《财务管理基础第13版》相关章节答案.ppt

Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualContentsChaptersPages1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.The Role of Financial ManagementThe Business, Tax, and Financial EnvironmentsThe Time Value of Money*The Valuation of Long-term Securities*Risk and Return*Financial Statement Analysis*Funds Analysis, Cash-flow Analysis, and Financial Planning*Overview of Working-capital ManagementCash and Marketable Securities ManagementAccounts Receivable and Inventory ManagementShort-term FinancingCapital Budgeting and Estimating Cash FlowsCapital Budgeting TechniquesRisk and Managerial (Real) Options in Capital Budgeting(some sections may be omitted in an abbreviated course)Required Returns and the Cost of CapitalOperating and Financial Leverage (may be omitted in an abbreviated course)Capital Structure DeterminationDividend PolicyThe Capital MarketLong-term Debt, Preferred Stock, and Common StockTerm Loans and Leases (may be omitted in an abbreviated course)Convertibles, Exchangeables, and WarrantsMergers and Other Forms of Corporate RestructuringInternational Financial Management9121932414961828893105112120134144157174184195201213225234251*Note: Some instructors prefer to cover Chapters 6 and 7 before going into Chapters 3-5. Thesechapters have been written so that this can be done without any problem. 本课程涉及的章节3© Pearson Education Limited 2008Chapter 1Chapter 3Chapter 4Chapter 5Chapter 6Chapter 15Chapter 16Chapter 17THE ROLE OF FINANCIAL MANAGEMENTTHE TIME VALUE OF MONEY*THE VALUATION OF LONG-TERM SECURITIES*RISK AND RETURN*FINANCIAL STATEMENT ANALYSIS*REQUIRED RETURNS AND THE COST OF CAPITALOPERATING AND FINANCIAL LEVERAGECAPITAL STRUCTURE DETERMINATION1语言资格考试PPTThe Role of Financial ManagementIncreasing shareholder value over time is the bottom lineof every move we make.ROBERT GOIZUETAFormer CEO, The Coca-Cola Company9© Pearson Education Limited 20082语言资格考试PPTChapter 1: The Role of Financial ManagementANSWERS TO QUESTIONS1. With an objective of maximizing shareholder wealth, capital will tend to be allocated to themost productive investment opportunities on a risk-adjusted return basis. Other decisionswill also be made to maximize efficiency. If all firms do this, productivity will beheightened and the economy will realize higher real growth. There will be a greater level ofoverall economic want satisfaction. Presumably people overall will benefit, but this dependsin part on the redistribution of income and wealth via taxation and social programs. In otherwords, the economic pie will grow larger and everybody should be better off if there is noreslicing. With reslicing, it is possible some people will be worse off, but that is the result ofa governmental change in redistribution. It is not due to the objective function ofcorporations.2. Maximizing earnings is a nonfunctional objective for the following reasons:a. Earnings is a time vector. Unless one time vector of earnings clearly dominates all othertime vectors, it is impossible to select the vector that will maximize earnings.b. Each time vector of earning possesses a risk characteristic. Maximizing expectedearnings ignores the risk parameter.c. Earnings can be increased by selling stock and buying treasury bills. Earnings willcontinue to increase since stock does not require out-of-pocket costs.d. The impact of dividend policies is ignored. If all earnings are retained, future earningsare increased. However, stock prices may decrease as a result of adverse reaction to theabsence of dividends.Maximizing wealth takes into account earnings, the timing and risk of these earnings, andthe dividend policy of the firm.3. Financial management is concerned with the acquisition, financing, and management ofassets with some overall goal in mind. Thus, the function of financial management can bebroken down into three major decision areas: the investment, financing, and assetmanagement decisions.4. Yes, zero accounting profit while the firm establishes market position is consistent with themaximization of wealth objective. Other investments where short-run profits are sacrificedfor the long-run also are possible.5. The goal of the firm gives the financial manager an objective function to maximize. He/shecan judge the value (efficiency) of any financial decision by its impact on that goal. Withoutsuch a goal, the manager would be "at sea" in that he/she would have no objective criterionto guide his/her actions.6. The financial manager is involved in the acquisition, financing, and management of assets.These three functional areas are all interrelated (e.g., a decision to acquire an assetnecessitates the financing and management of that asset, whereas financing andmanagement costs affect the decision to invest).7. If managers have sizable stock positions in the company, they will have a greaterunderstanding for the valuation of the company. Moreover, they may have a greaterincentive to maximize shareholder wealth than they would in the absence of stock holdings.However, to the extent persons have not only human capital but also most of their financial10© Pearson Education Limited 20083语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualcapital tied up in the company, they may be more risk averse than is desirable. If thecompany deteriorates because a risky decision proves bad, they stand to lose not only theirjobs but have a drop in the value of their assets. Excessive risk aversion can work to thedetriment of maximizing shareholder wealth as can excessive risk seeking, if the manager isparticularly risk prone.8. Regulations imposed by the government constitute constraints against which shareholderwealth can still be maximized. It is important that wealth maximization remain the principalgoal of firms if economic efficiency is to be achieved in society and people are to haveincreasing real standards of living. The benefits of regulations to society must be evaluatedrelative to the costs imposed on economic efficiency. Where benefits are small relative tothe costs, businesses need to make this known through the political process so that theregulations can be modified. Presently there is considerable attention being given inWashington to deregulation. Some things have been done to make regulations less onerousand to allow competitive markets to work.9. As in other things, there is a competitive market for good managers. A company must paythem their opportunity cost, and indeed this is in the interest of stockholders. To the extentmanagers are paid in excess of their economic contribution, the returns available toinvestors will be less. However, stockholders can sell their stock and invest elsewhere.Therefore, there is a balancing factor that works in the direction of equilibrating managers’pay across business firms for a given level of economic contribution.10. In competitive and efficient markets, greater rewards can be obtained only with greater risk.The financial manager is constantly involved in decisions involving a trade-off between thetwo. For the company, it is important that it do well what it knows best. There is littlereason to believe that if it gets into a new area in which it has no expertise that the rewardswill be commensurate with the risk that is involved. The risk-reward trade-off will becomeincreasingly apparent to the student as this book unfolds.11. Corporate governance refers to the system by which corporations are managed andcontrolled. It encompasses the relationships among a company’s shareholders, board ofdirectors, and senior management. These relationships provide the framework within whichcorporate objectives are set and performance is monitored.The board of directors sets company-wide policy and advises the CEO and other seniorexecutives, who manage the company’s day-to-day activities. The Board reviews andapproves strategy, significant investments, and acquisitions. The board also overseesoperating plans, capital budgets, and the company’s financial reports to commonshareholders.12. The controller’s responsibilities are primarily accounting in nature. Cost accounting, as wellas budgets and forecasts, would be for internal consumption. External financial reportingwould be provided to the IRS, the SEC, and the stockholders.The treasurer’s responsibilities fall into the decision areas most commonly associated withfinancial management: investment (capital budgeting, pension management), financing(commercial banking and investment banking relationships, investor relations, dividenddisbursement), and asset management (cash management, credit management).11© Pearson Education Limited 20084语言资格考试PPTThe Time Value of MoneyThe chief value of money lies in the fact that one lives ina world in which it is overestimated.H.L. MENCKENFrom A Mencken Chrestomathy19© Pearson Education Limited 20085语言资格考试PPTChapter 3: The Time Value of MoneyANSWERS TO QUESTIONS1. Simple interest is interest that is paid (earned) on only the original amount, or principal,borrowed (lent).2. With compound interest, interest payments are added to the principal and both then earninterest for subsequent periods. Hence interest is compounded. The greater the number ofperiods and the more times a period interest is paid, the greater the compounding and futurevalue.3. The answer here will vary according to the individual. Common answers include a savingsaccount and a mortgage loan.4. An annuity is a series of cash receipts of the same amount over a period of time. It is worthless than a lump sum equal to the sum of the annuities to be received because of the timevalue of money.5. Interest compounded continuously. It will result in the highest terminal value possible for agiven nominal rate of interest.6. In calculating the future (terminal) value, we need to know the beginning amount, theinterest rate, and the number of periods. In calculating the present value, we need to knowthe future value or cash-flow, the interest or discount rate, and the number of periods. Thus,there is only a switch of two of the four variables.7. They facilitate calculations by being able to multiply the cash-flow by the appropriatediscount factor. Otherwise, it is necessary to raise 1 plus the discount rate to the nth powerand divide. Prior to electronic calculators, the latter was quite laborious. With the advent ofcalculators, it is much easier and the advantage of present value tables is lessened.8. Interest compounded as few times as possible during the five years. Realistically, it is likelyto be at least annually. Compounding more times will result in a lower present value.9. For interest rates likely to be encountered in normal business situations the ‘‘Rule of 72’’ isa pretty accurate money doubling rule. Since it is easy to remember and involves acalculation that can be done in your head, it has proven useful.10. Decreases at a decreasing rate. The present value equation, 1/(1 +i)n, is such that as youdivide 1 by increasing (linearly) amounts of i, present value decreases towards zero, but at adecreasing rate.11. Decreases at a decreasing rate. The denominator of the present value equation increases atan increasing rate with n. Therefore, present value decreases at a decreasing rate.12. A lot. Turning to FVIF Table 3.3 in the chapter and tracing down the 3 percent column to25 years, we see that he will increase his weight by a factor of 2.09 on a compound basis.This translates into a weight of about 418 pounds at age 60.20© Pearson Education Limited 20086语言资格考试PPTn n=5=======mnVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualSOLUTIONS TO PROBLEMS1. a. FVn = P0(1 + i)n(i) FV3 = $100(2.0)3 = $100(8)(ii) FV3 = $100(1.10)3 = $100(1.331)(iii) FV3 = $100(1.0)3 = $100(1)= $800= $133.10= $100b. FVn = P0(1 + i) ; FVAn = R[([1 + i] – 1)/i](i) FV5 = $500(1.10)5 = $500(1.611)FVA5 = $100[([1.10]5 – 1)/(0.10)]= $100(6.105)(ii) FV5 = $500(1.05) = $500(1.276)FVA5 = $100[([1.05]5 – 1)/(0.05)]= $100(5.526)(iii) FV5 = $500(1.0)5 = $500(1)FVA5 = $100(5)*= $ 805.50610.50$1,416.00= $ 638.00552.60$1,190.60= $ 500.00500.00$1,000.00*[Note: We had to invoke l’Hospital’s rule in the special case where i = 0; in short,FVIFAn = n when i = 0.]c. FVn = P0(1 + i)n; FVADn = R[([1 + i]n – 1)/i][1 + i](i) FV6 = $500 (1.10)6 = $500(1.772)FVAD5 = $100 [([1.10]5 – 1)/(.10)] × [1.10]= $100(6.105)(1.10) =(ii) FV6 = $500(1.05)6 = $500(1.340)FVAD5 = $100[([1.05] 5 – 1)/(0.05)] × [1.05]= $100(5.526)(1.05)(iii) FV6 = $500(1.0)6 = $500(1)FVAD5 = $100(5)$ 886.00671.55$1,557.55$ 670.00580.23$1,250.23$ 500.00500.00$1,000.00d. FVn = PV0(1 + [i/m])(i) FV3 = $100(1 + [1/4])12 = $100(14.552)(ii) FV3 = $100(1 + [0.10/4])12 = $100(1.345)= $1,455.20= $ 134.5021© Pearson Education Limited 20087语言资格考试PPTf.=3=n===n=3=2=3=1=21==3=Chapter 3: The Time Value of Moneye. The more times a year interest is paid, the greater the future value. It is particularlyimportant when the interest rate is high, as evidenced by the difference in solutionsbetween Parts 1.a. (i) and 1.d. (i).FVn = PV0(1 + [i/m])mn; FVn = PV0(e)in(i) $100(1 + [0.10/1])10 = $100(2.594) = $259.40(ii) $100(1 + [0.10/2])20 = $100(2.653) = $265.30(iii) $100(1 + [0.10/4])40 = $100(2.685) = $268.50(iv) $100(2.71828)1 = $271.832. a. P0 = FVn[1/(1 + i)n](i) $100[1/(2)3] = $100(0.125)(ii) $100[1/(1.10) ] = $100(0.751)$12.50$75.10(iii) $100[1/(1.0)3] = $100(1)b. PVAn = R[(1 –[1/(1 + i) ])/i]=$100(i) $500[(1 – [1/(1 + .04)3])/0.04] =(ii) $500[(1 – [1/(1 + 0.25)3])/0.25c. P0 = FVn[1/(1 + i) ]$500(2.775)$500(1.952)$1,387.50$ 976.00(i) $100[1/(1.04)1] = $100(0.962)500[1/(1.04)2] = 500(0.925)1,000[1/(1.04) ] = 1,000(0.889)= $96.20462.50889.00$1,447.70(ii) $100[1/(1.25)1] = $100(0.800)500[1/(1.25) ] = 500(0.640)1,000[1/(1.25) ] = 1,000(0.512)= $80.00320.00512.00$ 912.00d. (i) $1,000[1/(1.04) ]$1,000(0.962) = $ 962.00500[1/(1.04) ]100[1/(1.04) 3 ]==500(0.925)100(0.889)==462.5088.90$1,513.40(ii) $1,000[1/(1.25) ] = $1,000(0.800)500[1/(1.25)2] = 500(0.640)100[1/(1.25) ] = 100(0.512)$ 800.00320.0051.20$1,171.20e. The fact that the cash flows are larger in the first period for the sequence in Part (d)results in their having a higher present value. The comparison illustrates the desirabilityof early cash flows.22© Pearson Education Limited 20088语言资格考试PPT145612345Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual3. $25,000 = R(PVIFA6%,12) = R(8.384)R = $25,000/8.384 = $2,9824. $50,000 = R(FVIFA8%,10) = R(14.486)R = $50,000/14.486 = $3,4525. $50,000 = R(FVIFA8%,10)(1 + 0.08) = R(15.645)R = $50,000/15.645 = $3,1966. $10,000 = $16,000(PVIFx%,3)(PVIFx%, 3) = $10,000/$16,000 = 0.625Going to the PVIF table at the back of the book and looking across the row for n = 3, wefind that the discount factor for 17 percent is 0.624 and that is closest to the number above.7. $10,000 = $3,000(PVIFAx%,4)(PVIFAx%,4) = $10,200/$3,000 = 3.4 Going to the PVIFAtable at the back of the book and looking across the row for n = 4, we find that the discountfactor for 6 percent is 3.465, while for 7 percent it is 3.387. Therefore, the note has animplied interest rate of almost 7 percent.8. YearSales$ 600,000=$ 500,000(1.2)23720,000864,0001,036,8001,244,1601,492,992=====600,000(1.2)720,000(1.2)864,000(1.2)1,036,800(1.2)1,244,160(1.2)9.Present ValueYear1–10 (annuity)1–5 (annuity)Amount$1,2002,0002,4001,9001,600Subtotal (a)1,4001,400Subtotal (b)Factor at 14%0.8770.7690.6750.5920.519.................................5.2163.433.................................Present Value$1,052.401,538.001,620.001,124.80830.40$6,165.60$7,302.40–4,806.20$2,496.20Total Present Value (a + b) .................................23© Pearson Education Limited 2008$8,661.809语言资格考试PPT===Chapter 3: The Time Value of Money10. AmountPresent Value Interest FactorPresent Value$1,0001/(1 + .10)10=0.386$3861,0001/(1 + .025)40 =0.3723721,0001/e(.10)(10)= 0.36836811.$1,000,000(1 + x%)100$1,000(1 + x%)100$1,000,000/$1,000 = 1,000Taking the square root of both sides of the above equation gives(1 + x%)50(FVIFAx%, 50) = 31.623Going to the FVIF table at the back of the book and looking across the row for n = 50, wefind that the interest factor for 7 percent is 29.457, while for 8 percent it is 46.901.Therefore, the implicit interest rate is slightly more than 7 percent.12. a. Annuity of $10,000 per year for 15 years at 5 percent. The discount factor in the PVIFAtable at the end of the book is 10.380.Purchase price = $10,000 × 10.380 = $103,800b. Discount factor for 10 percent for 15 years is 7.606Purchase price = $10,000 × 7.606 = $76,060As the insurance company is able to earn more on the amount put up, it requires a lowerpurchase price.c. Annual annuity payment for 5 percent = $30,000/10.380 = $2,890Annual annuity payment for 10 percent = $30,000/7.606 = $3,944The higher the interest rate embodied in the yield calculations, the higher the annualpayments.13. $190,000 = R(PVIFA17%, 20) = R(5.628)R = $190,000/5.628 = $33,76024© Pearson Education Limited 200810语言资格考试PPT123456789Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual14. a. PV0 = $8,000 = R(PVIFA1%,36)= R[(1 – [1/(1 + .01)36])/(0.01)] = R(30.108)Therefore, R = $8,000/30.108 = $265.71(1)(2)(3)(4)End ofMonth0101112131415161718192021222324252627282930313233343536InstallmentPayment--$ 265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.71265.88*$9,565.73Monthly Interest(4)t–1 × 0.01--$ 80.0078.1476.2774.3772.4670.5368.5866.6064.6162.6060.5758.5256.4454.3552.2450.1147.9545.7743.5741.3539.1136.8434.5532.2429.9127.5525.1722.7620.3317.8815.4012.9010.377.825.242.63$1,565.73PrincipalPayment(1) – (2)--$ 185.71187.57189.44191.34193.25195.18197.13199.11201.10203.11205.14207.19209.27211.36213.47215.60217.76219.94222.14224.36226.60228.87231.16233.47235.80238.16240.54242.95245.38247.83250.31252.81255.34257.89260.47263.25$8,000.00Principal AmountOwing At MonthEnd (4)t–1 – (3)$8,000.007,814.297,626.727,437.287,245.947,052.696,857.516,660.386,461.276,260.176,057.065,851.925,644.735,435.465,224.105,010.634,795.034,577.274,357.334,135.193,910.833,684.233,455.363,224.202,990.732,754.932,516.772,276.232,033.281,787.901,540.071,289.761,036.95781.61523.72263.250.00*The last payment is slightly higher due to rounding throughout.25© Pearson Education Limited 200811语言资格考试PPT123456789Chapter 3: The Time Value of Moneyb. PV0 = $184,000 = R(PVIFA10%, 25)= R(9.077)Therefore, R = $184,000/9.077 = $20,271.01(1)(2)(3)(4)End ofYear010111213141516171819202122232425InstallmentPayment--$ 20,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,271.0120,262.76*$506,767.00AnnualInterest(4)t–1 × 0.10--$ 18,400.0018,212.9018,007.0917,780.7017,531.6717,257.7316,956.4016,624.9416,260.3415,859.2715,418.0914,932.8014,398.9813,811.7813,165.8612,455.3411,673.7710,814.059,868.358,828.097,683.806,425.075,040.483,517.431,842.07$322,767.00PrincipalPayment(1) – (2)--$ 1,871.012,058.112,263.922,490.312,739.343,013.283,314.613,646.074,010.674,411.744,852.925,338.215,872.036,459.237,105.157,815.678,597.249,456.9610,402.6611,442.9212,587.2113,845.9415,230.5316,753.5818,420.69$184,000.00Principal AmountOwing At Year End(4)t–1 – (3)$ 184,000.00182,128.99180,070.88177,806.96175,316.65172,577.31169,564.03166,249.42162,603.35158,592.68154,180.94149,328.02143,989.81138,117.78131,658.55124,553.40116,737.73108,140.4998,683.5388,280.8776,837.9564,250.7450,404.8035,174.2718,420.690.00*The last payment is somewhat lower due to rounding throughout.15. $14,300 = $3,000(PVIFA15% ,n)(PVIFA15%,n) = $14,300/$3,000 = 4.767Going to the PVIFA table at the back of the book and looking down the column for i = 15%,we find that the discount factor for 8 years is 4.487, while the discount factor for 9 years is4.772. Thus, it will take approximately 9 years of payments before the loan is retired.16. a. $5,000,000 = R[1 + (0.20/1)]5 = R(2.488)R = $5,000,000/2.488 = $2,009,64626© Pearson Education Limited 200812语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualb. $5,000,000 = R[1 + (0.20/2)]10 = R(2.594)R = $5,000,000/2.594 = $1,927,525c. $5,000,000 = R[1 + (0.20/4)]20 = R(2.653)R = $5,000,000/2.653 = $1,884,659d. $5,000,000 = R(e)(0.20) (5) = R(2.71828)(1)R = $5,000,000/2.71828 = $1,839,39817. FV of Earl’s plan = ($2,000) × (FVIFA7%,10) × (FVIF7%,35)= ($2,000) × (13.816) × (10.677)= $295,027FV of Ivana’s plan = ($2,000) × (FVIFA7%, 35)= ($2,000) × (138.237)= $276,474Earl’s investment program is worth ($295,027 – $276,474) = $18,553 more at retirementthan Ivana’s program.18. Tip: First find the future value of a $1,000-a-year ordinary annuity that runs for 25 years.Unfortunately, this future value overstates our “true” ending balance because three of theassumed $1,000 deposits never occurred. So, we need to then subtract three future valuesfrom our “trial” ending balance: (1) the future value of $1,000 compounded for 25 – 5 = 20years; (2) the future value of $1,000 compounded for 25 – 7 = 18 years; and (3) the futurevalue of $1,000 compounded for 25 – 11 = 14 years. After collecting terms, we get thefollowing:FV25 = $1,000[(FVIFA5%, 25) – (FVIF5%, 20) – (FVIF5%, 18) – (FVIF5%,14)]= $1,000[(47.727) – (2.653) – (2.407) – (1.980)]= $1,000[40.687] = $40,68719. There are many ways to solve this problem correctly. Here are two:Cash withdrawals at the END of year ...Alt. %1This above pattern is equivalent to ...PVA9-- minus --PVA327© Pearson Education Limited 200813语言资格考试PPT–=–==×===2==12===Chapter 3: The Time Value of MoneyPVA9R(PVIFAִ05, 9)R(7.108)–PVA3R(PVIFAִ05, 3)R(2.723)==$100,000$100,000$100,000R(4.385)R= $100,000/(4.385)$100,000$22,805.02Cash withdrawals at the END of year ...Alt. %2This above pattern is equivalent to ...PVA6R(PVIFAִ05, 6)R(5.076)××(PVIF.05, 3)(PVIF.05, 3)(.864)==$100,000$100,000$100,000R(4.386)$100,000R=$100,000/(4.386)=$22,799.82NOTE: Answers to Alt. #1 and Alt. #2 differ slightly due to rounding in the tables.20. Effective annual interest rate = (1 + [i/m])m – 1a. (annually)b. (semiannually)c. (quarterly)d. (monthly)= (1 + [0.096/1])1 – 1= (1 + [0.096/2]) – 1= (1 + [0.096/4])4 – 1= (1 + [0.096/12]) – 10.09600.09830.09950.1003e. (daily)= (1 + [0.096/365])365–1=0.1007Effective annual interestrate with continuous compounding(e)i – 1f. (continuous)= (2.71828) .096 – 10.100821. (Note: You are faced with determining the present value of an annuity due. And, (PVIFA8%, 40)can be found in Table IV at the end of the textbook, while (PVIFA8%, 39) is not listed in thetable.)Alt. 1: PVAD40 = (1 + 0.08)($25,000)(PVIFA8%, 40)= (1.08)($25,000)(11.925) = $321,975Alt. 2: PVAD40 = ($25,000)(PVIFA8%, 39) + $25,000= ($25,000)[(1 – [1/(1 + 0.08)39])/0.08] + $25,000= ($25,000)(11.879) + $25,000 = $321,950NOTE: Answers to Alt. 1 and Alt. 2 differ slightly due to rounding.28© Pearson Education Limited 200814语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual22. For approximate answers, we can make use of the ‘‘Rule of 72’’ as follows:(i) 72/14 = 5.14 or 5% (to the nearest whole percent)(ii) 72/8 = 9%(iii) 72/2 = 36%For greater accuracy, we proceed as follows:(i) (1 + i)14 = 2(1 + i) = 21/14 = 2.07143 = 1.0508i = 5% (to the nearest whole percent)(ii) (1 + i)8 = 2(1 + i) = 21/8 = 2.125 = 1.0905i = 9% (to the nearest whole percent)(iii) (1 + i)2 = 2(1 + i) = 21/2 = 2.5 = 1.4142i = 41% (to the nearest whole percent)Notice how the “Rule of 72” does not work quite so well for high rates of growth such as thatseen in situation (iii).SOLUTIONS TO SELF-CORRECTION PROBLEMS1. a. Future (terminal) value of each cash-flow and total future value of each stream are asfollows (using Table I in the end-of-book Appendix):CASH-FLOWSTREAMPV0 FOR INDIVIDUAL CASH FLOWS RECEIVED ATEND OF YEARTOTALFUTUREVALUE12345WXYZ$146.40878.40--292.80$266.20------$242------$330----605$ 300--1,200300$1,284.60878.401,200.001,197.80b. Present value of each cash-flow and total present value of each stream (using Table II inthe end-of-book Appendix):CASH-FLOWSTREAMPV0 FOR INDIVIDUAL CASH FLOWS RECEIVED ATEND OF YEAR1 2 3 4 5TOTALFUTUREVALUEWXYZ$ 87.70526.20--175.40$153.80------$135.80----337.50$177.60------$155.70--622.80155.70$709.80526.20622.80668.6029© Pearson Education Limited 200815语言资格考试PPT=i1Chapter 3: The Time Value of Money2. a. FV10 Plan 1 = $500(FVIFA3.5%,20)= $500([(1 + .035)20 – 1]/[0.035]) = $14,139.84b. FV10 Plan 2 = $1,000(FVIFA7.5%, 10)= $1,000([(1 + 0.075)10 – 1]/[0.075]) = $14,147.09c. Plan 2 would be preferred by a slight margin -- $7.25.d. FV10 Plan 2 = $1,000(FVIFA7%,10)= $1,000([1 + 0.07)10 – 1]/[0.07]) = $13,816.45Now, Plan 1 would be preferred by a nontrivial $323.37 margin.3. Indifference implies that you could reinvest the $25,000 receipt for 6 years at X% toprovide an equivalent $50,000 cash-flow in year 12. In short, $25,000 would double in6 years. Using the “Rule of 72,” 72/6 = 12%Alternatively, note that $50,000 = $25,000(FVIFX%,6). Therefore, (FVIFX%,6) = $50,000/$25,000 = 2. In Table I in the Appendix at the end of the book, the interest factor for 6 yearsat 12 percent is 1.974 and that for 13 percent is 2.082. Interpolating, we haveX% = 12% +2.000 − 1.9742.082 − 1.974= 12.24%as the interest rate implied in the contract.For an even more accurate answer, recognize that FVIFX%, 6 can also be written as (1 + i)6.Then we can solve directly for i (and X% = i(100)) as follows:(1 + i) 6 =2(1 + i) =21/6 = 2.16671.1225=0.1225 or X%=12.25%4. a. PV0 = $7,000(PVIFA6%, 20 ) = $7,000(11.470) = $80,290b. PV0 = $7,000(PVIFA8%, 20) = $7,000(9.818) = $68,7265. a. PV0 = $10,000 = R(PVIFA14%, 4) = R(2.914)Therefore, R = $10,000/2.914 = $3,432 (to the nearest dollar).b.End ofYear0234(1)InstallmentPayment--$ 3,4323,4323,4323,432$13,728(2)Annual Interest(4)t–1 × 0.14--$1,4001,116791421$3,728(3)PrincipalPayment--$ 2,0322,3162,6413,011$10,000(4)Principal AmountOwing At Year End(4)t–1 – (3)$10,0007,9685,6523,011030© Pearson Education Limited 200816语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual6. When we draw a picture of the problem, we get $1,000 at the end of every even-numberedyear for years 1 through 20:TIP: Convert $1,000 every 2 years into an equivalent annual annuity (i.e., an annuity thatwould provide an equivalent present or future value to the actual cash flows) pattern.Solving for a 2-year annuity that is equivalent to a future $1,000 to be received at the end ofyear 2, we getFVA2 = $1,000 = R(FVIFA10%,2) = R(2.100)Therefore, R = $1,000/2.100 = $476.19. Replacing every $1,000 with an equivalent two-year annuity gives us $476.19 for 20 years.PVA20 = $476.19(PVIFA10%, 20) = $476.19(8.514) = $4,054.287. Effective annual interest rate = (1 + [i/m])m –1= (1 + [0.0706/4])4 – 1 = 0.07249 (approx. 7.25%)Therefore, we have quarterly compounding . And, investing $10,000 at 7.06% compoundedquarterly for 7 months (Note: 7 months equals 2 and 1/3 quarter periods), we get$10,000(1 + [0.0706/4])2.33 = $10,000(1.041669) = $10,416.698. FVA65 = $1,230(FVIFA5%, 65) = $1,230[([1 + 0.05]65 – 1)/(0.05)]= $1,230(456.798) = $561,861.54Our “penny saver” would have been better off by ($561,861.54 – $80,000) = $481,861.54 --or 48,186,154 pennies -- by depositing the pennies saved each year into a savings accountearning 5 percent compound annual interest.9. a. $50,000(0.08) = $4,000 interest payment$7,451.47 – $4,000 = $3,451.47 principal paymentb. Total installment payments – total principal payments= total interest payments$74,514.70 – $50,000 = $24,514.7031© Pearson Education Limited 200817语言资格考试PPTThe Valuation of Long-Term SecuritiesWhat is a cynic? A man who knows the price ofeverything and the value of nothing.OSCAR WILDE32© Pearson Education Limited 200818语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualANSWERS TO QUESTIONS1. The market value of a firm is the market price at which the firm trades in an openmarketplace. This value is often viewed as being the higher of the firm's liquidation value(i.e., amount that could be realized if the firm's assets are sold separately from its operatingorganization) or going concern value (i.e., amount a firm could be sold for as a continuingbusiness)2. The intrinsic value (or economic value) of a security could differ from its market value (orprice). Even in a market that is reasonably efficient and informed, the market price of asecurity will fluctuate about its intrinsic value. The less efficient and informed the marketmay be, the greater the likelihood that intrinsic value will differ from market value.3. Both bonds and preferred stocks are fixed-income securities. The interest payment ordividend is fixed at the time of issuance, is contractual, and occurs at regular intervals.Thus, we apply the same general approach to valuing bonds and preferred stock -- that is,we determine the present value of a fixed payment stream.4. The longer the maturity, the less important the principal payment, and the more importantthe interest payments in the bond's valuation. As a result, the principal payment acts less asa buffer against the effect of changes in yield on market price.5. The lower coupon bond will suffer the greater proportional market decline. Its incomestream is further in the future than that for the higher coupon bond, and hence subject tomore volatility.6. Dividends are all that investors as a whole receive. As shown in the chapter, a dividendcapitalization model does not preclude consideration of capital gains. In fact, it embodiesmarket price changes.7. The stock would be worth zero. There must be the prospect for an ultimate cash payment tosomeone for an investment to have value.8. As companies grow larger, growth becomes more difficult. Unless there is somecompetitive advantage or monopolistic position, most large companies grow roughly inkeeping with growth in the economy. A company can of course grow at an increasing ratefor a while, but increasing rates become increasingly harder to sustain in a competitiveeconomy. If increasing rates of growth could be sustained for a number of years, the valueof the stock would explode and approach infinity. This can be illustrated with the perpetualgrowth model where “g” is greater than “k”.9. A company could grow at this rate for a while, but not forever. At the end of 25 years, itwould be over 700 times larger. Obviously this cannot go on forever in real terms or thecompany will end up owning the world. The real rate of growth of the economies of theworld is single digit. Eventually, the growth of this company must taper off.10. She is right. The constant growth dividend valuation model states that P0 = D1/(ke – g).Multiplying both sides of this equation by (ke – g)/P0 reveals that (ke – g) equals D1/P0, or inother words, the expected dividend yield.33© Pearson Education Limited 200819语言资格考试PPT132.64.3Chapter 4: The Valuation of Long-Term Securities11. The ad does not reveal that the current value of this zero-coupon bond is nowhere close tobeing worth 1,000. For example, at a 10 percent discount rate this bond is only worth about$57.SOLUTIONS TO PROBLEMS1.DiscountEnd of Year2End of Six-month Period12345Payment$ 1001001,100Payment$ 50505050501,050Factor (14%)0.8770.7690.675Price per bondDiscountFactor (7%)0.9350.8730.8160.7630.7130.666Price per bondPresent Value$ 87.7076.90742.50$ 907.10Present Value$ 46.7543.6540.8038.1535.65699.30$ 904.303. Current price: P0 = Dp/kp = (0.08)($100)/(0.10) = $80.00Later price: P0 = Dp/kp = ($8)/(0.12) = $66.67The price drops by $13.33 (i.e., $80.00 – $66.67).Rate of return =$1 dividend + ($23 − $20) capital gain$20 original price= $4/$20 = 20%5. Phases 1 and 2: Present Value of Dividends to Be Received Over First 6 YearsEnd ofYearPresent Value Calculation(Dividend × PVIF18%,t)Pre sent Valueof DividendPhase123$2.00 (1.15)12.00 (1.15)22.00 (1.15)===$2.302.653.04× 0.847× 0.718× 0.609===$ 1.951.901.85134© Pearson Education Limited 200820语言资格考试PPTaseor ￿∑t ￿===+Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualPh4563.04(1.10)1 =3.04(1.10)2 =3.04(1.10)3 =3.34 × 0.5163.68 × 0.4374.05 × 0.370===1.721.611.502￿￿6 Dt ￿￿￿t =1 (1.18) ￿Phase 3: Present Value of Constant Growth ComponentDividend at the end of year 7 = $4.05(1.05) = $4.25$10.53Value of stock at the end of year 6 =D7(K e − g)$ 4.25(.18 − .05)= $32.69Present value of $32.69 at end of year 6 = ($32.69) (PVIF18%,6 )= ($32.69)(.370) = $12.10Present Value of StockV = $10.53 + $12.10 = $22.636. a. P0 = D1/(ke – g): ($1.50)/(0.13 – 0.09) = $37.50b. P0 = D1/(ke – g): ($1.50)/(0.16 – 0.11) = $30.00c. P0 = D1/(ke – g): ($1.50)/(0.14 – 0.10) = $37.50Either the present strategy (a) or strategy (c). Both result in the same market price per share.7. a. kp = Dp/P0: $8/$100 = 8 percentb. Solving for YTC by computer for the following equation$100 = $8/(1 +YTC)1 + $8/(1 + YTC)2 + $8/(1 + YTC)3+ $8/(1 + YTC)4 + $118/(1 + YTC)5we get YTC = 9.64 percent. (If the students work with present-value tables, they shouldstill be able to determine an approximation of the yield to call by making use of a trial-and-error procedure.)8. V = Dp/kp = [(0.09)($100)]/(0.12) = $9/(0.12) = $759. V = (I/2)(PVIFA7%, 30) +$45(12.409)$1,000(PVIF7%, 30)$1,000(0.131)=$558.41+$131= $689.4110. a. P0 = D1/(ke – g) = [D0(1 + g)]/(ke – g)$21 = [$1.40(1 + g)]/(0.12 – g)$21(0.12 – g) = $1.40(1 + g)35© Pearson Education Limited 200821语言资格考试PPT=2+++++￿X ￿￿￿$103.47 ￿￿$155.92￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿===2=Chapter 4: The Valuation of Long-Term Securities$2.52 – $21(g) = $1.40 + $1.40(g)$1.12 = $22.40(g)g = $1.12/$22.40 = 0.05 or 5 percentb. Expected dividend yield = D1/P0 = D0(1 + g)/P0= $1.40(1 + 0.05)/$21 = $1.47/$21 = 0.07c. Expected capital gains yield = g = 0.05.11. a.$1,120P0 = (I/2)/(semiannual yield)= ($45)/(semiannual yield)semiannual yield = $45/$1,120 = 0.0402b. (semiannual yield) × (2)(nominal annual) yield(0.0402)× (2)=0.0804c. (1 + semiannual yield)2 – 1 =(effective annual) yield(1 + 0.0402)–1 =0.082012. Trying a 4 percent semiannual YTM as a starting point for a trial-and-error approach, wegetP0 = $45(PVIFA4%, 20)= $45(13.590)$1,000(PVIF4%, 20)$1,000(0.456)= $611.55+$456=$1,067.55Since $1,067.55 is less than $1,120, we need to try a lower discount rate, say 3 percentP0 = $45(PVIFA3%, 20)= $45(14.877)= $669.47$1,000(PVIF3%, 20)$1,000(0.554)$554 = $1,223.47To approximate the actual discount rate, we interpolate between 3 and 4 percent as follows:￿￿￿￿￿ .03 $1,223.47 ￿￿￿￿￿￿￿￿￿￿￿￿￿￿.01￿￿￿￿￿ semiannual YTM $1,120,00￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿.15 $1,067.55 ￿X 103.47.01 $155.92Therefore, X =(.01) × ($103.47)$155.92= .0066and semiannual YTM = 0.03 + X = 0.03 + 0.0066 = 0.0366, or 3.66 percent. (The use of acomputer provides a precise semiannual YTM figure of 3.64 percent.)b. (semiannual YTM) × (2)(0.0366) × (2)c. (1 + semiannual YTM)2 – 1 =(1 + 0.0366) – 1(nominal annual) YTM0.0732(effective annual) YTM0.075436© Pearson Education Limited 200822语言资格考试PPT++++4Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual13. a. Old Chicago's 15-year bonds should show a greater price change than Red Frog's bonds.With everything being the same except for maturity, the longer the maturity, the greaterthe price fluctuation associated with a given change in market required return. Thecloser in time that you are to the relatively large maturity value being realized, the lessimportant are interest payments in determining the market price, and the less importantis a change in market required return on the market price of the security.b. (Red Frog):P0 = $45(PVIFA4%,10)= $45(8.111)$1,000(PVIF4%, 10)$1,000(0.676)= $365+$676=$1,041(Old Chicago):P0 = $45(PVIFA4%, 30)= $45(17.292)$1,000(PVIF4%,30)$1,000(0.308)= $778.14+$308=$1,086.14Old Chicago’s price per bond changes by ($1.086.14 – $1,000) = $86.14, while RedFrog’s price per bond changes by less than half that amount, or ($1,041 – $1,000) = $41.14. D0(1 + g)/(ke – g) = Va. $2(1 + 0.10)/(0.16 – 0.10) = $2.20/0.06 = $36.67b. $2(1 + 0.09)/(0.16 – 0.09) = $2.18/0.07 = $31.14c. $2(1 + 0.11)/(0.16 – 0.11) = $2.22/0.05 = $44.40SOLUTIONS TO SELF-CORRECTION PROBLEMS1. a, b.End ofDiscountPresentDiscountPresentyearPaymentFactor, 15%Value, 15%Factor, 12%Value, 12%_____________________________________________________________________________1–3$802.283$182.642.402$192.16Market value1,0800.572617.76$800.400.636686.88$879.04Note: Rounding error incurred by use of tables may sometimes cause slight differences inanswers when alternative solution methods are applied to the same cash flows.The market value of an 8 percent bond yielding 8 percent is its face value, of $1,000.37© Pearson Education Limited 200823语言资格考试PPT4343￿∑ (1.16)t ￿=Chapter 4: The Valuation of Long-Term Securitiesc. The market value would be $1,000 if the required return were 15 percent.End OfDiscountPresentYearPaymentFactor, 8%Value, 8%_____________________________________________________________________________1–3$ 1501,150Market value2.5770.735$ 386.55845.25$1,231.802.Phases 1 and 2: Present Value of Dividends to Be Received Over First 8 YearsEnd of YearPresent Value Calculation(Dividend × PVIF16%, t)Present Value of DividendPhase1Phase212345678or$1.60 (1.20)1 = $1.92 × 0.8621.60 (1.20)2 = 2.30 × 0.7431.60 (1.20) = 2.76 × 0.6411.60 (1.20) = 3.32 × 0.5523.32 (1.13)1 = 3.75 × 0.4763.32 (1.13)2 = 4.24 × 0.4103.32 (1.13) = 4.79 × 0.3543.32 (1.13)4 = 5.41 × 0.305￿￿8 Dt ￿￿￿t =1 ￿=========$ 1.661.711.771.831.791.741.701.65$13.85Phase 3: Present Value of Constant Growth ComponentDividend at the end of year 9 = $5.41(1.07) = $5.79Value of stock at the end of year 8 =D9 $5.79(k e − g) (.16 − .07)= $64.33Present value of $64.33 at end of year 8 = ($64.33) (PVF16%, 8)= ($64.33)(0.305) = $19.62Present Value of StockV = $13.85 + $19.62 = $33.4738© Pearson Education Limited 200824语言资格考试PPTt++++++++Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual3. The yield to maturity is higher than the coupon rate of 8 percent because the bond sells at adiscount from its face value. The (nominal annual) yield to maturity as reported in bondcircles is equal to (2 × semiannual YTM). The (effective annual) YTM is equal to (1 +semiannual YTM)2 – 1. The problem is set up as follows:20$935 = ∑t =1$40(1 + k d / 2)$1,000(1 + k d / 2)20= ($40) (PVIFAk d / 2,20 ) + MV(PVIFk d / 2,20 )a. Solving for kd/2 (the semiannual YTM) in this expression using a calculator, a computerroutine, or present value tables yields 4.5 percent.b. (i) The (nominal annual) YTM is then 2 × 4.5 percent = 9 percent.(ii) The (effective annual) YTM is (1 + 0.045)2 – 1 = 9.2025 percent.4. a. P0 = FV20(PVIFkd/2,20)( PVIFk d / 2,20 ) = P0/FV20 = $312/$1,000 = 0.312From Table II in the end-of-book Appendix, the interest factor for 20 periods at 6 percentis 0.312; therefore, the bond’s semiannual yield to maturity (YTM) is 6 percent.b. (i) (nominal annual) YTM = 2 × (semiannual YTM)= 2 × (0.06) = 12 percent(ii) (effective annual) YTM = (1 + semiannual YTM)2 – 1= (1 + 0.06)2 – 1 = 12.36 percent5. a. ke = (D1/P0) + g = ([D0(1 + g)]/P0) + g= ([$1(1 + 0.06)]/$20) + 0.06= 0.053 + 0.06 = 0.113b. expected dividend yield = D1/P0 = $1(1 + 0.06)/$20 = 0.053c. expected capital gains yield = g = 0.066. a. (i) V = ($140/2)(PVIFAִ06,6)$1,000(PVIF.06,6)=$70(4.917)+$1,000(0.705)=$344.19+$705=$1,049.19(ii) V = ($140/2)(PVIFAִ07, 6)= $70(4.767)= $333.69$1,000(PVIFִ07, 6)$1,000(0.666)$666 = $999.69* or $1,000(*Value should equal $1,000 when the nominal annual required return equals thecoupon rate; our answer differs from $1,000 only because of rounding in the Tablevalues used.)(iii) V = ($140/2)(PVIFA.08, 6)= $70(4.623)= $323.61$1,000(PVIF.08, 6)$1,000(0.630)$630 = $953.6139© Pearson Education Limited 200825语言资格考试PPTChapter 4: The Valuation of Long-Term Securitiesb. The value of this type of bond is based on simply discounting to the present the maturityvalue of each bond. We have already done that in answering Part (a) and those valuesare: (i) $705; (ii) $666; and (iii) $630.40© Pearson Education Limited 200826语言资格考试PPTRisk and ReturnTake calculated risks. That is quite different from beingrash.GENERAL GEORGE S. PATTON41© Pearson Education Limited 200827语言资格考试PPTChapter 5: Risk and ReturnANSWERS TO QUESTIONS1. Virtually none of the concepts presented would hold. Risk would not be a dimension ofconcern to the risk-neutral investor. The only concern would be with expected return, andmarket equilibrium would be in relation to seeking the highest expected return. If investorswere risk seekers, increased risk would provide positive utility and would be sought alongwith higher expected returns. Obviously there would be no risk-return trade-off of the typedescribed.2. The characteristic line depicts the expected relationship between excess returns (in excessof the risk-free rate) for the security involved and for the market portfolio. The beta is theslope of the characteristic line. [The alpha is the intercept on the vertical axis. It should bezero in theory, but may be positive or negative in practice.]3. Beta measures the responsiveness of changes in excess returns for the security involved tochanges in excess returns for the market portfolio. It tells us how attuned fluctuations inreturns for the stock are with those for the market. A beta of one indicates proportionalfluctuation and systematic risk; a beta greater than one indicates more than proportionalfluctuation; and a beta less than one indicates less than proportional fluctuation relative tothe market.4. Req. (Rj) = Rf + [E(Rm) – Rf] BetajRf = risk-free rate;Req. (Rj) = required rate of return for security j;E(R m ) = expected rate of return for the market portfolio;Betaj = beta for security j.5. No. The security market line (SML) can vary with changes in interest rates, investorpsychology, and perhaps with other factors.6. a. Lower the market price.b. Raise the market price.c. Lower the market price.d. Lower the market price.7. If you limit yourself to only common stock, you would seek out defensive stocks -- wherereturns tend to go up and down by less than those for the overall market. Therefore, thebetas would be less than 1.0. However, it is important to recognize that there are few stockswith betas of less than 0.5. Most have betas of 0.7 or more.8. The undervalued stock would lie above the security market line, thereby providing investorswith more expected return than required for the systematic risk involved. Investors wouldbuy the stock and cause it to rise in price. The higher price will result in a lower expectedreturn. Equilibrium is achieved when the expected return lies along the security market line.42© Pearson Education Limited 200828语言资格考试PPTb.Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualSOLUTIONS TO PROBLEMS1. a.Possible Return, Ri–.10.00.10.20.30Probability ofOccurrence, Pi.10.20.30.30.10Σ = 1.00(Ri)(Pi)–.10.00.03.06.03Σ = 0.11 = R(Ri – R )2(Pi)(–0.10 – 0.11)2 (.10)(.00 – 0.11)2 (.20)(0.10 – .11)2 (0.30)(0.20 – .11)2 (0.30)(0.30 – .11)2 (0.10)Σ = .0129 = σ2(0.0129).5 = 11.36% = σb. There is a 30 percent probability that the actual return will be zero (prob. E(R) = 0 is20%) or less (prob. E(R) < is 10%). Also, by inspection we see that the distribution isskewed to the left.2. a. For a return that will be zero or less, standardizing the deviation from the expectedvalue of return we obtain (0% – 20%)/15% = –1.333 standard deviations. Turning toTable V at the back of the book, 1.333 falls between standard deviations of 1.30 and1.35. These standard deviations correspond to areas under the curve of 0.0968 and0.0885 respectively. This means that there is approximately a 9 percent probabilitythat actual return will be zero or less. (Interpolating for 1.333, we find the probability tobe 9.13%).10 percent::20 percent:30 percent:40 percent:50 percent:Standardized deviation = (10% – 20%)/15% = –0.667. Probability of10 percent or less return = (approx.) 25 percent. Probability of 10percent or more return = 100% – 25% = 75 percent.50 percent probability of return being above 20 percent.Standardized deviation = (30% – 20%)/15% = +0.667. Probability of30 percent or more return = (approx.) 25 percent.Standardized deviation = (40% – 20%)/15% = +1.333. Probability of40 percent or more return = (approx.) 9 percent -- (i.e., the samepercent as in part (a).Standardized deviation = (50% – 20%)/15% = +2.00. Probability of 50percent or more return = 2.28 percent.43© Pearson Education Limited 200829语言资格考试PPTChapter 5: Risk and Return3. As the graph will be drawn by hand with the characteristic line fitted by eye, All of themwill not be same. However, students should reach the same general conclusions.The beta is approximately 0.5. This indicates that excess returns for the stock fluctuate lessthan excess returns for the market portfolio. The stock has much less systematic risk thanthe market as a whole. It would be a defensive investment.4. Req. (RA)Req. (RB)Req. (R C )Req. (RD)Req. (RE)=====0.070.070.070.070.07+++++(0.13 – 0.07) (1.5) =(0.13 – 0.07) (1.0) =(0.13 – 0.07) (0.6) =(0.13 – 0.07) (2.0) =(0.13 – 0.07) (1.3) =0.160.130.1060.190.148The relationship between required return and beta should be stressed.5. Expected return = 0.07 + (0.12 – 0.07)(1.67) = 0.1538, or 15.38%6. Perhaps the best way to visualize the problem is to plot expected returns against beta. Thisis done below. A security market line is then drawn from the risk-free rate through theexpected return for the market portfolio which has a beta of 1.0.44© Pearson Education Limited 200830语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualThe (a) panel, for a 10% risk-free rate and a 15% market return, indicates that stocks 1 and 2are undervalued while stock 4 is overvalued. Stock 3 is priced so that its expected returnexactly equals the return required by the market; it is neither overpriced nor underpriced.The (b) panel, for a 12% risk-free rate and a 16% market return, shows all of the stocksovervalued. It is important to stress that the relationships are expected ones. Also, with achange in the risk-free rate, the betas are likely to change.7. a.TickerSymbolWOOPSKBOOMJUDYUPDWNSPROUTRINGGEIEIOAmountInvested$ 6,00011,0009,0007,0005,00013,0009,000$60,000Proportion,Pi0.1000.1830.1500.1170.0830.2170.1501.000ExpectedReturn, Ri0.140.160.170.130.200.150.18Weighted Return,(Pi)(Ri)0.01400.02930.02550.01520.01670.03250.02700.1602Selena’s expected return is 0.1602 or 16.02 percent.45© Pearson Education Limited 200831语言资格考试PPTPi==Chapter 5: Risk and Returnb.TickerSymbolWOOPSKBOOMJUDYUPDWNSPROUTRINGGEIEIOAmountInvested$6,00011,0009,0007,00020,00013,0009,000$75,000Proportion,0.080.1470.1200.0930.2670.1730.1201.000ExpectedReturn, Ri0.140.160.170.130.200.150.18WeightedReturn, (Pi)(Ri)0.01120.02350.02040.01210.05340.02600.02160.1682The expected return on Selena’s portfolio increases to 16.82 percent, because theadditional funds are invested in the highest expected return stock.8. Required return0.10 + (0.15 – .10)(1.08)0.10 + .054 = 0.154 or 15.4 percentAssuming that the perpetual dividend growth model is appropriate, we getV = D1/(ke – g) = $2/(0.154 –0.11) = $2/0.044 = $45.459. a. The beta of a portfolio is simply a weighted average of the betas of the individualsecurities that make up the portfolio.Ticker SymbolNBSYUWHOSLURPWACHOBURPSHABOOMBeta1.400.800.601.801.050.90Proportion0.20.20.20.20.10.11.0Weighted Beta0.2800.1600.1200.3600.1050.0901.115The portfolio beta is 1.115.b. Expected portfolio return = 0.08 + (0.14 – 0.08)(1.115)= 0.08 + .0669 = 0.1469 or 14.69%10. a. Required return = 0.06 + (0.14 – 0.06)(1.50)= 0.06 + 0.12 = 0.18 or 18%Assuming that the constant dividend growth model is appropriate, we getV = D1/(ke – g) = $3.40/(0.18 – 0.06) = $3.40/0.12 = $28.3346© Pearson Education Limited 200832语言资格考试PPT22EFVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualb. Since the common stock is currently selling for $30 per share in the marketplace, whilewe value it at only $28.33 per share, the company’s common stock appears to be“overpriced”. Paying $30 per share for the stock would likely result in our receiving arate of return less than that required based on the stock’s systematic risk.Solution to Appendix A Problem:11. E(Rp) = (0.20)(0.08) + (0.30)(0.15) + (0.50)(0.12) = 0.121The standard deviation for the portfolio is found by summing up all the elements in thefollowing variance-covariance matrix and then taking the sum's square root.DEFD(0.2) (1) (.02)(0.2) (0.3) (0.4) (0.02) (0.16) (0.2) (0.5) (0.6) (0.02) (0.08)(0.3) (0.2) (0.4) (0.16) (0.02)(0.3)2 (1) (0.16)2(0.3) (0.5) (0.8) (0.16) (0.08)(0.5) (0.2) (0.6) (0.08) (0.02)(0.5) (0.3) (0.8) (0.08) (0.16) (0.5)2 (1) (0.08)2Therefore, the standard deviation of the portfolio equals:[(0.2)2(1)(0.02)2 + (0.3)2(1)(0.16)2 + (0.5)2 (1)(0.08)2+ 2(0.2)(0.3)(0.4)(0.02)(0.16) + 2(0.2)(0.5)(0.6)(0.02)(0.08)+ 2(0.3)(0.5)(0.8)(0.16)(0.08)].5 = [0.0073376].5 = 8.56%SOLUTIONS TO SELF-CORRECTION PROBLEMS1. a.PossibleReturn, Ri–0.100.050.200.350.50Probability ofOccurrence, Pi0.100.200.400.200.10Σ =1.00(R i )(P i )–0.0100.0100.0800.0700.050Σ = 0.200 = R(R i − R)2 (Pi )(–0.10 –0.20)2 (0.10)(0.05 – 0.20)2 (0.20)(0.20 – 0.20)2 (0.40)(0.35 – 0.20)2 (0.20)(0.50 – 0.20) 2 (0.10)Σ = 0.027 = σ2(0.027).5 = 16.43% = σb. For a return that will be zero or less, standardizing the deviation from the expectedvalue of return we obtain (0% – 20%)/16.43% = –1.217 standard deviations. Turning toTable V in the appendix at the back of the book, 1.217 falls between standard deviationsof 1.20 and 1.25. These standard deviations correspond to areas under the curve of0.1151 and 0.1056 respectively. This means that there is approximately an 11%probability that actual return will be zero or less.47© Pearson Education Limited 200833语言资格考试PPT=Chapter 5: Risk and ReturnFor a return that will be 10 percent or less, standardizing the deviation we obtain(10% – 20%)/16.43% = –0.609 standard deviations. Referring to Table V, we see thatthis corresponds to approximately 27%.For a return of 40% or more, standardizing the deviation we obtain (40% –0 20%)/16.43% = 1.217 standard deviations. This is the same as in our first instance involving azero return or less, except that it is to the right, as opposed to the left, of the mean.Therefore, the probability of a return of 40% or more is approximately 11%.2. a. R= 8% + (13% – 8%)1.45 = 15.25%b. If we use the perpetual dividend growth model, we would haveP0 =D1 $2 (1.10)k e − g 0.1525 − 0.10= $41.90c. R = 8% + (13% – 8%)0.80 = 12%P0 =$2(1.10)0.12 - 0.10= $110SOLUTION TO APPENDIX A SELF-CORRECTION PROBLEM3. Rp = (0.60)(0.10) + (0.40)(0.06) = 8.4%σp = [(0.6)2(1.0)(0.05)2 + 2(0.6)(0.4)(–.35) (0.05)(0.04) + (0.4)2(1.0)(0.04)2]0.5In the above expression, the middle term denotes the covariance (–0.35)(0.05)(0.04) timesthe weights of .6 and .4, all of which is counted twice -- hence the two in front. For the firstand last terms, the correlation coefficients for these weighted-variance terms are 1.0. Thisexpression reduces toσp = [0.00082].5 = 2.86%48© Pearson Education Limited 200834语言资格考试PPTFinancial Statement AnalysisFinancial statements are like a fine perfume – to besniffed but not swallowed.ABRAHAM BRILLOFF49© Pearson Education Limited 200835语言资格考试PPTChapter 6: Financial Statement AnalysisANSWERS TO QUESTIONS1. The purpose of a balance sheet is to present a picture of the firm’s financial position at onemoment in time. The income statement, on the other hand, depicts a summary of the firm’sprofitability over time.2. By analyzing trends, one is able to determine whether there has been improvement ordeterioration in the financial condition and performance of a firm. This is particularly usefulin the prediction of insolvency and the taking of remedial steps before insolvency can occur.3. Receivables and inventories undoubtedly dominate the current asset position of the firm.Moreover, the collection period is probably slow and there may be some hidden bad debts.Also, inventory turnover may be slow, indicating inefficiency and excessive investment ininventory. This question points to the fact that the current ratio is a very crude indicator ofliquidity and that one must analyze the specific current assets.4. A firm may generate a high return and still be technically insolvent for many reasons. Mostfrequently, the profitable firm is growing at a rate that cannot be supported by internalsources of funds, and external sources of funds beyond a point are unavailable.5. Both measures relate a balance sheet figure, which was the result of the last month, or so, ofsales, to annual income statement figures. Comparing a “stock” (balance sheet) item to a“flow” (income statement) item might involve a mismatch of variables. The stock item maynot be representative of how this variable looked over the period during which the flowoccurred. Therefore, where appropriate, we may need to use an “average” balance sheetfigure in order to better match the income statement flow item with a balance sheet stockfigure more representative of the entire period.6. A long-term creditor is interested in liquidity ratios because short-term creditors may forcebankruptcy, imposing some substantial costs on the long-term creditor.7. a. Liquidity ratios to insure payment of principal by the going concern and debt ratios as ameasure of protection of his/her principal in bankruptcy.b. The equity investor is interested in profitability ratios and ratios that provideinformation about risk.c. The fund manager is interested in profitability ratios to provide some assurance of thelong-run viability of the firm, leverage (debt) ratios to get an indication of risk, andliquidity ratios to determine if the firm is technically solvent.d. The president, as a manager, is interested in all the ratios, with particular emphasis onprofitability.8. The ratio of debt-to-equity and long-term debt to total capitalization both historically and incomparison with other companies. Coverage ratios give some indication of the firm’s abilityto service debt. With all of these ratios, comparisons with other companies in the industry aswell as over time add additional insight.9. Such a situation could come about if the company had invested its profits in large, slow-moving inventory, an addition to fixed assets, or in increased accounts receivable. A slow-moving inventory would be visible in a low inventory turnover ratio and in a below averagequick or acid-test ratio. An addition to fixed assets would be visible in the fixed asset50© Pearson Education Limited 200836语言资格考试PPTEFVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualturnover ratio. An increase in accounts receivable would be reflected in a lengtheningaverage collection period and, possibly, in a stretching of the receivable aging schedule.In addition, if the firm has recently suffered a decline in the market value of its securitiescarried at cost on the balance sheet, the firm could find itself in difficulty when attemptingto sell out to pay maturing obligations.10. Yes, it could. By increasing the turnover the company is really reducing its investment inexcessive stocks of inventory carrying a low or zero rate of return. The resulting inventoryis said to be more liquid or more readily convertible into cash. However, if the reduction ininventory levels is accomplished by a loss of sales due to stockouts, the increased turnoverratio may be unfavorable.The use of cost of goods sold in the ratio allows the analyst to separate the effects of anincreased gross margin (resulting from an increase in selling price or a decrease in costs)from the effects of a more efficient inventory management per se (high volume of sales fora given level of inventory investment).11. No. The appropriate standard varies by industry. What is a good ratio for one industry maynot be so for another. Also, no one financial ratio tells the whole story. Only by analyzingmultiple ratios can one get a reasonably complete picture of a firm’s financial condition andperformance.12. Both firms are equally profitable. Each has an “earning power” or return on investment(ROI) of 20%. An example of Firm A might be a grocery store such as Safeway or Winn-Dixie. An example of Firm B might be a retail department store.13. Short-term creditors look at balance sheet assets as a loan safety margin for repayment inthe event of default. The income statement is ignored because the impact of future earningson this safety margin is small over short time periods. Yet for that portion of short-termcredit renewed on a more or less permanent basis, the “earning power” of the firmrepresents the real margin of credit risk over the long-term regardless of initial assetstrength.14. The use of index analysis allows one to go behind some of the trends that are evident in atrend analysis of financial ratios. For example, if the current ratio deteriorates, indexanalysis permits one to determine the specific current assets and/or liabilities that arecausing this trend.SOLUTIONS TO PROBLEMS1.(a)Total Asset(b)Net Profit(a) × (b)Earning PowerCo.TurnoverMargin(ROI)A ($10M/$8M) = 1.25B ($20M/$10M) = 2.00($.7M/$10M) = 0.07($2M/$20M) = 0.100.08750.2000C ($8M/$6M)= 1.33($.8M/$8M) = 0.100.1333D ($5M/$2.5M) = 2.00($12M/$4M) = 3.00($17M/$8M) = 2.125($.5M/$5M) = 0.10($1.5M/$12M) = 0.125($1M/$17M) = 0.058851© Pearson Education Limited 20080.20000.37500.125037语言资格考试PPTf.i.Chapter 6: Financial Statement Analysis2. a. Current ratio = ($3,800 / $1,680) = 2.26b. Acid-test ratio = ($3,800 – $2,100)/ $1,680 = 1.01c. Average collection period = ($1,300 × 365 days)/$12,680 = 37.42 daysd. Inventory turnover = ($8,930/$2,100) = 4.25e. Debt to net worth = ($1,680 + $2,000)/$3,440 = 1.07LTD to total capitalization = ($2,000)/($2,000 + $3,440) = 0.37g. Gross profit margin = ($3,750)/$12,680) = 0.2957h. Net profit margin = ($670/$12,680) = 0.0528Return on equity = ($670/$3,440) = 0.19483. a. The return on investment declined because total asset turnover declined and the netprofit margin declined. Apparently, sales did not keep up with asset expansion or salesdecreased while assets did not. In either case, fixed costs would command a largerpercentage of the sales dollar, causing profitability on sales to decrease. The lowerprofitability on sales and lower asset turnover resulted in lower return on investment.b. The increase in debt came from short–term sources. Current assets increased relative tosales as is indicated by the inventory turnover and collection period. The current ratioand the acid–test ratio, however, decreased. This indicates a substantial increase incurrent liabilities.4. Profit after taxes = Sales × Net profit margin= $8,000 × 0.07 = $560Profit before taxes = $560/(1 – Tax rate)= $560/(1 – 0.44) = $1,000Taxes = $1,000 – $560 = $440Total liabilities = (Shareholders’ equity) × (Total liabilities/Shareholders’ equity)= ($3,750)(1/1) = $3,750Total liabilities & Equity = $3,750 + 3,750 = $7,500Current liabilities = Total Liabilities – Long–term debt= $3,750 – $2,650 = $1,100Bank loan = Current liabilities – Payables – Accruals= $1,100 – $400 – $200 = $500Total assets = Total liabilities & Equity = $7,500Current assets = Current liabilities × Current Ratio= $1,100 × 3 = $3,300Net fixed assets = Total assets – Current assets= $7,500 – $3,300 = $4,200Accounts receivable = [(Credit sales) × (Average collection period)]/360 days= [($8,000) × (45 days)]/360 days = $1,00052© Pearson Education Limited 200838语言资格考试PPTb.===×=Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualInventories = Current assets – Cash – Receivables= $3,300 – $500 – $1,000 = $1,800Cost of Goods Sold = (Inventories) × (Inventory turnover ratio)= $1,800 × 3 = $5,400Gross Profit = Sales – Cost of goods sold= $8,000 – $5,400 = $2,600Selling & Administrative Expenses = Gross profit – Interest – Profit before taxes= $2,600 – $400 – $1,000 = $1,2005. a. Cost of goods sold = (1 – Gross profit margin)(Net sales)= (1 – 0.20)($400,000) = $320,000Inventory turnover = Cost of goods sold/(average)InventoryTherefore, . . . (average) Inventory = Cost of goods sold/Inventory turnover= $320,000/4 = $80,000Average collection period =(average) Receivable × 360 daysAnnual credit sales45 days = ($50,000 × 360 days)/$400,0006. a. Earning power =Sales profitability × Asset efficiencyROIROIb. Total assets“New” ROI==Net profit margin × Total asset turnover($120,000/$6,000,000) × 6 = 0.12Sales/Total asset turnover = $6M/6 = $1MNet profit margin × Total asset turnover0.03 × ($6M/($1M × 1.2)) = 0.157. Interest on each issue:(9-1/4s)(12-3/8s)(10-1/4s)(14-1/2s)$2,500,000$1,500,000$1,000,000$1,000,000×××0.09250.123750.10250.145===$231,250185,625102,500145,000$664,375EBIT/Interest expense = interest coverage ratio $1,500,000/$664,375 = 2.2653© Pearson Education Limited 200839语言资格考试PPTChapter 6: Financial Statement Analysis8.20X120X220X320X4CashReceivablesInventoriesNet fixed assetsTotal assetsAccounts payableNotes payableAccrualsLong-term debtCommon stockRetained earnings100.00100.00100.00100.00100.00100.00100.00100.00100.00100.00100.0043.46129.35137.63105.72120.06139.52130.00131.25160.00100.00101.8519.63152.18174.98107.62138.38163.40150.00196.49160.00100.00111.0817.76211.21202.71121.32166.20262.42150.00265.70160.00100.00111.99Total liabilities &shareholders’ equity100.00120.06138.38166.20In the last three years, the company has increased its receivables and inventories ratherdramatically. While net fixed assets jumped in 20X4, changes were only modest in 20X2and 20X3. The basic problem is that retained earnings have grown at only a very slow rate,almost all of which occurred in 20X3. This is due to inadequate profitability, excessivedividends, or both. While the company increased its long-term debt in 20X2, it has not doneso since. The burden of financing has fallen on accounts payable and accruals, together withdrawing down the cash position and $50,000 in increased short-term borrowings (notespayable). The question would be whether payables are past due and whether employees arebeing paid on time. It is clear that the company cannot continue to expand its assets withoutincreasing its equity base in a significant way.9. a. (i) Current ratio = Current assets/Current liabilities= $13M/$8M = 162.5%(ii) Acid-test ratio = (Current assets - Inventories)/Current liabilities= $6M/$8M = 75%(iii) Receivable turnover = Annual credit sales/Receivables= $16M/$5M = 3.2x(iv) Inventory turnover = Cost of goods sold/Inventory= $12M/$7M = 1.7x(v) Long-term debt/Total capitalization= $12M/($12M + $4M + $6M)= $12M/$22M = 54.5%54© Pearson Education Limited 200840语言资格考试PPT=Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual(vi) Gross profit margin = (Sales - Cost of goods sold)/Sales= ($20M - $12M)/$20M = 40%(vii)Net profit margin(viii) Return on equity= Net income after taxes/Sales= $2M/$20M = 10%Net income after taxes − Dividends on preferred stockNet worth − Par value of preferred stock= $1,760,000/($10,000,000 - $4,000,000) = 29.3%(ix) Return on assets = Net income after taxes/Total assets= $2M/$30M = 6.7%(x) Total asset turnover = Sales/Total assets = $20M/$30M = 0.67x(xi) Interest coverage = EBIT/Interest charges= $4.4M/$1.2M = 3.67xb. (i) Ratios 1-5 uniformly indicate that liquidity is deteriorating.(ii) The gross profit margin (#6) remains relatively constant and at the industry norm,while the net profit margin (#7) is declining. This indicates that interest,depreciation, and selling and administrative expenses are rising relative to sales.(iii) Part of the margin decline is accounted for by the rapid rise in debt (#5). Thisincrease also explains why the return on equity (#8) has been rising while the returnon assets (#9) has been falling. The impact of the increase in debt and overalldecline in profitability is also shown by the reduction in coverage (#11).(iv) The intention of the authors was to depict a fundamentally deteriorating situationthat company officials had attempted to hide through the excessive use of financialleverage.c. (i) Primary interest should be in ratios 1-4. The overall reduction in liquidity, togetherwith the large amount involved and the lengthy terms, would argue against grantingthe credit. Of course, this argument would have to be balanced against theimportance to the vendor of this sale and possible repeat sales.(ii) If this were done, the new capitalization would be:Debt (long-term)Preferred stockCommon equity$16,000,0004,000,0006,000,000$26,000,00061.5%15.4%23.1%100.0%Pro forma interest coverage would be$4.4M/$1,760,000 = 2.5x(#11 pro forma.) The student should be especially concerned with this ratio. Inaddition, he/she would have to be concerned with all of the rest, as bothdeteriorating liquidity and profitability would affect a 10-year note of the company.There would appear to be little advantage in granting the loan.55© Pearson Education Limited 200841语言资格考试PPTChapter 6: Financial Statement Analysis(iii) An easy answer would be to point to the high rate of return on equity (#8) and say“buy”. On the other hand, the high degree of leverage (#5) and the decliningprofitability (#s 7, 8, and 9), would indicate caution. The student should at least beaware of the multitude of fundamentally negative factors involved.SOLUTIONS TO SELF-CORRECTION PROBLEMS1. Present current ratio = $800/$500 = 1.60.a. $700/$500 = 1.40. Current assets decline, and there is no change in current liabilities.b. $900/$600 = 1.50. Current assets and current liabilities each increase by the sameamount.c. $800/$500 = 1.60. Neither current assets nor current liabilities are affected.d. $760/$540 = 1.41. Current assets decline and current liabilities increase by the sameamount.2.20X120X220X3Current ratioAcid-test ratioAverage collection periodInventory turnoverTotal debt/equity1.190.43188.01.381.250.46227.51.401.200.40275.51.61Long-term debt/totalcapitalizationGross profit marginNet profit marginTotal asset turnoverReturn on assets0.330.2000.0752.800.210.320.1630.0472.760.130.320.1320.0262.240.06──────────────────────────────────────────────────The company’s profitability has declined steadily over the period. As only $50,000 isadded to retained earnings, the company must be paying substantial dividends.Receivables are growing at a slower rate, although the average collection period is stillvery reasonable relative to the terms given. Inventory turnover is slowing as well,indicating a relative buildup in inventories. The increase in receivables and inventories,coupled with the fact that shareholders’ equity has increased very little, has resulted inthe total debt-to-equity ratio increasing to what would have to be regarded on anabsolute basis as quite a high level.56© Pearson Education Limited 200842语言资格考试PPT3.== 1Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualThe current and acid-test ratios have fluctuated, but the current ratio is not particularlyinspiring. The lack of deterioration in these ratios is clouded by the relative buildup inboth receivables and inventories, evidencing a deterioration in the liquidity of these twoassets. Both the gross profit and net profit margins have declined substantially. Therelationship between the two suggests that the company has reduced relative expensesin 20X3 in particular. The buildup in inventories and receivables has resulted in adecline in the asset turnover ratio, and this, coupled with the decline in profitability, hasresulted in a sharp decrease in the return on assets ratio.Long − term debtEquity= 0.5 =Long − term debt$200,000Long-term debt =$100,000Total liabilities and shareholders’ equity = $400,000Total assets = $400,000SalesTotal assets= 2.5 =Sales$400,000Sales = $1,000,000Cost of goods sold = (1 − gross profit margin) (Sales)= (0.9) ($1,000,000) = $900,000Cost of good sold $900,000Inventory Inventory= 9 Inventory = $100,000Receivables × 360 days$1,000,000= 18 daysReceivables = $50,000Cash + $50,000$100,000Cash = $50,000Plant and equipment (plug figure on left-hand side of the balance sheet) = $200,000Balance SheetCashAccounts receivableInventoryPlant and equipmentTotal$ 50,00050,000100,000200,000$400,000Notes and payablesLong-term debtCommon stockRetained earningsTotal$100,000100,000100,000100,000$400,000_____________________________________________________________________________57© Pearson Education Limited 200843语言资格考试PPTChapter 6: Financial Statement Analysis4.Common-Size Analysis (%)CashReceivablesInventoriesCurrent assetsNet fixed assetsTotal assetsPayablesAccrualsBank loanCurrent liabilitiesLong-term debtShareholders’ equity20X17.927.528.463.836.2100.026.14.23.533.87.059.220X23.827.825.457.043.0100.028.65.08.742.39.748.020X31.734.027.663.336.7100.030.44.98.844.18.047.9Total liabilitiesand shareholders’ equitySalesCost of goods sold100.0100.072.0100.0100.074.4100.0100.073.5Selling, general, andadministrative expensesInterestProfit before taxesTaxesProfit after taxes19.20.68.23.34.916.51.37.83.04.817.11.28.23.54.758© Pearson Education Limited 200844语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualIndex Analysis (%)CashReceivablesInventoriesCurrent assetsNet fixed assetsTotal assetsPayablesAccrualsBank loanCurrent liabilitiesLong-term debtShareholders’ equity20X1100.0100.0100.0100.0100.0100.0___100.0100.0100.0100.0100.0100.020X269.0146.2128.7128.9171.6144.3___158.1171.4360.0180.7200.0117.020X336.0206.4161.8165.5169.1166.8194.0195.0420.0217.6190.0135.1Total liabilitiesand shareholders’ equitySalesCost of goods sold100.0___100.0100.0144.3___126.0130.3166.8137.8140.8Selling, general, andadministrative expensesInterestProfit before taxesTaxesProfit after taxes100.0100.0100.0100.0100.0___108.6257.5119.7115.9122.2___101.8273.9137.2147.7130.2________________________________________________________________The common-size analysis shows that cash declined dramatically relative to other current assetsand total assets in general. Net fixed assets surged in 20X2, but then fell back as a percentage ofthe total to almost the 20X1 percentage. The absolute amounts suggest that the company spentless than its depreciation on fixed assets in 20X3. With respect to financing, shareholders’ equityhas not kept up, so the company has had to use somewhat more debt percentage-wise. It appearsto be leaning more on trade credit as a financing source as payables increased percentage-wise.Bank loans and long-term debt also increased sharply in 20X2, no doubt to finance the bulge innet fixed assets. The bank loan remained about the same in 20X3 as a percentage of totalliabilities and shareholders’ equity, while long-term debt declined as a percentage. Profit aftertaxes slipped slightly as a percentage of sales over the 3 years. In 20X2, this decline was a resultof the cost of goods sold and interest expense, as other expenses and taxes declined as a59© Pearson Education Limited 200845语言资格考试PPTChapter 6: Financial Statement Analysispercentage of sales. In 20X3, cost of goods sold declined as a percentage of sales, but this wasmore than offset by increases in other expenses and taxes as percentages of sales.Index analysis shows much the same picture. Cash declined faster than total assets and currentassets, and receivables increased faster than these two benchmarks. Inventories fluctuated, butwere about the same percentage-wise to total assets in 20X3 as they were in 20X1. Net fixedassets increased more sharply than total assets in 20X2 and then fell back into line in 20X3. Thesharp increase in bank loans in 20X2 and 20X3 and the sharp increase in long-term debt in20X2, along with the accompanying increases in interest expenses, are evident. The percentageincreases in shareholders’ equity were less than those for total assets, so debt increased by alarger than for either of the other two items. With respect to profitability, net profits increasedless than sales, for the reasons indicated earlier.60© Pearson Education Limited 200846语言资格考试PPTRequired Returns and the Costof CapitalTo guess is cheap. To guess wrong is expensive.CHINESE PROVERB.144© Pearson Education Limited 200847语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualANSWERS TO QUESTIONS1. If the weights used in the calculations do not correspond to the proportions of financing thefirm intends to use, the computed weighted average cost will be a biased estimate of the realcost of capital of the firm.2. The principal qualification to its use is that existing as well as new investment proposals arealike with respect to risk. In other words, the proposal being judged should not alter the riskcomplexion of the firm as perceived by the suppliers of capital. Also, the costs of theindividual components of financing must be measured accurately and the weights must bemarginal in the sense of corresponding to the proportions with which the firm intends tofinance.3. Yes, these funds have a cost. In most cases, however, the cost is ignored because thesesources represent “built-in” financing of current assets. As current assets grow, payablesand accruals tend to grow as well.4. The tax shield associated with the use of debt funds would be lost, at least until profits wererestored. As a result, we would no longer multiply the before-tax cost of debt by one minusthe tax rate. The explicit cost of debt would be the before-tax cost or yield on the debtinstrument, which is considerably higher than the after-tax cost. Without the tax advantage,other methods of financing like leasing and preferred stock will become more attractive in arelative sense.5. Dividends per share are estimated out into the future, preferably out to infinity. Thediscount rate necessary to equate the present value of the expected future stream ofdividends with the present share price is determined. This is taken to be the cost of equitycapital. The critical factor in the model is the growth rate of future dividends. The pattern ofgrowth specified must correspond to the pattern expected by investors at the margin thatleads them to pay so many dollars for a share of stock.6. The critical assumption is that capital markets are perfect and that only the systematic riskof the firm is important. With market imperfections, such as bankruptcy costs, the total riskof the firm may take on a degree of importance. For example, the possibility of bankruptcywould be important to equityholders because the external drain of bankruptcy costs shouldthe firm become insolvent and would adversely affect them. As a result, investors would beconcerned with both systematic and unsystematic risk. The greater the importance of totalrisk the less relevant is the capital-asset pricing model approach.7. The firm’s before-tax cost of debt is used as a base to which a risk premium is added. Therisk premium is the difference in required return between stocks and bonds. For companiesoverall, this premium averages about 3 percent. However, it will vary by the company. If acompany could borrow at 13 percent and the premium were 3 percent, the required returnon equity would be 16 percent. The before-tax cost of debt funds will exceed the risk-freerate due to the presence of risk of default in corporate bonds.8. Proxy companies are used in place of the project or group of projects under consideration.The idea is to find a group of proxy companies that closely parallel the business representedby the project or group. These companies must be publicly traded and stand alone in thesense that they do not carry on other activities. One then takes some type of average of theirbetas (a median or modal value is perhaps best), and this average is used as a proxy for the145© Pearson Education Limited 200848语言资格考试PPTChapter 15: Required Returns and the Cost of Capitalbeta of the project or group. The required return on equity is then solved for in the usualway when employing the capital-asset pricing model. If debt is involved, it is blended inthrough a weighted average cost approach.9. A project-specific required return refers to the hurdle rate for a specific project as derivedwith the capital-asset pricing model approach. A group-specific required return is for adivision or some other subgroup of the firm where there is an aggregation of assets ofroughly the same risk.10. Management determines the acceptability of the project on the basis of the project’sexpected return in relation to the probability distribution of possible returns. The usualinformation is the mean and the standard deviation of the probability distribution. On thebasis of this information and management’s risk preferences, a decision is reached. The linkwith share price is indirect. It depends on how perceptive management is in determining thetrade-off of investors between profitability and risk. Moreover, systematic risk as opposedto total risk is likely to be the important thing, and this is not brought into play.11. The RADR approach to project selection calls for “adjusting” the required return, ordiscount rate, upward (downward) from the firm’s overall cost of capital for projects orgroups showing greater (less) than “average” risk. The CAPM approach could beconsidered as a special type of “risk-adjusted” method, but with any adjustment taking placerelative to a risk-free return base. The RADR approach, unlike the CAPM approach,generally relies on relatively informal, subjective ways of determining the required riskadjustment.12. For a group of projects, the correlation between returns of the various projects must betaken into account when computing the standard deviation (see Chapter 14). In other words,the diversification effect of projects is recognized. And in the absence of perfect correlation,the total risk of the group will be less than the sum of the parts.13. Empirically, companies in the same industry tend to have similar betas and required rates ofreturn. However, there are many exceptions. It depends on how similar the industrydefinition, the diversity of product lines of companies classified in the industry, and thevariation in financial risk of companies in the industry. One difficulty is with classifying amultiproduct company like General Electric. Aluminum companies, on the other hand, alldo about the same thing so that industry comparisons are very valid. Again, the key is thesimilarity of business and financial risk among companies, particularly the former.14. No. Eventually the equity base will need to be rebuilt and this will require retained earningsor common stock financing, both of which have a higher cost than debt funds. To use thecost of debt funds as the required return ignores this eventual need and in so doing makes noprovision for a premium for the business risk associated with the project.15. An increase in bankruptcy costs would increase the required rate of return for companies.The change should make companies more conscious of avoiding bankruptcy and analyzingthe risk associated with the particular project. In a capital-asset pricing model context, itwill work to make unsystematic risk more important. In other words, companies would needto pay some attention to the effect of a project on the overall or total risk of the company(systematic plus unsystematic), not just the impact on systematic risk.16. If the divisions have significantly different risks, a company should use different costs ofcapital for them. One approach is the capital-asset pricing model context using outside146© Pearson Education Limited 200849语言资格考试PPTkek o = ￿￿2.=Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualcompanies in about the same types of businesses as proxies for risk. Required rates of returnare determined for these proxy companies (based on stock-return data) and these rates areused as costs of capital for the divisions. In many, perhaps most, situations, multi-divisioncompanies have multiple risks. Therefore, the use of a company-wide cost of capital isinappropriate as an acceptance criterion.17. Value is created when projects are accepted, whose expected returns exceed the requiredreturns established by the financial markets. Returns in excess of what the financial marketsexpect, and require, are economic rents which will lead to a share price increase, all otherthings being the same.18. Through investment in assets, value is created by industry attractiveness and competitiveadvantage. These are largely the sources of value and allow a company to earn excessreturns, at least for a while.SOLUTIONS TO PROBLEMS1.BondsCommon StockTotals(1)Costki(2)Proportion of Total FinancingB/(B+S)S/(B+S)100%(1) × (2)Weighted Costki[B/(B+S)]ke[S/(B+S)]ki[B/(B+S)]+ke[S/(B+S)]Thus, ko = ki[B/(B+S)] + ke[S/(B+S)]or alternatively written￿￿ki (B) + k e (S) ￿￿￿￿￿￿￿￿￿(B + S) ￿ki = (kd)(1 – t) = (0.14)(0.6) = 8.4 percentk e =D1P0+g =(# of shares) (D1 )(# of shares) (P0 )+g$500,000$7,000,000+ 0.11 = 0.0714 + 0.11 = 18.14 percentko = ki[B/(B+S)] + ke[S/(B+S)]= (0.084)($3M/$10M) + (0.1814)($7M/$10M)= (0.084)(0.3) + (0.1814)(0.7) = 15.22 percent147© Pearson Education Limited 200850语言资格考试PPT=12345=6==D6Chapter 15: Required Returns and the Cost of Capital3. (January 20X1)k e =D1P0+g=$3$300+ 0.20 = 21 percent(January 20X2)4.P0 =D1 $3.45(Ke – g) (0.21 – 0.15)= $57.50DividendPresent ValuePresent ValueEnd of Year6 to ∞Per Share$ 2.2402.5092.8102.9793.1583.3470.12$25.511at 12 Percent$ 2.0002.0002.0001.8931.79215.826*$25.511at 13 Percent$ 1.9821.9651.9471.8271.71413.976**$23.4110.01Xke$25$0.511$2.100.13$23.411x0.1$0.511$2.10Therefore, x =(0.01)($0.511)$2.10= 0.0024ke = 0.12 + X = 0.12 + 0.0024 = 12.24 percent* Implied Value of Stock at End of Year 5D(0.12 – g)$3.347(0.12 – g)= $27.89Present Value of $27.89 at End of Year 5= ($27.89) (PVIF12%,5)= ($27.89)(0.56743) = $15.826**Implied Value of Stock at End of Year 5 = (0.13–g) =$3.347(0.13 – 0)= $25.75Present Value of $25.75 at end of year 5= ($25.75) (PVIF13%, 5)= ($25.75) (0.54276) = $13.976148© Pearson Education Limited 200851语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual5.(1)After-tax Cost(2)Proportion of Total Financing(1) × (2)Weighted CostDebenturesPreferred StockCommon Stock7.8%12.017.037.5%12.550.0100.0%2.93%1.508.5012.93% = ko6. Flotation costs of debt = $200,000 × 0.02 = $ 4,000Flotation costs of stock = $200,000 × 0.15 = 30,000$34,000NPV =$90,000.145− $600,000 − $34,000 = − $13,310The proposal should be rejected. Without flotation costs, however, the net present valuewould have been positive and the proposal acceptable.7. a. Cost of equity = 0.12 + (0.18 – 0.12) 1.28 = 19.68 percentCost of debt = 8 percent (given)Weighted-average required return for the project = 0.4(8%) + 0.6(19.68%) = 15 percent.b. The approach assumes that unsystematic risk is not a factor of importance, which mayor may not be the case. It assumes also that the average beta for the oil drillingequipment companies is a good surrogate for the systematic risk of the prospect.Finally, the estimates of the likely return on stocks in general and of the risk-free ratemust be accurate. If these assumptions hold, the figure obtained will be a realisticestimate of the project’s required rate of return.8. a. Required Return = 0.10 + (0.15 – 0.10)(1.10) = 15.5 percentb. Minimum Required Return = 0.10 + (0.15 – 0.10)(1.00) = 15 percentMaximum Required Return = 0.10 + (0.15 – 0.10)(1.40) = 17 percentc. Required Returnfor beta of 1.20 = 0.10 + (0.15 – 0.10)(1.20) = 16 percentRequired Returnfor beta of 1.30 = 0.10 + (0.15 – 0.10)(1.30) = 16.5 percentExpected value of required rate of return= (0.2)(0.15) + (0.3)(0.155) + (0.2)(0.16) + (0.2)(0.165) + (0.1)(.17)= 15.85 percent149© Pearson Education Limited 200852语言资格考试PPT01234Chapter 15: Required Returns and the Cost of Capital9. Using the RADR approach we would calculate the project’s net present value at themanagement-determined risk-adjusted discount rate:(1)——————————(2)————————————(1) × (2)———————Year————Expected Cash Flow——————————$–400,00050,00050,000150,000350,000Discount Factor at 15%————————————1.00000.86950.75610.65750.5718Present Value———————$–400,00043,48037,80598,625200,130$ –19,960Since the NPV is negative ($–19,960), we would reject the project. Alternatively, we couldcalculate the project’s IRR and compare it to the RADR, which we would use as a hurdlerate. In this case, the project’s IRR of 13.17 percent is less than the RADR of 15 percent, sowe would, once again, reject the project.10. The selection will depend on the risk preferences of the individual. Graphs of the plots areshown below. For the reasonable risk averter, the selection will probably be combinationE13, which has an expected net present value of $7,500 and a standard deviation of $5,600.(The E(NPV) vs. CV of NPV graph reinforces the implied preference for E13.) In this case,proposals #1 and #3 would be accepted and proposal #2 would be rejected. It should benoted that the combination of proposal #1 with existing investment projects results in anactual lowering of the standard deviation. This implies negative correlation between theproposal and existing projects.150© Pearson Education Limited 200853语言资格考试PPT==Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualSolution to Appendix A Problem:11. a.Peerless unlevered beta =β j[1+(B/S) (1 – Tc )]1.15 1.15[1 + (0.25) (1 − 0.41)] 1.15= 1.00Adjusted beta for Willie Suttonusing its debt-to-equity ratio of 0.75 = ßju [1 + (B/S)(1 – Tc)]= 1.00[1 + (0.75)(1 – 0.4)]= 1.00[1.45] = 1.45An adjusted beta of 1.45 is appropriate for the new venture if the assumptions of thecapital-asset pricing model hold, except for corporate taxes.b. ki = kd(1 – Tc) = 0.15(1 – 0.4) = 0.09ke = Rf + ( R m – Rf)ß = 0.13 + (0.17 – 0.13)1.45 = 0.188Since B/S = 0.75 and (B+S) = 1.00, thenB/(B+S) = (0.75)S/(1.75)S = (0.75/1.75) andS/(B+S) = S/(1.75)S = (1.00/1.75)Therefore, ko = (ki)(B/(B+S)) + (ke)(S/(B+S))= (0.09)(0.75/1.75) + (0.188)(1.00/1.75)= 14.6 percent151© Pearson Education Limited 200854语言资格考试PPT1NPV = ∑Chapter 15: Required Returns and the Cost of CapitalSolution to Appendix B Problem:12. a.Schedule for determining the present value of the interest tax-shield benefits related tothe new snow plow truckEnd ofYear023456(1)Debt OwedAt Year End(1)t–1 – $3,000$18,00015,00012,0009,0006,0003,0000(2)Annual Interest(1)t–1 × 0.12--$2,1601,8001,4401,080720360(3)Tax-ShieldBenefits(2) × 0.30--$648540432324216108(4)PV of Benefitsat 12%--$ 57943030820612255$1,700To an all-equity financed firm, the net present value of the project’s after-tax operating cashflows would be,6 $10,000t=1 (1 + 16)t− $30,000 = $6,850while the adjusted present value would be,APV = $6,850 + $1,700 – $1,000 = $7,550The project is acceptable.b. If the cash flows are $8,000 per year instead of $10,000, the net present value of theproject’s after-tax operating cash flows becomes –$520, while the adjusted presentvalue becomes,APV = –$520 + $1,700 –$1,000 = $180The project is still acceptable – but, barely.152© Pearson Education Limited 200855语言资格考试PPT1Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualSOLUTIONS TO SELF-CORRECTION PROBLEMS1. a. ke = D1/P0 + gD1 = D0(1.12) = $1(1.12) = $1.12ke = $1.12/$20 + 12% = 17.6%b. Through the trial-and-error approach illustrated in Chapters 3 and 4, one ends updetermining that the discount rate necessary to discount the cash dividend stream to $20must fall somewhere between 18 and 19 percent as follows:End of Year2345Dividend Per Share$1.201.441.732.072.49Present Value At 18%$1.021.031.051.071.09Present Value At 19%$1.011.021.031.031.04Present value, years 1-5$5.26$5.13Year 6 dividend = $2.49 (1.10) = $2.74Market prices at the end of year 5 using a constant growth dividendvaluation model: P5 = D6/(ke – g)P5 = $2.74/(0.18 – 0.10) = $34.25,P5 = $2.74/(0.19 – 0.10) = $30.44Present value at time 0 for amounts received at end of year 5:$34.25 at 18% = $14.97,$30.44 at 19% = $12.76153© Pearson Education Limited 200856语言资格考试PPT=1Chapter 15: Required Returns and the Cost of Capital18%19%Present value of years 1 – 5Present value of years 6 – ∞Present value of all dividends$ 5.2614.97$ 20.23$ 5.1312.76$ 17.89Therefore, the discount rate is closer to 18 percent than it is to 19 percent. Interpolating,we get0.18$20.230.01Xke$20.00$0.23$2.340.19$17.89X $0.230.01 $2.34Therefore, X =(0.01) ($0.23)$2.34= 0.0010and ke = 0.18 + X = 0.18 + 0.0010 = 18.10 percent, which is the estimated return on equitythat the market requires.2.SituationEquation: Rf + ( R m – Rf)ßReturn Required10%+ (15% – 10%) 1.0015.0%234514%8%11%10%+ (18% – 14%) 0.70+ (15% – 8%) 1.20+ (17% – 11%) 0.80+ (16% – 10%) 1.9016.816.415.821.4The greater the risk-free rate, the greater the expected return on the market portfolio, and thegreater the beta, the greater will be the required return on equity, all other things being thesame. In addition, the greater the market risk premium (R m – R f ) , the greater the requiredreturn, all other things being the same.3. Cost of debt = 15%(1 – 0.4) = 9%Cost of preferred stock = 13%Cost of equity for Health Foods division= 0.12 + (0.17 – 0.12) 0.90 = 16.5%Cost of equity for Specialty Metals division= 0.12 + (0.17 – 0.12) 1.30 = 18.5%154© Pearson Education Limited 200857语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualWeighted-average required return for Health Foods division= 9% (0.3) + 13%(0.1) + 16.5% (0.6) = 13.9%Weighted average required return for Specialty Metals division= 9% (0.3) + 13%(0.1) + 18.5% (0.6) = 15.1%As mentioned in the text, a conceptual case can be made for adjusting the nonequity costs offinancing the two divisions for differences in systematic risks. However, we have notdone so.4. a. The coefficients of variation (standard deviation/ NPV ) for the alternatives are as follows:Existing projects (E)Plus project 1 (E1)Plus project 2 (E2)Plus project 1 and 2 (E12)0.500.600.430.49Graphs of risk versus return are shown below. A moderately risk-averse decision maker willprobably prefer the existing projects plus both new projects to any of the other threepossible combinations. If this is the case, both new projects will be accepted. The actualdecision will depend on your risk preferences. A very risk-averse individual might preferthe existing projects plus only project 2. Presumably, these preferences will be influencedby the presence of bankruptcy costs.155© Pearson Education Limited 200858语言资格考试PPTChapter 15: Required Returns and the Cost of Capitalb. If the CAPM approach leads to a different decision, the key to deciding would be theimportance of market imperfections. As indicated earlier, if a company’s stock is tradedin imperfect markets, if the possibility of insolvency is substantive, and if bankruptcycosts are significant, more reliance should be placed on a total variability approachbecause it recognizes unsystematic plus systematic risk. If things point to minimalmarket imperfections, more reliance should be placed on the CAPM results.156© Pearson Education Limited 200859语言资格考试PPTOperating and Financial LeverageIt does not do to leave a live dragon out of yourcalculations, if you live near him.J.R.R. TOLKIEN, THE HOBBIT157© Pearson Education Limited 200860语言资格考试PPTf.i.Chapter 16: Operating and Financial LeverageANSWERS TO QUESTIONS1. Operating Leverage is the use of fixed operating costs associated with the production ofgoods or services. The degree of operating leverage (DOL) is the percentage change in afirm’s operating profit (EBIT) resulting from a 1 percent change in output (sales). DOL isused to study the sensitivity of the variability in EBIT to the variability in sales. The DOLprovides a quantitative measure of this sensitivity that is caused by the presence ofoperating leverage.2. a. Fixed;b. Variable;c. Variable;d. Fixed – but, variable at management’s discretion;e. Fixed – but, variable at management’s discretion;Variable;g. Variable;h. Fixed – but, somewhat variable at management’s discretion;Fixed – but, variable at management’s discretion;All costs are variable in the long run.3. Students may find Eqs. (16-3) and (16-4) of help in explaining the probable effect of achange in a firm’s operations on the break-even point. Of course, an increase in any costwill raise the break-even point.a. Lower the break-even point.b. Raise the break-even point.c. Raise the break-even point.d. Will not affect the break-even point.e. The break-even point would not be affected unless the quality of A/R deteriorates. If thequality of A/R deteriorates, the total cost curve would shift up, resulting in a higherbreak-even point.4. All businesses have at least some business risk even if they have no financial risk.5. No, this is not always the case. It is true that the presence of fixed operating costs will causea change in the volume of sales to result in a more than proportional change in operatingprofits. But, even firms with larger fixed costs will have a low sensitivity to changes in sales(i.e., a low DOL) if they operate well above their respective break-even points.6. You can have a high DOL and still have low business risk if sales and the production coststructure are stable. You can have a low DOL and high business risk if sales and/or theproduction cost structure are/is volatile.7. Financial leverage is the use of fixed cost financing. The degree of financial leverage(DFL) is the percentage change in the firm’s earnings per share (EPS) resulting from a 1percent change in operating profit (EBIT). DFL is used to study the sensitivity of thevariability in EPS to the variability in EBIT. The DFL provides a quantitative measure ofthis sensitivity caused by the presence of financial leverage.158© Pearson Education Limited 200861语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual8. Both operating and financial leverage involve the use of fixed costs. The former is due tofixed operating costs associated with the production of goods or services, while the latter isdue to the existence of fixed financing costs. Both types of leverage, affect the level andvariability of the firm’s after-tax earnings and, hence, the firm’s overall risk and return.However, while financial leverage is acquired by choice, operating leverage often is not.Operating leverage is often dictated by the physical requirements of the firm’s operations.9. Yes. Eq. (16.14) shows that the degree of financial leverage is a function of the level ofEBIT and the fixed charges of financing.10. The objective of business firms is not to maximize EPS. It is to maximize shareholder’swealth. A high EPS often requires incurring high risk. Stock price may decrease as a resultof the high level financial risks required to increase EPS.11. An electric utility has much higher fixed costs in a relative sense than does the typicalmanufacturing company. Also, its revenues are much more stable and predictable. Despite ahigh amount of operating leverage, overall business risk is relatively low. As a result,electric utilities are able to take on significant financial risk. The typical manufacturingcompany has higher business risk and balances this with lower financial risk.12. Whether or not, the debt-to-equity ratio is a good proxy for the cash flow ability of the firmto service debt depends on the situation. There should be a rough correspondence betweenthe two. However, the debt-to-equity ratio tells us nothing about the level or variability ofcash flows. While there is certainly a close association between the debt-to-equity ratio andthe magnitude of debt payments, differences in maturity and times in the past when variousdebt instruments were issued, make the relationship not one-to-one. As a result, the debt-to-equity ratio must be regarded as an index approximation of financial risk. Still, it isfrequently used.13. The chapter has provided analytical tools to evaluate the financial structure of the firm. TheEBIT-EPS chart, cash flow available to service debt, comparison of debt ratios to industrynorms, the evaluation of the attitudes of creditors and stockholders, and the effect onsecurity ratings can be used to determine the debt-to-equity ratio that will maximize thevalue of the firm.14. Coverage ratios should be compared with those of other companies in similar lines ofbusiness. Where significant deviations occur, the reasons should be carefully explored. Ifthe average coverage ratio for the industry is used as a target, the firm could determine theamount of debt to employ by applying this ratio to the firm’s earnings. However, it isimportant to determine the appropriateness of the industry average to the situation. Acoverage ratio is based on expected earnings or cash flow. It tells nothing about theprobability of earnings or cash flow falling. The probability of cash insolvency should beanalyzed as well.15. While earnings per share will increase as long as the firm is able to earn more on theemployment of the funds than their interest or preferred-dividend cost, risk to the commonshareholders increases as well. After a point, the increased risk more than offsets theincrease in expected earnings per share. At that point, market price per share declines withfinancial leverage. Clearly this is undesirable.159© Pearson Education Limited 200862语言资格考试PPTChapter 16: Operating and Financial Leverage16. An increase in the debt of a company will increase the amount of periodic interest andprincipal payments. The additional cash obligation for each increment in debt can bedetermined for each future period. The next step is to determine a probability distribution ofpossible ending cash balances for various future periods. Such distributions are based oncash flows together with the beginning cash balance. It is then an easy matter to see at whatpoint further increments in debt results in the probability of running out of cash, exceedingsome limit tolerance, such as 5 percent.17. Most companies are concerned with the effect a debt decision will have on its bond ratings,both for prestige reasons and because of the interest rate they will have to pay onborrowings. Moreover, if a rating is lowered below Baa, the company’s bonds no longer areconsidered “investment grade” and no longer appeal to institutional investors. The ratingagencies look at the debt ratio and the cash-flow coverage ratios. If these ratios deteriorate,the rating agencies may well lower the company’s rating in the credit and capital markets.Some companies will not issue further debt, even if they do, bond rating will be lowered.While this is not sufficient grounds to stop issuing debt, as other things should beconsidered. A company cannot ignore the effect of a financial leverage decision on itssecurity ratings.SOLUTIONS TO PROBLEMS1. a. Q = $880,000/$200 = 4,400 units$24,000 = [Q(P – V) –FC](1 – t)$24,000 = [4,400($200 – $150) – FC](0.60)$24,000 = $132,000 – FC(0.60)FC = $180,000b. QBE = $180,000/($200 –$150) = 3,600 unitsSBE = 3,600($200) = $720,000 – or, alternatively –SBE = $180,000/[1 – ($150/$200)] = $720,000c. DOL4,000 units = 4,000/(4,000 – 3,600) = 10.0DOL4,400 units = 4,400/(4,400 – 3,600) = 5.5DOL4,800 units = 4,800/(4,800 – 3,600) = 4.0DOL5,200 units = 5,200/(5,200 – 3,600) = 3.25DOL5,600 units = 5,600/(5,600 – 3,600) = 2.8DOL6,000 units = 6,000/(6,000 – 3,600) = 2.5160© Pearson Education Limited 200863语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manuald. The graph shows that the sensitivity of a firm’s operating profit to changes in salesdecreases further, as the firm operates above its break-even point. The company isoperating close to its break-even point. Therefore, at its current monthly sales level of4,400 units, its sensitivity to sales changes is quite high. Its DOL at 4,400 units is 5.5 –meaning any percent change in operating profits will be 5.5 times as large as the percentchange in sales that causes it.2. a. QBE = $180,000/($250 – $150) = 1,800 unitsb. QBE = $160,000/($200 – $150) = 3,200 unitsc. QBE = $240,000/(4200 – $140) = 4,000 units3. a. QBE = $1,200/($100 – $20) = 15 horsesb. EBIT = 40($100 – $20) – $1,200 = $2,0004. a. Using an expected level of EBIT of $1 million, the earnings per share are:Plan1234EBIT (in thousands)InterestEBTTaxesEATPreferred dividendsEACSNumber of sharesEPS$1,0000$1,000500$ 5000$ 500250$ 2.00$1,000240$ 760380$ 3800$ 380175$ 2.17$1,000400$ 600300$ 3000$ 300125$ 2.40$1,000400$ 600300$ 300150$ 15075$ 2.00161© Pearson Education Limited 200864语言资格考试PPTChapter 16: Operating and Financial LeverageThe intercepts on the horizontal axis for the four plans are $0, $240,000, $400,000, and$700,000 respectively. With this information, the EBIT-EPS indifference chart is:b. The “dominant” financing plans are #1, #3, and #4. For the EBIT indifference pointbetween Plans #1 and #3, we have:(EBIT1, 3 – 0) (0.5) / 250,000 = (EBIT1, 3 – $400,000) (0.5) / 125,000(0.5) (EBIT1, 3) (125,000) = (0.5) (EBIT1, 3) (250,000) – (0.5) ($400,000) (250,000)– (62,500) (EBIT1, 3) = – $50,000,000,000EBIT1,3 = $800,000For the indifference point between Plans #3 and #4, we have:(EBIT3, 4 – $400,000)(0.5)/125,000 = [(EBIT3, 4 – $400,000)(0.5) – $150,000]/75,000(0.5)(EBIT3, 4)(75,000) – (0.5)($400,000)(75,000) =(0.5)(EBIT3, 4)(125,000) – (0.5)($400,000)(125,000) – ($150,000)(125,000)(37,500)(EBIT3, 4) – $15,000,000,000 = (62,500)(EBIT3, 4) – $43,750,000,000(25,000)(EBIT3, 4) = – $28,750,000,000EBIT3, 4 = $1,150,000c. Plan #1 (all equity) dominates up to $800,000 in EBIT, Plan #3 (half debt, half equity)from $800,000 to $1,150,000 in EBIT, and Plan #4 (debt, preferred, and equity) after$1,150,000 in EBIT. The best plan depends upon the likely level of EBIT and thelikelihood of falling below an indifference point.162© Pearson Education Limited 200865语言资格考试PPT=I1, I2t=Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual5. a. (000s omitted)Additional-financing PlansPresent(1)(2)(3)(4)HalfCapitalStructureAllCommonAll8% BondsAllPreferredCommon andHalf BondsEBITInterestEBTTaxesEATPref. Stk.DividendEACSSharesoutstandingEPS$1,000120$ 880440$ 440---$ 440100$ 4.40$1,000120$ 880440$ 440---$ 440150$ 2.93$1,000360$ 640320$ 320---$ 320100$ 3.20$1,000120$ 880440$ 440210$ 230100$ 2.30$1,000240$ 760380$ 380---$ 380125$ 3.04b. The important thing in graphing the alternatives is to include the $120,000 in interest onexisting bonds in all of the additional-financing plans. The mathematical formula fordetermining the indifference point is:(EBIT1,2 – I1 ) (1 – t) – PD1NS1(EBIT1,2 – I2 ) (1 – t) – PD2NS2where EBIT1, 2 = the EBIT indifference point between the two alternative financingmethods that we are concerned with – in this case, methods 1 and 2;= annual interest paid under financing methods 1 and 2;PD1, PD2NS1, NS2= annual preferred stock dividend paid under financing methods 1 and 2;= corporate tax rate;= number of shares of common stock to be outstandingunder financing methods 1 and 2;Comparing Plan #1 (all common) with Plan #2 (all bonds), we have:(EBIT1,2 - $120,000) (0.5)150,000(EBIT1,2 - $360,000) (0.5)100,000(0.5) (EBIT1, 2) (100,000) – (0.5) ($120,000) (100,000) =(.5) (EBIT1,2) (150,000) – (0.5) ($360,000) (150,000)(50,000) (EBIT1,2) – (75,000) (EBIT1,2) = $6,000,000,000 – $27,000,000,000– (25,000) (EBIT1,2) = – $21,000,000,000EBIT1,2 = $840,000163© Pearson Education Limited 200866语言资格考试PPT==Chapter 16: Operating and Financial LeverageAbove $840,000 in EBIT, debt is more favorable (in terms of EPS); below $840,000 inEBIT, common is more favorable.Comparing Plan #1 (all common) with Plan #3 (all preferred), we have:(EBIT1,3 – $120,000) (0.5)150,000(EBIT1,3 – $120,000) (0.5) – $210,000100,000(0.5) (EBIT1,3) (100,000) – (0.5) ($120,000) (100,000) =(0.5) (EBIT1,3) (150,000) – (0.5) ($120,000) (150,000)– ($210,000) (150,000)(50,000) (EBIT1,3) – (75,000) (EBIT1,3) =$6,000,000,000 - $9,000,000,000 – $31,500,000,000– (25,000) (EBIT1,3) = – $34,500,000,000EBIT1,3 = $1,380,000Above $1,380,000 in EBIT, Plan #3 (all preferred) is more favorable (in terms of EPS);below $1,380,000 in EBIT, Plan #1 (all common) is more favorable.Comparing Plan #1 (all common) with Plan #4 (half common, half bonds) we have:(EBIT1,4 – $120,000) (0.5)150,000(EBIT1,4 – $240,000) (0.5)125,000(0.5) (EBIT1, 4) (125,000) – (0.5) ($120,000) (125,000) =(0.5) (EBIT1,4) (150,000) – (0.5) ($240,000) (150,000)(62,500) (EBIT1,4) – (75,000) (EBIT1,4) =$7,500,000,000 – $18,000,000,000– (12,500) (EBIT1,4) = – $10,500,000,000EBIT1,4 = $840,000 (the same figure as under the Plan #1 vs. Plan #2 comparison)Above $840,000 in EBIT, Plan #4 (half common, half bonds) is more favorable (interms of EPS); below $840,000 in EBIT, Plan #1 (all common) is more favorable.For the Plan #2 (all bonds) versus Plan #3 (all preferred) comparison, the bondalternative dominates the preferred alternative by $0.90 per share throughout all levelsof EBIT.For the Plan #2 (all bonds) versus Plan #4 (half common, half bonds) comparison, theindifference point is again $840,000 in, EBIT.164© Pearson Education Limited 200867语言资格考试PPT=Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualFor the Plan #3 (all preferred) versus Plan #4 (half common, half bonds) comparison,we have:(EBIT3,4 – $120,000) (0.5) – $210,000100,000(EBIT3,4 – $240,000) (0.5)125,000(0.5) (EBIT3,4) (125,000) – (0.5) ($120,000) (125,000)– ($210,000) (125,000) = (0.5) (EBIT3,4) (100,000) – (0.5) ($240,000) (100,000)(62,500) (EBIT3,4) – (50,000) (EBIT3,4) =$7,500,000,000 + $26,250,000,000 – $12,000,000,000(12,500) (EBIT3,4) = $21,750,000,000EBIT3,4 = $1,740,000Above $1,740,000 in EBIT, preferred is more favorable (in terms of EPS); below$1,740,000 in EBIT, half common and half bonds is more favorable.These exact indifference points can be used to check graph approximations.6. a. The level of expected EBIT is only moderately above the indifference point of$840,000. Moreover, the variance of possible outcomes is great and there isconsiderable probability that the actual EBIT will be below the indifference point. Atwo-thirds probability corresponds to one standard deviation on either side of the meanof a normal distribution. If the distribution is approximately normal, σ = $1,000,000 –$600,000 = $400,000. The standardized difference from the mean to the indifferencepoint is:($840,000 – $1,000,000) / $400,000 = – 0.4Looking at a normal distribution table, found in any statistics text, we find that thiscorresponds to a 34.5 percent probability that the actual EBIT will be below $840,000.While the choice of alternatives depends upon one’s risk preferences, the level andvariability of EBIT points to the “all common stock” alternative.b. Here the level of expected EBIT is significantly above the indifference point and thevariability is less. If the distribution is approximately normal, s = $1,500,000 –$1,300,000 = $200,000. The standardized difference from the mean to the indifferencepoint is:($840,000 – $1,500,000) / $200,000 = – 3.3The probability of actual EBIT falling below the indifference point is negligible. Thesituation in this case favors the “all bond” alternative.165© Pearson Education Limited 200868语言资格考试PPT$$Chapter 16: Operating and Financial Leverage7. a.Additional-financing AlternativesCommonDebtPreferredEBIT (000s omitted)Interest on existing debtInterest on new debtEarnings before taxesTaxesEarnings after taxesDividends on existingpreferred stockDividends on newpreferred stockEarnings available tocommon shareholdersNumber of common sharesoutstandingEarnings per share (EPS)$6,00080005,2001,8203,38000$3,3801,350$ 2.50$6,000.0800.0550.04,650.01,627.53,022.50.00.0$3,022.51,100.02.75$6,00080005,2001,8203,3800500$2,8801,100$ 2.62b. (1)Additional-financing AlternativesCommonDebtPreferredEBIT (000s omitted)Interest on existing debtInterest on new debtEarnings before taxesTaxesEarnings after taxesDividends on existingpreferred stockDividends on newpreferred stockEarnings available tocommon shareholdersNumber of common sharesoutstandingEarnings per share (EPS)$3,00080002,2007701,43000$1,4301,350$ 1.06$3,000.0800.0550.01,650.0577.51,072.50.00.0$1,072.51,100.00.98$3,00080002,2007701,4300500$1,4301,100$ 0.85166© Pearson Education Limited 200869语言资格考试PPT$$Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualb. (2)Additional-financing AlternativesCommonDebtPreferredEBIT (000s omitted)Interest on existing debtInterest on new debtEarnings before taxesTaxesEarnings after taxesDividends on existingpreferred stockDividends on newpreferred stockEarnings available tocommon shareholdersNumber of common sharesoutstandingEarnings per share (EPS)$4,00080003,2001,1202,08000$2,0801,350$ 1.54$4,000.0800.0550.02,650.0927.51,772.50.00.0$1,772.51,100.00.57$4,00080003,2001,2202,0800500$1,5801,100$ 1.44b. (3)Additional-financing AlternativesCommonDebtPreferredEBIT (000s omitted)Interest on existing debtInterest on new debtEarnings before taxesTaxesEarnings after taxesDividends on existingpreferred stockDividends on newpreferred stockEarnings available tocommon shareholdersNumber of common sharesoutstandingEarnings per share (EPS)$8,00080007,2002,5204,68000$4,6801,350$ 3.47$8,000.0800.0550.06,650.02,327.54,322.50.00.0$4,322.51,100.03.93$8,00080007,2002,5204,6800500$4,1801,100$ 3.80167© Pearson Education Limited 200870语言资格考试PPTChapter 16: Operating and Financial Leveragec. (1)Additional-financing AlternativesCommonDebtPreferredEBIT (000s omitted)Interest on existing debtInterest on new debtEarnings before taxesTaxesEarnings after taxesDividends on existingpreferred stockDividends on newpreferred stockEarnings available tocommon shareholdersNumber of common sharesoutstandingEarnings per share (EPS)$6,00080005,2002,3922,80800$2,8081,350$ 2.08$6,0008005504,6502,1392,51100$2,5111,100$ 2.28$6,00080005,2002,3922,8080500$2,3081,100$ 2.10c. (2)Additional-financing AlternativesCommonDebtPreferredEBIT (000s omitted)Interest on existing debtInterest on new debtEarnings before taxesTaxesEarnings after taxesDividends on existingpreferred stockDividends on newpreferred stockEarnings available tocommon shareholdersNumber of common sharesoutstandingEarnings per share (EPS)$6,00080005,2001,8203,38000$3,3801,350$ 2.50$6,0008005504,8001,6803,12000$3,1201,100$ 2.84$6,00080005,2001,8203,3800350$3,0301,100$ 2.75168© Pearson Education Limited 200871语言资格考试PPT$$2,0001 − .40$35,0001 − .36Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualc. (3)Additional-financing AlternativesCommonDebtPreferredEBIT (000s omitted)Interest on existing debtInterest on new debtEarnings before taxesTaxesEarnings after taxesDividends on existingpreferred stockDividends on newpreferred stockEarnings available tocommon shareholdersNumber of common sharesoutstandingEarnings per share (EPS)$6,00080005,2001,8203,38000$3,3801,225$ 2.76$6,000.0800.0550.04,650.01,627.53,022.50.00.0$3,022.51,100.02.75$6,00080005,2001,8203,3800500$2,8801,100$ 2.628. (000s omitted)Boehm-Gau: Interest Coverage = $5,000 / $1,600 = 3.13Debt-service Coverage =$5,000$1,600 += 1.01Northern California: Interest Coverage = $100,000 / $45,000 = 2.22Debt-service Coverage =$100,000$45,000 += 1.00The question of with which company one feels more comfortable depends on the businessrisk. Inasmuch as an electric utility has stable cash flows and Northern California is large, itis no doubt the safer loan despite the lower coverage ratios. The fact that the debt-servicecoverage ratio is 1.0 means that some of the debt will probably have to be renewed or“rolled over” at maturity. However, this is typical for an electric utility.9. Matching, we get,CompanyABCDTD/TA0.560.640.470.42LTD/Total Cap0.430.660.080.26IndustryChemicalAirlineSupermarketApparel Maker169© Pearson Education Limited 200872语言资格考试PPTChapter 16: Operating and Financial LeverageThe supermarket is likely to have the highest portion of total debt in the form of accountspayable and a short-term liability, because purchases make up a large portion of total costs.Therefore, we would expect it to have the greatest disparity between the two debt ratios.The airline would be expected to have the highest debt ratio, most of which is long-termdebt, used to finance aircraft. Here the ratio of total debt to total assets is slightly less thanthe ratio of long-term debt to total capitalization. An apparel maker will have a sizeableamount of accounts payable, but will also have some long-term debt used to finance fixedassets. Finally, the chemical company is determined largely by elimination. Such a companyhas current liabilities, but relies heavily on long-term debt to finance fixed assets.SOLUTIONS TO SELF-CORRECTION PROBLEMS1. a.QBE =$3M$2.00 − $1.75= 12 million half pintsb.SBE =$3M1 − ($1.75 / $2.00)= $24 million in annual salesc.d.QBE =QBE =$3M$2.00 - $1.68$3.75M$2.00 - $1.75= 9.375 million half pints= 15 million half pintsDOL 16 million units =16M(16M -12M)= 4e.(15 percent) × 4 = 60% increase in EBIT2. a. (Percent change in sales) × DOL = Percent change in EBIT(20 percent) × 2 = 40% change in EBITTherefore, $1,000 × (1 + 0.40) = $1,400b.DOL10,000 units =10,00010,000 – QBE=2Therefore, QBE must equal 5,000 units.DOL12,000 units =12,00012,000 - 5,000= 1.7170© Pearson Education Limited 200873语言资格考试PPT$=Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual3. a. (000s omitted)PreferredCommonDebtStockStockOperating profit (EBIT)Interest on existing debtInterest on new debtProfit before taxesTaxes$ 1,500360560580232$ 1,500360---$ 1,140456$ 1,500360----$ 1,140456Profit after taxes$348$684$684Preferred stock dividend----480----Earnings available tocommon shareholders$348$204$684Number of sharesEarnings per share800$ 0.435800$ 0.2551,050$ 0.651b.Approximate indifference points:Debt (1) and common (3): $2.7 million in EBITPreferred (2) and common (3): $3.7 million in EBITDebt dominates preferred by the same margin throughout. There is no indifference pointbetween these two alternative financing methods.Mathematically, the indifference point between debt (1) and common (3), with 000somitted, isDebt (1)(EBIT1,3 – $920) (1 – 0.40) – 0800Common Stock (3)(EBIT1,3 – $360) (1 – 0.40) – 01,050171© Pearson Education Limited 200874语言资格考试PPT= ￿=￿=Chapter 16: Operating and Financial LeverageCross-multiplying and rearranging, we obtain(EBIT1,3) (0.60) (1,050) – ($920) (0.60) (1,050)= (EBIT1,3) (0.60) (800) – ($360) (0.60) (800)(EBIT1,3) (630) – ($579,600) = (EBIT1,3) (480) – ($172,800)(EBIT1,3) (150) = $406,800EBIT1,3 = $2,712Note that for the debt alternative, the total before-tax interest is $920, and this is theintercept on the horizontal axis. For the preferred stock alternative, we divide $480 by(1 – 0.4) to get $800. When this is added to $360 in interest on existing debt, theintercept becomes $1,160.c. Debt (1):DFLEBIT of $1.5M =Preferred (2):$1,500,000$1,500,000 – $920,000= 2.59DFLEBIT of $1.5M =Common (3):$1,500,000$1,500,000 – $360,000 – [$480,000 / (1 – .40)]= 4.41DFLEBIT of $1.5M =$1,500,000$1,500,000 – $360,000= 1.32d. For the present EBIT level, common is clearly preferable. EBIT would need to increaseby $2,712,000 – $1,500,000 = $1,212,000 before an indifference point with debt isreached. One would want to be comfortably above this indifference point before astrong case for debt should be made. The lower the probability that actual EBIT will fallbelow the indifference point, the stronger the case that can be made for debt, all otherthings being the same.4.DQLQ unitsPercentage change inoperating profit (EBIT)Percentage change inoutput (or sales)￿￿￿￿ ∆Q(P − V) ￿￿￿Q(P − V) − FC ￿∆Q / QWhich reduces to: DOLQ units =Q (P – V)Q (P – V) – FCDividing both the numerator and denominator by (P – V) producesDOLQ units = – [FC / (P – V)] – QBE172© Pearson Education Limited 200875语言资格考试PPT===Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual5. a. Total annual interest is determined as follows:15% of $2.4 million13% of $3.0 million18% of $2.0 million$ 360,000390,000360,000$1,110,000Interest coverage ratio = $2,000,000 / $1,110,000 = 1.80Total annual principal payments = $100,000 + $150,000 = $250,000Debt − servicecoverage =ratio$2,000,000$1,110,000 + [$250,000 / (1 − .50)]= 1.24b. Required deviation of EBIT from its mean value before ratio in question becomes 1 : 1:Interest coverage: $1,110,000 – $2,000,000 = –$890,000Debt-service coverage: $1,610,000 – $2,000,000 = –$390,000Standardizing each deviation from the mean produces the following Z-scores:Interest coverage:−$890,000$1,500,000= − 0.593 standard deviations (left of the mean)Debt-service coverage:−$390,000$1,500,000= − 0.260 standard deviations (left of the mean)Table V in the Appendix at the end of the book can be used to determine the proportionof the area under the normal curve, that is, Z-standard deviations left of the mean. Thisproportion corresponds to the probability that an EBIT figure will occur that producescoverage ratios lower than 1 : 1. For interest coverage and debt-service coverage, ratiosless than 1 : 1 of these probabilities are approximately 28 percent and 40 percent,respectively. These probabilities assume that the distribution of possible EBITs isnormal.c. There is a substantial probability of 40 percent that the company will fail to cover itsinterest and principal payments. Its debt ratio (using either book or market values) ismuch higher than the industry norm of 0.47. Although the information is limited, basedon what we have, it would appear that Archimedes has too much debt. However, otherfactors, such as liquidity, may mitigate against this conclusion.6. Aberez has a lower debt ratio than its industry norm. Vorlas has a higher ratio relative to itsindustry. Both companies exceed modestly their industry norms with respect to interestcoverage. The lower debt/equity ratio and higher interest coverage for Vorlas’s industrysuggest that its industry might have more business risk than the industry of which Aberez isa part. The liquidity ratio of Aberez is higher than the industry norm, while that for Vorlas itis lower than the industry norm. Although all three financial ratios for Vorlas are better thanthose of Aberez’s, they are relatively lower to the industry norm. Finally, the bond rating ofAberez is much better than is that of Vorlas, being an Aa grade and higher than the industrynorm. The bond rating of Vorlas is one grade below the very lowest grade for investment-grade bonds. It is also lower than the typical company's bond rating in the industry. If theindustry norms are reasonable representations of underlying business and financial risk, wewould say that Vorlas had the greater degree of risk.173© Pearson Education Limited 200876语言资格考试PPTCapital Structure DeterminationWhen you have eliminated the impossible, whateverremains, however improbable, must be the truth.SHERLOCK HOLMESIN THE SIGN OF THE FOUR174© Pearson Education Limited 200877语言资格考试PPTVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualANSWERS TO QUESTIONS1. The net operating income (NOI) approach and the Modigliani-Miller (M&M) approach, inthe absence of taxes, are identical in form. The only difference is that M&M specify thebehavioral characteristics that cause the average cost of capital to remain constant. M&Mprovide a set of assumptions necessary to show the mechanism of arbitrage equilibratingreturns from similar investments.2. The optimal capital structure would differ from one industry to another because eachindustry has a different level of business risk. The higher the level of business risk, thelower the amount of financial risk that might be incurred and vice versa. Even within anindustry, the competitive position of a firm, the growth potential, and the caliber ofmanagement may cause a higher degree of business risk.3. Many factors influence the interest rate a firm must pay for debt funds. Some factors areexternal to the firm. For example, the expected inflation rate, the Federal Reserve’s activityin the capital and money markets, and the productivity of capital, are external to the firm.Other factors such as the magnitude and variability of earnings, the stability of management,the debt-to-equity ratio, type and quality of assets, bond rating, the maturity of the bonds,etc., are internal factors that affect the rate paid on debt funds.4. The total-value principle states that a corporation is valued on the basis of its earnings’potential and its business risk. The total “pie” of value stays the same regardless of how it issliced. Therefore, no matter how the pie is divided between debt, equity, and other claims,the total value of the firm stays the same. There is a conservation of investment value, sothat the sum of the parts equals the whole and the whole does not change with changes infinancial leverage.5. Arbitrage implies that an identical product cannot sell for different prices in differentmarkets. If it does, arbitragers will buy in one market and sell in another to earn an arbitrageprofit with no risk to them. These actions will cause the price of one asset to rise and theprice of the other to fall until equilibrium is achieved, at which time there will be no furtheropportunity for arbitrage profit. As applied to capital structure, if two companies are said tobe the same other than one is levered while the other is not, arbitrage supposedly wouldcause the total value of the two firms to be the same. With market imperfections, however,this need not be the case, though the elimination of arbitrage profits is central to marketequilibration as it applies, among other things, to the issue of capital structure.6. Without financial-market imperfections, variation in capital structure would have no impacton share price. Capital structure decisions would be irrelevant, as suggested by Modigliani-Miller. Market imperfections take us away from a frictionless world and reduce theeffectiveness of arbitrage. As a result, different financial liabilities and common stock canhave different costs on a certainty equivalent basis. The two most important imperfectionswith respect to capital structure are probably income taxes and bankruptcy costs. Their jointimpact was taken up in the chapter. Other imperfections include agency costs, transactioncosts on the sale of stocks and bonds by investors, flotation costs to the corporation, legalrestrictions governing investor behavior, and restrictions on margin loans and short sales.7. Bankruptcy costs include out-of-pocket expenses to lawyers, accountants, appraisers,trustees, and others as well as the loss of economic value that often occurs as a companyapproaches bankruptcy and is not able to operate efficiently. Agency costs include costs of175© Pearson Education Limited 200878语言资格考试PPTChapter 17: Capital Structure Determinationshareholders monitoring the actions of management and lenders monitoring the actions of acompany. Auditing fees, appraiser fees, bonding fees, and the cost of protective covenantsare examples of agency costs. These costs tend to increase at an increasing rate beyondsome point of financial leverage. Therefore, bankruptcy and agency costs eventually offsetthe net tax benefit associated with the employment of debt funds by the corporation. Theybound the solution so that there is an optimal capital structure.8. For reasons of prudence as well as legal reasons, institutional investors will not lend moneyto a company that has excessive financial leverage. Both the investors, under stateregulations and ERISA, cannot take excessive risks. Therefore, there comes a point infinancial leverage where they will not extend loans even though the firm may be willing topay a higher interest rate. The judgment of whether financial leverage is excessive is usuallymade after studying debt ratios as well as the cash-flow ability of the company to servicedebt. Often, regulators rely on the rating agencies to determine whether a company is toorisky when the debt is publicly held.9. Without the payment of taxes, the corporate tax-shield due to debt, disappears and so toodoes the major economic argument to the use of debt. As a result, the optimal capitalstructure would entail much less debt than if a company were to pay taxes at the fullcorporate tax rate.10. Debt financing would decrease on a relative basis, all other things being the same. The taxadvantage associated with debt would be reduced. Equity financing would increase on arelative basis, all other things being the same.11. The tax effect associated with debt and equity financing would be the same, as opposed tothe tax advantage presently enjoyed by debt financing. As a result, equity financing wouldincrease relative to debt financing. Corporations as a whole would move towards lowerdebt-to-equity ratios.12. If there is asymmetric information between management and investors, the former mightsignal via capital structure. The implication is that management would not bind itself to thedebt-servicing schedule, unless it believed the company had operating cash flows in thefuture to adequately service such debt. The capital structure change represents an explicitstatement about expected future earnings. In this context, the issuance of debt is “goodnews”, whereas the issuance of equity would be regarded as “bad news” by investors.176© Pearson Education Limited 200879语言资格考试PPTOIESBVkoOkoVBSOIEkeVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s ManualSOLUTIONS TO PROBLEMS1. a.Net operating incomeInterest on debtEarnings available to common shareholders (O – I)$10,000,0001,400,000$ 8,600,000keEquity capitalization rate÷0.125b.Market value of stock (E/ke)Market value of debtTotal value of firm (B + S)Implied overall capitalization rate [ki(B/V) + ke(S/V)] oralternatively (O/V)Net operating incomeOverall capitalization rateTotal value of firm (B + S)Market value if debtMarket value of stock (V – B)Net operating incomeInterest on debtEarnings available to common shareholders (O – I)Implied equity capitalization rate (E/S)177© Pearson Education Limited 2008$68,800,00020,000,000$88,800,0000.1126126$10,000,000÷ 0.1126126$88,800,00030,000,000$58,800,000$10,000,0002,100,000$ 7,900,0000.1343580语言资格考试PPTIPChapter 17: Capital Structure Determination2. a. (i) Sell your Gottahave stock for $22,500.(ii) Borrow $20,000 at 12 percent interest. This personal debt is equal to 1 percent ofGottahave debt.(iii) Buy 1 percent of the stock of the Wannabee Company for $40,000 and still have$22,500 + $20,000 – $40,000 = $2,500 left over for other investments.Return on investment in WannabeeLess: interest paid ($20,000 × 0.12)Net return$6,0002,400$3,600Your net dollar return, $3,600, is the same as it was for your investment inGottahave. However, your personal cash outlay of $20,000 ($40,000 less personalborrowings of $20,000) is $2,500 less than your previous $22,500 investment inGottahave.b. When there is no further opportunity for employing fewer funds and achieving the sametotal dollar return, the arbitrage process will cease. At this point, the total value of thetwo firms must be the same, as must their average costs of capital.3. a. $400,000 in debt. The market price per share of common stock is highest at this amountof financial leverage.b.(000s omitted)# sharesBEBITEBTEAT100908070605040ki---5.00%5.005.255.506.007.00$0100200300400500600EPS$1.251.331.441.561.721.902.08$250250250250250250250$10.0010.0010.5010.7511.0010.509.50$ 0.010.020.031.544.060.084.0ke = EPS/P12.5%13.313.714.515.618.121.8$250.0240.0230.0218.5206.0190.0166.0S = (# shares) × P$1,000.0900.0840.0752.5660.0525.0380.0$125.00120.00115.00109.25103.0095.0083.00V=B+S$1000.01000.01040.01052.51060.01025.0980.0178© Pearson Education Limited 200881语言资格考试PPT=+=+=+=+=+=+=0Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualki(B/V)+ke(S/V)=ko(12.5%)($1,000/$1,000.0)12.50%(5.00%)($100/$1,000.0)(5.00%)($200/$1,040.0)(5.25%)($300/$1,052.5)(5.50%)($400/$1,060.0)(6.00%)($500/$1,025.0)(7.00%)($600/$980.0)(13.3%)($900.0/$1,000.0)(13.7%)($840.0/$1,040.0)(14.5%)($752.5/$1,052.5)(15.6%)($660.0/$1,060.0)(18.1%)($525.0/$1,025.0)(21.8%)($380/$980.0)12.4712.0311.8611.7912.2012.74c. Yes. The optimal capital structure – the one possessing the lowest overall cost of capital– involves $400,000 in debt.4. a.All-equityDebt and EquityEBITInterest to debt holdersEBTTaxes (0.40)Incomes available to common shareholdersIncome to debt holders plus incomeavailable to shareholders$1,000,000$1,000,000400,000$ 600,000$ 600,000$1,000,000450,000$ 550,000220,000$ 330,000$ 780,000b. Present value of tax-shield benefits = (B)(tc) = ($3,000,000)(0.40) = $1,200,000c. Value of all-equity financed firm = EAT/ke = $600,000/(0.20) = $3,000,000Value of recapitalized firm = $3,000,000 + $1,200,000 = $4,200,000179© Pearson Education Limited 200882语言资格考试PPT=+=+=+=+=+=+=+=+=Chapter 17: Capital Structure Determination5.(in millions)(3)(4)(5)(2)PV of tax- shieldPV ofValue of(1)Debt$012345678Value of UnleveredFirm$101010101010101010benefits(1) × 0.22$0.000.220.440.660.881.101.321.541.76BankruptcyCosts$0.000.000.050.100.200.400.701.101.60Levered Firm(2) + (3) – (4)$10.0010.2210.3910.5610.6810.70*10.6210.4410.16*The optimal amount of debt would be $5 million.6. a. without bankruptcy costs[ki × (B/V)]+[ke × (S/V)]=ko(10.00%) (1.00)10.000%(4.00%) (0.10)(4.00%) (0.20)(4.25%) (0.30)(4.50%) (0.40)(5.00%) (0.50)(5.50%) (0.60)(6.25%) (0.70)(7.50%) (0.80)(10.50%) (0.90)(11.00%) (0.80)(11.50%) (0.70)(12.25%) (0.60)(13.25%) (0.50)(14.50%) (0.40)(16.00%) (0.30)(18.00%) (0.20)180© Pearson Education Limited 20089.850%9.600%9.325%9.150%9.125%9.100%9.175%9.600%83语言资格考试PPT=+=+=+=+=+=+=+=+=Van Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manualb. with bankruptcy costs[ki × (B/V)]+[ke × (S/V)]=ko(10.00%)(1.00)10.000%(4.00%)(0.10)(4.00%)(0.20)(4.25%)(0.30)(4.50%)(0.40)(5.00%)(0.50)(5.50%)(0.60)(6.25%)(0.70)(7.50%)(0.80)(10.50%)(0.90)(11.25%) (0.80)(12.00%)(0.70)(13.00%)(0.60)(14.50%)(0.50)(16.25%)(0.40)(18.50%)(0.30)(21.00%)(0.20)9.850%9.800%9.675%9.600%9.750%9.800%9.925%10.200%With bankruptcy costs, the optimal capital structure is 40 percent debt in contrast to 60percent bankruptcy costs.7. According to the notion of asymmetric information between management and investors, thecompany should issue the overvalued security, or at least the one that is not undervalued inits mind. This would be debt in the situation described in the problem. Investors would beaware of management’s likely behavior and would view the event as “good news”. Thestock price might rise, all other things being the same, if this information was not otherwiseconveyed.In contrast, if the common stock were believed to be overvalued, management would wantto issue common stock. This assumes it wishes to maximize the wealth of existingstockholders. Investors would regard this announcement as “bad news”, and the stock pricemight decline. Information effects through financing would assume that the information isnot otherwise known by the market. Management usually has a bias in thinking that thecommon stock of the company is undervalued.181© Pearson Education Limited 200884语言资格考试PPTOVBSOIEOVBSOIEChapter 17: Capital Structure DeterminationSOLUTIONS TO SELF-CORRECTION PROBLEMS1. a. Qwert Typewriter Company:Net operating income$ 360,000koOverall capitalization rate÷0.18Total value of the firm (B + S)Market value of debt (50%)Market value of stock (50%)Net operating incomeInterest on debt (13%)Earnings available to common shareholders (O – I)$2,000,0001,000,000$1,000,000$ 360,000130,000$ 230,0002% of $230,000 = $4,600Implied equity capitalization rate, ke = E/S = $230,000/$1,000,000 = 23 percentb. Yuiop Typewriters, Inc.:Net operating income$ 360,000koOverall capitalization rate÷0.18Total value of the firm (B + S)Market value of debt (20%)Market value of stock (80%)Net operating incomeInterest on debt (13%)Earnings available to common shareholders (O – I)$2,000,000400,000$1,600,000$ 360,00052,000$ 308,000Implied equity capitalization rate, ke = E/S = $308,000/$1,600,000 = 19.25 percentYuiop has a lower equity capitalization rate than Qwert, because Yuiop uses less debt inits capital structure. As the equity capitalization rate is a linear function of the debt-to-equity ratio when we use the net operating income approach, the decline in equitycapitalization rate exactly offsets the disadvantage of not employing so much in the wayof “cheaper” debt funds.182© Pearson Education Limited 200885语言资格考试PPT=+=+=+ofVan Horne and Wachowicz , Fundamentals of Financial Management, 13th edition, Instructor’s Manual2. Value of firm if unlevered:Earnings before interest and taxesInterestEarnings before taxesTaxes (40 percent)Earnings after taxes$ 3,000,0000$ 3,000,0001,200,000$ 1,800,000Equity capitalization rate, ke÷0.18Value of the firm (unlevered)Value with $4 million in debt:$10,000,000Value oflevered firm=Value of firmif unlevered$10,000,000$11,600,000Present value oftax-shield benefits of debt($4,000,000) (0.40)Value with $7 million in debt:$10,000,000($7,000,000)(0.40)=$12,800,000Due to the tax subsidy, the firm is able to increase its value in a linear manner with moredebt.3. (In millions):(1)Level(2)Firm(3)PV of Tax-Shield(4)PV of Bankruptcy,ValueBenefits Of DebtAgency & IncreasedValue of FirmDebt$05101520*2530Unlevered$15151515151515(1) × 0.20$0123456Interest Costs$0.00.00.61.22.03.25.0(2)+(3)–(4)$15.016.016.416.817.016.816.0*The market value of the firm is maximized with $20 million in debt.183© Pearson Education Limited 200886语言资格考试PPT•202087语言资格考试PPT•2020。