daily (BankDaily).a.Based on effective annual rates, which bank would you prefer?b.Suppose BankAnnual is only offering one-year Certificates of Deposit and if you withdraw your moneyearly you lose all interest. How would you evaluate this additional piece of information when making your decision?SOLUTION:a.Effective Annual Rate: BankAnnual = 8%.Effective Annual Rate BankDaily = [1 + .075]365 - 1 = .07788 = 7.788%365Based on effective annual rates, you would prefer BankAnnual (you will earn more money.)b.If BankAnnual’s 8% annual return is conditioned upon leaving the money in for one full year, I would need tobe sure that I did not need my money within the one year period. If I were unsure of when I might need the money, it might be safer to go for BankDaily. The option to withdraw my money whenever I might need it will cost me the potential difference in interest:FV (BankAnnual) = $1,000 x 1.08 = $1,080FV (BankDaily) = $1,000 x 1.07788 = $1,077.88Difference = $2.12.16.What are the effective annual rates of the following:a.12% APR compounded monthly?b.10% APR compounded annually?c.6% APR compounded daily?SOLUTION:Effective Annual Rate (EFF) = [1 + APR] m - 1ma.(1 + .12)12 - 1 = .1268 = 12.68%12b.(1 + .10)- 1 = .10 = 10%1c.(1 + .06)365 - 1 = .0618 = 6.18%36517.Harry promises that an investment in his firm will double in six years. Interest is assumed to be paid quarterly and reinvested. What effective annual yield does this represent?EAR=(1.029302)4-1=12.25%18.Suppose you know that you will need $2,500 two years from now in order to make a down payment on a car.a.BankOne is offering 4% interest (compounded annually) for two-year accounts, and BankTwo is offering4.5% (compounded annually) for two-year accounts. If you know you need $2,500 two years from today,how much will you need to invest in BankOne to reach your goal? Alternatively, how much will you need to invest in BankTwo? Which Bank account do you prefer?b.Now suppose you do not need the money for three years, how much will you need to deposit today inBankOne? BankTwo?SOLUTION:PV = $2,500= $2,311.39(1.04)2PV = $2,500= $2,289.32(1.045)2You would prefer BankTwo because you earn more; therefore, you can deposit fewer dollars today in order to reach your goal of $2,500 two years from today.b.PV = $2,500= $2,222.49(1.04)3PV = $2,500= $2,190.74(1.045)3Again, you would prefer BankTwo because you earn more; therefore, you can deposit fewer dollars today in order to reach your goal of $2,500 three years from today.19.Lucky Lynn has a choice between receiving $1,000 from her great-uncle one year from today or $900 from her great-aunt today. She believes she could invest the $900 at a one-year return of 12%.a.What is the future value of the gift from her great-uncle upon receipt? From her great-aunt?b.Which gift should she choose?c.How does your answer change if you believed she could invest the $900 from her great-aunt at only 10%?At what rate is she indifferent?SOLUTION:a. Future Value of gift from great-uncle is simply equal to what she will receive one year from today ($1000). Sheearns no interest as she doesn’t receive the money until next year.b. Future Value of gift from great-aunt: $900 x (1.12) = $1,008.c. She should choose the gift from her great-aunt because it has future value of $1008 one year from today. Thegift from her great-uncle has a future value of $1,000. This assumes that she will able to earn 12% interest on the $900 deposited at the bank today.d. If she could invest the money at only 10%, the future value of her investment from her great-aunt would only be$990: $900 x (1.10) = $990. Therefore she would choose the $1,000 one year from today. Lucky Lynn would be indifferent at an annual interest rate of 11.11%:$1000 = $900 or (1+i) = 1,000 = 1.1111(1+i)900i = .1111 = 11.11%20.As manager of short-term projects, you are trying to decide whether or not to invest in a short-term project that pays one cash flow of $1,000 one year from today. The total cost of the project is $950. Your alternative investment is to deposit the money in a one-year bank Certificate of Deposit which will pay 4% compounded annually.a.Assuming the cash flow of $1,000 is guaranteed (there is no risk you will not receive it) what would be alogical discount rate to use to determine the present value of the cash flows of the project?b.What is the present value of the project if you discount the cash flow at 4% per year? What is the netpresent value of that investment? Should you invest in the project?c.What would you do if the bank increases its quoted rate on one-year CDs to 5.5%?d.At what bank one-year CD rate would you be indifferent between the two investments?SOLUTION:a.Because alternative investments are earning 4%, a logical choice would be to discount the project’s cash flowsat 4%. This is because 4% can be considered as your opportunity cost for taking the project; hence, it is your cost of funds.b.Present Value of Project Cash Flows:PV = $1,000= $961.54(1.04)The net present value of the project = $961.54 - $950 (cost) = $11.54The net present value is positive so you should go ahead and invest in the project.c.If the bank increased its one-year CD rate to 5.5%, then the present value changes to:PV = $1,000= $947.87(1.055)Now the net present value is negative: $947.87 - $950 = - $2.13. Therefore you would not want to invest in the project.d.You would be indifferent between the two investments when the bank is paying the following one-year interestrate:$1,000 = $950 hence i = 5.26%(1+i)21.Calculate the net present value of the following cash flows: you invest $2,000 today and receive $200 one year from now, $800 two years from now, and $1,000 a year for 10 years starting four years from now. Assume that the interest rate is 8%.SOLUTION:Since there are a number of different cash flows, it is easiest to do this problem using cash flow keys on the calculator:22.Your cousin has asked for your advice on whether or not to buy a bond for $995 which will make one payment of $1,200 five years from today or invest in a local bank account.a.What is the internal rate of return on the bond’s cash flows? What additional information do you need tomake a choice?b.What advice would you give her if you learned the bank is paying 3.5% per year for five years(compounded annually?)c.How would your advice change if the bank were paying 5% annually for five years? If the price of thebond were $900 and the bank pays 5% annually?SOLUTION:a.$995 x (1+i)5 = $1,200.(1+i)5 = $1,200$995Take 5th root of both sides:(1+i) =1.0382i = .0382 = 3.82%In order to make a choice, you need to know what interest rate is being offered by the local bank.b.Upon learning that the bank is paying 3.5%, you would tell her to choose the bond because it is earning a higherrate of return of 3.82% .c.If the bank were paying 5% per year, you would tell her to deposit her money in the bank. She would earn ahigher rate of return.5.92% is higher than the rate the bank is paying (5%); hence, she should choose to buy the bond.23.You and your sister have just inherited $300 and a US savings bond from your great-grandfather who had left them in a safe deposit box. Because you are the oldest, you get to choose whether you want the cash or the bond. The bond has only four years left to maturity at which time it will pay the holder $500.a.If you took the $300 today and invested it at an interest rate 6% per year, how long (in years) would ittake for your $300 to grow to $500? (Hint: you want to solve for n or number of periods. Given these circumstances, which are you going to choose?b.Would your answer change if you could invest the $300 at 10% per year? At 15% per year? What otherDecision Rules could you use to analyze this decision?SOLUTION:a.$300 x (1.06)n = $500(1.06)n = 1.6667n log 1.06 = log 1.6667n = .510845 = 8.77 Years.0582689You would choose the bond because it will increase in value to $500 in 4 years. If you tookthe $300 today, it would take more than 8 years to grow to $500.b.You could also analyze this decision by computing the NPV of the bond investment at the different interest rates:In the calculations of the NPV, $300 can be considered your “cost” for acquiring the bond since you will give up $300 in cash by choosing the bond. Note that the first two interest rates give positive NPVs for the bond, i.e. you should go for the bond, while the last NPV is negative, hence choose the cash instead. These results confirm the previous method’s results.24.Suppose you have three personal loans outstanding to your friend Elizabeth. A payment of $1,000 is due today, a $500 payment is due one year from now and a $250 payment is due two years from now. You would like to consolidate the three loans into one, with 36 equal monthly payments, beginning one month from today. Assume the agreed interest rate is 8% (effective annual rate) per year.a.What is the annual percentage rate you will be paying?b.How large will the new monthly payment be?SOLUTION:a.To find the APR, you must first compute the monthly interest rate that corresponds to an effective annual rate of8% and then multiply it by 12:1.08 = (1+ i)12Take 12th root of both sides:1.006434 = 1+ ii = .006434 or .6434% per monthOr using the financial calculator:b.The method is to first compute the PV of the 3 loans and then compute a 36 month annuity payment with thesame PV. Most financial calculators have keys which allow you to enter several cash flows at once. This approach will give the user the PV of the 3 loans.Note: The APR used to discount the cash flows is the effective rate in this case, because this method is assuming annual compounding.25.As CEO of ToysRFun, you are offered the chance to participate, without initial charge, in a project that produces cash flows of $5,000 at the end of the first period, $4,000 at the end of the next period and a loss of $11,000 at the end of the third and final year.a.What is the net present value if the relevant discount rate (the company’s cost of capital) is 10%?b.Would you accept the offer?c.What is the internal rate of return? Can you explain why you would reject a project which has aninternal rate of return greater than its cost of capital?SOLUTION:At 10% discount rate:Net Present Value = - 0 + $5,000 + $4,000 - $11,000 = - 413.22(1.10)(1.10)2 (1.10)3c.This example is a project with cash flows that begin positive and then turn negative--it is like a loan. The 13.6% IRR is therefore like an interest rate on that loan. The opportunity to take a loan at 13.6% when the cost of capital is only 10% is not worthwhile.26.You must pay a creditor $6,000 one year from now, $5,000 two years from now, $4,000 three years from now, $2,000 four years from now, and a final $1,000 five years from now. You would like to restructure the loan into five equal annual payments due at the end of each year. If the agreed interest rate is 6% compounded annually, what is the payment?SOLUTION:Since there are a number of different cash flows, it is easiest to do the first step of this problem using cash flow keys on the calculator. To find the present value of the current loan payments:27.Find the future value of the following ordinary annuities (payments begin one year from today and all interest rates compound annually):a.$100 per year for 10 years at 9%.b.$500 per year for 8 years at 15%.c.$800 per year for 20 years at 7%.d.$1,000 per year for 5 years at 0%.e.Now find the present values of the annuities in a-d.f.What is the relationship between present values and future values?SOLUTION:Future Value of Annuity:e.f.The relationship between present value and future value is the following:FV = PV x (1+i)n28.Suppose you will need $50,000 ten years from now. You plan to make seven equal annual deposits beginning three years from today in an account that yields 11% compounded annually. How large should the annual deposit be?SOLUTION:You will be making 7 payments beginning 3 years from today. So, we need to find the value of an immediate annuity with 7 payments whose FV is $50,000:29.Suppose an investment offers $100 per year for five years at 5% beginning one year from today.a.What is the present value? How does the present value calculation change if one additional payment isadded today?b.What is the future value of this ordinary annuity? How does the future value change if one additionalpayment is added today?SOLUTION:$100 x [(1.05)5] - 1 = $552.56.05If you were to add one additional payment of $100 today, the future value would increase by:$100 x (1.05)5 = $127.63. Total future value = $552.56 + $127.63 = $680.19.Another way to do it would be to use the BGN mode for 5 payments of $100 at 5%, find the future value of that, and then add $100. The same $680.19 is obtained.30.You are buying a $20,000 car. The dealer offers you two alternatives: (1) pay the full $20,000 purchase price and finance it with a loan at 4.0% APR over 3 years or (2) receive $1,500 cash back and finance the rest at a bank rate of 9.5% APR. Both loans have monthly payments over three years. Which should you choose? SOLUTION:31.You are looking to buy a sports car costing $23,000. One dealer is offering a special reduced financing rate of 2.9% APR on new car purchases for three year loans, with monthly payments. A second dealer is offering a cash rebate. Any customer taking the cash rebate would of course be ineligible for the special loan rate and would have to borrow the balance of the purchase price from the local bank at the 9%annual rate. How large must the cash rebate be on this $23,000 car to entice a customer away from the dealer who is offering the special 2.9% financing?SOLUTION:of the 2.9% financing.32.Show proof that investing $475.48 today at 10% allows you to withdraw $150 at the end of each of the next 4 years and have nothing remaining.SOLUTION:You deposit $475.48 and earn 10% interest after one year. Then you withdraw $150. The table shows what happensAnother way to do it is simply to compute the PV of the $150 annual withdrawals at 10% : it turns out to be exactly $475.48, hence both amounts are equal.33.As a pension manager, you are considering investing in a preferred stock which pays $5,000,000 per year forever beginning one year from now. If your alternative investment choice is yielding 10% per year, what is the present value of this investment? What is the highest price you would be willing to pay for this investment? If you paid this price, what would be the dividend yield on this investment?SOLUTION:Present Value of Investment:PV = $5,000,000 = $50,000,000.10Highest price you would be willing to pay is $50,000,000.Dividend yield = $5,000,000 = 10%.$50,000,00034. A new lottery game offers a choice for the grand prize winner. You can receive either a lump sum of $1,000,000 immediately or a perpetuity of $100,000 per year forever, with the first payment today. (If you die, your estate will still continue to receive payments). If the relevant interest rate is 9.5% compounded annually, what is the difference in value between the two prizes?SOLUTION:The present value of the perpetuity assuming that payments begin at the end of the year is:$100,000/.095 = $1,052,631.58If the payments begin immediately, you need to add the first payment. $100,000 + 1,052,632 = $1,152,632.So the annuity has a PV which is greater than the lump sum by $152,632.35.Find the future value of a $1,000 lump sum investment under the following compounding assumptions:a.7% compounded annually for 10 yearsb.7% compounded semiannually for 10 yearsc.7% compounded monthly for 10 yearsd.7% compounded daily for 10 yearse.7% compounded continuously for 10 yearsa.$1,000 x (1.07)10 = $1,967.15b.$1,000 x (1.035)20 = $1,989.79c.$1,000 x (1.0058)120 = $2,009.66d.$1,000 x (1.0019178)3650 = $2,013.62e.$1,000 x e.07x10 = $2,013.7536.Sammy Jo charged $1,000 worth of merchandise one year ago on her MasterCard which has a stated interest rate of 18% APR compounded monthly. She made 12 regular monthly payments of $50, at the end of each month, and refrained from using the card for the past year. How much does she still owe? SOLUTION:Sammy Jo has taken a $1,000 loan at 1.5% per month and is paying it off in monthly installments of $50. We could work out the amortization schedule to find out how much she still owes after 12 payments, but a shortcut on the financial calculator is to solve for FV as follows:37.Suppose you are considering borrowing $120,000 to finance your dream house. The annual percentage rate is 9% and payments are made monthly,a.If the mortgage has a 30 year amortization schedule, what are the monthly payments?b.What effective annual rate would you be paying?c.How do your answers to parts a and b change if the loan amortizes over 15 years rather than 30?EFF = [1 + .09]1238.Suppose last year you took out the loan described in problem #37a. Now interest rates have declined to 8% per year. Assume there will be no refinancing fees.a.What is the remaining balance of your current mortgage after 12 payments?b.What would be your payment if you refinanced your mortgage at the lower rate for 29 years? SOLUTION:Exchange Rates and the Time Value of Money39.The exchange rate between the pound sterling and the dollar is currently $1.50 per pound, the dollar interest rate is 7% per year, and the pound interest rate is 9% per year. You have $100,000 in a one-year account that allows you to choose between either currency, and it pays the corresponding interest rate.a.If you expect the dollar/pound exchange rate to be $1.40 per pound a year from now and are indifferentto risk, which currency should you choose?b.What is the “break-even” value of the dollar/pound exchange rate one year from now?SOLUTION:a.You could invest $1 today in dollar-denominated bonds and have $1.07 one year from now. Or you couldconvert the dollar today into 2/3 (i.e., 1/1.5) of a pound and invest in pound-denominated bonds to have .726667(i.e., 2/3 x 1.09) pounds one year from now. At an exchange rate of $1.4 per pound, this would yield 0.726667(1.4) = $1.017 (this is lower than $1.07), so you would choose the dollar currency.b.For you to break-even the .726667 pounds would have to be worth $1.07 one year from now, so the break-evenexchange rate is $1.07/.726667 or $1.4725 per pound. So for exchange rates lower than $1.4725 per pound one year from now, the dollar currency will give a better return.。