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博迪《金融学》第2版名校考研真题【视频讲解】一、单选题1．以下货币制度中会发生劣币驱逐良币现象的是（）。
[中央财大2011金融硕士] A．金银双本位B．金银平行本位C．金币本位D．金汇兑本位【答案】A【解析】金银双本位制下金、银两种金属同时被法律承认为货币金属，金、银铸币都可自由铸造，都有无限的法定支付能力。
当金银铸币各按其本身所包含的价值并行流通时，市场上的商品就出现了金银两重价格，而这两重价格随金银市场比价的不断变动而变动。
为了克服由此造成的紊乱，很多国家用法律规定了金币与银币的比价。
但金银市场比价并不会由于法定比例的确定而不再发生变化。
于是法定比价和市场比价之间可能会出现差异，价值被高估的货币渐渐被贮藏，而劣币充斥市场。
金银平行本位是金银两种本位币按其所含金属的实际价值流通，国家对两种货币的交换不加规定，而由市场上的金银的实际比价自由确定金币和银币比价的货币制度。
在金本位制下，每单位的货币价值等同于若干重量的黄金（即货币含金量）；当不同国家使用金本位时，国家之间的汇率由它们各自货币的含金量之比——铸币平价（Mint Parity）来决定。
金汇兑本位制（Gold Exchange Standard）又称“虚金本位制”，该国货币一般与另一个实行金本位制或金块本位制国家的货币保持固定的比价，并在后者存放外汇或黄金作为平准基金，从而间接实行了金本位制。
实际上，它是一种带有附属性质的货币制度。
当然，无论金块本位制或金汇兑本位制，都是削弱了的金本位制，很不稳定。
而这种脆弱的制度经过1929年～1933年的世界经济危机，终于全部瓦解。
2．面值为100元的永久性债券票面利率是10%，当市场利率为8%时，该债券的理论市场价格应该是（）元。
[中央财大2011金融硕士]A．100B．125C．110D．1375【答案】B 【解析】该债券的理论市场价格应该是（元）125%8%10100=⨯==m r C P 。
3．实际利率为3%，预期通货膨胀率为6%，则名义利率水平应该近似地等于（）。
博迪《金融学》第2版课章节练习及详解第5章居民户的储蓄和投资决策一、概念题１．持久收入假说（武汉大学2002研；南开大学2008研）答：持久收入假说由美国经济学家米尔顿·弗里德曼（M．Friedman）提出，认为消费者的消费支出主要不是由他的现期收入决定，而是由他的永久收入决定。
所谓永久收入是指消费者可以预计到的长期收入。
永久收入大致可以根据观察到的若干年收入的数值之加权平均数计得，距现在的时间越近，权数越大；反之，则越小。
根据这种理论，政府想通过增减税收来影响总需求的政策是不能奏效的，因为人们减税而增加的收入，并不会立即用来增加消费。
与生命周期假说不同的是，持久收入假说偏重于个人如何预测自己未来收入问题。
持久收入假说认为：（1）消费不只同现期收入相联系，而是以一生或永久的收入作为消费决策的依据。
（2）一次性暂时收入变化引起的消费支出变动甚小，即其边际消费倾向很低，甚至近于零，但来自永久收入变动的消费倾向很大，甚至接近于1。
（3）当政府想用税收政策影响消费时，如果减税或增税只是临时性的，则消费者并不会受到很大影响，只有永久性税收变动，政策才会有明显效果。
2．跨期预算约束与最优消费选择费雪认为，人们在消费时会受到一些限制，这些约束包括：预算约束（即人们可以为自己进行消费所支出的数额大小）和跨期预算约束（即人们可以为自己在当前消费和未来消费所支付的数额大小）。
假定消费者的一生可以分为两个时期：第一个时期是青年时期，第二个时期是老年时期。
用1y 和1c 分别表示消费者在第一个时期的收入和消费，用2y 和2c 分别表示消费者在第二个时期的收入和消费。
再假定消费者有机会进行借贷或储蓄，因此他在任何一个时期的消费都可以大于或小于那一时期的收入。
第一个时期的储蓄或借贷：11s y c =-（0s >表示储蓄，0s <表示借贷），第二个时期的消费：()221c r s y =++，其中r 为实际利率。
博迪《金融学》第2版课后习题及详解第15章期权市场与或有索取权市场一、概念题1．或有索取权（contingent claim）答：或有索取权是一类范围广泛的资产或证券，这种资产未来的收益取决于其他资产或某些不确定事件的结果。
常见的或有索权权有债务和权益资本的或有索取权。
（1）债务资本的或有索取权：债务资本体现为借债的公司承诺在某一确定的时间支付给债权人一笔固定的金额。
一般地，假设债权人得到在年末将获得金额为F的支付承诺。
如果公司年末的价值X，等于或大于F，债权人将获得F。
显然，如果公司不足以支付承诺的金额，公司将会“破产”。
无论这些资产价值多少，它将被迫变现。
债权人所得到的是X。
从数学上来看，这意味着债权人拥有对X和F之间较小数额的索取权。
图15-1表示债权人报酬结构的本质。
图15-1债权人报酬结构的本质（2）权益资本的或有索取权：股东在年末对公司价值的索取权等于支付给债权人之后的剩余部分。
当然，如果公司的价值等于或少于承诺支付给债权人的数额，股东什么都得不到。
用数学公式来表达，如果X＞F，股东的索取权是X－F；如果X≤F，股东的索取权等于0。
图15-1描述了这一关系。
总之，债权人的索取权和股东的索取权之和总是等于公司期末的价值。
2．买入期权（call）答：买入期权又称“买方期权”、“看涨期权”、“多头期权”、“敲进”，是指期权买方在合约到期日或有效期内按照预先敲定的交割价格从期权卖方手中买入某种金融资产或商品的权利，是期权交易的种类之一。
购买这种期权以人们预测市场价格将有上涨趋势为前提。
投资者在支付一定的期权费取得该种期权后，在合约到期日或到期日之前的有效期限内，若市场价格超过协定价格与期权费之和的水平，则可通过行使期权以协定价格买入合约规定的一定数量的金融资产或商品，再以市场价格卖出，从而获利。
在市场价格上涨引起期权费上升的情况下，持有者也可在合约有效期限内以较高的期权费转售该种期权，从而获利。
博迪《金融学》第2版课章节练习及详解第12章投资组合机会和选择一、概念题1．有效组合（efficient portfolio）（中央财大2012金融硕士；上海财大2000研）答：有效组合指在期望收益率一定时其风险（即标准差）最低的证券组合，或者指在风险一定时其期望收益率最高的证券组合。
有效边界上的点对应的证券组合也称为有效组合。
图12-1有效边界具体来讲，在所有可行的投资组合中，如果证券组合的特征由期望收益率和收益率方差来表示，则投资者需要在E-δ坐标系中的可行域中寻找最好的点，但不可能在可行域中找到一点被所有投资者都认为是最好的。
按照投资者的共同偏好规则，可以排除那些被所有投资者都认为差的组合，排除后余下的这些组合就是有效证券组合。
根据有效组合的定义，有效组合不止一个，描绘在可行域的图形中，如图粗实线部分它是可行域的上边界部分，也即有效边界ABC曲线段（图12-1）。
对于可行域内部及下边界上的任意可行组合，均可以在有效边界上找到一个有效组合比它好。
但有效边界上的不同组合，比如B和C，按共同偏好规则不能区分好差。
因而有效组合相当于有可能被某位投资者选作最佳组合的候选组合，不同投资者可以在有效边界上获得任一位置。
作为一个理性投资者，且厌恶风险，则他不会选择有效边界以外的点。
此外，A点是一个特殊的位置，它是上边界和下边界的交汇点，这一点所代表的组合在所有可行组合中方差最小，因而被称作最小方差组合。
2．市场证券组合（market portfolio）（上海财大2002研）答：市场证券组合指个人或机构投资者所持有的各种与整个资本市场的构成完全相同的有价证券组合的总称，通常包括各种类型的债券、股票及存款单等。
证券组合的分类通常以组合的投资目标为标准。
证券组合按不同标准可以分为避税型、收入型、增长型、收入和增长混合型、货币市场型、国际型及指数化型等。
投资者构建证券组合的原因主要有：①降低风险。
资产组合理论证明，证券组合的风险随着组合所包含证券数量的增加而降低，资产间关联性极低的多元化证券组合可以有效地降低非系统风险。
博迪《金融学》第2版课后习题及详解第1章金融学一、概念题1．金融学（finance）答：金融学是一项针对人们怎样跨期配置稀缺资源的研究。
其主要研究货币领域的理论及货币资本资源的配置与选择、货币与经济的关系及货币对经济的影响、现代银行体系的理论和经营活动的经济学科，是当代经济学的一个相对独立而又极为重要的分支。
金融学所涵盖的内容极为丰富，诸如货币原理、货币信用与利息原理、金融市场与银行体系、储蓄与投资、保险、信托、证券交易、货币理论、货币政策、汇率及国际金融等。
2．金融体系（financial system）答：金融体系是金融市场以及其他金融机构的集合，这些集合被用于金融合同的订立以及资产和风险的交换。
金融体系是由连接资金盈余者和资金短缺者的一系列金融中介机构和金融市场共同构成的一个有机体，包括股票、债券和其他金融工具的市场、金融中介（如银行和保险公司）、金融服务公司（如金融咨询公司）以及监控管理所有这些单位的管理机构等。
研究金融体系如何发展演变是金融学科的重要方面。
3．资产（assets）答：资产是指个人、公司或者组织拥有的具有商业或交换价值的任何物品，它能在未来产生经济利益，资产有三个非常重要的特征：①能在未来产生经济利益；②由实体控制；③由过去发生的事项或交易产生。
在国民账户体系中，资产是指经济资产，即所有者能对其行使所有权，并在持有或使用期间可以从中获得经济利益的资源或实体。
资产可分为金融资产和非金融资产两大类。
金融资产是指以价值形态或以金融工具形式存在的资产，它包括金融债权以及货币黄金和特别提款权。
非金融资产是指非金融性的资产，它包括生产资产和非生产资产。
在企业财务会计中，资产是指由过去的交易和事项所形成的，并由企业拥有或控制，预期会给企业带来经济利益的资源。
按流动性可分为流动资产和非流动资产两大类。
流动资产是指企业可以在一年或超过一年的一个营业周期内变现或者耗用的资产。
非流动资产是指不能在一年或者超过一年的一个营业周期内变现或耗用的资产。
博迪《金融学》第2版课后习题及详解第3章管理财务健康状况和业绩一、概念题1．账面价值（book values）答：账面价值是指会计账面所表现的资产价值，分为资产的账面价值和公司的账面价值。
资产的账面价值是指公司的资产在会计账簿上表现的价值，即原来购进资产的价值（资产的成本）减去折旧。
在固定资产购置当期，资产的账面价值等于当期市场价值加上运输、安装、调试等费用。
在固定资产正式投产营运后，每一会计期间都会对该资产计提折旧。
资产的账面价值会随着累计折旧的增加而减少，直到该资产报废时其账面价值仅剩残值，进而转销该资产。
公司的账面价值，是指公司资产负债表上所列示的资产总额减去负债、优先股之后的差额。
账面价值以历史成本为基础，它与一项资产或一个公司的市场价值关系不大。
2．无形资产（intangible assets）答：无形资产是指企业为生产商品、提供劳务、出租给他人，或为管理目的而持有的、没有实物形态的非货币性长期资产，如专利权、商标权、著作权、土地使用权、非专利技术、专营权、商誉等。
无形资产的特征有：①不具有实物形态；②可以在一个以上会计期间为企业提供经济利益；③有偿取得；④提供的未来经济利益具有很大的不确定性；⑤用于生产商品或提供劳务、出租给他人或为了行政管理目的而持有。
无形资产按形成来源不同可分为购入的、自创的、投资者投入的、接受捐赠的无形资产等；按能否辨认可分为可辨认无形资产和不可辨认无形资产。
无形资产只有在该资产产生的经济利益很可能流入企业、该资产的成本能够可靠地计量时，企业才能加以确认。
3．商誉（goodwill）答：商誉是指企业在经营活动中所具有的优越获利能力的潜在经济价值，是一种不可辨认的无形资产。
商誉由企业的良好信誉、产品的较高质量和市场占有率、可靠的销售网络、有效的内部管理、先进的技术、优越的地理位置等因素形成。
其特征是：①商誉与企业整体相关，不能单独存在；②形成商誉的因素无法单独计值；③商誉与形成商誉过程中所发生的成本无关，它是一种获得超额收益的能力。
博迪《⾦融学》第2版课后习题及详解（居民户的储蓄和投资决策）【圣才出品】博迪《⾦融学》第2版课后习题及详解第5章居民户的储蓄和投资决策⼀、概念题1．⼈⼒资本（human capital）答：⼈⼒资本是指劳动者受到教育、培训、实践经验、迁移、保健等⽅⾯的投资⽽获得的知识和技能的积累，亦称“⾮物⼒资本”。
由于这种知识与技能可以为其所有者带来⼯资等收益，因⽽形成了⼀种特定的资本——⼈⼒资本。
任何使⼈⼒资本增值的活动都是⼈⼒资本投资，包括医疗和保健、在职⼈员培训、正规教育、成⼈教育与培训、迁移者⼯作搜寻等等。
⼈⼒资本投资的决策是⼀种收益与成本的权衡，其成本包括：实际的费⽤或直接的费⽤、放弃的⼯资报酬以及⼼理成本。
投资的预期收益可能是以各种形式表现出来的，⽐如较⾼的未来收⼊、终⾝⼯作满意程度的提⾼、对娱乐活动欣赏⽔平的提⾼以及欣赏兴趣的增长等。
2．永久性收⼊（permanent income）答：永久性收⼊是指消费者可以预期到的长期收⼊，即预期在较长时期中（3年以上）可以维持的稳定的收⼊流量。
永久性收⼊是弗⾥德曼持久收⼊假说中的重要概念，⼤致可以根据所观察到的若⼲年收⼊的数值的加权平均数来计算，估算持久收⼊的计算公式为：YP T=Y T-1＋θ（Y T－Y T-1）=θY T－（1－θ）Y T-1（0＜θ＜1）式中，YP T为现期永久性收⼊，Y T为现期收⼊，Y T-1为前期收⼊，θ为加权数。
该公式说明，现期的永久性收⼊等于前期收⼊和两个时期收⼊变动的⼀定⽐率，或者说等于现期收⼊和前期收⼊的加权平均数。
加权数的⼤⼩取决于⼈们对未来收⼊的预期，这种预期要根据过去的经验进⾏修改，称为适应性预期。
如果⼈们认为前期和后期收⼊变动的时间较长，θ就⼤；反之，前期和后期收⼊变动的时间较短，θ就⼩。
3．跨期预算约束（inter-temporal budget constraint）答：跨期预算约束是指决定⼀⽣消费计划时⾯临的约束条件，即⼀⽣的消费开⽀和遗产的现值等于包括初始财产和未来劳动收⼊在内的⼀⽣资源的现值。
博迪《金融学》第2版课后习题及详解博迪的《金融学》第2版是一本广泛使用的金融学教材，其中的课后习题对于学生理解和掌握金融学概念和理论具有重要意义。
本文将选取一些具有代表性的课后习题，并提供详细的解答和分析。
答：金融学是一项针对人们怎样跨期配置稀缺资源的研究。
它涉及货币、投资、证券、银行、保险、基金等领域，主要研究如何在不确定的环境下对资源进行跨时期分配，以实现最大化的收益或满足特定的目标。
金融体系（financial system）答：金融体系是金融市场以及其他金融机构的集合，这些集合被用于金融合同的订立以及资产和风险的交换。
它是由连接资金盈余者和资金短缺者的一系列金融中介机构和金融市场共同构成的一个有机体，包括股票、债券和其他金融工具的市场、金融中介（如银行和保险公司）、金融服务公司（如金融咨询公司）以及监控管理所有这些单位的管理机构等。
研究金融体系如何发展演变是金融学科的重要方面。
假设某个投资者在2022年购买了一张面值为1000元，年利率为5%的债券，并在2023年以1100元的价格卖出。
请问该投资者的年化收益率是多少？(1100 - 1000) / 1000 × 100% = 10%其中，分子部分为投资者获得的收益，分母部分为投资者的初始投资金额。
答：现代金融学的三个主要理论包括资本资产定价模型（CAPM）、有效市场假说（EMH）和现代投资组合理论（MPT）。
资本资产定价模型（CAPM）是一种用来决定资产合理预期收益的模型，它认为资产的预期收益与该资产的系统性风险有关。
在投资决策中，投资者可以通过比较不同资产的预期收益与其系统性风险来确定最优投资组合。
有效市场假说（EMH）认为市场是有效的，即市场上的价格反映了所有可用信息。
根据这个理论，投资者无法通过分析信息来获取超额收益。
然而，在实践中，许多研究表明市场并非完全有效，投资者可以通过分析和利用信息来获得超额收益。
现代投资组合理论（MPT）是由Harry Markowitz于20世纪50年代提出的，它认为投资者应该通过多元化投资来降低风险。
兹维博迪金融学第二版试题库12TBChapter TwelvePortfolio Opportunities and ChoiceThis chapter contains 30 multiple choice questions, 10 short problems, and 5 longer problems.Multiple Choice1. A person's wealth portfolio consists of all one’s ________ and ________.(a)retained earnings; credit(b)stocks; bonds(c)assets; liabilities(d)student loans; mortgagesAnswer: (c)2.The principle of diversification usually applies to all ________.(a)risk averse people(b)risk neutral people(c)risk tolerant people(d)b and cAnswer: (a)3.Which of the following decisions can be considered part of portfolio selection?(a)Whether to buy or rent one’s house(b)What kind of life insurance to purchase(c)Whether to invest in stocks or bonds(d)All of the aboveAnswer: (d)12-14.An insurance policy that guarantees a person an income for as long as one lives is termed a ________.(a)lump sum payment(b)life annuity(c)perpetual annuity(d)life perpetuityAnswer: (b)5.The ________ is the length of time between decisions to revise portfolios, whereas the ________ isthe total length of time for which one plans.(a)trading horizon; decision horizon(b)planning horizon; decision horizon(c)decision horizon; trading horizon(d)decision horizon; planning horizonAnswer: (d)6.In making portfolio-selection decisions, people can in general achieve a ________ expected rate ofreturn by exposing themselves to ________ risk.(a)higher; no(b)higher; greater(c)higher; lower(d)lower; greaterAnswer: (b)7.The ________ the assets that make up the portfolio is found to be a very important factor whenconsidering the ability of diversification to reduce the riskiness of an investor's portfolio.(a)expected return of(b)variance of(c)correlation among(d)skewness amongAnswer: (c)12-28.Risk tolerance can be influenced by which of the following characteristics?(a)job status(b)age(c)wealth(d)all of the aboveAnswer: (d)9.The ________ is defined as a security that offers a perfectly predictable rate of return in terms of theunit of account and the length of the investor's decision horizon.(a)riskless asset(b)risky asset(c)30-day bond(d)30-day debentureAnswer: (a)10.A portfolio contains one risky asset and one riskless asset. The expected rate of return on the riskyasset is 0.13 and the riskless rate is 0.05. The standard deviation of the risky asset is 0.2, and the standard deviation of the portfolio is 0.075. What is the expected rate of return on the portfolio using the trade-off line?(a)0.0490(b)0.0800(c)0.0980(d)0.1175Answer: (b)11.An investor has a $100,000 investment to allocate between a risky asset and a riskless asset. Theequation for the trade-off line is determined to be E(r) = 0.05 + 0.09w. If the investor is requiring a portfolio composition corresponding to an expected rate of return of 0.11, how much should be invested in the risky asset?(a)$18,181(b)$33,333(c)$66,667(d)$81,819Answer: (c)12-312.An investor has a $100,000 investment to allocate between a risky asset and a riskless asset. Theequation for the trade-off line is determined to be E(r) = 0.07 + 0.12w. If the investor is requiring a portfolio composition corresponding to an expected rate of return of 0.17, how much should beinvested in the riskless asset?(a)$16,667(b)$29,412(c)$70,588(d)$83,333Answer: (a)13.An investor has a $100,000 investment to allocate between a risky asset and a riskless asset. Theequation for the trade-off line is determined to be E(r) = 0.07 + 0.12w. If the investor requires aportfolio composition corresponding to an expected rate of return of 0.17, what is the corresponding standard deviation of the portfolio? The standard deviation of risky asset is 0.3.(a)0.05(b)0.25(c)0.49(d)0.83Answer: (b)14.The expected rate of return on a risky asset is 0.13 and the riskless rate is 0.06. The standard deviationof the risky asset is 0.25. What happens to the slope of the trade-off line if the riskless rate changes to0.05 per year and the expected return on the risky asset changes to 0.14?(a)No change(b)The slope of the line falls from 36% to 28%(c)The slope of the line rises from 28% to 36%(d)The slope of the line rises from 52% to 56%Answer: (c)15.The formula for the trade-off line between risk and expected return is ________.(a)E(r) = r f+ w[E(r s) –r f](b)E(r) = r f+ [E(r s) –r f](c)E(r) = r f+ w[E(r s) + r f](d)all of the aboveAnswer: (a)12-416.In the trade-off line, the risk premium depends on ________(a)the risk premium of the risky asset(b)the proportion of the portfolio invested in the risky asset(c)the risk premium of the riskless asset(d)both a and bAnswer: (d)17.When one of the two assets in a portfolio is riskless, thestandard deviation of its rate of return and itscorrelation with other asset are________.(a)greater than zero but less than positive one(b)less than zero but greater than negative one(c)zero(d)none of the aboveAnswer: (c)18.The expected rate of return on a risky asset is 0.16 and the riskless rate is 0.07. The standard deviationof the risky asset is 0.2. What happens to the slope of the trade-off line if the riskless rate changes to .06 per year and the expected return on the risky asset changes to 0.15?(a)no change(b)the slope rises from 0.45 to 0.5(c)the slope falls from 0.5 to 0.45(d)the slope falls from 0.45 to 0.4Answer: (a)19.A portfolio contains a riskless asset with an expected rate of return of 0.06 and a risky asset with anexpected rate of return of 0.15. The standard deviation of the risky asset is 0.25. If the expected rate of return of this portfolio is 0.10, what is its standard deviation?(a)0.11(b)0.14(c)0.22(d)0.44Answer: (a)12-5Consider a portfolio of two risky assets with the following distribution of rates of return on risky assets for questions 20 and21. The portfolio is 55% Risky Asset 1 and 45% Risky Asset 2, and the correlation coefficient is 0.4.Risky Asset 1 Risky Asset 2MeanStandard Deviation 0.160.250.090.1820.What is the mean of this portfolio?(a)0.1215(b)0.1285(c)0.2005(d)0.2185Answer: (b)21.What is the standard deviation of this portfolio?(a)0.15958(b)0.18541(c)0.25467(d)0.34378Answer: (b)Consider a portfolio of two risky assets with the following distribution of rates of return on risky assets for questions 22 and 23. The portfolio is 70% Risky Asset 1 and 30% Risky Asset 2, and the correlation coefficient is 0.3.Risky Asset 1 Risky Asset 2MeanStandard Deviation 0.120.160.200.3022.What is the mean of this portfolio?(a)0.1716(b)0.1600(c)0.1414(d)0.1320Answer: (c)12-623.What is the standard deviation of this portfolio?(a)0.16338(b)0.14368(c)0.02669(d)0.02064Answer: (a)24.In practice, the vast majority of assets are positively correlated with each other because they are allaffected by ________.(a)common economic factors(b)firm specific factors(c)potential lawsuits(d)managerial inefficienciesAnswer: (a)25.A mutual fund company offers a safe money market fund whose current rate is 0.04. The samecompany also offers an equity fund with an aggressive growth objective, which historically has exhibited an expected return of 0.25 and a standard deviation of 0.30. Derive the equation for the risk-reward trade-off line.(a)E(r) = 0.04 + 0.25σ(b)E(r) = 0.04 + 0.7σ(c)E(r) = 0.04 + 0.21σ(d)E(r) = 0.04 + 0.83σAnswer: (b)26.The ________ refers to the set of portfolios of risky assets offering the highest possible expected rateof return for any given standard deviation.(a)minimum portfolio frontier(b)effective portfolio frontier(c)expected portfolio frontier(d)efficient portfolio frontierAnswer: (d)12-727.The optimal combination of risky assets is found as ________ between a straight line representing theriskless asset and the efficient frontier of risky assets.(a)the point of bisection(b)the point of intersection(c)the point of tangency(d)the point of highest returnAnswer: (c)28.The power of diversification to reduce the riskiness of an investor’s portfolio depends on the________ among the assets that make up the portfolio.(a)expected returns(b)variances(c)correlations(d)none of the aboveAnswer: (c)29.In the context of the optimal combination of risky assets, in order to decide on the menu of assetchoices to offer its customers a financial intermediary shouldconsider:(a)investor preferences(b)the expected returns and standard deviations of the risky assets(c)both a and b(d)neither a nor bAnswer: (b)30.An investor has $100,000 invested in a portfolio that is composed of a tangency portfolio and ariskless asset, such that 35% is in the tangency portfolio and 65% is in the riskless asset. If thetangency portfolio is composed of 43.75% Risky Asset A and 56.25% Risky Asset B, which of the following accurately displays the amount of money invested in each component of the portfolio?(a)$35,000 in Riskless Asset; $43,750 in Risky Asset A; $56,250 in Risky Asset B(b)$65,000 in Riskless Asset; $43,750 in Risky Asset A; $56,250 in Risky Asset B(c)$35,000 in Riskless Asset; $28,437.50 in Risky Asset A; $36,562.50 in Risky Asset B(d)$65,000 in Riskless Asset; $15,312.50 in Risky Asset A; $19,687.50 in Risky Asset BAnswer: (d)12-8Short Problems1.Discuss the time horizons as they relate to portfolio planning.Answer:In formulating a plan for portfolio selection you begin bydetermining our goals and timehorizons. The planning horizon is the total length of time for which one plans. Thelongest time horizon would typically correspond to the retirement goal and would be thebalance of one’s lifetime. There are also shorter planning horizons that correspond tospecific financial goals, such as paying for a child’s education. The decision horizon isthe length of time between decisions to revise the portfolio. The length of the decisionhorizon is controlled by the individual, within certain limits. The shortest possibledecision horizon is the trading horizon, defined as the minimum time interval over whichinvestors can revise their portfolios.2.What is the riskless asset if the unit of account is the Japanese Yen and the length of the decisionhorizon is a month?Answer:The Japanese Yen one-month zero-coupon bond.3.Describe the steps involved in the portfolio optimization process.Answer:(1) Find the optimal combination of risky assets.(2) Mix this optimal risk-asset portfolio with the riskless asset.12-94.Who would you expect to be more risk tolerant, a young investor or an elderly one? An investor ormoderate means or a wealthy one?A young person with a secure job can look forward to a long period of earning a salarythat will probably increase with the rate of inflation. For her, investment in stocks wouldnot be as risky as for an older person who needs to ensure a steady source of income forthe rest of his life. A wealthier individual may be willing to take more risks (than a poorerperson) because his capacity to take bigger gambles and lose is higher. That is, he maystill be quite wealthy after his losses.5.An investor has a $100,000 investment to allocate betweena risky asset and a riskless asset. Theequation for the trade-off line is determined to be E(r) = 0.05 + 0.07w. If the investor requires aportfolio composition corresponding to an expected rate of return of 0.10, how much should beinvested in the risky asset? In the riskless asset?Answer:E(r) = 0.05 + 0.07w0.10 = 0.05 + 0.07w0.05 = 0.07w0.71429 = wThe investor should invest $71,429 in the risky asset and $28,571 in the riskless asset. 6.An investor has $75,000 to allocate between a risky asset and a riskless asset. The equation for the trade-off line is determined to be E(r) = 0.06 + 0.1w. If the investor requires a portfolio composition with an expected rate of return of 0.12, how much should be invested in each asset?E(r) = 0.06 + 0.1w0.12 = 0.06 + 0.1w0.06 = 0.1w0.6 = w0.6($75,000) = $45,000 should be invested in the risky asset0.4($75,000 = $30,000 should be invested in the riskless assetThere would have to be 16 million uncorrelated drugs in the portfolio.12-107.Consider the portfolio of two risky assets with the following distribution of rates of return on riskassets.Risky Asset 1 Risky Asset 2MeanStandard Deviation 0.170.230.100.19What are the mean and standard deviation of a portfolio that is 60% Risky Asset 1 and 40% Risky Asset 2 if the correlation coefficient is 0.3?Answer:E(r) = wE(r1) + (1 - w)E(r2)= 0.6(0.17) + 0.4(0.10)= 0.142The mean is 14.2%σ2= w2σ12 + (1 - w)2σ22 + 2w(1-w)ρ1,2σ1σ2= (0.6)2(0.23)2 + (0.4)2(0.19)2 + 2(0.6)(0.4)(0.3)(0.23)(0.19) σ2= 0.03111σ= 0.17639The standard deviation is 17.6%8.An investor has a $150,000 investment to allocate betweena risky asset and a riskless asset. Theexpected rate of return for the risky asset is 0.18 and the expected rate of return for the riskless asset is 0.07. The standard deviation of the risky asset is 0.2. If the investor requires a portfoliocomposition corresponding to an expected rate of return of 0.15, what is the standard deviation of the portfolio?Answer:Use the trade-off line to find w:E(r) = r f + w[E(r s) – r f)0.15 = 0.07 + w[0.18 – 0.07]0.15 = 0.07 + 0.11w0.08 = 0.11w0.7272 = wSo the standard deviation of the portfolio is 0.2(0.7272) = 0.1455.12-119.Discuss how to create efficient portfolios when the raw materials are two risky assets and a risklessasset.Answer:Let us now summarize what we have learned about creating efficient portfolios when the rawmaterials are two risky assets and a riskless asset. There is a single portfolio of the two riskyassets that it is best to combine with the riskless asset. We call this particular risky portfolio the optimal combination of riskyassets. The preferred portfolio is always some combination of this tangency portfolio and the riskless asset10.The expected rate of return on a risky asset is 0.19 and the riskless rate is 0.05. The standard deviationof the risky asset is 0.3.a. What happens to the slope of the trade-off line if the riskless rate decreases to 0.04 and theexpected return on the risky asset increases to 0.2?b. What happens to the slope of the trade-off line if the riskless rate increases to 0.06 and theexpected return on the risky assets increases to 0.2?Answer:a. Slope = (E(r s) –r f)/σsSlope of original scenario: (0.19 – 0.05)/0.3 = 0.14/0.3 = 0.467 Slope in revised scenario: (0.20 – 0.04)/0.3 = 0.16/0.3 = 0.533 The slope rises from 0.467 to 0.533.b.Slope of original scenario: (0.19 – 0.05)/0.3 = 0.14/0.3 = 0.467 Slope in revised scenario: (0.20 – 0.06)/0.3 = 0.14/0.3 = 0.467 The slope is unchanged.12-12Longer Problems1. A mutual fund advertises a money market fund whose current rate is 0.06, and is deemed “safe.” Inaddition, the mutual fund also offers an equity fund that is considered very aggressive in terms of growth. Historical expected returns are 0.30 with a standard deviation of 0.25.(a) Derive the risk-reward trade-off line.(b) For each unit of extra risk that an investor bears, how much extra expected return willresult?(c) What allocation should be placed in the money market fund if an investor desires anexpected return of 18%?Answer:(a) E(r) = r f + w[E(r s) – r f)= 0.06 + w[0.3 – 0.06]= 0.06 +0 .24w= 0.06 +0 .24(σ/0.25)= 0.06 + 0.96σ(b) For each unit of extra risk that an investor bears, the extra expected return will be 0.96(the slope of the risk-reward line)(c) 0.18 = 0.06 + w[0.30 - 0.06]0.18 = 0.06 + 0.24w0.12 = 0.24w0.5 = wInvest 50% in the money market fund and 50% in the equity fund.12-132.Suppose you are the manager of a mutual fund and a client comes to you wanting to invest 65% of aportfolio into your mutual fund and the remaining 35% into a “safe” money market fund. The mutual fund that you manage has an expected rate of return of 0.18 and a standard deviation of 0.25. The money market fund rate is 0.065.(a) If your client invests as described above, what is the expected return and standarddeviation of his portfolio?(b) The fund that you manage has the following stocks andtheir corresponding proportions:Stock X: 30%, Stock Y: 35%, and Stock Z: 35%If we include the position in the riskless asset, what are the investment proportions ofyour client’s portfolio?Answer:(a) E(r) = r f + w[E(r s) – r f)= 0.065 +0 .65[0.18 – 0.065]= 0.065 + 0.65[0.115]= 0.13975σ= 0.65 (0.25)= 0.1625(b) Stock X: (0.65 x 30%) = 19.50%Stock Y: (0.65 x 35%) = 22.75%Stock Z: (0.65 x 35%) = 22.75%Riskless Asset: = 35.00%Total = 100.00%12-143.If we have many risky assets to choose from, how do we determine the optimal combination of riskyassets?Answer:When there are many risky assets we use a two-step method of portfolio constructionsimilar to the one used in the previous section. In the first step, we consider portfoliosconstructed from the risky assets only, and in the second step we find the tangencyportfolio of risky assets to combine with the riskless asset. Because the computationinvolves a lot of number crunching, it is best done using computers. The efficientportfolio frontier is defined as the set of portfolios of risky assets offering the highestpossible expected rate of return for any given standard deviation. The reason theindividual basic assets lie inside the efficient frontier is that there is usually somecombination of two or more basic securities that has a higher expected rate of returnthan the basic security for the same standard deviation.The optimal combination of risky assets is found as the point of tangency between astraight line from the point representing the riskless asset and the efficient frontier ofrisky assets. The straight line connecting the riskless asset and the tangency pointrepresenting the optimal combination or risky assets is the best feasible risk rewardtradeoff line.4.Suppose you have the following two stocks:Risky Asset A Risky Asset BMean 0.10 0.18Standard Deviation 0.12 0.25_____________________________________________________The minimum-variance portfolio of these assets requires investment proportions of 83.92% ofRisky Asset A and 16.08% of Risky Asset B. The correlation between the two stocks is 0.1?What is the corresponding expected return and standarddeviation of the portfolio?Answer:The corresponding E(r) = w1 E(r1) + (1 - w1) E(r2)= 0.8392 (0.1) + 0.1608 (0.18)= 0.113The corresponding σ2= w12σ12 + (1 - w1)2σ22 + 2w(1 - w1) ρ1,2σ1σ2σ2= 0.01257So σ= 0.11212-155.Is it true that investing in stocks is less risky in the long run than the short run? Why or why not?Answer:There is a widespread—but mistaken—belief that stocks are less risky in the long run than in the short run. Based on this belief, it is generally inferred that you should invest more of your money in stocks the longer your planned holding period. Two propositions have been used to persuadeskeptics that this so-called time diversification effect is valid: The longer the investor’s holdi ng period, the smaller the standard deviation of the annualized rate of return on stocks.The longer the investor’s holding period, the lower the probability that stocks will earn a rate of return less than the corresponding risk-free interest rate on bonds.Although they are true, these propositions do not support the validity of the claim that stocks are less risky in the long run than in the short run or that you should invest more in stocks because you have a longer planned holding period. Let us explain why. First, the fact that the standarddeviation of the annualized rate of return on an investmentin stocks declines as the length of the holding period increases is merely an artifact of expressing investment performance in terms of the annualized rate of return. There is no genuine diversification in this situation. You care about the amount of wealth that you will have at the end of the holding period, and there is no decline in its standard deviation. For example, compare the results of investing all of your money in stocks versus risk-free bonds for one year and for 25 years. Even though the standard deviation of your annualized rate of return for the 25-year period is approximately one-fifth of the one-year result, the standard deviation of your ending wealth for the 25-year holding period is five times greater than the one-year standard deviation. Second, it is true that the longer the holding period, thelower the probability of a shortfall, defined as the stock portfolio’s earning less than the ri sk-free interest rate over that same period. However, the risk of a shortfall depends on its severity when it happens as well as its probability of happening. If we consider measures of risk that take account of both the severity and the probability of a shortfall, there is no decline in risk as the holdingperiod lengthens. For example, consider as a measure of risk the price of insuring a stock portfolio against a shortfall. It actually increases with the length of the holding period.12-16。
Chapter FourAllocating Resources Over TimeThis chapter contains 46 multiple-choice questions, 18 short problems and 9 longer problems. Multiple Choice1.________ is the process of going from present value to future value, whereas ________ isfinding the present value of some future amount.(a)Discounting; compounding(b)Compounding; annualizing(c)Compounding; discounting(d)Discounting; leasingAnswer: (c)2.________ refers to the interest rate at which money received before the end of the planninghorizon can be reinvested.(a)Internal rate(b)Reinvestment rate(c)Cost of equity(d)Compound interestAnswer: (b)3.The difference between an immediate annuity and an ordinary annuity is ________.(a)the number of periods(b)the amount of the payments(c)the interest rate(d)the timing of the paymentsAnswer: (d)4.The preferred stock of Tavistock Realty offers a cash dividend of $2.28 per year and it isselling at a price of $110 per share. What is the yield of Tavistock Realty preferred stock?(a)2.07%(b)2.12%(c)2.28%(d)48.25%Answer: (a)5.Consider the situation where you have won a $10 million lottery to be received in 25 annualequal payments of $400,000. What will happen to the present value of these winnings if the interest rate increases during the next 25 years?(a)it will not change(b)it will be worth more(c)it will be worth less(d)it cannot be determinedAnswer: (c)6.What is the effective annual rate on a bank account that has APR of 8 percent with interestcompounded quarterly?(a)6.12%(b)8.24%(c)8.48%(d)17.17%Answer: (b)7.You take out a loan with an APR of 10% with monthly compounding. What is the effectiveannual rate on your loan?(a)23.87%(b)21.6%(c)19.56%(d)18%Answer: (a)8.The CFO of CyberHelp Inc. has $250,000 in cash today that he wants to invest. How muchwill this investment be worth in four years if the current interest rate is 8%?(a)$270,000(b)$330,000(c)$340,125(d)$342,150Answer: (c)9.If you purchase a $12,000 certificate of deposit today with an APR of 14%, with quarterlycompounding, what will the CD be worth when it matures in 5 years?(a)$20,846.99(b)$20,865.60(c)$23,104.97(d)$23,877.47Answer: (d)10.The CFO of CyberChain Inc. plans to unleash a media campaign that is expected to cost $15million four years from today. How much cash should she set aside to pay for this if the current interest rate is 13%?(a)$9.2 million(b)$13.3 million(c)$14.4 million(d)$16.9 millionAnswer: (a)11.The NPV is a measure of how much your ________ wealth changes as a result of your choiceand if the NPV is ________it does not pay to undertake that choice.(a)future; negative(b)current; negative(c)current; positive(d)future; positiveAnswer: (b)12.The ________ is the rate that one can earn somewhere else if one did not invest in the projectunder evaluation.(a)opportunity cost of capital(b)cost of debt(c)cost of equity(d)weighted average cost of capitalAnswer: (a)13.You are trying to decide whether or not to buy a bond for $990 that will make one paymentfor $1,050 four years from today. What is the internal rate of return on the bond’s cash flows?(a)1.06%(b)1.48%(c)10.6%(d)14.8%Answer: (b)14.Calculate the NPV of the following cash flows: you invest $3,000 today and receive $300 oneyear from now, $700 two years from now, and $1,100 starting four years from now. Assume that the interest rate is 7%.(a)–$1,962.62(b)–$1,269.04(c)$1,269.04(d)$1,962.62Answer: (b)15.After each payment of an amortized loan, the outstanding balance is reduced by the amountof principal repaid. Therefore, the portion of the payment that goes toward the payment of interest is ________ than the previous period’s interest payment and the portion going toward repayment of principal is ________ than the previous period’s.(a)greater; lower(b)lower; lower(c)greater; greater(d)lower; greaterAnswer: (d)16.The present value of a future amount can be calculated with the equation ________.(a) PV = FV(1 + i)n(b) PV = FV(1 + i)(n)(c) PV = FV/(1 + i)n[NOTE: this should be formatted as a stacked fraction](d) PV = FV/(1 + i)(n) [NOTE: this should be formatted as a stacked fraction]Answer: (c)17.To compute the future value of a present amount use the compound amount factor defined as________.(a) FV = PV(1 + i)n(b) FV = PV(1 + i)(n)(c) FV = PV/(1 + i)n [NOTE: this should be formatted as a stacked fraction](d) FV = PV/(1 + i)(n) [NOTE: this should be formatted as a stacked fraction]Answer: (a)18.The earnings of BGB Computers have grown from $3.20 to $6.90 in 6 years. Determine theannual compound rate.(a)1.14%(b)13.7%(c)15.6%(d)115.6%Answer: (b)19.In five years you intend to go to graduate school. For each of your four years in graduateschool, you need to have a fund that will provide $25,000 per year at the beginning of each year. If the interest rate is 9% throughout, how much must you put in the fund today?(a)$64,996(b)$57,379(c)$50,184(d)$16,249Answer: (b)20.As part of your new job at CyberInc. the company is providing you with a new Jeep. Yourfirm will lease this $34,000 Jeep for you. The terms of the lease are seven annual payments at an interest rate of 10%, which will fully amortize the cost of the car. What is the annual lease payment?(a)$6,984.39(b)$5,342.86(c)$4,857.14(d)$3,584.00Answer: (a)21.A rule of thumb with using the internal rate of return is to invest in a project if the IRR is________ the opportunity cost of capital.(a)greater than(b)less than(c)less than or equal to(d)one-half ofAnswer: (a)22.When considering the timeframe of an investment, a rule followed by some is to choose theinvestment with ______ payback period.(a)the longest(b)the shortest(c)no(d)an infiniteAnswer: (b)23.A major problem with using the internal rate of return rule is ________.(a)there may be multiple cash outflows and multiple cash inflows(b)the internal rate of return may not exist(c)the internal rate of return may not be unique(d)all of the aboveAnswer: (d)24.The NPV is the difference between the ________ value of all ________ cash inflowsminus the ________ value of all current and future cash outflows.(a)future; present; present(b)present; future; present(c)present; present; future(d)present; future; futureAnswer: (b)25.When considering effective interest rates, as the compounding frequency increases, theeffective annual rate gets ________ and ________ but approaches ________.(a)larger; larger; a limit(b)smaller; smaller; a limit(c)larger; larger; infinity(d)smaller; smaller; infinityAnswer: (a)26.In 10 years you wish to own your business. How much will you have in your bankaccount at the end of 10 years if you deposit $300 each quarter (assume end of the period deposits)? Assume the account is paying an interest rate of 12% compounded quarterly.(a)$20,220(b)$21,060(c)$21,626(d)$22,620Answer: (d)27.The director of marketing for CyberProducts Inc. plans to unleash a media blitz that isexpected to cost $4.7 million three years from today. How much cash should she set aside today to pay for this if the current interest rate is 11%?(a) $6.43 million(b) $4.23 million(c) $3.62 million(d) $3.44 millionAnswer: (d)28.If you purchased a $10,000 certificate of deposit today with an APR of 12%, with monthlycompounding, what would be the CD worth when it matures in 6 years?(a) $56,340(b) $20,468(c) $19,738(d) $5,066Answer: (b)29.The manufacturing manager of CyberProducts Inc. estimates that she can save the company$16,000 cash per year over the next 8 years by implementing a recycling plan. What is the value of the savings today if the appropriate interest rate for the firm is 9%? Assume cash flows occur at the end of the year.(a) $64,240(b) $88,557(c) $96,527(d) $128,000Answer: (b)30.If the exchange rate between the U.S. dollar and the French Franc is $0.17 per French Franc,the dollar interest rate is 5.5% per year, and the French Franc interest rate is 4.5% per year, what is the "break-even" value of the future dollar/French Franc exchange rate one year from now?a)$0.172 per FFb)$0.179 per FFc)$5.827 per FFd)$5.882 per FFAnswer: (a)31.In any time value of money calculation, the cash flows and the interest rate must bedenominated ________.a)in the same currencyb)in different currenciesc)in terms of a third currencyd)in terms of the ECUAnswer: (a)32.If the exchange rate between the U.S. dollar and the Japanese yen is $0.00745 per yen, thedollar interest rate is 6% per year, and the Japanese interest rate is 7% per year, what is the “break-even” value of the future dollar/yen exchange rate one year from now?a)$135.49 per yenb)$134.23 per yenc)$0.00752 per yend)$0.00738 per yenAnswer: (d)33.Consider the situation where you are trying to decide if you should invest in a Swiss projector an American project. Both projects require an initial outlay of $15,000. The Swiss project will pay you 17,100 Swiss Francs per year for 6 years, whereas the American one will pay you $11,000 per year for 6 years. The dollar interest rate is 5% per year, the Swiss Franc interest rate is 6% per year, and the current dollar price of a Swiss Franc is $0.68 per Swiss Franc. Which project has the higher NPV?a)the U.S. project; its NPV is $55,832b)the U.S. project; its NPV is $40,833c)the Swiss project; its NPV is $42,179d)the Swiss project; its NPV is $57,178Answer: (c)34.The ________ is the rate denominated in dollars or in some other currency, and the ________is denominated in units of consumer goods.a)nominal interest rate; inflation interest rateb)nominal interest rate; real interest ratec)real interest rate; inflation interest rated)real interest rate; nominal interest rateAnswer: (b)35.Consider the situation where you are trying to decide if you should invest in a British projector U.S. project. Both projects require an initial outlay of $55,000. The British project will pay you 30,000 pounds per year for 6 years, whereas the American one will generate $40,000 per year for 6 years. The British interest rate is 5% per year, and the American interest rate is 6% per year; the current dollar price of a pound sterling is $1.6320 per pound sterling. Which project has the higher NPV?a)choose the U.S. one, it has a NPV of $196,693b)choose the U.S. one, it has a NPV of $141,693c)choose the British one, it has a NPV of $248,506d)choose the British one, it has a NPV of $193,506Answer: (d)36.What is the real interest rate if the nominal interest rate is 9% per year and the rate ofinflation is 6% per year?a) 1.5%b) 2.75%c) 2.83%d)7.5%Answer: (c)37.What is the nominal interest rate if the real rate of interest is 4.5% and the rate of inflation is6% per year?a)10.5%b)10.77%c)10.86%d)14.5%Answer: (b)38.What is the real rate of interest if the inflation rate is 6% per year and the nominal interestrate per year is 12.5%?a) 1.32%b) 6.13%c) 5.78%d)11.79%Answer: (b)pute the real future value, to the nearest dollar, of $2,000 in 35 years time. The realinterest rate is 3.2%, the nominal interest rate is 8.36%, and the rate of inflation is 5%.a)$6,023b)$6,853c)$33,223d)$11,032Answer: (a)40.The real interest rate is 3.2%, the nominal interest rate is 8.36% and the rate of inflation is 5%.We are interested in determining the future value of $200 in 35 years time. What is the future price level?a) 2.91b) 3.012c) 5.516d)16.61Answer: (c)41.Suppose your child is 9 years old and you are planning to open a fund to provide for thechild’s college education. Currently, tuition for one year of college is $22,000. How much must you invest now in order to pay enough for the first year of college nine years from now, if you think you can earn a rate of interest that is 4% more than the inflation rate?a)$21,154b)$16,988c)$15,585d)$15,457Answer: (d)42.Suppose you have a child who is 10 years old and you are planning to open a fund to providefor the child’s college education. Currently, tuition for one year is $22,000. Your child is planning to travel for two years before starting college. How much must you invest now in order to pay enough for the first year of college ten years from now, if you think you can earna rate of interest that is 5% more than the inflation rate?a)$10,190b)$13,506c)$13,660d)$20,952Answer: (b)43.When considering a plan for long run savings, if one does not have an explicit forecast ofinflation, then one can make plans in terms of:a)constant real payments and a real rate of interestb)constant nominal payments and a nominal rate of interestc)constant real payments and a nominal rate of interestd)constant nominal payments and a real rate of interestAnswer: (a)44.If the real rate is 4% and the rate of inflation is 6%, what is the nominal rate?a)8.16%b)10.16%c)10.24%d)10.36%Answer: (c)45.You have an investment opportunity with a nominal rate of 6% compounded daily. If youwant to have $100,000 in your investment account in 15 years, how much should you deposit today, to the nearest dollar?a.$43,233b.$41,727c.$40,930d.$40,660Answer: (d)46.You have determined the present value of an expected cash inflow stream. Which of thefollowing would cause the stream to have a higher present value?a)The discount rate increases.b)The cash flows are paid over a shorter period of time.c)The discount rate decreases.d)Statements (b) and (c) are both correct.Answer: (d)Short Problems1.CyberNow is opening an office in the U.S. CyberNow expects cash flows to be $500,000 forthe first year, $530,000 for the second year, $560,000 in the third year. If CyberNow uses 12 percent as its discount rate, what is the present value of the cash flows? Assume cash flows are made at the end of the year.Answer: PV = FV/(1 + i)n= 500,000/(1.12)1 + 530,000/(1.12)2 + 560,000/(1.12)3= 446,429 + 422,513 + 398,597= $1,267,5392. GeorgiaSun Inc. has preferred stock that pays an annual dividend of $10.50. If the securityhas no maturity (an “infinite” life), what is its value to an investor who wishes to obtain an8.5 percent rate of return?Answer: PV of a level Perpetuity = $10.50/0.085= $123.533.Let us suppose you have a choice between investing in a bank savings account that pays 9%compounded annually (Bank Yearly) and one that pays 8.5% compounded daily (Bank Daily).(Assume this is based on 365 days). Using only effective annual rates, which bank would you prefer?Answer: Effective annual rate: Bank Yearly = 9%Effective annual rate: Bank Daily = [1 + 0.085/365]365– 1= 8.87%You would prefer Bank Yearly because you will earn more money.4.Steptoe’s bank account has a floating interest rate on certain deposits. That is, every year theinterest rate is adjusted. Four years ago Steptoe deposited $35,000 into the bank account, when interest rates were 6%. The following year the rate was 6.5%, last year the rate was 8% and this year the rate fell to 7.5%. How much will be in his account at the end of the year?Assume annual compounding.Answer: Amount = $35,000 x 1.06 x 1.065 x 1.08 x 1.075= $45,872.855.Calculate the net present value of the following cash flows: you invest $4,000 today andreceive $400 one year from now, $900 two years from now and $2000 three years from now.Assume the interest rate is 9%.Answer: NPV = $400/(1.09) +$900/(1.09)2 + $2,000(1.09)3–$4,000= $366.97 + $757.51 + $1,544.37 – $4,000= $ -1,331.156.The manufacturing manager of CyberNow Inc. estimates that she can save the company$20,000 cash per year over the next 5 years by implementing a recycling plan. What is the value of the savings today if the appropriate interest rate for the firm is 8%. Assume that cash flows occur at the end of the year.Answer:n i PV FV PMT Result5 8 ? 0 $20,000 PV = $79,854.207.Stroll Inc. has been offered a $2,000,000 jet under a 10 year loan agreement. The loanrequires Stroll Inc. to make equal, annual, end-of-year payments that include both principal and interest on the outstanding balance. The interest rate on the loan is 11%. Calculate the amount of these annual payments.Answer:n i PV FV PMT Result10 11 –$2,000,000 0 ? PMT = $339,602.85 8.Herb Flint decides to put $2,000 a year into an IRA fund over his 35 year working life andthen retire. Assume the deposits are made at the end of the year. If the account earns 11% compounded annually, what will Herb have in the account when he retires?Answer:n i PV FV PMT Result35 11 0 ? $2,000 FV = $683,179.119.Regarding retirement funds, there is some debate as to whether investors should invest at thebeginning of the year rather than at the end of the year. If an investor invests $2,000 per year at 12% over a 35 year period, what is the difference between the two funds?Answer: End of Year Fund:n i PV FV PMT Result35 12 0 ? $2,000 PV = $863,326.99Under an immediate annuity the entire amount earns interest for an additional year. So the FV for the immediate annuity is $863,326.99 X 1.12 = $996,926.23.Therefore the difference between the funds is: $996,926.23 – $863,326.99 = $103,599.24 10.You have the chance to buy a bond for $900 that will make one payment of $1,100 six yearsfrom today. What is the internal rate of return in the bond’s cash flows?Answer: 900(1 + i)6 = 1,100(1 + i)6 = 1.222i = (1.222)1/6 - 1i= 3.40%11.Consider the situation where you are trying to decide if you should invest in an Australianproject or an American project. Both projects require an initial outlay of $20,000. TheAustralian project will pay you Aust $40,000 per year for 6 years, whereas the American one will generate $25,000 per year for 6 years. The Australian dollar interest rate is 6% per year and the American interest rate is 5% per year; the current dollar price of an Australian dollar is $0.65 per Australian dollar. Which project has the higher NPV?Answer:American Project:n i PV FV PMT PV Result6 5 ? 0 $25,000 $126,892Australian Project:n i PV FV PMT PV Result6 6 ? 0 $40,000 $196,693 (Aust)NPV US project = $126,892 - $20,000 = $106,892Today the Australian project is worth A$196,693 x $0.65 per Aust= $127,850.45 (in U.S. dollars)NPV Aust project = $127,850.45 - $20,000 = $107,850.45Choose the Australian project since it has a higher NPV.12.If the exchange rate between the U.S. dollar and the Dutch Guilder is $0.49903 per Guilder,the dollar interest rate is 7% per year and the Dutch interest rate is 8% per year, what is the “break-even” value of the future dollar/Guilder exchange rate one year from now?Answer:Today One Year From Now$1 @7% $1.072.00389 Guilders @8% 2.16420 Guilders“Break-even” point = $1.07/2.16420 Guilders= $0.49441 per Guilder13.What is the real rate of interest if the nominal rate is 11.5% per year and the rate of inflationis 7% per year?Answer:Real interest rate = Nominal interest rate – rate of inflation1 + rate of inflation= 0.115 – 0.071.07= 0.04206Real interest rate = 4.21%14.I have $200 today and am interested in finding out what its equivalent real future value willbe in 40 years. What are the two ways I have available to me in computing the real future value?Answer:pute the future value using the real rate of interest.pute the nominal future value using the nominal rate, and then deflate it tofind the real future value.15.The real rate of interest is 3.756%, the nominal rate of interest is 10.5% and the rate ofinflation is 6.5%. What is the real future value of $2,000 in 40 years time? Show bothmethods.Answer:Method One:Real future value = $,2000 x 1.0375640= $8,741Method Two:Nominal future value = $2,000 x 1.10540= $108,522.83Future price level = 1.06540= 12.16Real FV = nominal future valuefuture price level= $108,522.8312.416= $8,74116.As part of your new job at CyberInc. the company is providing you with a new Jeep. Yourfirm will lease this $34,000 Jeep for you. The terms of the lease are seven annual payments at an interest rate of 10%, which will fully amortize the cost of the car. Assuming that allpayments are made on time and no additional money is paid towards the lease in any year, what percent of the 5th payment will go towards repayment of principal?Answer:n i PV FV PMT Result7 10 –$34,000 0 ? PMT = $6,984.39The monthly payment = $6,984.39Of the monthly payment, principal = $5,247% principal repayment in 5th payment =$5,247/$6,984.39= 75.12%17.You have decided to buy a car that costs $35,000. The dealer offers you a 5 year loan withmonthly payments of $814 per month. What is the annual interest rate on the loan?Answer:n i PV FV PMT Result60 ? –$35,000 0 $814 i = 1.165The annual nominal interest rate = 1.165 * 12= 13.98% per year18.A subscription to the magazine “National Tattler” states that you can purchase a one yearsubscription for $45 today, which can be renewed after a year at this rate. Alternately, you can purchase a two year subscription for $80 today. If you wish to subscribe to the magazine for two years and your required rate of return is 9% per year, which subscription offer should you choose?Answer:PV of the two year subscription = $80PV of one year subscription and renewal = $45 + 45/1.09= $86.28The two year subscription is the cheaper alternative.Longer Problems1.Heathcliff is currently 25 years old and expects to retire at age 65. Suppose that Heathclifftakes a job immediately and can earn $35,000 for the remainder of his working life. What is the present value of his future earnings?Answer:n i PV FV PMT Result40 5 ? 0 $35,000 PV = $600,5682.In order to finance your dream home, you are considering borrowing $120,000. The annualpercentage rate is 9% and payments are made annually over 5 years. Construct the loan-amortization schedule for the annual paymentsAnswer:n i PV FV PMT Result5 9 –$120,000 0 ? PMT = $30,856Loan Amortization Schedule is as follows:3.You are 60 years old and are considering whether it pays to buy an annuity from an insurancecompany. For a cost of $25,000, the insurance company will pay you $3,000 per year for the rest of your life. If you can earn 8% per year on your money in a bank account and expect to live until age 80, is it worth buying the annuity? What implied interest rate is the insurance company paying you?Answer: First compute the present value of the annuity.n i PV FV PMT Result20 8 ? 0 $3,000 PV = $29,454.44Now compute the NPV of the investment of the annuity:NPV = $29,454.44 - $25,000= $4,454.44So the annuity looks worth buying.To compute the implied interest rate on the annuity, we need to find the discountrate that makes the NPV zero. On a financial calculator, we find the answer to be10.32% per year.4. Gemma Peel is 30 years today and she wishes to accumulate enough money over the next 35 years to provide for a 20 year retirement annuity of $100,000 at the beginning of each year, starting with her 65th birthday. Assume the rate of the return over the entire period will be 11%. What is the present value of this annuity?Answer:n i PV FV PMT Result20 11 ? 0 $100,000 PV = $883,9295. The exchange rate between the Canadian dollar and the U.S. dollar is currently $0.69190 perCanadian dollar, the dollar interest rate is 6% per year, and the Canadian dollar interest rate is7% per year. You have $100,000 in a one-year account that allows you to choose betweeneither currency and it pays the corresponding interest rate. What is the “break-even” value ofthe dollar/Canadian dollar exchange rate one year from now?Answer:U.S. today One year from now$1 @6% $1.06Canadian today One year from now$1.44530(Cdn) @7% $1.54647“Break-even” point = $1.06/1.54647 (Cdn dollar)= $0.68543 per Canadian dollar6.Assume that you have just taken out a $300,000 30 year mortgage with monthly payments atan annual 8 percent rate. At the end of the 3rd year (after 36 payments), you begin paying anadditional $100 each month towards the mortgage. That is, for months 37 onward you makethe scheduled payment plus an extra $100 each month. To the nearest whole number, howmany additional payments (payments in addition to the first 36) must you make before themortgage is paid off?Answer:First compute the monthly payment-PV FV Interest N Result________-300,000 0 0.67 360 360 PMT = $2,201.29Initially, you made $2,201.29 for the first three years. After 36 payments, the remaining balance = $291,840.45. After period 37, compute number of additional payments now that your monthly paymentis $2,301.29.PV FV Interest PMT Result__-$291,840.45 0 0.67 $2,301.29 N = 281You must make 281 additional payments before the mortgage is paid off.7.The company you work for has been experiencing financial difficulties and has just filed areorganization plan. Three years ago, one of the firm’s creditors lent the firm $80,000 on a ten year annual payment loan at a 15% interest rate. Immediately after the firm made the third payment, as a result of the court settlement, the creditor agreed to decrease the current outstanding balance of the loan by 20%, to lower the interest rate to 10%, and to increase the remaining term of the loan to 15 years. What wi ll be the new annual payments on the firm’s loan, assuming all these changes take place?Answer:Under the original plan, your firm had annual payment obligations of:n i PV FV PMT Result10 15 –$80,000 0 ? PMT = $15,940Originally, your firm had to pay $15,940 per year to its creditors.After the third balance, the remaining balance = $66,318Under the new arrangement, new outstanding balance = $66,318 X 0.80= $53,054Under the new payment arrangement, annual payments are:n i PV FV PMT Result15 10 –$53,054 0 ? PMT = $6,975.218.Five banks offer CDs at the following stated annual percentage rates:Bank A: 10% APR compounded annuallyBank B: 9.8% APR compounded semiannuallyBank C: 9.6% APR compounded quarterlyBank D: 9.5% APR compounded monthlyBank E: 9.4% APR compounded dailyAnton has inherited $150,000 and decides to invest the money in a 20 year CD. He decides to invest the money with Bank E. If Anton had invested his money in the CD offering the best rate instead of Bank E, how much more money would he have had after 20 years?Answer:First determine the effective annual rates at each bank.Bank A: Effective Annual Rate = 10% per yearBank B: Effective Annual Rate = 10.04% per yearBank C: Effective Annual Rate = 9.95% per yearBank D: Effective Annual Rate = 9.92% per yearBank E: Effective Annual Rate = 9.85% per yearBest Account = Bank BAfter 20 years, the FV at Bank B:n i PV FV PMT Result20 10.04 –$150,000 ? 0 FV = $1,016,489.49Compare the above with the FV at Bank E after 20 years:n i PV FV PMT Result20 9.85 –$150,000 ? 0 FV = $981,957.03If Anton had invested with Bank B, he would have earned $1,016,489.49 - $981,957.03 = $34,532.46 more.。
