university of Saskatchewan公司财务导论(金融学)3
公司财务学导论ppt课件
公司财务学导论
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公司的资产负债表
营运资本净额决策
流动资产 营运 资本 净额
流动负债 长期负债
固定资产 1有形固定资产
公司需要多少短期 现金流量来支付其 账单
2 无形固定资产
所有这权益
公司财务学导论
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资产负债表左右两边项目的内容及相互关系构成了公司 财务学的研究内容：
1．企业应该投资于什么样的长期资产？(资产负债表的左下方 )
（4）期权理论。
（5）资本结构理论。
公司财务学导论
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• 三、财务管理的重要性
财务管理在一个企业的经营管理中有着举足轻重的 位置，许多决策都直接影响到企业的生存和发展。
企业组织结构图
公司财务学导论
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董事会 执行总裁
营销副总裁
财务副总裁
生产副总裁
财务主管
会计主管
资本预算经理 现金经理 信用经理 税务经理 成本会计经理
管理内容。
公司财务学导论
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•二、财务管理学的发展历史回顾
财务管理学作为独立的学科始于19世纪末20世纪初。 1897年，托马斯·格林纳（Thomos Greene）出版 了《公司理财》，1920年亚瑟·斯通（Arthor Stone） 出版了《公司财务策略》，财务管理学逐渐地从微 观经济学中分离出来，成为一门独立的学科。
公司财务学导论
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财务经理（CFO）
为了为公司创造价值，财务经理需做:
1. 制定精明的投资策略.
2. 制定精明的融资策略.
3.
例如股息分配政策的决定、重大投资计划
的通过和发行债券、股票的决定权等，财务总监
虽不直接做出这些重大决定，但要为最后的决策
1公司金融导论mup
金融学
货币银行学 国际金融学
何谓金融学?
2024/7/11
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Webster字典:“To Finance”定义为“筹集或提 供资本(To Raise Or Provide Funds or Capital For)” ;
《华尔街日报》在其新开的公司金融(Corporate Finance)的固定版面中将(公司)金融定义为“为 业务提供融资的业务(Business Of Financing Businesses)” ;
《新帕尔格雷夫货币金融大辞典》(The New Palgrave Dictionary Of Money And Finance):” 金融以其不同的中心点和方法论而成为经济学的 一个分支，其中心点是资本市场的运营、资本资 产的供给和定价。 ”其方法论是使用相近的替代 物给金融契约和工具定价。罗斯概括了“Finance” 的四大课题：“有效率的市场”、“收益和风 险”、“期权定价理论”和“公司金融”。
公司理论应该是公司金融学的基础，而公司理论在很大程度上是 个法律问题。
过去的研究者往往给定公司的存在，而被动地讨论金融问题，公 司金融被视同为财务管理。
2024/7/11
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当前公司金融最有意义的课题： 从法律的角度研究公司金融。 以资本成本为核心研究公司金融。 资本结构 公司治理 公司价值评估
2024/7/11
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第11章 套利定价理论(APT)211 11．1 因素模型：公告．意外和期望收益211 11．2 风险：系统性和非系统性212 11．3 系统风险和贝塔系数213 11．4 投资组合与因素模型215 11．5 贝塔系数与期望收益218 11．6 资本资产定价模型和套利定价模型220 11．7 资产定价的实证研究方法221 第12章 风险．资本成本和资本预算227 12．1 权益资本成本227 12．2 贝塔的估计229 12．3 贝塔的确定232 12．4 基本模型的扩展234 12．5 伊士曼化学公司的资本成本估计237 12．6 降低资本成本240
公司理财导论
资产合计
=
负债+所有者权益合计 负债 所有者权益合计
Discussion
• What does the Corporate Finance aim to resolve? • What are the three main decisions that a financial manager needs to make? • How does the balance-sheet form when the financial manager makes the three decisions?
Total Value of Assets: Total Firm Value to Investors: Current Liabilities Long-Term Debt
How can the firm raise the money for the required investments?
Corporate Finance
About the Author
• 斯蒂芬 罗斯（Stephen A.Ross）现任 斯蒂芬·A·罗斯（ 罗斯 ）现任MIT斯 斯 隆管理学院教授， 隆管理学院教授，是在金融学和经济学领域著述 最广泛的学者之一。 最广泛的学者之一。他因提出套利定价理论而闻 名于世，并在信号理论、代理理论、期权定价、 名于世，并在信号理论、代理理论、期权定价、 利率的期限结构等领域做出了重要贡献。 利率的期限结构等领域做出了重要贡献。 • 罗斯教授曾任美国金融学会主席，目前担任一些 罗斯教授曾任美国金融学会主席， 学术和实务杂志的编委。 学术和实务杂志的编委。同时还担任加利福尼亚 技术公司（ 技术公司（CalTech）管理人、大学退休权益基 ）管理人、 金（College Retirement Equity Fund）董事长， ）董事长， 罗尔-罗斯资产管理公司联合主席 罗斯资产管理公司联合主席。 罗尔 罗斯资产管理公司联合主席。
公司理财导论(ppt67张)
“一个企业所做的每一个决定都有其 财务上的含义，而任何一个对企业财 务状况产生影响的决定就是该企业的 财务决策。因此，从广义上讲，一个 企业所做的任何事情都属于公司理财 的范畴。”
——达摩达兰
传说
在很久很久以前，一个主人雇了三个忠实的仆人 一次，主人要出远门一年，他把自己的全部积蓄（30 枚金币）交给三位仆人保管，每人10枚 一年后，当主人回到家，三位仆人如下汇报 A：我把金币埋在安全的地方，现在完好无损 B：我把金币借给别人，现在连本带利共有11枚 C：我用金币去做生意，现在共有14枚 问题：哪位仆人值得赞扬？
要求： 关注一家上市公司 每人（或以小组为单位）对一家上市公 司的财务状况、投资、融资、公司治理 等予以关注，进行课堂交流。
财务管理与会计学科体系中其他课程之 间的关系
该课程需要的背景知识 会计学基础、经济学知识、管理学背景、 金融学知识
《财务管理》是考研、职称考试、资格考试中的 必考科目 CPA 考试科目（6+1）： 第一阶段：专业考试 会计、审计、财务成本管理、税法、经济法、 公司战略与风险管理 第二阶段：综合考试
公司制：现代企业最重要的组织形式， 公司是一个独立的“法人” 公司章程 P7 三类直接利益主体：股东、董事、高 层管理人员
中级会计师考试科目： 经济法、会计实务、财务管理
国际上与财务管理相关的各种资格认证考试 (CFA、CFP）陆续登陆中国 2008年CFA学员平均薪资 CFA一级学员收入：基本薪金RMB240,000加上 奖金RMB102,400， 总计年收入为RMB342,400
CFA二级学员收入：基本薪金RMB436,000加上奖 金RMB156,000， 总计年收入为RMB592,000 CFA三级学员收入：基本薪金RMB514,800加上奖 金RMB423,600， 总计年收入为RMB938,400
公司理财罗斯版1-导论
金融工具与融资方式
1 2 3
金融工具的定义和分类
金融工具是用来交换资金和转移风险的凭证，可 以分为股票、债券、衍生品等类型。
融资方式的种类
融资方式是指企业筹集资金的方式，包括内部融 资、债务融资、股权融资等，不同的融资方式具 有不同的成本和风险。
金融工具的交易和定价
金融工具的交易和定价涉及到市场供求关系、风 险水平、利率等多个因素，是公司理财中需要关 注的重要问题。
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02
03
04
财务计划与预算
制定公司的财务计划和预算， 以指导公司的财务活动。
财务分析与控制
定期评估公司的财务状况，识 别问题并采取措施进行改进。
财务风险管理
识别和管理与公司财务相关的 风险，包括市场风险、信用风
险和操作风险等。
财务决策
制定公司的投资、融资和股息 政策，以实现公司的财务目标
。
02 公司理财的环境
社会责任
公司理财也需考虑社会责任， 通过合理经营和资源利用，为
社会做出贡献。
投资决策
投资项目评估
资本预算
投资决策需要对项目进行全面的评估，包 括市场需求、技术可行性、财务效益等方 面。
投资决策需要进行资本预算，对项目的投 资成本和预期收益进行预测和评估。
风险评估
投资组合选择
投资决策需要对项目风险进行评估，包括 市场风险、技术风险、财务风险等，并制 定相应的风险控制措施。
金融政策与法规
金融政策的种类和影响
金融政策是指政府通过货币政策、财政政策等手段对经济进 行调控的政策，这些政策会影响到企业的融资成本和市场环 境。
法律法规对企业理财的影响
企业的理财活动需要遵守相关的法律法规，如公司法、证券 法、会计法等，这些法律法规对企业融资、投资等方面都有 重要的影响。
昆士兰大学 公司理财Lecture3
Dividend Policies
Residual dividend policy Smoothed dividend policy Constant payout policy
Company may decide to buy back own shares
Managers and Payout Decisions
Is There an Optimal Dividend Policy?
With perfect capital markets
Dividends do not impact shareholder wealth
19/6
Dividend Timetable
3/7 9/7 27/8
With capital market imperfections, the following views exist:
Legal Considerations
Dividends
Must be paid from profit, not capital Cannot be paid if it would make the company insolvent May be restricted by loan agreements and covenants Must observe priority rights of preference shares
A fixed investment or capital budgeting program No transaction costs, or other market imperfections (e.g. tax, information asymmetry) No taxes — investors are indifferent between receiving dividends or capital gains
财务管理专业导论(第三学期专题PPT课件
2）政府及非营利组织会计改革
• 我国企业会计改革已经比较成功，但非企业会计严重 滞后。而国际发展趋势是，非企业会计要引入企业会 计的理念、原则和方法，引入企业财务管理理念、财 务报告理念。因此我们要加强非企业会计制度改革。
• 非企业单位的改革是分步走的： 第一步：医院、学校会计制度 第二步：事业单位财务规则和事业单位会计准则 第三步：政府会计准则体系
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关于农村会计改革，我国发布了三个制度：《农村 经济合作组织会计制度》、《农村集体经济会计制 度》、《农村信用社会计制度》，为规范农村会计 核算和监督提供了制度保障。
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2010年2月中纪委、财政部、农业部、民政部联合印 发《关于进一步加强村级会计委托代理服务工作指导 意见的通知》（财会〔2010〕4号），要求强化村级 会计委托代理机构建设，完善工作规范，落实工作经 费，把做好村级会计委托代理服务工作作为推进农村 集体财务管理规范化建设，加强农村集体资金资产资 源管理，促进农村党风廉政建设、基层民主政治建设 和社会主义新农村建设的一项重要工作。
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②应对国际金融危机，中国支持建立全球统一的高质 量会计准则，积极推进中国会计准则持续国际趋同。
为应对国际金融危机，2008年11月，G20华盛顿峰会 提出了应对金融危机的对策，以及改进IASB治理结构 和建立全球统一的高质量会计准则的目标。
中国高度赞赏和支持IASB为应对国际金融危机和落实 G20、FSB要求所做的不懈努力，积极推进中国会计准 则持续国趋同。
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1）企业会计准Leabharlann 的持续趋同• 财政部正式发布了《中国企业会计准则与国际财务报 告准则持续趋同路线图》，这个路线图主要强调三个 方面的内容：
①中国企业会计准则的建设、趋同、实施、等效已经 取得了卓越的成效。
university of Saskatchewan公司财务导论(金融学)1
Fall 2003COMM 2032Why Study Finance?•Personal well-being¾Spend money smartly, e.g., mortgage, car loan¾Retirement planning¾Planning for your (or your kids) education¾Personal investment•Corporate business decisionsFall 2003COMM 2033ObjectivesWhat is Corporate Finance? Answer will be structuredaround the following questions:•What are the basic decisions of corporate finance?•Who is responsible for decisions concerning corporate finance?•How do corporate financial decisions depend on the legal form of the firm?•What is the economic environment in which(corporate) financial decisions have to be undertaken?•What does modern corporate finance see as an appropriate goal for the firm?Fall 2003COMM 2034What is Corporate Finance ?Corporate finance can be seen as a set of decisions made by a business that affects its finances. The following groups of decisions can be distinguished:•expenditure of funds (“Capital Budgeting ")•sources of funds (“Capital Structure ")•short-term cash flows ("Working Capital Management ")Capital BudgetingBasic Issue : Allocation of funds among alternativeinvestment opportunities.Question : Optimal allocation of funds? => Objective forcapital budgeting (“maximization of the market value of the firm's common stocks" or ???)Capital budgeting decisions are not independent of otherdecisions of the firm like:•Market analysis:¾Forecasts: Input costs, Sales.¾Macroeconomic trends: Interest rates, Exchangerates etc.•R & D decisions.Capital StructureMarket value of a firm corresponds to thevalue of two forms of securities: Bonds (loan agreements) and Stocks (share certificates).Fall 2003COMM 2037Difference: Stocks and BondsQuestion : What is the essential differencebetween stocks and bonds?•Both are contingent claims on the total valueof the firmwhere X: Total value of the firm, and F: Promised payoff (debt) to debtholders.Fall 2003COMM 2038Working Capital ManagementShort term finance: Management of short-term cashflows => Management of gaps of cash in-and outflows.What is managed isFall 2003COMM 2039Decision Makers in Corporate FinanceQuestion : Who is responsible for decisions concerning corporate finance ?The Financial Manager:•His/her objective: Create value:¾Buy assets that generate more cash than theycost¾sell financial instruments that raise more cashthan they cost•His/her position held: Vice president financeFall 2003COMM 20310Hypothetical Organization ChartCash Manager Credit Manager Capital Expenditures Financial PlanningTreasurer Tax Manager Cost AccountingManager Financial AccountingManagerData ProcessingManagerControllerVice President andChief Financial Officer (CFO)President and Chief Operations Officer (COO)Chairman of the Board and Chief Executive Officer (CEO)Board of Directors© 1999 McGraw-Hill Ryerson LimitedLegal Forms of CompaniesThere are three legal forms of businessorganization:•Sole Proprietorship •Partnership¾General Partnership ¾Limited Partnership•CorporationSole ProprietorshipFall 2003COMM 20313Partnership (*)General Partnership: all debts, Limited Partnership: equity contributionFall 2003COMM 20314Corporation•Important feature: Separation of Ownership and ControlFall 2003COMM 20315Separation of Ownership and ControlBoard of DirectorsManagementAssetsDebtEquityShareholdersDebtholders© 1999 McGraw-Hill Ryerson Limited Fall 2003COMM 20316Environment of Corporate FinanceEconomic institutions and partners for financialdecisions of the firm .•Financial institutions : Banks, Investmentdealers, insurance companies, pension funds => Financial Intermediation•Money and Capital Markets : Short-term-debt securities (T-bills, bankers acceptance) vs. Long-term securities (long-term debt and shares of stocks)Cash Flows between the Firm andthe Financial MarketsT a x e sFirm Invests in assets (B)Current assets Fixed assetsCash flowfrom firm (C)Financial marketsShort-term debt Long-term debt Equity sharesGovernment(D)Firm issues securities (A)Retainedcash flows (E)Dividends and debt payments (F)© 1999 McGraw-Hill Ryerson LimitedObjective of the Firm•Neoclassical Economics: Profit maximization.¾Problems: Ignores time dimension and thereforeuncertainty of future cash flows•Neolithic Finance: Net Present (NPV) Value maximization.¾Problems: recognizes time dimension but notuncertainty.•“Modern" Finance: Efficient markets for diversification of risk exist.¾Investors will want the firm to make decisionswhich max. current value of its stock.Fall 2003COMM 20319Informational AsymmetriesQuestion:Is the picture of “Modern" corporatefinance too idealistic?•Are markets informationally efficient?¾Insider information ¾Market timing•How do informational asymmetries affect theseparation of ownership and control? ¾Agency ProblemsFall 2003COMM 20320Conflict: Stockholders vs. ManagersPrincipal-Agent Problem : How can shareholders(Principal) design a mechanism which gives managers (Agents) an incentive to work in their interest? =>Reduce agency costs.•Warrants and Stock Option Plans: Managers haveright to buy shares when share price increases ¾Does it work? (financial sense article )•Incentives for stockholders to play active role duringthe annual meeting to elect the board of directors and improve their information.•Take-over threats•Competition in the managerial labour market.Fall 2003COMM 20321Conflict: Stockholders vs. BondholdersSource : Different residual claims contingent upondefault. => Creditors dislike actions which increase leverage and therefore default probability.Tools :•Covenants (investment policy, dividend policy)•Protective Puts (Option to get principal backcontingent upon critical events)•Taking Equity Stakes and Warrant (Hedging ofdefault risk by convertible debt instruments.)。
英国布里斯托大学财务分析课程25页PPT
Cash from share issues
Dividends and cash from share repurchases
Shareholders
Cash from Secondary sale of shares Shareholders
Source: Penman, p. 8
What are we doing?
Why are we doing it?
• Social welfare:
– The activity of analysts make markets efficient. Therefore, contribution to efficient allocation of resources.
• Financial analysts are: – information intermediaries; they digest information and provide summary information to the public/less sophisticated investors. – especially important where capital markets are well developed.
• Note of caution in regard of financial statement analysis:
– Financial statement analysis can be done for various purposes: credit analysis, competitive benchmarking, analysis of mergers and acquisitions, etc.
公司财务原理Principles of Corporate Finance(11th edition)_课后习题答案Chap003
CHAPTER 3Valuing BondsAnswers to Problem Sets1. a. Does not change. The coupon rate is set at time of issuance.b. Price falls. Market yields and prices are inversely related.c. Yield rises. Market yields and prices are inversely related.Est. Time: 01-052. a. If the coupon rate is higher than the yield, then investors must beexpecting a decline in the capital value of the bond over its remaining life.Thus, the bond’s price must be greater than its face value.b. Conversely, if the yield is greater than the coupon, the price will be belowface value and it will rise over the remaining life of the bond.Est. Time: 01-053. The yield over six months is 2.7/2 = 1.35%.The six-month coupon payment is $6.25/2 = $3.125.There are 18 years between today (2012) and 2030; since coupon payments are listed every six months, there will be 36 payment periods.Therefore, PV = $3.125 / 1.0135 + $3.125 / (1.0135)2 + . . . $103.125 / (1.0135)36 = $150.35.Est. Time: 01-054. Yields to maturity are about 4.3% for the 2% coupon, 4.2% for the 4% coupon,and 3.9% for the 8% coupon. The 8% bond had the shortest duration (7.65years), the 2% bond the longest (9.07 years).The 4% bond had a duration of 8.42 years.Est. Time: 01-055. a. Fall. Example: Assume a one-year, 10% bond. If the interest rate is 10%,the bond is worth $110/1.1 = $100. If the interest rate rises to 15%, the bond isworth $110/1.15 = $95.65.b. Less (e.g., see 5a —if the bond yield is 15% but the coupon rate is lower at 10%, the price of the bond is less than $100).c.Less (e.g., with r = 5%, one-year 10% bond is worth $110/1.05 = $104.76).d. Higher (e.g., if r = 10%, one-year 10% bond is worth $110/1.1 = $100, while one-year 8% bond is worth $108/1.1 = $98.18).e.No. Low-coupon bonds have longer durations (unless there is only one period to maturity) and are therefore more volatile (e.g., if r falls from 10% to 5%, the value of a two-year 10% bond rises from $100 to $109.3 (a rise of 9.3%). The value of a two-year 5% bond rises from $91.3 to $100 (a rise of 9.5%).Est. Time: 01-056. a. Spot interest rates. Yield to maturity is a complicated average of theseparate spot rates of interest.b. Bond prices. The bond price i s determined by the bond’s cash flows andthe spot rates of interest. Once you know the bond price and the bond’s cash flows, it is possible to calculate the yield to maturity.Est. Time: 01-057. a. 4%; each bond will have the same yield to maturity.b.PV = $80/(1.04) + $1,080/(1.04)2 = $1,075.44.Est. Time: 01-058. a. PV ()221110515r r +++=b.PV ()2110515y y +++=c. Less (it is between the one-year and two-year spot rates). Est. Time: 01-059. a. The two-year spot rate is r 2 = (100/99.523).5 – 1 = 0.24%.The three-year spot rate is r 3 = (100/98.937).33 – 1 = 0.36%. The four-year spot rate is r 4 = (100/97.904).25 – 1 = 0.53%. The five-year spot rate is r 5 = (100/96.034).2 – 1 = 0.81%.b. Upward-sloping.c. Higher (the yield on the bond is a complicated average of the separatespot rates).Est. Time: 01-0510. a. Price today is $108.425; price after one year is $106.930.b. Return = (8 + 106.930)/108.425 - 1 = .06, or 6%.c. If a bond’s yie ld to maturity is unchanged, the return to the bondholder isequal to the yield.Est. Time: 01-0511. a. False. Duration depends on the coupon as well as the maturity.b. False. Given the yield to maturity, volatility is proportional to duration.c. True. A lower coupon rate means longer duration and therefore highervolatility.d. False. A higher interest rate reduces the relative present value of (distant)principal repayments.Est. Time: 01-0512.Est. Time: 06-1013. 7.01%; the extra return that you earn for investing for two years rather than oneyear is 1.062/1.05 – 1 = .0701.Est. Time: 01-0514. a. Real rate = 1.10/1.05 – 1 = .0476, or 4.76%.b. The real rate does not change. The nominal rate increases to 1.0476 ×1.07 – 1 = .1209, or 12.09%.Est. Time: 01-0515. With annual coupon payments:=+⎥⎦⎤⎢⎣⎡⨯-⨯=1010(1.06)100(1.06)0.0610.0615PV €92.64 Est. Time: 01-0516. a. $10,231.64(1.026)10,000(1.026)0.02610.0261275PV 2020=+⎥⎦⎤⎢⎣⎡⨯-⨯=b.Interest Rate PV of Interest PV ofFace Value PV of Bond1.0% $5,221.54 $9,050.63 $14,272.17 2.0% 4,962.53 8,195.44 13,157.973.0% 4,721.38 7,424.70 12,146.08 4.0% 4,496.64 6,729.71 11,226.365.0% 4,287.02 6,102.71 10,389.736.0% 4,091.31 5,536.76 9,628.067.0% 3,908.41 5,025.66 8,934.07 8.0% 3,737.34 4,563.87 8,301.219.0% 3,577.18 4,146.43 7,723.61 10.0% 3,427.11 3,768.89 7,196.00 11.0% 3,286.36 3,427.29 6,713.64 12.0% 3,154.23 3,118.05 6,272.28 13.0% 3,030.09 2,837.97 5,868.06 14.0% 2,913.35 2,584.19 5,497.54 15.0% 2,803.49 2,354.13 5,157.62Est. Time: 06-1017.Purchase price for a six-year government bond with 5% annual coupon:1,108.34(1.03)1,000(1.03)0.0310.03150PV 66$=+⎥⎦⎤⎢⎣⎡⨯-⨯= The price one year later is equal to the present value of the remaining five years of the bond:1,091.59(1.03)1,000(1.03)0.0310.03150PV 55$=+⎥⎦⎤⎢⎣⎡⨯-⨯= Rate of return = [$50 + ($1,091.59 – $1,108.34)]/$1,108.34 = 3.00% Price one year later (yield = 2%):1,141.40(1.02)1,000(1.02)0.0210.02150PV 55$=+⎥⎦⎤⎢⎣⎡⨯-⨯=Rate of return = [$50 + ($1,141.40 – $1,108.34)]/$1,108.34 = 7.49%.Est. Time: 06-1018. The key here is to find a combination of these two bonds (i.e., a portfolio ofbonds) that has a cash flow only at t = 6. Then, knowing the price of the portfolio and the cash flow at t = 6, we can calculate the six-year spot rate. We begin byspecifying the cash flows of each bond and using these and their yields tocalculate their current prices:Investment Yield C1. . . C5C6Price6% bond 12% 60 . . . 60 1,060 $753.3210% bond 8% 100 . . . 100 1,100 $1,092.46 From the cash flows in years 1 through 5, we can see that buying two 6% bonds produces the same annual payments as buying 1.2 of the 10% bonds. To seethe value of a cash flow only in year 6, consider the portfolio of two 6% bondsminus 1.2 10% bonds. This portfolio costs:($753.32 × 2) – (1.2 ⨯ $1,092.46) = $195.68The cash flow for this portfolio is equal to zero for years 1 through 5 and, for year 6, is equal to:(1,060 × 2) – (1.2 ⨯ 1,100) = $800Thus:$195.68 ⨯ (1 + r6)6 = $800r6 = 0.2645 = 26.45%Est. Time: 06-1019. Downward sloping. This is because high-coupon bonds provide a greaterproportion of their cash flows in the early years. In essence, a high-coupon bond is a ―shorter‖ bond than a low-coupon bond of the same maturity.Est. Time: 01-0520. a.Year Discount Factor Forward Rate1 1/1.05 = 0.9522 1/(1.054)2 = 0.900 (1.0542 /1.05) – 1 = 0.0580 = 5.80%3 1/(1.057)3 = 0.847 (1.0573 /1.0542 ) – 1 = 0.0630 = 6.30%4 1/(1.059)4 = 0.795 (1.0594 /1.0573 ) – 1 = 0.0650 = 6.50%5 1/(1.060)5 = 0.747 (1.0605 /1.0594 ) – 1 = 0.0640 = 6.40%b. i. 5%, two-year bond:$992.79(1.054)10501.0550PV 2=+=ii. 5%, five-year bond:$959.34(1.060)1,050(1.059)50(1.057)50(1.054)501.0550PV 5432=++++=iii. 10%, five-year bond:$1,171.43(1.060)1,100(1.059)100(1.057)100(1.054)1001.05100PV 5432=++++=c. First, we calculate the yield for each of the two bonds. For the 5% bond, this means solving for r in the following equation:5432r)(11,050r)(150)(150)(150150$959.34+++++++++=r r r r = 0.05964 = 5.964%For the 10% bond:5432r)(11,100r)(1100r)(1100r)(1100r 1100$1,171.43+++++++++=r = 0.05937 = 5.937%The yield depends upon both the coupon payment and the spot rate at the time of the coupon payment. The 10% bond has a slightly greater proportion of its total payments coming earlier, when interest rates are low, than does the 5% bond. Thus, the yield of the 10% bond is slightly lower.d. The yield to maturity on a five-year zero-coupon bond is the five-year spot rate, here 6.00%.e. First, we find the price of the five-year annuity, assuming that the annual payment is $1:Now we find the yield to maturity for this annuity:r = 0.05745 = 5.745%$4.2417(1.060)1.059)(11.057)(11.054)(111.051P V 5432=++++=5432r)(11r)(11r)(11r)(11r 11$4.2417+++++++++=f. The yield on the five-year note lies between the yield on a five-year zero-coupon bond and the yield on a five-year annuity because the cash flowsof the Treasury bond lie between the cash flows of these other twofinancial instruments during a period of rising interest rates. That is, theannuity has fixed, equal payments; the zero-coupon bond has onepayment at the end; and the bond’s payments are a combination of these. Est. Time: 06-1021. To calculate the duration, consider the following table similar to Table 3.4:The duration is the sum of the year × fraction of total value column, or 6.395 years.The modified duration, or volatility, is 6.395/(1 + .04) = 6.15.The price of the 3% coupon bond at 3.5%, and 4.5% equals $969.43 and $911.64, respectively. This price difference ($57.82) is 5.93% of the original price, which is very close to the modified duration.Est. Time: 06-1022.a. If the bond coupon payment changes from 9% as listed in Table 3.4 to 8%,then the following calculation for duration can be made:A decrease in the coupon payment will increase the duration of the bond, as theduration at an 8% coupon payment is 5.778 years.The volatility for the bond in Table 3.4 with an 8% coupon payment is:5.778/(1.04) = 5.556.The bond therefore becomes less volatile if the couponpayment decreases.b. For a 9% bond whose yield increases from 4% to 6%, the duration can becalculated as follows:There is an inverse relationship between the yield to maturity and the duration.When the yield goes up from 4% to 6%, the duration decreases slightly. Thevolatility can be calculated as follows: 5.595/(1.06) = 5.278. This shows that the volatility decreases as well when the yield increases.Est. Time: 06-1023. The duration of a perpetual bond is: [(1 + yield)/yield].The duration of a perpetual bond with a yield of 5% is:D5 = 1.05/0.05 = 21 yearsThe duration of a perpetual bond yielding 10% is:D10 = 1.10/0.10 = 11 yearsBecause the duration of a zero-coupon bond is equal to its maturity, the 15-year zero-coupon bond has a duration of 15 years.Thus, comparing the 5% perpetual bond and the zero-coupon bond, the 5%perpetual bond has the longer duration. Comparing the 10% perpetual bond and the 15-year zero, the zero has a longer duration.Est. Time: 06-1024. Answers will differ. Generally, we would expect yield changes to have thegreatest impact on long-maturity and low-coupon bonds.Est. Time: 06-1025. The new calculations are shown in the table below:26. We will borrow $1,000 at a five-year loan rate of 2.5% and buy a four-year strippaying 4%. We may not know what interest rates we will earn on the last year(4 5), but our $1,000 will come due, and we put it under our mattress earning0% if necessary to pay off the loan.Let’s turn to present value calculations: As shown above, the cost of the strip is$854.80. We will receive proceeds from the 2.5% loan = $1,000/(1.025)5 =$883.90. Pocket the difference of $29.10, smile, and repeat.The minimum sensible value would set the discount factors used in year 5 equal to that of year 4, which would assume a 0% interest rate from year 4 to 5. Wecan solve for the interest rate where 1/(1 + r)5 = 0.8548, which is roughly 3.19%. Est. Time: 06-1027.a. If the expectations theory of term structure is right, then we can determinethe expected future one-year spot rate (at t = 3) as follows: investing $100in a three-year instrument at 4.2% gives us $100(1 + .042)3 = 113.136.Investing $100 in a four-year instrument at 4.0% gives us $100 × (1+.04)4= 116.986. This reveals a one-year spot rate from year 3 to 4 of ($116.98– 113.136)/113.136 = 3.4%.b. If investing in long-term bonds carries additional risks, then the riskequivalent of a one-year spot rate in year 3 would be even less (reflectingthe fact that some risk premium must be built into this 3.4% spot rate).Est. Time: 06-1028.a. Your nominal return will be 1.082 -1 = 16.64% over the two years. Yourreal return is (1.08/1.03) × (1.08/1.05) - 1 = 7.85%.b. With the TIPS, the real return will remain at 8% per year, or 16.64% overtwo years. The nominal return on the TIPS will equal (1.08 × 1.03) × (1.08× 1.05) – 1 = 26.15%.Est. Time: 01-0529. The bond price at a 5.3% yield is:1,201.81(1.053)1,000(1.053)0.05310.0531100PV 55$=+⎥⎦⎤⎢⎣⎡⨯-⨯= If the yield decreases to 5.9%, the price would rise to:1,173.18(1.059)1,000(1.059)0.05910.0591100PV 55$=+⎥⎦⎤⎢⎣⎡⨯-⨯=30. Answers will vary by the interest rates chosen.a. Suppose the YTM on a four-year 3% coupon bond is 2%. The bond is selling for:08.038,1$3=+⎥⎦⎤⎢⎣⎡⨯-⨯=44(1.02)1,000(1.02)0.0210.0210PVIf the YTM stays the same, one year later the bond will sell for:84.028,1$3=+⎥⎦⎤⎢⎣⎡⨯-⨯=33(1.02)1,000(1.02)0.0210.0210PVThe return over the year is [$30 + (1,028.84 - 1,038.08)]/$1,038.08= 0.02, or 2%.b. Suppose the YTM on a four-year 3% coupon bond is 4%. The bond is sellingfor:70.963$3=+⎥⎦⎤⎢⎣⎡⨯-⨯=44(1.04)1,000(1.04)0.0410.0410PV If the YTM stays the same, one year later the bond will sell for:25.972$3=+⎥⎦⎤⎢⎣⎡⨯-⨯=33(1.04)1,000(1.04)0.0410.0410PVThe return over the year is [$30+(972.25-963.70)]/$963.70 = 0.04, or 4%.Est. Time: 06-1031. Spreadsheet problem; answers will vary.Est. Time: 06-1032. Arbitrage opportunities can be identified by finding situations where the impliedforward rates or spot rates are different.We begin with the shortest-term bond, Bond G, which has a two-year maturity.Since G is a zero-coupon bond, we determine the two-year spot rate directly by finding the yield for Bond G. The yield is 9.5%, so the implied two-year spot rate (r 2) is 9.5%. Using the same approach for Bond A, we find that the three-yearspot rate (r 3) is 10.0%.Next we use Bonds B and D to find the four-year spot rate. The followingposition in these bonds provides a cash payoff only in year four: a long position in two of Bond B and a short position in Bond D.Cash flows for this position are:[(–2 ⨯ $842.30) + $980.57] = –$704.03 today[(2 ⨯ $50) – $100] = $0 in years 1, 2 and 3[(2 ⨯ $1,050) – $1,100] = $1,000 in year 4 We determine the four-year spot rate from this position as follows:4)4r (1$1,000$704.03+= r 4 = 0.0917 = 9.17%Next, we use r 2, r 3, and r 4 with one of the four-year coupon bonds to determine r 1. For Bond C:978.74r 1120(1.0917)1,120(1.100)120(1.095)120r 1120$1,065.2814321++=++++= r 1 = 0.3867 = 38.67%Now, in order to determine whether arbitrage opportunities exist, we use thesespot rates to value the remaining two four-year bonds. This produces thefollowing results: for Bond B, the present value is $854.55, and for Bond D, thepresent value is $1,005.07. Since neither of these values equals the currentmarket price of the respective bonds, arbitrage opportunities exist. Similarly, the spot rates derived above produce the following values for the three-year bonds: $1,074.22 for Bond E and $912.77 for Bond F.Est. Time: 11-1533. We begin with the definition of duration as applied to a bond with yield r and anannual payment of C in perpetuity:We first simplify by dividing both the numerator and the denominator by C :The denominator is the present value of a perpetuity of $1 per year, which isequal to (1/r ). To simplify the numerator, we first denote the numerator S andthen divide S by (1 + r ):Note that this new quantity [S /(1 + r )] is equal to the square of denominator in the duration formula above, that is:Therefore:Thus, for a perpetual bond paying C dollars per year:++++++++++++++++++=t 32t 32r)(1C r)(1C r)(1C r 1C r)(1tC r)(13C r)(12C r 11C DUR ++++++++++++++++++=t32t 32r)(11r)(11r)(11r 11r)(1t r)(13r)(12r)(11DUR+++++++++=++1t 432r)(1t r)(13r)(12r)(11r)(1S 2t 32r)(11r)(11r)(11r 11r)(1S ⎪⎪⎭⎫ ⎝⎛+++++++++=+ 22r r 1S r 1r)(1S +=⇒⎪⎭⎫ ⎝⎛=+rr 1r)/(11r r 1DUR 2+=⨯+=Est. Time: 06-1034. We begin with the definition of duration as applied to a common stock with yield rand dividends that grow at a constant rate g in perpetuity:We first simplify by dividing each term by [C (1 + g )]:The denominator is the present value of a growing perpetuity of $1 per year,which is equal to [1/(r - g )]. To simplify the numerator, we first denote thenumerator S and then divide S by (1 + r ):Note that this new quantity [S/(1 + r )] is equal to the square of denominator in the duration formula above, that is:Therefore:Thus, for a perpetual bond paying C dollars per year:Est. Time: 11-15++++++++++++++++++++++++++=t t 3322t t 3322r)(1g)C(1r)(1g)C(1r)(1g)C(1r 1g)C(1r)(1g)tC(1r)(1g)3C(1r)(1g)2C(1r 1g)1C(1DUR ++++++++++++++++++++++++=--t1t 322t 1t 322r)(1g)(1r)(1g)(1r)(1g 1r 11r)(1g)t(1r)(1g)3(1r)(1g)2(1r 11DUR ++++++++++++=++-1t 2t 4232r)(1g)t(1r)(1g)3(1r)(1g)2(1r)(11 r)(1S 2t 1t 322r)(1g)(1r)(1g)(1r)(1g 1r 11r)(1S ⎪⎪⎭⎫ ⎝⎛++++++++++++=+- 22g)(r r 1S g r 1r)(1S -+=⇒⎪⎪⎭⎫ ⎝⎛-=+g r r 1g)](r /[11g)(r r 1DUR 2-+=-⨯-+=35. a. We make use of the one-year Treasury bill information in order to determine the one-year spot rate as follows:1r 1$100$93.46+= r 1 = 0.0700 = 7.00%The following position provides a cash payoff only in year two: a longposition in 25 two-year bonds and a short position in 1 one-year Treasurybill. Cash flows for this position are:[(–25 ⨯ $94.92) + (1 ⨯ $93.46)] = –$2,279.54 today[(25 ⨯ $4) – (1 ⨯ $100)] = $0 in year 1(25 ⨯ $104) = $2,600 in year 2 We determine the two-year spot rate from this position as follows:2)2r (1$2,600$2,279.54+= r 2 = 0.0680 = 6.80%The forward rate f 2 is computed as follows:f 2 = [(1.0680)2/1.0700] – 1 = 0.0660 = 6.60%The following position provides a cash payoff only in year 3:a long position in the three-year bond and a short position equal to (8/104)times a package consisting of a one-year Treasury bill and a two-yearbond.Cash flows for this position are:[(–1 ⨯ $103.64) + (8/104) ⨯ ($93.46 + $94.92)] = –$89.15 today[(1 ⨯ $8) – (8/104) ⨯ ($100 + $4)] = $0 in year 1[(1 ⨯ $8) – (8/104) ⨯ $104] = $0 in year 21 ⨯ $108 = $108 in year 3 We determine the three-year spot rate from this position as follows:3)3r (1$108$89.15+= r 3 = 0.0660 = 6.60%The forward rate f 3 is computed as follows:f 3 = [(1.0660)3/(1.0680)2] – 1 = 0.0620 = 6.20%b.We make use of the spot and forward rates to calculate the price of the 4% coupon bond:The actual price of the bond ($950) is significantly greater than the pricededuced using the spot and forward rates embedded in the prices of theother bonds ($931.01). Hence, a profit opportunity exists. In order to takeadvantage of this opportunity, one should sell the 4% coupon bond shortand purchase the 8% coupon bond.Est. Time: 11-1536. a. We can set up the following three equations using the prices of bonds A, B,and C:Using bond A: $1,076.19 = $80/(1+r 1) + $1,080/(1+r 2)2Using bond B: $1,084.58 = $80/(1+r 1) + $80/(1+r 2)2 + $1,080 / (1+r 3)3Using bond C: $1,076.20 = $80/(1+r 1) + $80/(1+r 2)2 + $80/(1+r 3)3 + $1,080/(1+r 4)4 We know r 4 = 6% so we can substitute that into the last equation. Now wehave three equations and three unknowns and can solve this with variablesubstitution or linear programming to get r 1 = 3%, r 2 = 4%; r 3 = 5%, r 4 = 6%.b.We will want to invest in the underpriced C and borrow money at thecurrent spot market rates to construct an offsetting position. For example,we might borrow $80 at the one-year rate of 3%, $80 at the two-year rateof 4%, $80 at the three-year rate of 5%, and $1,080 at the four-year rate of6%. Of course the PV amount we will receive on these loans is $1,076.20.Now we purchase the discounted bond C at $1,040 and use the proceedsof this bond to repay our loans as they come due. We can pocket thedifference of $36.20, smile, and repeat. Est. Time: 11-15$931.01(1.062)(1.066)(1.07)1040(1.066)(1.07)40(1.07)40P =++=。