公司财务原理Principles of Corporate Finance(11th edition)_课后习题答案Chap005

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习题答案PrinciplesofCorporateFinance第十版Chapter14

习题答案PrinciplesofCorporateFinance第⼗版Chapter14 CHAPTER 14An Overview of Corporate Financing Answers to Problem Sets1. a. Falseb. Truec. True2. a. 40,000/.50 = 80,000 sharesb. 78,000 sharesc. 2,000 shares are held as Treasury stockd. 20,000 sharese. See table belowf. See table below3. a. 80 votesb. 10 X 80 = 800 votes.4. a. subordinatedb. floating ratec. convertibled. warrante. common stock; preferred stock.5. a. Falseb. Truec. False6. a. Par value is $0.05 per share, which is computed as follows:$443 million/8,863 million sharesb. The shares were sold at an average price of:[$443 million + $70,283 million]/8,863 million shares = $7.98c. The company has repurchased:8,863 million – 6,746 million = 2,117 million sharesd. Average repurchase price:$57,391 million/2,117 million shares = $27.11 per share.e. The value of the net common equity is:$443 million + $70,283 million + $44,148 million – $57,391 million= $57,483 million7. a. The day after the founding of Inbox:Common shares ($0.10 par value) $ 50,000Additional paid-in capital 1,950,000Retained earnings 0Treasury shares 0Net common equity $ 2,000,000b. After 2 years of operation:Common shares ($0.10 par value) $ 50,000Additional paid-in capital 1,950,000Retained earnings 120,000Treasury shares 0Net common equity $ 2,120,000c. After 3 years of operation:Common shares ($0.10 par value) $ 150,000 Additional paid-in capital 6,850,000Retained earnings 370,000Treasury shares 0Net common equity $ 7,370,0008. a.Common shares ($1.00 par value) $1,008Additional paid-in capital 5,444Retained earnings 16,250Treasury shares (14,015)Net common equity $8,687b.Common shares ($1.00 par value) $1,008Additional paid-in capital 5,444Retained earnings 16,250Treasury shares (14,715)Net common equity $7,9879. One would expect that the voting shares have a higher price because theyhave an added benefit/responsibility that has value.10. a.Gross profits $ 760,000Interest 100,000EBT $ 660,000Tax (at 35%) 231,000Funds available to common shareholders $ 429,000b.Gross profits (EBT) $ 760,000Tax (at 35%) 266,000Net income $ 494,000Preferred dividend 80,000Funds available to common shareholders $ 414,00011. Internet exercise; answers will vary.12. a. Less valuableb. More valuablec. More valuabled. Less valuable13. Answers may differ. Some key events of the financial crisis through the end of2008 include:June 2007: Bear Stearns pledges $3.2 billion to aid one of its ailing hedge funds Sept. 2007: Northern Rock receives emergency funding from the Bank of England Oct. 2007: Citigroup begins a string of writedowns based on mortgage losses Dec. 2007: Fed establishes Term Auction Facility linesJan. 2008: Ratings agencies threaten to downgrade Ambac and MBIA (major bond issuers)Feb. 2008: Economic stimulus package signed into lawMar. 2008: JPMorgan purchases Bear Stearns with support from the FedMar. 2008: SEC proposes ban on naked short sellingJuly 2008: FDIC takes over IndyMac BankSept. 2008: Lehman forced into bankruptcyB of A purchases Merrill Lynch10 banks create $70 billion liquidity fundAIG debt downgradedRMC money market fund “breaks the buck”Treasury bailout plan voted down in the HouseOct. 2008: 9 large banks agree to capital injection from TreasuryRevised bailout plan passes in HouseConsumer confidence hits lowest point on recordThe NY Fed has an excellent timeline of events at:/doc/24f5ef393968011ca30091d5.html /research/global_economy/Crisis_Timeline.pdf14. Answers will differ. Some purported causes of the financial crisis include:Long periods of very low interest rates leading to easy credit conditionsHigh leverage ratiosThe bursting of the US housing market bubbleHigh rates of default on subprime mortgagesMassive losses on investments in mortgage backed securitiesOpaque derivative markets and amplified losses through credit default swaps High rates of unemployment and job losses 15.a.For majority voting, you must own or otherwise control the votes of a simple majority of the shares outstanding, i.e., one-half of the shares outstanding plus one. Here, with 200,000 shares outstanding, you must control the votes of 100,001 shares. b.With cumulative voting, the directors are elected in order of the total number of votes each receives. With 200,000 shares outstanding and five directors to be elected, there will be a total of 1,000,000 votes cast. To ensure you can elect at least one director, you must ensure that someone else can elect at most four directors. That is, you must have enough votes so that, even if the others split their votes evenly among five other candidates, the number of votes your candidate gets would be higher by one.Let x be the number of votes controlled by you, so that others control (1,000,000 - x) votes. To elect one director:Solving, we find x = 166,666.8 votes, or 33,333.4 shares. Because there are no fractional shares, we need 33,334 shares.15x000,000,1x +-=。

快速弄懂基本金融知识的书籍

快速弄懂基本金融知识的书籍以下是一些快速帮助你了解基本金融知识的书籍：1. 《金融学原理》（Principles of Corporate Finance）- 该书由布雷利（Brealey）、迈尔斯（Myers）和艾伦（Allen）合著，是一本经典的金融学教材，概述了基本的金融概念和原理。

2. 《金融市场的智慧》（A Random Walk Down Wall Street）-作者伯顿·马尔基尔（Burton Malkiel）通过通俗易懂的语言介绍了金融市场的基本知识和投资策略，帮助读者理解金融市场中的机会和风险。

3. 《资本市场论》（Capital Markets: Institutions and Instruments）- 作者弗兰克·法伊（Frank J. Fabozzi）等人合著的这本书详细介绍了各种资本市场和金融工具，包括债券、股票、衍生品等，对投资者和金融从业人员都非常有用。

4. 《金融工程入门》（Introduction to Financial Engineering）-这本书由萨蒙·杜（Samuel Dumas）和菲利普·桑德松（Philippe Santoni）合著，对金融工程学科进行了概述，介绍了金融衍生品、投资组合理论和风险管理等主题。

5. 《经济学原理》（Principles of Economics）- 作者尼·格里高利·曼昆（N. Gregory Mankiw）的这本书是一本广泛使用的经济学教材，可以帮助读者理解经济原理和金融市场的运作方式。

这些书籍都是基本金融知识的入门读物，通过阅读它们，你可以快速了解金融领域的基本概念和原理。

然而，请注意，金融是一个庞大的领域，对于深入理解和应用金融知识，可能需要进一步研究和学习。

PrinciplesofCorporateFinance英文第十版习题解答Chap005

PrinciplesofCorporateFinance英⽂第⼗版习题解答Chap005CHAPTER 5Net Present Value and Other Investment CriteriaAnswers to Problem Sets1. a. A = 3 years, B = 2 years, C = 3 yearsb. Bc. A, B, and Cd. B and C (NPV B = $3,378; NPV C = $2,405)e. Truef. It will accept no negative-NPV projects but will turn down some withpositive NPVs. A project can have positive NPV if all future cash flows areconsidered but still do not meet the stated cutoff period.2. Given the cash flows C0, C1, . . . , C T, IRR is defined by:It is calculated by trial and error, by financial calculators, or by spreadsheetprograms.3. a. $15,750; $4,250; $0b. 100%.4. No (you are effectively “borrowing” at a rate of interest highe r than theopportunity cost of capital).5. a. Twob. -50% and +50%c. Yes, NPV = +14.6.6. The incremental flows from investing in Alpha rather than Beta are -200,000;+110,000; and 121,000. The IRR on the incremental cash flow is 10% (i.e., -200 + 110/1.10 + 121/1.102 = 0). The IRR on Beta exceeds the cost of capital and so does the IRR on the incremental investment in Alpha. Choose Alpha.7. 1, 2, 4, and 68. a. $90.91.10)(1$10001000NP V A -=+-=$$4,044.7310)(1.$1000(1.10)$1000(1.10)$4000(1.10)$1000(1.10)$10002000NP V 5432B +=+++++-=$$39.4710)(1.$1000.10)(1$1000(1.10)$1000(1.10)$10003000NP V 542C +=++++-=$ b.Payback A = 1 year Payback B = 2 years Payback C = 4 years c. A and Bd.$909.09.10)(1$1000P V 1A ==The present value of the cash inflows for Project A never recovers the initial outlay for the project, which is always the case for a negative NPV project. The present values of the cash inflows for Project B are shown in the third row of the table below, and the cumulative net present values are shown in the fourth row:C 0 C 1C 2C 3C 4C 5-2,000.00 +1,000.00 +1,000.00 +4,000.00 +1,000.00 +1,000.00-2,000.00909.09 826.45 3,005.26 683.01 620.92-1,090.91 -264.46 2,740.803,423.81 4,044.73Since the cumulative NPV turns positive between year two and year three,the discounted payback period is:years 2.093,005.26264.462=+The present values of the cash inflows for Project C are shown in the third row of the table below, and the cumulative net present values are shown in the fourth row:C 0C 1C 2C 3 C 4C 5-3,000.00 +1,000.00 +1,000.00 0.00 +1,000.00 +1,000.00-3,000.00 909.09 826.450.00 683.01 620.92 -2,090.91 -1,264.46-1,264.46-581.45 39.47Since the cumulative NPV turns positive between year four and year five,the discounted payback period is:years 4.94620.92581.454=+e. Using the discounted payback period rule with a cutoff of three years, the firm would accept only Project B.9. a.When using the IRR rule, the firm must still compare the IRR with the opportunity cost of capital. Thus, even with the IRR method, one must specify the appropriate discount rate.b.Risky cash flows should be discounted at a higher rate than the rate used to discount less risky cash flows. Using the payback rule is equivalent to using the NPV rule with a zero discount rate for cash flows before the payback period and an infinite discount rate for cash flows thereafter. 10.The two IRRs for this project are (approximately): –17.44% and 45.27% Between these two discount rates, the NPV is positive. 11.a.The figure on the next page was drawn from the following points: Discount Rate0% 10% 20%NPV A +20.00 +4.13 -8.33 NPV B +40.00 +5.18 -18.98b.From the graph, we can estimate the IRR of each project from the point where its line crosses the horizontal axis:IRR A = 13.1% and IRR B = 11.9%c. The company should accept Project A if its NPV is positive and higherthan that of Project B; that is, the company should accept Project A if thediscount rate is greater than 10.7% (the intersection of NPV A and NPV B on the graph below) and less than 13.1%.d. The cash flows for (B – A) are:C0 = $ 0C1 = –$60C2 = –$60C3 = +$140Therefore:Discount Rate0% 10% 20%NPV B-A +20.00 +1.05 -10.65IRR B-A = 10.7%The company should accept Project A if the discount rate is greater than10.7% and less than 13.1%. As shown in the graph, for these discountrates, the IRR for the incremental investment is less than the opportunitycost of capital.12. a.Because Project A requires a larger capital outlay, it is possible that Project A has both a lower IRR and a higher NPV than Project B. (In fact, NPV A is greater than NPV B for all discount rates less than 10 percent.) Because the goal is to maximize shareholder wealth, NPV is the correct criterion.b.To use the IRR criterion for mutually exclusive projects, calculate the IRR for the incremental cash flows:C 0C 1C 2IRRA -B -200 +110 +121 10%Because the IRR for the incremental cash flows exceeds the cost of capital, the additional investment in A is worthwhile. c.81.86$(1.09)$3001.09$250400NPV 2A =++-=$ $79.10(1.09)$1791.09$140200NPV 2B =++-=$ 13.Use incremental analysis:C 1C 2 C 3Current arrangement -250,000 -250,000 +650,000 Extra shift -550,000 +650,000 0 Incremental flows -300,000+900,000 -650,000The IRRs for the incremental flows are (approximately): 21.13% and 78.87% If the cost of capital is between these rates, Titanic should work the extra shift.14. a..82010,0008,18210,000)( 1.1020,00010,000PI D ==--+-=.59020,00011,81820,000)( 1.1035,00020,000PI E ==--+-=b.Each project has a Profitability Index greater than zero, and so both areacceptable projects. In order to choose between these projects, we must use incremental analysis. For the incremental cash flows:0.3610,0003,63610,000)( 1.1015,00010,000PI D E ==--+-=-The increment is thus an acceptable project, and so the larger project should be accepted, i.e., accept Project E. (Note that, in this case, the better project has the lower profitability index.)15.Using the fact that Profitability Index = (Net Present Value/Investment), we find:Project Profitability Index 1 0.22 2 -0.02 3 0.17 4 0.14 5 0.07 6 0.18 70.12Thus, given the budget of $1 million, the best the company can do is to acceptProjects 1, 3, 4, and 6.If the company accepted all positive NPV projects, the market value (compared to the market value under the budget limitation) would increase by the NPV of Project 5 plus the NPV of Project 7: $7,000 + $48,000 = $55,000Thus, the budget limit costs the company $55,000 in terms of its market value. 16.The IRR is the discount rate which, when applied to a project’s cash flows, yields NPV = 0. Thus, it does not represent an opportunity cost. However, if eachproject’s cash flows could be invested at that project’s IRR, then the NPV of each project would be zero because the IRR would then be the opportunity cost of capital for each project. The discount rate used in an NPV calculation is the opportunity cost of capital. Therefore, it is true that the NPV rule does assume that cash flows are reinvested at the opportunity cost of capital.17.a.C 0 = –3,000 C 0 = –3,000 C 1 = +3,500 C 1 = +3,500 C 2 = +4,000 C 2 + PV(C 3) = +4,000 – 3,571.43 = 428.57 C 3 = –4,000 MIRR = 27.84%b.2321 1.12C 1.12xC xC -=+(1.122)(xC 1) + (1.12)(xC 2) = –C 3 (x)[(1.122)(C 1) + (1.12C 2)] = –C 3)()21231.12C )(C (1.12C -x +=0.4501.12)(4,00)(3,500(1.124,000x 2=+=)()0IRR)(1x)C -(1IRR)(1x)C -(1C 2210=++++0IRR)(10)0.45)(4,00-(1IRR)(10)0.45)(3,50-(13,0002=++++- Now, find MIRR using either trial and error or the IRR function (on afinancial calculator or Excel). We find that MIRR = 23.53%.It is not clear that either of these modified IRRs is at all meaningful.Rather, these calculations seem to highlight the fact that MIRR really has no economic meaning.18.Maximize: NPV = 6,700x W + 9,000x X + 0X Y – 1,500x Z subject to:10,000x W + 0x X + 10,000x Y + 15,000x Z ≤ 20,000 10,000x W + 20,000x X – 5,000x Y – 5,000x Z ≤ 20,000 0x W - 5,000x X– 5,000x Y – 4,000x Z ≤ 20,000 0 ≤ x W ≤ 1 0 ≤ x X ≤ 1 0 ≤ x Z ≤ 1Using Excel Spreadsheet Add-in Linear Programming Module:Optimized NPV = $13,450with x W = 1; x X = 0.75; x Y = 1 and x Z = 0If financing available at t = 0 is $21,000:Optimized NPV = $13,500with x W = 1; x X = (23/30); x Y = 1 and x Z = (2/30)Here, the shadow price for the constraint at t = 0 is $50, the increase in NPV for a $1,000 increase in financing available at t = 0.In this case, the program viewed x Z as a viable choice even though the NPV of Project Z is negative. The reason for this result is that Project Z provides a positive cash flow in periods 1 and 2.If the financing available at t = 1 is $21,000:Optimized NPV = $13,900with x W = 1; x X = 0.8; x Y = 1 and x Z = 0Hence, the shadow price of an additional $1,000 in t =1 financing is $450.。

金融工程师必读的十本经典书籍推荐

金融工程师必读的十本经典书籍推荐金融工程师是负责研究和分析金融市场，设计和实施金融产品和模型的专业人士。

要成为一名优秀的金融工程师，不仅需要具备扎实的数理统计、金融知识和技术能力，还需要不断学习和更新自己的知识。

本文将推荐十本经典的金融工程师必读书籍，帮助读者提升专业素养和技能。

一、《Options, Futures and Other Derivatives》（期权、期货与其他衍生产品）作者：John C. Hull这本书是金融工程领域的经典教材，系统详细地介绍了期权、期货和其他衍生产品的基本原理和应用。

它涵盖了各种金融工具的定价、交易策略和风险管理方法，对于理解金融市场和衍生品的运作机制非常有帮助。

二、《Financial Modeling》（金融建模）作者：Simon Benninga这本书主要介绍了金融建模的基本理论和方法，包括财务分析、风险管理、衍生品定价等方面。

作者通过大量的实例和案例，让读者能够具备建立和应用金融模型的能力，是一本非常实用的教材。

三、《A Random Walk Down Wall Street》（华尔街的随机漫步）作者：Burton G. Malkiel这本书是投资领域的经典之作，对于金融工程师来说，了解投资市场的行为和规律非常重要。

作者通过深入浅出的方式，介绍了股票、债券、基金等各类金融工具的投资原理和策略，帮助读者更好地理解资本市场。

四、《Hedge Fund Market Wizards》（对冲基金市场巫师）作者：Jack D. Schwager这本书收录了一些对冲基金行业的成功人士的采访，他们分享了自己的投资经验和策略。

通过这些真实案例，读者可以学习到对冲基金行业的专业知识和实践经验，对于发展自己的投资技能非常有帮助。

五、《Quantitative Investment Analysis》（量化投资分析）作者：Richard A. DeFusco等这本书是量化投资领域的经典教材，详细介绍了量化投资的理论基础、模型构建和策略应用。

企业财务管理的书

企业财务管理的书以下是一些经典的企业财务管理的书籍：1.《财务管理》（Fundamentals of Financial Management）-作者：Eugene F. Brigham, Joel F. Houston此书是一本权威的财务管理教材，涵盖了企业财务管理的基本原理和实践，包括资本预算、资本结构、股息政策等重要议题。

2.《企业财务管理》（Corporate Finance）-作者：Stephen A. Ross, Randolph W. Westerfield, Jeffrey Jaffe这本书提供了关于企业财务的全面介绍，包括投资决策、融资决策、盈利能力分析等关键内容。

它还涵盖了现代财务理论和实践的最新发展。

3.《财务管理原理》（Principles of Corporate Finance）-作者：Richard A. Brealey, Stewart C. Myers, Franklin Allen该书提供了一种综合的财务管理框架，涵盖了投资、融资和资本结构等方面的内容。

它还涵盖了风险管理和国际财务管理等重要议题。

4.《财务管理与政策》（Financial Management and Policy）-作者：James C. Van Horne, John M. Wachowicz Jr.这本书强调了财务决策的战略性和长期连续性，探讨了企业财务管理与企业价值创造之间的关系。

它还包括现代财务理论、融资策略和金融市场分析等内容。

5.《财务管理：理论与实践》（Financial Management: Theoryand Practice）-作者：Eugene F. Brigham, Michael C. Ehrhardt 这本书提供了对财务管理的理论和实践的综合介绍。

它讲解了投资决策、资本预算、融资决策等财务管理的核心概念，并提供了实际案例和应用。

这些书籍都是企业财务管理领域的经典著作，适合学习和了解企业财务管理的原理和实践。

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 =++=。

适合老总看的财务书

以下是几本适合老总阅读的财务书籍，这些书籍深入浅出地介绍了财务知识和管理实践，对于提升老总的财务素养和决策能力有很大帮助：1. 《财务智慧：如何理解数字的真正含义》（The Financial Wisdom of Warren Buffett）：作者是著名的投资大师沃伦·巴菲特（Warren Buffett）的前儿媳玛丽·巴菲特（Mary Buffett）和戴维·克拉克（David Clark）。

这本书以简洁易懂的方式解释了财务报表的基本概念和分析方法，帮助读者更好地理解公司的财务状况。

2. 《财务报表分析与证券定价》（ Financial Statement Analysis and Security Valuation）：作者是斯蒂芬·H·佩因曼（Stephen H. Penman）。

这本书是一本经典的财务分析教材，详细介绍了财务报表分析的方法和技巧，以及如何利用财务信息进行证券定价。

3. 《公司财务原理》（Principles of Corporate Finance）：作者是理查德·B·布雷利（Richard B. Brealey）、斯图尔特·C·迈尔斯（Stewart C. Myers）和艾伦·J·马库斯（Alan J. Marcus）。

这本书是一本广泛使用的公司财务教材，涵盖了财务管理的各个方面，包括资本预算、融资决策、风险管理等。

4. 《读懂财务报表》（Reading Financial Statements for Dummies）：作者是史蒂文·M·布拉格（Steven M. Bragg）。

这本书是一本通俗易懂的财务入门读物，通过简单的案例和解释，帮助读者了解财务报表的基本内容和分析方法。

这些书籍都是财务领域的经典之作，内容深入浅出，适合不同层次的读者阅读。

Principles of Corporate Finance 英文第十版习题解答Chap001

CHAPTER 1Goals and Governance of the FirmAnswers to Problem Sets1. a. realb. executive airplanesc. brand namesd. financiale. bondsf. investmentg. capital budgetingh. financing2. c, d, e, and g are real assets. Others are financial.3. a. Financial assets, such as stocks or bank loans, are claims held byinvestors. Corporations sell financial assets to raise the cash to invest inreal assets such as plant and equipment. Some real assets are intangible.b. Capital budgeting means investment in real assets. Financing meansraising the cash for this investment.c. The shares of public corporations are traded on stock exchanges and canbe purchased by a wide range of investors. The shares of closely heldcorporations are not traded and are not generally available to investors.d. Unlimited liability: investors are responsible for all the firm’s debts. A soleproprietor has unlimited liability. Investors in corporations have limitedliability. They can lose their investment, but no more.e. A corporation is a separate legal “person” with unlimited life. Its ownershold shares in the business. A partnership is a limited-life agreement toestablish and run a business.4. c, d.5. b, c.6. Separation of ownership and management typically leads to agency problems,where managers prefer to consume private perks or make other decisions fortheir private benefit -- rather than maximize shareholder wealth.7. a. Assuming that the encabulator market is risky, an 8% expected return onthe F&H encabulator investments may be inferior to a 4% return on U.S.government securities.b. Unless their financial assets are as safe as U.S. government securities,their cost of capital would be higher. The CFO could consider what theexpected return is on assets with similar risk.8. Shareholders will only vote for (a) maximize shareholder wealth. Shareholderscan modify their pattern of consumption through borrowing and lending, matchrisk preferences, and hopefully balance their own checkbooks (or hire a qualified professional to help them with these tasks).9. If the investment increases the firm’s wealth, it will increase the value of the firm’sshares. Ms. Espinoza could then sell some or all of these more valuable shares in order to provide for her retirement income.10. As the Putnam example illustrates, the firm’s value typically falls by significantlymore than the amount of any fines and settlements. The firm’s reput ation suffers in a financial scandal, and this can have a much larger effect than the fines levied.Investors may also wonder whether all of the misdeeds have been contained. 11. Managers would act in shareholders’ interests because they have a legal dut y toact in their interests. Managers may also receive compensation, either bonusesor stock and option payouts whose value is tied (roughly) to firm performance.Managers may fear personal reputational damage that would result from notacting in shareho lders’ interests. And m anagers can be fired by the board ofdirectors, which in turn is elected by shareholders. If managers still fail to act inshareholders’ interests, shareholders may sell their shares, lowering the stockprice, and potentially creating the possibility of a takeover, which can again lead tochanges in the board of directors and senior management.12. Managers that are insulated from takeovers may be more prone to agencyproblems and therefore more likely to act in their own interests rather than in shareholders’. If a firm instituted a new takeover defense, we might expect to see the value of its shares decline as agency problems increase and lessshareholder value maximization occurs. The counterargument is that defensive measures allow managers to negotiate for a higher purchase price in the face of a takeover bid – to the benefit of shareholder value.Appendix Questions :1. Both would still invest in their friend’s business. A invests and receives $121,000for his investment at the end of the year (which is greater than the $120,000 it would receive from lending at 20%). G also invests, but borrows against the $121,000 payment, and thus receives $100,833 today.2. a. He could consume up to $200,000 now (foregoing all future consumption) orup to $216,000 next year (200,000*1.08, foregoing all consumption this year). To choose the same consumption (C) in both years, C = (200,000 – C) x 1.08 or C = $103,846.203,704200,000220,000216,000Dollars Next YearDollars Nowb. He should invest all of his wealth to earn $220,000 next year. If he consumesall this year, he can now have a total of $203,703.7 (200,000 x 1.10/1.08) this year or $220,000 next year. If he consumes C this year, the amount available for next year’s consumption is (203,703.7 – C) x 1.08. To get equal consumption in both years, set the amount consumed today equal to the amount next year:C = (203,703.7 – C) x 1.08C = $105,769.2。

公司财务原理(第9版)课件10

McGraw Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved
Measuring Betas
GE
20.00
10- 12
Price data: July 2001 – June 2006
30.00
Price data: July 2001 – June 2006
20.00
10.00
Intel return, %
R2 =
.30
0.00 -20.00 -10.00 0.00 10.00 20.00
B = 2.22
-10.00
-20.00
-30.00
Slope determined from plotting the line of best fit.
10- 6
requity = rf + Bequity ( rm - rf )
COC = rportfolio = rassets rassets = WACC = rdebt (D) + requity (E) (V) (V)
E, D, and V are all market values of Equity, Debt and Total Firm Value
GE return, %
15.00 10.00 5.00 0.00 -20.00 -10.00 0.00 -5.00 -10.00 -15.00 -20.00 Market return, % 10.00 20.00
R2 = .17 B = .83
Slope determined from plotting the line of best fit.

principles of corporate finance—chap012-精品文档

• Agency costs: the costs that the principal incurs when dealing with an agent • Actions of agents:
– Moral hazard: when the principal cannot monitor the agent actions, while the interest of agent is diverged from principal Employees do not work hard
– Asian Financial Crisis: because banks believed that they were “too big to fail,” they made excessively risky loans.
• Entrenching investment: reinvestment in projects that CEO is familiar with
Chapter 12
Agency Problems, Compensation, and Performance Measurement
McGraw-Hill/Irwin
Topics Covered
• Incentives and Compensation • Measuring and Rewarding Performance: Residual Income and EVA • Bias in Accounting Measures of Performance
Incentive Issues
• Monitoring - Reviewing the actions of managers and providing incentives to maximize shareholder value. – Monitors: Shareholders, board directors, lenders, auditors, security analysts, rival companies • Free Rider Problem - When owners rely on the efforts of others to monitor the company. • Management Compensation - How to pay managers so as to reduce the cost and need for monitoring and to maximize shareholder value. – Marketization of CEOs contracts • Incentive Compensation - the portion of an employee's salary that is related to performance, and not a guaranteed payment – Stock options, restricted stock, performance shares

公司财务原理Principles of Corporate Finance(11th edition)_课后习题答案Chap005

CHAPTER 5Net Present Value and Other Investment CriteriaAnswers to Problem Sets1. a. A = 3 years, B = 2 years, C = 3 years.b. Bc. A, B, and Cd. B and C (NPV B = $3,378;NPV C = $2,405)e. True. The payback rule ignores all cash flows after the cutoff date,meaning that future years’ cash inflows are not considered. In addition, thepayback rule ignores the timing of cash inflows. For example, for apayback rule set at two years, a project with a payback period of one yearis given equal weight as a project with a payback period of two years.f. It will accept no negative-NPV projects, but will turn down some withpositive NPVs. A project can have positive NPV if all future cash flows areconsidered but still do not meet the stated cutoff period.Est. time: 6 – 102. Given the cash flows C0, C1, . . . , C T, IRR is defined by:It is calculated by trial and error, by financial calculators, or by spreadsheetprograms.Est. time: 1 – 53. a. $15,750; $4,250; $0b. 100%Est. time: 1 – 54. No (you are effectively “borrowing” at a rate of interest highe r than theopportunity cost of capital).Est. time: 1 – 55 a. Two. There are multiple internal rates of return for a project when thereare changes in the sign of the cash flows.b. −50% and +50%. The NPV for the project using both of these IRRs is 0.c. Yes, NPV = +14.6.Est. time: 1 – 56. The incremental flows from investing in Alpha rather than Beta are −200,000;+110,000; and 121,000. The IRR on the incremental cash flow is 10% (i.e., −200 + 110/1.10 + 121/1.102 = 0). The IRR on Beta exceeds the cost of capital and so does the IRR on the incremental investment in Alpha. Choose Alpha.Est. time: 1 – 57. 1, 2, 4, and 6The profitability index for each project is shown below:Start with the project with the highest profitability index and go from there. Project2 has the highest profitability index and has an initial investment of $5,000. Thenext highest profitability index is for Project 1, which has an initial investment of $10,000. The next highest is Project 4, which will cost $60,000 up front. So far we have spent $75,000. Projects 5 and 6 both have profitability indexes of .2, but we only have $15,000 left to spend, so we will add Project 6 to our list. This gives us Projects 1, 2, 4, and 6.Est. time: 1 – 58. a. $90.91.10)(1$10001000NPV A -=+-=$ $4,044.7310)(1.$1000(1.10)$1000(1.10)$4000(1.10)$1000(1.10)$10002000NPV 5432B +=+++++-=$ $39.4710)(1.$1000.10)(1$1000(1.10)$1000(1.10)$10003000NPV 542C +=++++-=$ Projects B and C have positive NPVs.b. Payback A = one yearPayback B = two yearsPayback C = four yearsc. A and Bd.$909.09.10)(1$1000PV 1A == The present value of the cash inflows for Project A never recovers the initialoutlay for the project, which is always the case for a negative NPV project.The present values of the cash inflows for Project B are shown in the thirdrow of the table below, and the cumulative net present values are shownin the fourth row:C 0C 1 C 2 C 3 C 4 C 5 -2,000.00+1,000.00 +1,000.00 +4,000.00 +1,000.00 +1,000.00 -2,000.00909.09 826.45 3,005.26 683.01 620.92 -1,090.91 -264.46 2,740.80 3,423.81 4,044.73Since the cumulative NPV turns positive between year 2 and year 3, the discounted payback period is:years 2.093,005.26264.462=+The present values of the cash inflows for Project C are shown in the third row of the table below, and the cumulative net present values are shown in the fourth row:C 0 C 1 C 2 C 3 C 4 C 5-3,000.00 +1,000.00 +1,000.000.00 +1,000.00 +1,000.00 -3,000.00 909.09 826.450.00 683.01 620.92 -2,090.91 -1,264.46 -1,264.46 -581.45 39.47Since the cumulative NPV turns positive between year 4 and year 5, thediscounted payback period is:years 4.94620.92581.454=+e. Using the discounted payback period rule with a cutoff of three years, thefirm would accept only Project B.Est. time: 11– 159. a. When using the IRR rule, the firm must still compare the IRR with theopportunity cost of capital. Thus, even with the IRR method, one mustspecify the appropriate discount rate.b. Risky cash flows should be discounted at a higher rate than the rate usedto discount less risky cash flows. Using the payback rule is equivalent tousing the NPV rule with a zero discount rate for cash flows before thepayback period and an infinite discount rate for cash flows thereafter.Est. time: 1 – 510.The two IRRs for this project are (approximately): –17.44% and 45.27%. Between these two discount rates, the NPV is positive.Est. time: 06 - 1011. a.The figure on the next page was drawn from the following points:Discount Rate 0% 10% 20%NPV A +20.00 +4.13 -8.33NPV B +40.00 +5.18 -18.98b. From the graph, we can estimate the IRR of each project from the pointwhere its line crosses the horizontal axis:IRR A = 13.1% and IRR B = 11.9%This can be checked by calculating the NPV for each project at theirrespective IRRs, which give an approximate NPV of 0.c.The company should accept Project A if its NPV is positive and higherthan that of Project B; that is, the company should accept Project A if thediscount rate is greater than 10.7% (the intersection of NPV A and NPV B onthe graph below) and less than 13.1% (the internal rate of return).d. The cash flows for (B–A) are:C0 = $ 0C1 = –$60C2 = –$60C3 = +$140Therefore:Discount Rate0% 10% 20%NPV B−A+20.00 +1.05 -10.65IRR B − A = 10.7%The company should accept Project A if the discount rate is greater than10.7% and less than 13.1%. As shown in the graph, for these discountrates, the IRR for the incremental investment is less than the opportunitycost of capital.Est. time: 06 - 1012. a. Because Project A requires a larger capital outlay, it ispossible that Project A has both a lower IRR and a higher NPV thanProject B. (In fact, NPV A is greater than NPV B for all discount rates lessthan 10%.) Because the goal is to maximize shareholder wealth, NPV isthe correct criterion.b. To use the IRR criterion for mutually exclusive projects, calculate theIRR for the incremental cash flows:C 0 C 1 C 2 IRRA -B −200 +110 +121 10%Because the IRR for the incremental cash flows exceeds the cost ofcapital, the additional investment in A is worthwhile. c. 81.86$(1.09)3001.09250400NPV 2A =++-= $79.10(1.09)1791.09140200NPV 2B =++-= Est. time: 06 - 1013. Use incremental analysis:C 1 C 2 C 3Current Arrangement −250,000 −250,000 +650,000Extra Shift −550,000 +650,000 0Incremental Flows −300,000 +900,000 -650,000The IRRs for the incremental flows are (approximately): 21.13% and 78.87%If the cost of capital is between these rates, Titanic should work the extra shift.Est. time: 06 - 1014.a. First calculate the NPV for each project.The NPV for Project D is: $=-+=D 20,000NPV 10,0008,181.821.10The NPV for Project E is:=-+=E 35,000NPV 20,000$11,818.181.10Profitability index = NPV/initial investment.For Project D: Profitability index = 8,181.82/10,000 = .82.For Project E: Profitability index = 11,818.18/20,000 −.59.b. Each project has a profitability index greater than zero, and so both areacceptable projects. In order to choose between these projects, we must use incremental analysis. For the incremental cash flows:0.3610,0003,63610,000)( 1.1015,00010,000PI D E ==--+-=- The increment is thus an acceptable project, and so the larger project should be accepted, i.e., accept Project E. (Note that, in this case, the better project has the lower profitability index.)Est. time: 11 - 1515. Using the fact that profitability index = (net present value / investment), we find:ProjectProfitability Index 10.22 2−0.02 30.17 40.14 50.07 60.18 7 0.12 Thus, given the budget of $1 million, the best the company can do is to acceptProjects 1, 3, 4, and 6.If the company accepted all positive NPV projects, the market value (compared to the market value under the budget limitation) would increase by the NPV ofProject 5 plus the NPV of Project 7: $7,000 + $48,000 = $55,000.Thus, the budget limit costs the company $55,000 in terms of its market value.Est. time: 06 - 1016. The IRR is the discount rate wh ich, when applied to a project’s cash flows, yieldsNPV = 0. Thus, it does not represent an opportunity cost. However, if eachproject’s cash flows could be invested at that project’s IRR, then the NPV of each project would be zero because the IRR would then be the opportunity cost ofcapital for each project. The discount rate used in an NPV calculation is theopportunity cost of capital. Therefore, it is true that the NPV rule does assume that cash flows are reinvested at the opportunity cost of capital.Est. time: 06 - 1017.a.C 0 = –3,000 C 0 = –3,000C 1 = +3,500 C 1 = +3,500C 2 = +4,000 C 2 + PV(C 3) = +4,000 – 3,571.43 = 428.57C 3 = –4,000 MIRR = 27.84%b. 2321 1.12C 1.12xC xC -=+ (1.122)(xC 1) + (1.12)(xC 2) = –C 3(x)[(1.122)(C 1) + (1.12C 2)] = –C 3)()2123 1.12C )(C (1.12C -x += 0.4501.12)(4,00)(3,500(1.124,000x 2=+=)() 0IRR)(1x)C -(1IRR)(1x)C -(1C 2210=++++ 0IRR)(10)0.45)(4,00-(1IRR)(10)0.45)(3,50-(13,0002=++++- Now, find MIRR using either trial and error or the IRR function (on afinancial calculator or Excel). We find that MIRR = 23.53%.It is not clear that either of these modified IRRs is at all meaningful.Rather, these calculations seem to highlight the fact that MIRR really hasno economic meaning. Est. time: 11 - 15 18. Maximize:NPV = 6,700x W + 9,000x X + 0X Y – 1,500x Z subject to: 10,000x W + 0x X + 10,000x Y + 15,000x Z ≤ 20,00010,000x W + 20,000x X – 5,000x Y – 5,000x Z ≤ 20,0000x W - 5,000x X – 5,000x Y – 4,000x Z ≤ 20,0000 ≤ x W ≤ 10 ≤ x X ≤ 10 ≤ x Z ≤ 1Using Excel Spreadsheet Add-in Linear Programming Module:Optimized NPV = $13,450with x W = 1; x X = 0.75; x Y = 1 and x Z = 0If financing available at t = 0 is $21,000:Optimized NPV = $13,500with x W = 1; x X = (23/30); x Y = 1 and x Z = (2/30)Here, the shadow price for the constraint at t = 0 is $50, the increase in NPV for a $1,000 increase in financing available at t = 0.In this case, the program viewed x Z as a viable choice even though the NPV ofProject Z is negative. The reason for this result is that Project Z provides apositive cash flow in periods 1 and 2.If the financing available at t = 1 is $21,000:Optimized NPV = $13,900with x W = 1; x X = 0.8; x Y = 1 and x Z = 0Hence, the shadow price of an additional $1,000 in t =1 financing is $450.Est. time: 11 - 15。

公司财务原理Principles of Corporate Finance(11th edition)_课后习题答案Chap002

CHAPTER 2How to Calculate Present ValuesAnswers to Problem Sets1. If the discount factor is .507, then .507 x 1.126 = $1.Est time: 01-052. DF x 139 = 125. Therefore, DF =125/139 = .899.Est time: 01-053. PV = 374/(1.09)9 = 172.20.Est time: 01-054. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003.Est time: 01-055. FV = 100 x 1.158 = $305.90.Est time: 01-056. NPV = −1,548 + 138/.09 = −14.67 (cost today plus the present value of theperpetuity).Est time: 01-057. PV = 4/(.14 − .04) = $40.Est time: 01-058. a. PV = 1/.10 = $10.b. Since the perpetuity will be worth $10 in year 7, and since that is roughlydouble the present value, the approximate PV equals $5.You must take the present value of years 1–7 and subtract from the totalpresent value of the perpetuity:PV = (1/.10)/(1.10)7 = 10/2= $5 (approximately).c. A perpetuity paying $1 starting now would be worth $10, whereas aperpetuity starting in year 8 would be worth roughly $5. The differencebetween these cash flows is therefore approximately $5. PV = $10 – $5=$5 (approximately).d. PV = C/(r−g) = 10,000/(.10-.05) = $200,000.Est time: 06-109. a. PV = 10,000/(1.055) = $7,835.26 (assuming the cost of the car does notappreciate over those five years).b. The six-year annuity factor [(1/0.08) – 1/(0.08 x (1+.08)6)] = 4.623. Youneed to set aside (12,000 × six-year annuity factor) = 12,000 × 4.623 =$55,475.c. At the end of six years you would have 1.086 × (60,476 - 55,475) = $7,935. Est time: 06-1010. a. FV = 1,000e.12 x 5 = 1,000e.6 = $1,822.12.b. PV = 5e−.12 x 8 = 5e-.96 = $1.914 million.c. PV = C (1/r– 1/re rt) = 2,000(1/.12 – 1/.12e.12 x15) = $13,912.Est time: 01-0511.a. FV = 10,000,000 x (1.06)4 = 12,624,770.b. FV = 10,000,000 x (1 + .06/12)(4 x 12) = 12,704,892.c. FV = 10,000,000 x e(4 x .06) = 12,712,492.Est time: 01-0512.a. PV = $100/1.0110 = $90.53.b. PV = $100/1.1310 = $29.46.c. PV = $100/1.2515 = $3.52.d. PV = $100/1.12 + $100/1.122 + $100/1.123 = $240.18.Est time: 01-05 13. a.⇒=+=0.905r 11DF 11r 1 = 0.1050 = 10.50%.b. 0.819.(1.105)1)r (11DF 2222==+=c. AF 2 = DF 1 + DF 2 = 0.905 + 0.819 = 1.724.d.PV of an annuity = C ⨯ [annuity factor at r % for t years]. Here:$24.65 = $10 ⨯ [AF 3]AF 3 = 2.465e. AF 3 = DF 1 + DF 2 + DF 3 = AF 2 + DF 32.465 = 1.724 + DF 3DF 3 = 0.741Est time: 06-1014. The present value of the 10-year stream of cash inflows is:6$886,739.6(1.14)0.1410.141 $170,000PV 10=⎥⎦⎤⎢⎣⎡⨯-⨯= Thus:NPV = –$800,000 + $886,739.66 = +$86,739.66At the end of five years, the factory’s value will be the present value of the fiveremaining $170,000 cash flows:6$583,623.7(1.14)0.1410.141 $170,000PV 5=⎥⎦⎤⎢⎣⎡⨯-⨯= Est time: 01-0515.$23,696.151.12$50,0001.12$68,0001.12$80,0001.12$92,0001.12$92,000 1.12$85,0001.12$80,0001.12$75,0001.12$57,0001.12$50,000$380,000(1.12)C NPV 109876543210t t t =++++++++++-==∑=0Est time: 01-0516.a.Let S t = salary in year t.∑=-=301t t1t (1.08)(1.05)40,000PV 3$760,662.5(1.08).05)-(.08(1.05).05)-(.081 43030=⎥⎦⎤⎢⎣⎡⨯-⨯=000,0b.PV(salary) x 0.05 = $38,033.13Future value = $38,033.13 x (1.08)30 = $382,714.30c.$38,980.30 (1.08)0.0810.081$C (1.08)0.0810.081 C $r)(1r 1r 1 C PV 2020t =⎥⎥⎦⎤⎢⎢⎣⎡⨯-=⎥⎦⎤⎢⎣⎡⨯-⨯=⎥⎦⎤⎢⎣⎡+⨯-⨯=382,714.30382,714.30Est time: 06-10 17.Period Present Value 0-400,000.001 +100,000/1.12 = +89,285.712 +200,000/1.122 = +159,438.783+300,000/1.123 = +213,534.07Total = NPV = $62,258.56Est time: 01-0518.We can break this down into several different cash flows, such that the sum ofthese separate cash flows is the total cash flow. Then, the sum of the present values of the separate cash flows is the present value of the entire project. (All dollar figures are in millions.) ▪ Cost of the ship is $8 million PV = -$8 million▪Revenue is $5 million per year, and operating expenses are $4 million. Thus, operating cash flow is $1 million per year for 15 years.million. million $$8.559(1.08)0.0810.081 115=⎥⎦⎤⎢⎣⎡⨯-⨯=PV ▪ Major refits cost $2 million each and will occur at times t = 5 and t = 10. PV = (-$2 million)/1.085 + (-$2 million)/1.0810 = -$2.288 million. ▪Sale for scrap brings in revenue of $1.5 million at t = 15. PV = $1.5 million/1.0815 = $0.473 million.Adding these present values gives the present value of the entire project:NPV = -$8 million + $8.559 million - $2.288 million + $0.473 million NPV = -$1.256 millionEst time: 06-1019. a. PV = $100,000.b. PV = $180,000/1.125 = $102,136.83.c. PV = $11,400/0.12 = $95,000.d. 4.$107,354.2(1.12)0.1210.121 $19,000PV 10=⎥⎦⎤⎢⎣⎡⨯-⨯=e. PV = $6,500/(0.12 - 0.05) = $92,857.14.Prize (d) is the most valuable because it has the highest present value.Est time: 01-0520.Mr. Basset is buying a security worth $20,000 now, which is its present value. The unknown is the annual payment. Using the present value of an annuity formula, we have:$2,653.90 (1.08)0.0810.081000,20$C (1.08)0.0810.081 C 000,20$r)(1r 1r 1 C PV 1212t =⎥⎥⎦⎤⎢⎢⎣⎡⨯-=⎥⎦⎤⎢⎣⎡⨯-⨯=⎥⎦⎤⎢⎣⎡+⨯-⨯=Est time: 01-0521. Assume the Zhangs will put aside the same amount each year. One approach tosolving this problem is to find the present value of the cost of the boat and then equate that to the present value of the money saved. From this equation, we can solve for the amount to be put aside each year.PV(boat) = $20,000/(1.10)5 = $12,418PV(savings) = annual savings ⎥⎦⎤⎢⎣⎡⨯-⨯5(1.10)0.1010.101 Because PV(savings) must equal PV(boat):Annual savings 418,12$ =⎥⎦⎤⎢⎣⎡⨯-⨯5(1.10)0.1010.101 Annual savings $3,276(1.10)0.1010.101$12,4185=⎥⎦⎤⎢⎣⎡⨯-= Another approach is to use the future value of an annuity formula:$20,0005.10)(1 savings Annual =⎥⎥⎦⎤⎢⎢⎣⎡-+⨯10.1 Annual savings = $ 3,276Est time: 06-1022.The fact that Kangaroo Autos is offe ring “free credit” tells us what the cash payments are; it does not change the fact that money has time value. A 10% annual rate of interest is equivalent to a monthly rate of 0.83%:r monthly = r annual /12 = 0.10/12 = 0.0083 = 0.83%The present value of the payments to Kangaroo Autos is:8$8,93(1.0083)0.008310.00831$300$1,00030=⎥⎦⎤⎢⎣⎡⨯-⨯+ A car from Turtle Motors costs $9,000 cash. Therefore, Kangaroo Autosoffers the better deal, i.e., the lower present value of cost.Est time: 01-05 23.The NPVs are: at 5%$117,687(1.05)$870,0001.05$30,000$700,000NPV 2=+--=⇒ at 10% $46,281(1.10)870,0001.10$30,000$700,000NPV 2=+--=⇒at 15% $16,068(1.15)870,0001.15$30,000$700,000NPV 2-=+--=⇒ The figure below shows that the project has zero NPV at about 13.5%.As a check, NPV at 13.5% is:$1.78(1.135)870,0001.135$30,000$700,000NPV 2-=+--=Est time: 06-10 24.a.This is the usual perpetuity, and hence:$1,428.570.07$100r C PV ===b. This is worth the PV of stream (a) plus the immediate payment of $100:PV = $100 + $1,428.57 = $1,528.57c.The continuously compounded equivalent to a 7% annually compoundedrate is approximately 6.77%, because:Ln(1.07) = 0.0677 ore 0.0677 = 1.0700 Thus:$1,477.100.0677$100r C PV ===Note that the pattern of payments in part (b) is more valuable than the pattern of payments in part (c). It is preferable to receive cash flows at the start of every year than to spread the receipt of cash evenly over the year; with the former pattern of payment, you receive the cash more quickly.Est time: 06-1025. a. PV = $1 billion/0.08 = $12.5 billion.b. PV = $1 billion/(0.08 – 0.04) = $25.0 billion.c. billion. $9.818(1.08)0.0810.081billion $1PV 20=⎥⎦⎤⎢⎣⎡⨯-⨯= d.The continuously compounded equivalent to an 8% annually compounded rate is approximately 7.7%, because:Ln(1.08) = 0.0770 ore 0.0770 = 1.0800 Thus:billion $10.203e 0.07710.0771billion $1PV )(0.077)(20=⎥⎦⎤⎢⎣⎡⨯-⨯= This result is greater than the answer in Part (c) because the endowmentis now earning interest during the entire year.Est time: 06-1026. With annual compounding: FV = $100 ⨯ (1.15)20 = $1,636.65.With continuous compounding: FV = $100 ⨯ e (0.15×20) = $2,008.55.Est time: 01-0527. One way to approach this problem is to solve for the present value of:(1) $100 per year for 10 years, and(2) $100 per year in perpetuity, with the first cash flow at year 11.If this is a fair deal, these present values must be equal, and thus we can solve for the interest rate (r ).The present value of $100 per year for 10 years is:⎥⎦⎤⎢⎣⎡+⨯-⨯=10r)(1(r)1r 1$100PV The present value, as of year 10, of $100 per year forever, with the first paymentin year 11, is: PV 10 = $100/r . At t = 0, the present value of PV 10 is:⎥⎦⎤⎢⎣⎡⨯⎥⎦⎤⎢⎣⎡+=r $100r)(11PV 10 Equating these two expressions for present value, we have:⎥⎦⎤⎢⎣⎡⨯⎥⎦⎤⎢⎣⎡+=⎥⎦⎤⎢⎣⎡+⨯-⨯r $100r)(11r)(1(r)1r 1$1001010 Using trial and error or algebraic solution, we find that r = 7.18%.Est time: 06-1028. Assume the amount invested is one dollar.Let A represent the investment at 12%, compounded annually.Let B represent the investment at 11.7%, compounded semiannually. Let C represent the investment at 11.5%, compounded continuously.After one year:FV A = $1 ⨯ (1 + 0.12)1= $1.1200FV B = $1 ⨯ (1 + 0.0585)2 = $1.1204 FV C = $1 ⨯ e (0.115 ⨯ 1)= $1.1219After five years:FV A = $1 ⨯ (1 + 0.12)5= $1.7623FV B = $1 ⨯ (1 + 0.0585)10 = $1.7657 FV C = $1 ⨯ e (0.115 ⨯ 5)= $1.7771 After twenty years:FV A = $1 ⨯ (1 + 0.12)20= $9.6463FV B = $1 ⨯ (1 + 0.0585)40 = $9.7193 FV C = $1 ⨯ e (0.115 ⨯ 20)= $9.9742 The preferred investment is C.Est time: 06-1029.Because the cash flows occur every six months, we first need to calculate the equivalent semiannual rate. Thus, 1.08 = (1 + r /2)2 => r = 7.846 semiannually compounded APR. Therefore the rate for six months is 7.846/2, or 3.923%:147,846039231039230103923010001000001009$).(..,$,$PV =⎥⎦⎤⎢⎣⎡⨯-⨯+=Est time: 06-1030. a. Each installment is: $9,420,713/19 = $495,827.$4,761,724(1.08)0.0810.081$495,827PV 19=⎥⎦⎤⎢⎣⎡⨯-⨯=b.If ERC is willing to pay $4.2 million, then:⎥⎦⎤⎢⎣⎡+⨯-⨯=19r)(1r 1r 1$495,827$4,200,000 Using Excel or a financial calculator, we find that r = 9.81%.Est time: 06-10 31. a.3$402,264.7(1.08)0.0810.081$70,000PV 8=⎥⎦⎤⎢⎣⎡⨯-⨯=b.Year Beginning-of-Year Balance ($) Year-End Interest on Balance ($) Total Year-End Payment ($) Amortization of Loan ($) End-of-Year Balance ($) 1 402,264.73 32,181.18 70,000.00 37,818.82 364,445.91 2 364,445.91 29,155.67 70,000.00 40,844.33 323,601.58 3 323,601.58 25,888.13 70,000.00 44,111.87 279,489.71 4 279,489.71 22,359.18 70,000.00 47,640.82 231,848.88 5 231,848.88 18,547.91 70,000.00 51,452.09 180,396.79 6 180,396.79 14,431.74 70,000.00 55,568.26 124,828.54 7 124,828.54 9,986.28 70,000.00 60,013.72 64,814.82864,814.825,185.1970,000.0064,814.810.01Est time: 06-1032. This is an annuity problem with the present value of the annuity equal to$2 million (as of your retirement date), and the interest rate equal to 8%with 15 time periods. Thus, your annual level of expenditure (C) is determined as follows:$233,659 (1.08)0.0810.081$2,000,000C (1.08)0.0810.081 C $2,000,000r)(1r 1r 1 C PV 1515t =⎥⎥⎦⎤⎢⎢⎣⎡⨯-=⎥⎦⎤⎢⎣⎡⨯-⨯=⎥⎦⎤⎢⎣⎡+⨯-⨯=With an inflation rate of 4% per year, we will still accumulate $2 million as of ourretirement date. However, because we want to spend a constant amount per year in real terms (R, constant for all t ), the nominal amount (C t ) must increase each year. For each year t : R = C t /(1 + inflation rate)t Therefore:PV [all C t ] = PV [all R ⨯ (1 + inflation rate)t ] = $2,000,000$2,000,0000.08)(1.04)0(1....08)0(10.04)(10.08)(1.04)0(1R 15152211=⎥⎦⎤⎢⎣⎡+++++++++⨯ R ⨯ [0.9630 + 0.9273 + . . . + 0.5677] = $2,000,000 R ⨯ 11.2390 = $2,000,000 R = $177,952Alternatively, consider that the real rate is.03846.1=-++0.04)(1.08)0(1 Then, redoingthe steps above using the real rate gives a real cash flow equal to:$177,952=⎥⎥⎦⎤⎢⎢⎣⎡⨯-= (1.03846)0.0384610.038461$2,000,000C 15Thus C 1 = ($177,952 ⨯ 1.04) = $185,070, C 2 = $192,473, etc.Est time: 11-15 33. a.9$430,925.8(1.055)0.05510.0551$50,000PV 12=⎥⎦⎤⎢⎣⎡⨯-⨯=b.The annually compounded rate is 5.5%, so the semiannual rate is:(1.055)(1/2) – 1 = 0.0271 = 2.71%Since the payments now arrive six months earlier than previously:PV = $430,925.89 × 1.0271 = $442,603.98Est time: 06-1034. In three years, the balance in the mutual fund will be:FV = $1,000,000 × (1.035)3 = $1,108,718The monthly shortfall will be: $15,000 – ($7,500 + $1,500) = $6,000. Annual withdrawals from the mutual fund will be: $6,000 × 12 = $72,000. Assume the first annual withdrawal occurs three years from today, when the balance in the mutual fund will be $1,108,718. Treating the withdrawals as an annuity due, we solve for t as follows:r)(1r)(1r 1r 1C PV t +⨯⎥⎦⎤⎢⎣⎡+⨯-⨯= 1.035(1.035)0.03510.0351$72,000$1,108,718t ⨯⎥⎦⎤⎢⎣⎡⨯-⨯= Using Excel or a financial calculator, we find that t = 21.38 years.Est time: 06-10 35. a. PV = 2/.12 = $16.667 million.b. PV = 939.14$=⎥⎦⎤⎢⎣⎡⨯-⨯20(1.12)0.1210.121$2million.c. PV = 2/(.12-.03) = $22.222 milliond. PV = 061.18$=⎥⎦⎤⎢⎣⎡⨯-⨯2020(1.12).03)-(0.12 1.03.03)-(0.121$2million.Est time: 06-1036. a. First we must determine the 20-year annuity factor at a 6% interest rate.20-year annuity factor = [1/.06 – 1/.06(1.06)20) = 11.4699.Once we have the annuity factor, we can determine the mortgagepayment.Mortgage payment = $200,000/11.4699 = $17,436.91.b.c. Nearly 69% of the initial loan payment goes toward interest($12,000/$17,436.79 = .6882). Of the last payment, only 6% goestoward interest (987.24/17,436.79 = .06).After 10 years, $71,661.21 has been paid off ($200,000 – remainingbalance of $128,338.79). This represents only 36% of the loan. Thereason that less than half of the loan has paid off during half of its lifeis due to compound interest.Est time: 11-1537. a. Using the Rule of 72, the time for money to double at 12% is 72/12,or six years. More precisely, if x is the number of years for money todouble, then:(1.12)x = 2Using logarithms, we find:x (ln 1.12) = ln 2 x = 6.12 yearsb.With continuous compounding for interest rate r and time period x :e rx = 2Taking the natural logarithm of each side:rx = ln(2) = 0.693Thus, if r is expressed as a percent, then x (the time for money to double) is: x = 69.3/(interest rate, in percent).Est time: 06-10 38.Spreadsheet exercise.Est time: 11-1539.. a. This calls for the growing perpetuity formula with a negative growth rate(g = –0.04):million $14.290.14million$20.04)(0.10million $2PV ==--=b.The pipeline’s value at year 20 (i.e., at t = 20), assuming its cash flows lastforever, is:gr g)(1C g r C PV 2012120-+=-= With C 1 = $2 million, g = –0.04, and r = 0.10:million $6.3140.14million$0.8840.140.04)(1million)($2PV 2020 ==-⨯=Next, we convert this amount to PV today, and subtract it from the answerto Part (a):million $13.35(1.10)million$6.314million $14.29PV 20=-=Est time: 06-10。

公司财务原理第九版第三章

PV of Cash Flow PV 0
cash flow discount C1 r rate
McGraw Hill/Irwin
PV DF C t
Ct (1 r )
t
Replacing “1” with “t” allows the formula to be used for cash flows that exist at any point in time
McGraw Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved
PV
100 (1.07)
1

200 (1 077)
2
265.88
McGraw Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved
3- 10
Present Values
$200
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved
3- 15
Short Cuts
Sometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods. These tools allow us to cut through the calculations quickly.

PrinciplesofCorporationFinance课程设计

Principles of Corporation Finance 课程设计本文将详细介绍 Principles of Corporation Finance（公司金融原理）课程的设计，包括教学目标、内容大纲、学生评估等方面。

教学目标Principles of Corporation Finance 是一个重要的金融课程，是为学生提供金融管理和决策技能的根本课程，重点培养学生的企业理财能力和财务管理能力，使他们能够理解复杂的企业金融问题并应用相关的模型和工具解决这些问题。

具体来说，本课程的教学目标包括：1.理解企业金融的基本概念和原理；2.掌握企业财务管理的基本技术和工具；3.能够分析企业的财务状况和经营绩效；4.能够评估投资项目的风险和回报；5.能够应用现代金融理论和工具解决实际企业金融问题。

内容大纲1.Introduction to Corporation Finance–Corporation Finance vs. Personal Finance–Forms of Businesses–Concepts of Risk and Return–Stock and Bond Markets2.Financial Statements and Cash Flow–Financial Statements Analysis–Cash Flow and Financial Planning3.Time Value of Money–Future Value and Present Value–Annuities and Perpetuities–Applications of Time Value of Money4.Bond Valuation and Interest Rates–Bond Prices and Yields–Interest Rates and Time Value of Money–Term Structure of Interest Rates and Yield Curve5.Stock Valuation and Stock Markets–Stock Prices and Dividend Policy–Market Efficiency and Behavioral Finance–Portfolio Theory and Market Indexes6.Capital Budgeting and Investment Decision Rules–Capital Budgeting Process and Net Present Value (NPV)–Internal Rate of Return (IRR) and Payback Period7.Capital Structure and Cost of Capital–Optimal Capital Structure and FinancialLeverage–Cost of Debt and Cost of Equity–Weighted Average Cost of Capital (WACC)8.Dividend Policy and Stock Repurchases–Dividend Payment and Stock Repurchases–Stock Dividends and Stock Splits9.Risk Management and Derivatives–Derivatives and Risk Management–Options and Hedging Strategies10.International Corporate Finance•Exchange Rates and International Trade•Global Financial Markets and Capital Flows•Financing Multinational Corporations教学方法本课程采用讲授、案例分析和课堂讨论相结合的教学方法。

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