罗斯《公司理财》第9版精要版英文原书课后部分章节答案

The present value of the four new outlets is only $954,316.78. The outlets are worth less than they cost. The Trojan Pizza Company should not make the investment because the NPV is –$45,683.22. If the Trojan Pizza Company requires a 15 percent rate of return, the new outlets are not a good investment.SPREADSHEET APPLICATIONSHow to Calculate Present Values with Multiple Future Cash Flows Using a SpreadsheetWe can set up a basic spreadsheet to calculate the present values of the individual cash flows as follows. Notice that we have simply calculated the present values one at a time and added them up:Summary and Conclusions1. Two basic concepts, future value and present value, were introduced in the beginning of thischapter. With a 10 percent interest rate, an investor with $1 today can generate a future value of $1.10 in a year, $1.21 [=$1 × (1.10)2] in two years, and so on. Conversely, present value analysis places a current value on a future cash flow. With the same 10 percent interest rate, a dollar to be received in one year has a present value of $.909 (=$1/1.10) in year 0. A dollar to be received in two years has a present value of $.826 [=$1/(1.10)2].2. We commonly express an interest rate as, say, 12 percent per year. However, we can speak ofthe interest rate as 3 percent per quarter. Although the stated annual interest rate remains 12 percent (=3 percent × 4), the effective annual interest rate is 12.55 percent [=(1.03)4 – 1]. In other words, the compounding process increases the future value of an investment. The limiting case is continuous compounding, where funds are assumed to be reinvested every infinitesimal instant.3. A basic quantitative technique for financial decision making is net present value analysis. Thenet present value formula for an investment that generates cash flows (C i) in future periods is:The formula assumes that the cash flow at date 0 is the initial investment (a cash outflow).4. Frequently, the actual calculation of present value is long and tedious. The computation of thepresent value of a long-term mortgage with monthly payments is a good example of this. We presented four simplifying formulas:5. We stressed a few practical considerations in the application of these formulas:1. The numerator in each of the formulas, C, is the cash flow to be received one full periodhence.2. Cash flows are generally irregular in practice. To avoid unwieldy problems, assumptions tocreate more regular cash flows are made both in this textbook and in the real world.3. A number of present value problems involve annuities (or perpetuities) beginning a fewperiods hence. Students should practice combining the annuity (or perpetuity) formula withthe discounting formula to solve these problems.4. Annuities and perpetuities may have periods of every two or every n years, rather thanonce a year. The annuity and perpetuity formulas can easily handle such circumstances.5. We frequently encounter problems where the present value of one annuity must beequated with the present value of another annuity.Concept Questions1. Compounding and Period As you increase the length of time involved, what happens tofuture values? What happens to present values?2. Interest Rates What happens to the future value of an annuity if you increase the rate r?What happens to the present value?3. Present Value Suppose two athletes sign 10-year contracts for $80 million. In one case, we’retold that the $80 million will be paid in 10 equal installments. In the other case, we’re told that the $80 million will be paid in 10 installments, but the installments will increase by 5 percent per year.Who got the better deal?4. APR and EAR Should lending laws be changed to require lenders to report EARs instead ofAPRs? Why or why not?5. Time Value On subsidized Stafford loans, a common source of financial aid for collegestudents, interest does not begin to accrue until repayment begins. Who receives a bigger subsidy,a freshman or a senior? Explain.Use the following information to answer the next five questions:Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor Corporation, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal, TMCC promised to repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive nothing until then. Investors paid TMCC $24,099 for each of these securities; so they gave up $24,099 on March 28, 2008, for the promise of a $100,000 payment 30 years later.6. Time Value of Money Why would TMCC be willing to accept such a small amount today($24,099) in exchange for a promise to repay about four times that amount ($100,000) in the future?7. Call Provisions TMCC has the right to buy back the securities on the anniversary date at aprice established when the securities were issued (this feature is a term of this particular deal).What impact does this feature have on the desirability of this security as an investment?8. Time Value of Money Would you be willing to pay $24,099 today in exchange for $100,000 in30 years? What would be the key considerations in answering yes or no? Would your answerdepend on who is making the promise to repay?9. Investment Comparison Suppose that when TMCC offered the security for $24,099 the U.S.Treasury had offered an essentially identical security. Do you think it would have had a higher or lower price? Why?10. Length of Investment The TMCC security is bought and sold on the New York StockExchange. If you looked at the price today, do you think the price would exceed the $24,099 original price? Why? If you looked in the year 2019, do you think the price would be higher or lower than today’s price? Why?Questions and Problems: connect™BASIC (Questions 1–20)1. Simple Interest versus Compound Interest First City Bank pays 9 percent simple intereston its savings account balances, whereas Second City Bank pays 9 percent interest compounded annually. If you made a $5,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years?2. Calculating Future Values Compute the future value of $1,000 compounded annually for1. 10 years at 6 percent.2. 10 years at 9 percent.3. 20 years at 6 percent.4. Why is the interest earned in part (c) not twice the amount earned in part (a)?3. Calculating Present Values For each of the following, compute the present value:4. Calculating Interest Rates Solve for the unknown interest rate in each of the following:5. Calculating the Number of Periods Solve for the unknown number of years in each of thefollowing:6. Calculating the Number of Periods At 9 percent interest, how long does it take to doubleyour money? To quadruple it?7. Calculating Present Values Imprudential, Inc., has an unfunded pension liability of $750million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8.2 percent, what is the present value of this liability?8. Calculating Rates of Return Although appealing to more refined tastes, art as a collectiblehas not always performed so profitably. During 2003, Sotheby’s sold the Edgar Degas bronze sculpture Petite Danseuse de Quartorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his annual rate of return on this sculpture?9. Perpetuities An investor purchasing a British consol is entitled to receive annual paymentsfrom the British government forever. What is the price of a consol that pays $120 annually if the next payment occurs one year from today? The market interest rate is 5.7 percent.10. Continuous Compounding Compute the future value of $1,900 continuously compounded for1. 5 years at a stated annual interest rate of 12 percent.2. 3 years at a stated annual interest rate of 10 percent.3. 10 years at a stated annual interest rate of 5 percent.4. 8 years at a stated annual interest rate of 7 percent.11. Present Value and Multiple Cash Flows Conoly Co. has identified an investment projectwith the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24 percent?12. Present Value and Multiple Cash Flows Investment X offers to pay you $5,500 per year fornine years, whereas Investment Y offers to pay you $8,000 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 22 percent?13. Calculating Annuity Present Value An investment offers $4,300 per year for 15 years, withthe first payment occurring one year from now. If the required return is 9 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?14. Calculating Perpetuity Values The Perpetual Life Insurance Co. is trying to sell you aninvestment policy that will pay you and your heirs $20,000 per year forever. If the required return on this investment is 6.5 percent, how much will you pay for the policy? Suppose the Perpetual Life Insurance Co. told you the policy costs $340,000. At what interest rate would this be a fair deal? 15. Calculating EAR Find the EAR in each of the following cases:16. Calculating APR Find the APR, or stated rate, in each of the following cases:17. Calculating EAR First National Bank charges 10.1 percent compounded monthly on itsbusiness loans. First United Bank charges 10.4 percent compounded semiannually. As a potential borrower, to which bank would you go for a new loan?18. Interest Rates Well-known financial writer Andrew Tobias argues that he can earn 177percent per year buying wine by the case. Specifically, he assumes that he will consume one $10 bottle of fine Bordeaux per week for the next 12 weeks. He can either pay $10 per week or buy a case of 12 bottles today. If he buys the case, he receives a 10 percent discount and, by doing so, earns the 177 percent. Assume he buys the wine and consumes the first bottle today. Do you agree with his analysis? Do you see a problem with his numbers?19. Calculating Number of Periods One of your customers is delinquent on his accounts payablebalance. You’ve mutually agreed to a repayment schedule of $600 per month. You will charge .9 percent per month interest on the overdue balance. If the current balance is $18,400, how long will it take for the account to be paid off?20. Calculating EAR Friendly’s Quick Loans, Inc., offers you “three for four or I knock on yourdoor.” This means you get $3 today and repay $4 when you get your paycheck in one week (orelse). What’s the effective annual return Friendly’s earns on this lending business? If you were brave enough to ask, what APR would Friendly’s say you were paying?INTERMEDIATE (Questions 21–50)21. Future Value What is the future value in seven years of $1,000 invested in an account with astated annual interest rate of 8 percent,1. Compounded annually?2. Compounded semiannually?3. Compounded monthly?4. Compounded continuously?5. Why does the future value increase as the compounding period shortens?22. Simple Interest versus Compound Interest First Simple Bank pays 6 percent simpleinterest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years?23. Calculating Annuities You are planning to save for retirement over the next 30 years. To dothis, you will invest $700 a month in a stock account and $300 a month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent.When you retire, you will combine your money into an account with an 8 percent return. How much can you withdraw each month from your account assuming a 25-year withdrawal period?24. Calculating Rates of Return Suppose an investment offers to quadruple your money in 12months (don’t believe it). What rate of return per quarter are you being offered?25. Calculating Rates of Return You’re trying to choose between two different investments, bothof which have up-front costs of $75,000. Investment G returns $135,000 in six years. Investment H returns $195,000 in 10 years. Which of these investments has the higher return?26. Growing Perpetuities Mark Weinstein has been working on an advanced technology in lasereye surgery. His technology will be available in the near term. He anticipates his first annual cash flow from the technology to be $215,000, received two years from today. Subsequent annual cash flows will grow at 4 percent in perpetuity. What is the present value of the technology if the discount rate is 10 percent?27. Perpetuities A prestigious investment bank designed a new security that pays a quarterlydividend of $5 in perpetuity. The first dividend occurs one quarter from today. What is the price of the security if the stated annual interest rate is 7 percent, compounded quarterly?28. Annuity Present Values What is the present value of an annuity of $5,000 per year, with thefirst cash flow received three years from today and the last one received 25 years from today? Usea discount rate of 8 percent.29. Annuity Present Values What is the value today of a 15-year annuity that pays $750 a year?The annuity’s first payment occurs six years from today. The annual interest rate is 12 percent for years 1 through 5, and 15 percent thereafter.30. Balloon Payments Audrey Sanborn has just arranged to purchase a $450,000 vacation homein the Bahamas with a 20 percent down payment. The mortgage has a 7.5 percent stated annualinterest rate, compounded monthly, and calls for equal monthly payments over the next 30 years.Her first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of year 8. There were no other transaction costs or finance charges. How much will Audrey’s balloon payment be in eight years?31. Calculating Interest Expense You receive a credit card application from Shady BanksSavings and Loan offering an introductory rate of 2.40 percent per year, compounded monthly for the first six months, increasing thereafter to 18 percent compounded monthly. Assuming you transfer the $6,000 balance from your existing credit card and make no subsequent payments, how much interest will you owe at the end of the first year?32. Perpetuities Barrett Pharmaceuticals is considering a drug project that costs $150,000 todayand is expected to generate end-of-year annual cash flows of $13,000, forever. At what discount rate would Barrett be indifferent between accepting or rejecting the project?33. Growing Annuity Southern California Publishing Company is trying to decide whether to reviseits popular textbook, Financial Psychoanalysis Made Simple. The company has estimated that the revision will cost $65,000. Cash flows from increased sales will be $18,000 the first year. These cash flows will increase by 4 percent per year. The book will go out of print five years from now.Assume that the initial cost is paid now and revenues are received at the end of each year. If the company requires an 11 percent return for such an investment, should it undertake the revision? 34. Growing Annuity Your job pays you only once a year for all the work you did over theprevious 12 months. Today, December 31, you just received your salary of $60,000, and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5 percent of your annual salary in an account that will earn 9 percent per year. Your salary will increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today?35. Present Value and Interest Rates What is the relationship between the value of an annuityand the level of interest rates? Suppose you just bought a 12-year annuity of $7,500 per year at the current interest rate of 10 percent per year. What happens to the value of your investment if interest rates suddenly drop to 5 percent? What if interest rates suddenly rise to 15 percent?36. Calculating the Number of Payments You’re prepared to make monthly payments of $250,beginning at the end of this month, into an account that pays 10 percent interest compounded monthly. How many payments will you have made when your account balance reaches $30,000? 37. Calculating Annuity Present Values You want to borrow $80,000 from your local bank tobuy a new sailboat. You can afford to make monthly payments of $1,650, but no more. Assuming monthly compounding, what is the highest APR you can afford on a 60-month loan?38. Calculating Loan Payments You need a 30-year, fixed-rate mortgage to buy a new home for$250,000. Your mortgage bank will lend you the money at a 6.8 percent APR for this 360-month loan. However, you can only afford monthly payments of $1,200, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $1,200?39. Present and Future Values The present value of the following cash flow stream is $6,453when discounted at 10 percent annually. What is the value of the missing cash flow?40. Calculating Present Values You just won the TVM Lottery. You will receive $1 million todayplus another 10 annual payments that increase by $350,000 per year. Thus, in one year you receive $1.35 million. In two years, you get $1.7 million, and so on. If the appropriate interest rate is 9 percent, what is the present value of your winnings?41. EAR versus APR You have just purchased a new warehouse. To finance the purchase, you’vearranged for a 30-year mortgage for 80 percent of the $2,600,000 purchase price. The monthly payment on this loan will be $14,000. What is the APR on this loan? The EAR?42. Present Value and Break-Even Interest Consider a firm with a contract to sell an asset for$135,000 three years from now. The asset costs $96,000 to produce today. Given a relevant discount rate on this asset of 13 percent per year, will the firm make a profit on this asset? At what rate does the firm just break even?43. Present Value and Multiple Cash Flows What is the present value of $4,000 per year, at adiscount rate of 7 percent, if the first payment is received 9 years from now and the last payment is received 25 years from now?44. Variable Interest Rates A 15-year annuity pays $1,500 per month, and payments are madeat the end of each month. If the interest rate is 13 percent compounded monthly for the first seven years, and 9 percent compounded monthly thereafter, what is the present value of the annuity? 45. Comparing Cash Flow Streams You have your choice of two investment accounts.Investment A is a 15-year annuity that features end-of-month $1,200 payments and has an interest rate of 9.8 percent compounded monthly. Investment B is a 9 percent continuously compounded lump-sum investment, also good for 15 years. How much money would you need to invest in B today for it to be worth as much as Investment A 15 years from now?46. Calculating Present Value of a Perpetuity Given an interest rate of 7.3 percent per year,what is the value at date t = 7 of a perpetual stream of $2,100 annual payments that begins at date t = 15?47. Calculating EAR A local finance company quotes a 15 percent interest rate on one-year loans.So, if you borrow $26,000, the interest for the year will be $3,900. Because you must repay a total of $29,900 in one year, the finance company requires you to pay $29,900/12, or $2,491.67, per month over the next 12 months. Is this a 15 percent loan? What rate would legally have to be quoted? What is the effective annual rate?48. Calculating Present Values A 5-year annuity of ten $4,500 semiannual payments will begin 9years from now, with the first payment coming 9.5 years from now. If the discount rate is 12 percent compounded monthly, what is the value of this annuity five years from now? What is the value three years from now? What is the current value of the annuity?49. Calculating Annuities Due Suppose you are going to receive $10,000 per year for five years.The appropriate interest rate is 11 percent.1. What is the present value of the payments if they are in the form of an ordinary annuity?What is the present value if the payments are an annuity due?2. Suppose you plan to invest the payments for five years. What is the future value if thepayments are an ordinary annuity? What if the payments are an annuity due?3. Which has the highest present value, the ordinary annuity or annuity due? Which has thehighest future value? Will this always be true?50. Calculating Annuities Due You want to buy a new sports car from Muscle Motors for$65,000. The contract is in the form of a 48-month annuity due at a 6.45 percent APR. What will your monthly payment be?CHALLENGE (Questions 51–76)51. Calculating Annuities Due You want to lease a set of golf clubs from Pings Ltd. The leasecontract is in the form of 24 equal monthly payments at a 10.4 percent stated annual interest rate, compounded monthly. Because the clubs cost $3,500 retail, Pings wants the PV of the lease payments to equal $3,500. Suppose that your first payment is due immediately. What will your monthly lease payments be?52. Annuities You are saving for the college education of your two children. They are two yearsapart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $35,000 per year per child, payable at the beginning of each school year. The annual interest rate is 8.5 percent. How much money must you deposit in an account each year to fund your children’s education? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of college.53. Growing Annuities Tom Adams has received a job offer from a large investment bank as aclerk to an associate banker. His base salary will be $45,000. He will receive his first annual salary payment one year from the day he begins to work. In addition, he will get an immediate $10,000 bonus for joining the company. His salary will grow at 3.5 percent each year. Each year he will receive a bonus equal to 10 percent of his salary. Mr. Adams is expected to work for 25 years.What is the present value of the offer if the discount rate is 12 percent?54. Calculating Annuities You have recently won the super jackpot in the Washington StateLottery. On reading the fine print, you discover that you have the following two options:1. You will receive 31 annual payments of $175,000, with the first payment being deliveredtoday. The income will be taxed at a rate of 28 percent. Taxes will be withheld when the checks are issued.2. You will receive $530,000 now, and you will not have to pay taxes on this amount. Inaddition, beginning one year from today, you will receive $125,000 each year for 30 years.The cash flows from this annuity will be taxed at 28 percent.Using a discount rate of 10 percent, which option should you select?55. Calculating Growing Annuities You have 30 years left until retirement and want to retirewith $1.5 million. Your salary is paid annually, and you will receive $70,000 at the end of the current year. Your salary will increase at 3 percent per year, and you can earn a 10 percent return on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year?56. Balloon Payments On September 1, 2007, Susan Chao bought a motorcycle for $25,000. Shepaid $1,000 down and financed the balance with a five-year loan at a stated annual interest rate of8.4 percent, compounded monthly. She started the monthly payments exactly one month after thepurchase (i.e., October 1, 2007). Two years later, at the end of October 2009, Susan got a new job and decided to pay off the loan. If the bank charges her a 1 percent prepayment penalty based on the loan balance, how much must she pay the bank on November 1, 2009?57. Calculating Annuity Values Bilbo Baggins wants to save money to meet three objectives.First, he would like to be able to retire 30 years from now with a retirement income of $20,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $320,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to his nephew Frodo. He can afford to save $1,900 per month for the next 10 years.If he can earn an 11 percent EAR before he retires and an 8 percent EAR after he retires, how much will he have to save each month in years 11 through 30?58. Calculating Annuity Values After deciding to buy a new car, you can either lease the car orpurchase it with a three-year loan. The car you wish to buy costs $38,000. The dealer has a special leasing arrangement where you pay $1 today and $520 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at an 8 percent APR. You believe that you will be able to sell the car for $26,000 in three years. Should you buy or lease the car? What break-even resale price in three years would make you indifferent between buying and leasing?59. Calculating Annuity Values An All-Pro defensive lineman is in contract negotiations. Theteam has offered the following salary structure:All salaries are to be paid in a lump sum. The player has asked you as his agent to renegotiate the terms. He wants a $9 million signing bonus payable today and a contract value increase of $750,000. He also wants an equal salary paid every three months, with the first paycheck three months from now. If the interest rate is 5 percent compounded daily, what is the amount of his quarterly check? Assume 365 days in a year.60. Discount Interest Loans This question illustrates what is known as discount interest. Imagineyou are discussing a loan with a somewhat unscrupulous lender. You want to borrow $20,000 for one year. The interest rate is 14 percent. You and the lender agree that the interest on the loan will be .14 × $20,000 = $2,800. So, the lender deducts this interest amount from the loan up front and gives you $17,200. In this case, we say that the discount is $2,800. What’s wrong here?61. Calculating Annuity Values You are serving on a jury. A plaintiff is suing the city for injuriessustained after a freak street sweeper accident. In the trial, doctors testified that it will be five years before the plaintiff is able to return to work. The jury has already decided in favor of the plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award to cover the following: (1) The present value of two years’ back pay. The plaintiff’s annual salary for the last two years would have been $42,000 and $45,000, respectively. (2) The present value of five years’ future salary. You assume the salary will be $49,000 per year. (3) $150,000 for pain and suffering. (4) $25,000 for court costs. Assume that the salary payments are equal amounts paid at the end of each month. If the interest rate you choose is a 9 percent EAR, what is the size of the settlement? If you were the plaintiff, would you like to see a higher or lower interest rate?62. Calculating EAR with Points You are looking at a one-year loan of $10,000. The interest rateis quoted as 9 percent plus three points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are very common with home mortgages. The interest rate quotation in this example requires the borrower to pay three points to the lender up front and repay the loan later with 9 percent interest. What rate would you actually be paying here? What is the EAR for a one-year loan with a quoted interest rate of 12 percent plus two points? Is your answer affected by the loan amount?63. EAR versus APR Two banks in the area offer 30-year, $200,000 mortgages at 6.8 percent andcharge a $2,100 loan application fee. However, the application fee charged by Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged by I. M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not required with nonrefundable。

CHAPTER 8INTEREST RATES AND BOND VALUATION1.The price of a pure discount (zero coupon) bond is the present value of the par. Remember, even though there are no coupon payments, the periods are semiannual to stay consistent with coupon bond payments. So, the price of the bond for each YTM is:a. P = $1,000/(1 + .05/2)20 = $610.27b. P = $1,000/(1 + .10/2)20 = $376.89c. P = $1,000/(1 + .15/2)20 = $235.412.The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes a semiannual coupon. The price of the bond at each YTM will be:a.P = $35({1 – [1/(1 + .035)]50 } / .035) + $1,000[1 / (1 + .035)50]P = $1,000.00When the YTM and the coupon rate are equal, the bond will sell at par.b.P = $35({1 – [1/(1 + .045)]50 } / .045) + $1,000[1 / (1 + .045)50]P = $802.38When the YTM is greater than the coupon rate, the bond will sell at a discount.c.P = $35({1 – [1/(1 + .025)]50 } / .025) + $1,000[1 / (1 + .025)50]P = $1,283.62When the YTM is less than the coupon rate, the bond will sell at a premium.We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as:PVIF R,t = 1 / (1 + r)twhich stands for Present Value Interest FactorPVIFA R,t= ({1 – [1/(1 + r)]t } / r )which stands for Present Value Interest Factor of an AnnuityThese abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in the remainder of the solutions key.3.Here we are finding the YTM of a semiannual coupon bond. The bond price equation is:P = $1,050 = $39(PVIFA R%,20) + $1,000(PVIF R%,20)Since we cannot solve the equation directly for R, using a spreadsheet, a financialcalculator, or trial and error, we find:R = 3.547%Since the coupon payments are semiannual, this is the semiannual interest rate. TheYTM is the APR of the bond, so:YTM = 2 3.547% = 7.09%4.Here we need to find the coupon rate of the bond. All we need to do is to set up the bondpricing equation and solve for the coupon payment as follows:P = $1,175 = C(PVIFA3.8%,27) + $1,000(PVIF3.8%,27)Solving for the coupon payment, we get:C = $48.48Since this is the semiannual payment, the annual coupon payment is:2 × $48.48 = $96.96And the coupon rate is the annual coupon payment divided by par value, so:Coupon rate = $96.96 / $1,000 = .09696 or 9.70%5.The price of any bond is the PV of the interest payment, plus the PV of the par value.The fact that the bond is denominated in euros is irrelevant. Notice this problem assumes an annual coupon. The price of the bond will be:P = €84({1 – [1/(1 + .076)]15 } / .076) + €1,000[1 / (1 + .076)15]P = €1,070.186.Here we are finding the YTM of an annual coupon bond. The fact that the bond is denominated in yen is irrelevant. The bond price equation is:P = ¥87,000 = ¥5,400(PVIFA R%,21) + ¥100,000(PVIF R%,21)Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find:R = 6.56%Since the coupon payments are annual, this is the yield to maturity.7.The approximate relationship between nominal interest rates (R), real interest rates (r),and inflation (h) is:R = r + hApproximate r = .05 –.039 =.011 or 1.10%The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:(1 + R) = (1 + r)(1 + h)(1 + .05) = (1 + r)(1 + .039)Exact r = [(1 + .05) / (1 + .039)] – 1 = .0106 or 1.06%8.The Fisher equation, which shows the exact relationship between nominal interest rates,real interest rates, and inflation, is:(1 + R) = (1 + r)(1 + h)R = (1 + .025)(1 + .047) – 1 = .0732 or 7.32%9. The Fisher equation, which shows the exact relationship between nominal interest rates,real interest rates, and inflation, is:(1 + R) = (1 + r)(1 + h)h = [(1 + .17) / (1 + .11)] – 1 = .0541 or 5.41%10.The Fisher equation, which shows the exact relationship between nominal interest rates,real interest rates, and inflation, is:(1 + R) = (1 + r)(1 + h)r = [(1 + .141) / (1.068)] – 1 = .0684 or 6.84%11.The coupon rate, located in the first column of the quote is 6.125%. The bid price is:Bid price = 119:19 = 119 19/32 = 119.59375% $1,000 = $1,195.9375The previous day’s ask price is found by:Previous day’s asked price = Today’s asked price – Change = 119 21/32 – (–17/32) = 120 6/32The previous day’s price in dollars was:Previous day’s dollar price = 120.1875% $1,000 = $1,201.87512.This is a premium bond because it sells for more than 100% of face value. The current yield is:Current yield = Annual coupon payment / Asked price = $75/$1,347.1875 = .0557 or 5.57%The YTM is located under the “Asked yield” column, so the YTM is 4.4817%.The bid-ask spread is the difference between the bid price and the ask price, so:Bid-Ask spread = 134:23 – 134:22 = 1/32Intermediate13. Here we are finding the YTM of semiannual coupon bonds for various maturity lengths.The bond price equation is:P = C(PVIFA R%,t) + $1,000(PVIF R%,t)Miller Corporation bond:P0 = $45(PVIFA3.5%,26) + $1,000(PVIF3.5%,26) = $1,168.90P1 = $45(PVIFA3.5%,24) + $1,000(PVIF3.5%,24) = $1,160.58P3 = $45(PVIFA3.5%,20) + $1,000(PVIF3.5%,20) = $1,142.12P8 = $45(PVIFA3.5%,10) + $1,000(PVIF3.5%,10) = $1,083.17P12= $45(PVIFA3.5%,2) +$1,000(PVIF3.5%,2) = $1,019.00P13= $1,000Modigliani Company bond:P0 = $35(PVIFA4.5%,26) + $1,000(PVIF4.5%,26) = $848.53P1 = $35(PVIFA4.5%,24) + $1,000(PVIF4.5%,24) = $855.05P3 = $35(PVIFA4.5%,20) + $1,000(PVIF4.5%,20) = $869.92P8 = $35(PVIFA4.5%,10) + $1,000(PVIF4.5%,10) = $920.87P12= $35(PVIFA4.5%,2) +$1,000(PVIF4.5%,2) = $981.27P13= $1,000All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called “pull to par.” In both cases, the largest percentage price changes occur at the shortest maturity lengths.Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately. This is because we calculate the clean price of the bond.14.Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, sothe initial YTM on both bonds is the coupon rate, 8 percent. If the YTM suddenly rises to 10 percent:P Laurel= $40(PVIFA5%,4) + $1,000(PVIF5%,4) = $964.54P Hardy= $40(PVIFA5%,30) + $1,000(PVIF5%,30) = $846.28The percentage change in price is calculated as:Percentage change in price = (New price – Original price) / Original price∆P Laurel% = ($964.54 – 1,000) / $1,000 = –0.0355 or –3.55%∆P Hardy% = ($846.28 – 1,000) / $1,000 = –0.1537 or –15.37%If the YTM suddenly falls to 6 percent:P Laurel= $40(PVIFA3%,4) + $1,000(PVIF3%,4) = $1,037.17P Hardy= $40(PVIFA3%,30) + $1,000(PVIF3%,30) = $1,196.00∆P Laurel% = ($1,037.17 – 1,000) / $1,000 = +0.0372 or 3.72%∆P Hardy% = ($1,196.002 – 1,000) / $1,000 = +0.1960 or 19.60%All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in interest rates. Notice also that for the same interest rate change, the gain froma decline in interest rates is larger than the loss from the same magnitude change. For aplain vanilla bond, this is always true.15.Initially, at a YTM of 10 percent, the prices of the two bonds are:P Faulk= $30(PVIFA5%,16) + $1,000(PVIF5%,16) = $783.24P Gonas= $70(PVIFA5%,16) + $1,000(PVIF5%,16) = $1,216.76If the YTM rises from 10 percent to 12 percent:P Faulk= $30(PVIFA6%,16) + $1,000(PVIF6%,16) = $696.82P Gonas= $70(PVIFA6%,16) + $1,000(PVIF6%,16) = $1,101.06The percentage change in price is calculated as:Percentage change in price = (New price – Original price) / Original price∆P Faulk% = ($696.82 – 783.24) / $783.24 = –0.1103 or –11.03%∆P Gonas% = ($1,101.06 – 1,216.76) / $1,216.76 = –0.0951 or –9.51% If the YTM declines from 10 percent to 8 percent:P Faulk= $30(PVIFA4%,16) + $1,000(PVIF4%,16) = $883.48P Gonas= $70(PVIFA4%,16) + $1,000(PVIF4%,16) = $1,349.57∆P Faulk% = ($883.48 – 783.24) / $783.24 = +0.1280 or 12.80%∆P Gonas% = ($1,349.57 – 1,216.76) / $1,216.76 = +0.1092 or 10.92% All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates.16.The bond price equation for this bond is:P0 = $960 = $37(PVIFA R%,18) + $1,000(PVIF R%,18)Using a spreadsheet, financial calculator, or trial and error we find:R = 4.016%This is the semiannual interest rate, so the YTM is:YTM = 2 ⨯ 4.016% = 8.03%The current yield is:Current yield = Annual coupon payment / Price = $74 / $960 = .0771 or 7.71%The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter:Effective annual yield = (1 + 0.04016)2– 1 = .0819 or 8.19%17.The company should set the coupon rate on its new bonds equal to the required return.The required return can be observed in the market by finding the YTM on outstanding bonds of the company. So, the YTM on the bonds currently sold in the market is:P = $1,063 = $50(PVIFA R%,40) + $1,000(PVIF R%,40)Using a spreadsheet, financial calculator, or trial and error we find:R = 4.650%This is the semiannual interest rate, so the YTM is:YTM = 2 ⨯ 4.650% = 9.30%18. Accrued interest is the coupon payment for the period times the fraction of the periodthat has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = $84/2 × 4/6 = $28And we calculate the clean price as:Clean price = Dirty price – Accrued interest = $1,090 – 28 = $1,06219. Accrued interest is the coupon payment for the period times the fraction of the periodthat has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = $72/2 × 2/6 = $12.00And we calculate the dirty price as:Dirty price = Clean price + Accrued interest = $904 + 12 = $916.0020.To find the number of years to maturity for the bond, we need to find the price of thebond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as:Current yield = .0842 = $90/P0P0 = $90/.0842 = $1,068.88Now that we have the price of the bond, the bond price equation is:P = $1,068.88 = $90{[(1 – (1/1.0781)t ] / .0781} + $1,000/1.0781tWe can solve this equation for t as follows:$1,068.88 (1.0781)t = $1,152.37 (1.0781)t– 1,152.37 + 1,000152.37 = 83.49(1.0781)t1.8251 = 1.0781tt = log 1.8251 / log 1.0781 = 8.0004 ≈ 8 yearsThe bond has 8 years to maturity.21.The bond has 10 years to maturity, so the bond price equation is:P = $871.55 = $41.25(PVIFA R%,20) + $1,000(PVIF R%,20)Using a spreadsheet, financial calculator, or trial and error we find:R = 5.171%This is the semiannual interest rate, so the YTM is:YTM = 2 5.171% = 10.34%The current yield is the annual coupon payment divided by the bond price, so:Current yield = $82.50 / $871.55 = .0947 or 9.47%22.We found the maturity of a bond in Problem 20. However, in this case, the maturity isindeterminate. A bond selling at par can have any length of maturity. In other words, when we solve the bond pricing equation as we did in Problem 20, the number of periods can be any positive number.Challenge23.To find the capital gains yield and the current yield, we need to find the price of the bond.The current price of Bond P and the price of Bond P in one year is:P: P0 = $90(PVIFA7%,5) + $1,000(PVIF7%,5) = $1,082.00P1 = $90(PVIFA7%,4) + $1,000(PVIF7%,4) = $1,067.74Current yield = $90 / $1,082.00 = .0832 or 8.32%The capital gains yield is:Capital gains yield = (New price – Original price) / Original priceCapital gains yield = ($1,067.74 – 1,082.00) / $1,082.00 = –0.0132 or –1.32% The current price of Bond D and the price of Bond D in one year is:D: P0 = $50(PVIFA7%,5) + $1,000(PVIF7%,5) = $918.00P1 = $50(PVIFA7%,4) + $1,000(PVIF7%,4) = $932.26Current yield = $50 / $918.00 = 0.0545 or 5.45%Capital gains yield = ($932.26 – 918.00) / $918.00 = 0.0155 or 1.55% All else held constant, premium bonds pay a high current income while having price depreciation as maturity nears; discount bonds pay a lower current income but have price appreciation as maturity nears. For either bond, the total return is still 7%, but this return is distributed differently between current income and capital gains.24.a. The rate of return you expect to earn if you purchase a bond and hold it until maturity is the YTM. The bond price equation for this bond is:P0 = $1,140 = $90(PVIFA R%,10) + $1,000(PVIF R%,10)Using a spreadsheet, financial calculator, or trial and error we find:R = YTM = 7.01%b. To find our HPY, we need to find the price of the bond in two years. The price ofthe bond in two years, at the new interest rate, will be:P2 = $90(PVIFA6.01%,8) + $1,000(PVIF6.01%,8) = $1,185.87To calculate the HPY, we need to find the interest rate that equates the price wepaid for the bond with the cash flows we received. The cash flows we receivedwere $90 each year for two years, and the price of the bond when we sold it. Theequation to find our HPY is:P0 = $1,140 = $90(PVIFA R%,2) + $1,185.87(PVIF R%,2)Solving for R, we get:R = HPY = 9.81%The realized HPY is greater than the expected YTM when the bond was boughtbecause interest rates dropped by 1 percent; bond prices rise when yields fall.25.The price of any bond (or financial instrument) is the PV of the future cash flows. Eventhough Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is:P M = $800(PVIFA4%,16)(PVIF4%,12) + $1,000(PVIFA4%,12)(PVIF4%,28) +$20,000(PVIF4%,40)P M = $13,117.88Notice that for the coupon payments of $800, we found the PVA for the coupon payments, and then discounted the lump sum back to today.Bond N is a zero coupon bond with a $20,000 par value; therefore, the price of the bond is the PV of the par, or:P N = $20,000(PVIF4%,40) = $4,165.7826.To find the present value, we need to find the real weekly interest rate. To find the realreturn, we need to use the effective annual rates in the Fisher equation. So, we find the real EAR is:(1 + R) = (1 + r)(1 + h)1 + .107 = (1 + r)(1 + .035)r = .0696 or 6.96%Now, to find the weekly interest rate, we need to find the APR. Using the equation for discrete compounding:EAR = [1 + (APR / m)]m– 1We can solve for the APR. Doing so, we get:APR = m[(1 + EAR)1/m– 1]APR = 52[(1 + .0696)1/52– 1]APR = .0673 or 6.73%So, the weekly interest rate is:Weekly rate = APR / 52Weekly rate = .0673 / 52Weekly rate = .0013 or 0.13%Now we can find the present value of the cost of the roses. The real cash flows are an ordinary annuity, discounted at the real interest rate. So, the present value of the cost of the roses is:PVA = C({1 – [1/(1 + r)]t } / r)PVA = $8({1 – [1/(1 + .0013)]30(52)} / .0013)PVA = $5,359.6427.To answer this question, we need to find the monthly interest rate, which is the APRdivided by 12. We also must be careful to use the real interest rate. The Fisher equation uses the effective annual rate, so, the real effective annual interest rates, and the monthly interest rates for each account are:Stock account:(1 + R) = (1 + r)(1 + h)1 + .12 = (1 + r)(1 + .04)r = .0769 or 7.69%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0769)1/12– 1]APR = .0743 or 7.43%Monthly rate = APR / 12Monthly rate = .0743 / 12Monthly rate = .0062 or 0.62%Bond account:(1 + R) = (1 + r)(1 + h)1 + .07 = (1 + r)(1 + .04)r = .0288 or 2.88%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0288)1/12– 1]APR = .0285 or 2.85%Monthly rate = APR / 12Monthly rate = .0285 / 12Monthly rate = .0024 or 0.24%Now we can find the future value of the retirement account in real terms. The future value of each account will be:Stock account:FVA = C {(1 + r )t– 1] / r}FVA = $800{[(1 + .0062)360 – 1] / .0062]}FVA = $1,063,761.75Bond account:FVA = C {(1 + r )t– 1] / r}FVA = $400{[(1 + .0024)360 – 1] / .0024]}FVA = $227,089.04The total future value of the retirement account will be the sum of the two accounts, or: Account value = $1,063,761.75 + 227,089.04Account value = $1,290,850.79Now we need to find the monthly interest rate in retirement. We can use the same procedure that we used to find the monthly interest rates for the stock and bond accounts, so:(1 + R) = (1 + r)(1 + h)1 + .08 = (1 + r)(1 + .04)r = .0385 or 3.85%APR = m[(1 + EAR)1/m– 1]APR = 12[(1 + .0385)1/12– 1]APR = .0378 or 3.78%Monthly rate = APR / 12Monthly rate = .0378 / 12Monthly rate = .0031 or 0.31%Now we can find the real monthly withdrawal in retirement. Using the present value of an annuity equation and solving for the payment, we find:PVA = C({1 – [1/(1 + r)]t } / r )$1,290,850.79 = C({1 – [1/(1 + .0031)]300 } / .0031)C = $6,657.74This is the real dollar amount of the monthly withdrawals. The nominal monthly withdrawals will increase by the inflation rate each month. To find the nominal dollar amount of the last withdrawal, we can increase the real dollar withdrawal by the inflation rate. We can increase the real withdrawal by the effective annual inflation rate since we are only interested in the nominal amount of the last withdrawal. So, the last withdrawal in nominal terms will be: FV = PV(1 + r)tFV = $6,657.74(1 + .04)(30 + 25)FV = $57,565.3028.In this problem, we need to calculate the future value of the annual savings after the fiveyears of operations. The savings are the revenues minus the costs, or:Savings = Revenue – CostsSince the annual fee and the number of members are increasing, we need to calculate the effective growth rate for revenues, which is:Effective growth rate = (1 + .06)(1 + .03) – 1Effective growth rate = .0918 or 9.18%The revenue for the current year is the number of members times the annual fee, or:Current revenue = 500($500)Current revenue = $250,000The revenue will grow at 9.18 percent, and the costs will grow at 2 percent, so the savings each year for the next five years will be:Year Revenue Costs Savings1 $ 272,950.00 $ 76,500.00 $ 196,450.002 298,006.81 78,030.00 219,976.813 325,363.84 79,590.60 245,773.244 355,232.24 81,182.41 274,049.825 387,842.55 82,806.06 305,036.49Now we can find the value of each year’s savi ngs using the future value of a lump sum equation, so:FV = PV(1 + r)tYear Future Value1 $196,450.00(1 + .09)4 = $277,305.212 $219,976.81(1 + .09)3 = 284,876.353 $245,773.24(1 + .09)2 = 292,003.184 $274,049.82(1 + .09)1 = 298,714.315 305,036.49Total future value of savings = $1,457,935.54He will spend $500,000 on a luxury boat, so the value of his account will be:Value of account = $1,457,935.54 – 500,000Value of account = $957,935.54Now we can use the present value of an annuity equation to find the payment. Doing so, we find:PVA = C({1 – [1/(1 + r)]t } / r )$957,935.54 = C({1 – [1/(1 + .09)]25 } / .09)C = $97,523.83CHAPTER 91.We need to find the required return of the stock. Using the constant growth model, wecan solve the equation for R. Doing so, we find:R = (D1 / P0) + g = ($2.85 / $58) + .06 = .1091 or 10.91%2.The dividend yield is the dividend next year divided by the current price, so the dividendyield is:Dividend yield = D1 / P0 = $2.85 / $58 = .0491 or 4.91%The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so:Capital gains yield = 6%3.We know the stock has a required return of 13 percent, and the dividend and capitalgains yield are equal, so:Dividend yield = 1/2(.13) = .065 = Capital gains yieldNow we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so:D1 = .065($64) = $4.16This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year:D1 = D0(1 + g)We can solve for the dividend that was just paid:$4.16 = D0 (1 + .065)D0 = $4.16 / 1.065 = $3.914.The price of a share of preferred stock is the dividend divided by the required return.This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember that most preferred stock pays a fixed dividend, so the growth rate is zero. Using this equation, we find the price per share of the preferred stock is:R = D/P0 = $6.40/$103 = .0621 or 6.21%5.This stock has a constant growth rate of dividends, but the required return changes twice.To find the value of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever.The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So:P6 = D6(1 + g) / (R–g) = D0(1 + g)7/ (R–g) = $2.75(1.06)7/ (.11 – .06) = $82.70Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is:P3= $2.75(1.06)4/ 1.14 + $2.75(1.06)5/ 1.142 + $2.75(1.06)6/ 1.143 + $82.70 / 1.143 P3= $64.33Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is:P0= $2.75(1.06) / 1.16 + $2.75(1.06)2/ (1.16)2+ $2.75(1.06)3/ (1.16)3+ $64.33 /(1.16)3P0= $48.126.The price of a stock is the PV of the future dividends. This stock is paying five dividends,so the price of the stock is the PV of these dividends using the required return. The price of the stock is:P0 = $13 / 1.11 + $16 / 1.112 + $19 / 1.113 + $22 / 1.114 + $25 / 1.115 = $67.927.Here we need to find the dividend next year for a stock experiencing differential growth.We know the stock price, the dividend growth rates, and the required return, but not the dividend. First, we need to realize that the dividend in Year 3 is the current dividend times the FVIF. The dividend in Year 3 will be:D3 = D0(1.30)3And the dividend in Year 4 will be the dividend in Year 3 times one plus the growth rate, or:D4 = D0(1.30)3(1.18)The stock begins constant growth after the 4th dividend is paid, so we can find the price of the stock in Year 4 as the dividend in Year 5, divided by the required return minus the growth rate. The equation for the price of the stock in Year 4 is:P4= D4(1 + g) / (R– g)Now we can substitute the previous dividend in Year 4 into this equation as follows:P4 = D0(1 + g1)3(1 + g2) (1 + g3) / (R–g3)P4= D0(1.30)3(1.18) (1.08) / (.13 – .08) = 56.00D0When we solve this equation, we find that the stock price in Year 4 is 56.00 times as large as the dividend today. Now we need to find the equation for the stock price today.The stock price today is the PV of the dividends in Years 1, 2, 3, and 4, plus the PV of the Year 4 price. So:P0= D0(1.30)/1.13 + D0(1.30)2/1.132+ D0(1.30)3/1.133+ D0(1.30)3(1.18)/1.134+56.00D0/1.134We can factor out D0 in the equation, and combine the last two terms. Doing so, we get: P0 = $65.00 = D0{1.30/1.13 + 1.302/1.132 + 1.303/1.133 + [(1.30)3(1.18) + 56.00] / 1.134} Reducing the equation even further by solving all of the terms in the braces, we get:$65 = $39.86D0D0 = $65.00 / $39.86 = $1.63This is the dividend today, so the projected dividend for the next year will be:D1 = $1.63(1.30) = $2.128.The price of a share of preferred stock is the dividend payment divided by the requiredreturn. We know the dividend payment in Year 5, so we can find the price of the stock in Year 4, one year before the first dividend payment. Doing so, we get:P4 = $7.00 / .06 = $116.67The price of the stock today is the PV of the stock price in the future, so the price today will be:P0 = $116.67 / (1.06)4 = $92.419.To find the number of shares owned, we can divide the amount invested by the stockprice. The share price of any financial asset is the present value of the cash flows, so, tofind the price of the stock we need to find the cash flows. The cash flows are the two dividend payments plus the sale price. We also need to find the aftertax dividends since the assumption is all dividends are taxed at the same rate for all investors. The aftertax dividends are the dividends times one minus the tax rate, so:Year 1 aftertax dividend = $1.50(1 – .28)Year 1 aftertax dividend = $1.08Year 2 aftertax dividend = $2.25(1 – .28)Year 2 aftertax dividend = $1.62We can now discount all cash flows from the stock at the required return. Doing so, we find the price of the stock is:P = $1.08/1.15 + $1.62/(1.15)2 + $60/(1+.15)3P = $41.62The number of shares owned is the total investment divided by the stock price, which is: Shares owned = $100,000 / $41.62Shares owned = 2,402.9810.The required return of a stock consists of two components, the capital gains yield and thedividend yield. In the constant dividend growth model (growing perpetuity equation), the capital gains yield is the same as the dividend growth rate, or algebraically:R = D1/P0 + gWe can find the dividend growth rate by the growth rate equation, or:g = ROE ×bg = .16 × .80g = .1280 or 12.80%This is also the growth rate in dividends. To find the current dividend, we can use the information provided about the net income, shares outstanding, and payout ratio. The total dividends paid is the net income times the payout ratio. To find the dividend per share, we can divide the total dividends paid by the number of shares outstanding. So: Dividend per share = (Net income × Payout ratio) / Shares outstandingDividend per share = ($10,000,000 × .20) / 2,000,000Dividend per share = $1.00Now we can use the initial equation for the required return. We must remember that the equation uses the dividend in one year, so:R = D1/P0 + gR = $1(1 + .1280)/$85 + .1280R = .1413 or 14.13%11. a.If the company does not make any new investments, the stock price will be thepresent value of the constant perpetual dividends. In this case, all earnings are paiddividends, so, applying the perpetuity equation, we get:P = Dividend / RP = $8.25 / .12P = $68.75。

罗斯《公司理财》（第9版）课后习题第1章公司理财导论一、概念题1．资本预算（capital budgeting）答：资本预算是指综合反映投资资金来源与运用的预算，是为了获得未来产生现金流量的长期资产而现在投资支出的预算。

资本预算决策也称为长期投资决策，它是公司创造价值的主要方法。

资本预算决策一般指固定资产投资决策，耗资大，周期长，长期影响公司的产销能力和财务状况，决策正确与否影响公司的生存与发展。

完整的资本预算过程包括：寻找增长机会，制定长期投资战略，预测投资项目的现金流，分析评估投资项目，控制投资项目的执行情况。

资本预算可通过不同的资本预算方法来解决，如回收期法、净现值法和内部收益率法等。

2．货币市场（money markets）答：货币市场指期限不超过一年的资金借贷和短期有价证券交易的金融市场，亦称“短期金融市场”或“短期资金市场”，包括同业拆借市场、银行短期存贷市场、票据市场、短期证券市场、大额可转让存单市场、回购协议市场等。

其参加者为各种政府机构、各种银行和非银行金融机构及公司等。

货币市场具有四个基本特征：①融资期限短，一般在一年以内，最短的只有半天，主要用于满足短期资金周转的需要；②流动性强，金融工具可以在市场上随时兑现，交易对象主要是期限短、流动性强、风险小的信用工具，如票据、存单等，这些工具变现能力强，近似于货币，可称为“准货币”，故称货币市场；③安全性高，由于货币市场上的交易大多采用即期交易，即成交后马上结清，通常不存在因成交与结算日之间时间相对过长而引起价格巨大波动的现象，对投资者来说，收益具有较大保障；④政策性明显，货币市场由货币当局直接参加，是中央银行同商业银行及其他金融机构的资金连接的主渠道，是国家利用货币政策工具调节全国金融活动的杠杆支点。

货币市场的交易主体是短期资金的供需者。

需求者是为了获得现实的支付手段，调节资金的流动性并保持必要的支付能力，供应者提供的资金也大多是短期临时闲置性的资金。

罗斯《公司理财》第9版精要版英文原书课后部分章节答案详细»1 / 17 CH5 11，13，18，19，20 11. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = $1,000,000 / (1.10) 80 = $488.19 13. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r) t Solving for r, we get: r = (FV / PV) 1 / t –1 r = ($1,260,000 / $150) 1/112 – 1 = .0840 or 8.40% To find the FV of the first prize, we use: FV = PV(1 + r) t FV = $1,260,000(1.0840) 33 = $18,056,409.94 18. To find the FV of a lump sum, we use: FV = PV(1 + r) t FV = $4,000(1.11) 45 = $438,120.97 FV = $4,000(1.11) 35 = $154,299.40 Better start early! 19. We need to find the FV of a lump sum. However, the money will only be invested for six years, so the number of periods is six. FV = PV(1 + r) t FV = $20,000(1.084)6 = $32,449.33 20. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r) t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln($75,000 / $10,000) / ln(1.11) = 19.31 So, the money must be invested for 19.31 years. However, you will not receive the money for another two years. From now, you’ll wait: 2 years + 19.31 years = 21.31 years CH6 16，24，27，42，58 16. For this problem, we simply need to find the FV of a lump sum using the equation: FV = PV(1 + r) t 2 / 17 It is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get: FV = $2,100[1 + (.084/2)] 34 = $8,505.93 24. This problem requires us to find the FV A. The equation to find the FV A is: FV A = C{[(1 + r) t – 1] / r} FV A = $300[{[1 + (.10/12) ] 360 – 1} / (.10/12)] = $678,146.38 27. The cash flows are annual and the compounding period is quarterly, so we need to calculate the EAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get: EAR = [1 + (APR / m)] m – 1 EAR = [1 + (.11/4)] 4 – 1 = .1146 or 11.46% And now we use the EAR to find the PV of each cash flow as a lump sum and add them together: PV = $725 / 1.1146 + $980 / 1.1146 2 + $1,360 / 1.1146 4 = $2,320.36 42. The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the $1,150 monthly payments is: PV A = $1,150[(1 – {1 / [1 + (.0635/12)]} 360 ) / (.0635/12)] = $184,817.42 The monthly payments of $1,150 will amount to a principal payment of $184,817.42. The amount of principal you will still owe is: $240,000 – 184,817.42 = $55,182.58 This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be: Balloon payment = $55,182.58[1 + (.0635/12)] 360 = $368,936.54 58. To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is: PV = $99 + $450{1 –[1 / (1 + .07/12) 12(3) ]} / (.07/12) = $14,672.91 The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is: PV = $23,000 / [1 + (.07/12)] 12(3) = $18,654.82 The PV of the decision to purchase is: $32,000 – 18,654.82 = $13,345.18 3 / 17 In this case, it is cheaper to buy the car than leasing it since the PV of the purchase cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same. In other words, the PV of the decision to buy should be: $32,000 – PV of resale price = $14,672.91 PV of resale price = $17,327.09 The resale price that would make the PV of the lease versus buy decision is the FV ofthis value, so: Breakeven resale price = $17,327.09[1 + (.07/12)] 12(3) = $21,363.01 CH7 3，18，21，22，31 3. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = $75({1 – [1/(1 + .0875)] 10 } / .0875) + $1,000[1 / (1 + .0875) 10 ] = $918.89 We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PV A equation, it is common to abbreviate the equations as: PVIF R,t = 1 / (1 + r) t which stands for Present V alue Interest Factor PVIFA R,t = ({1 – [1/(1 + r)] t } / r ) which stands for Present V alue Interest Factor of an Annuity These abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key. 18. The bond price equation for this bond is: P 0 = $1,068 = $46(PVIFA R%,18 ) + $1,000(PVIF R%,18 ) Using a spreadsheet, financial calculator, or trial and error we find: R = 4.06% This is thesemiannual interest rate, so the YTM is: YTM = 2 4.06% = 8.12% The current yield is:Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61% The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield = (1 + 0.0406) 2 – 1 = .0829 or 8.29% 20. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $74/2 × 2/6 = $12.33 And we calculate the clean price as: 4 / 17 Clean price = Dirty price –Accrued interest = $968 –12.33 = $955.67 21. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $68/2 × 4/6 = $22.67 And we calculate the dirty price as: Dirty price = Clean price + Accrued interest = $1,073 + 22.67 = $1,095.67 22. To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as: Current yield = .0755 = $80/P 0 P 0 = $80/.0755 = $1,059.60 Now that we have the price of the bond, the bond price equation is: P = $1,059.60 = $80[(1 – (1/1.072) t ) / .072 ] + $1,000/1.072 t We can solve this equation for t as follows: $1,059.60(1.072) t = $1,111.11(1.072) t –1,111.11 + 1,000 111.11 = 51.51(1.072) t2.1570 = 1.072 t t = log 2.1570 / log 1.072 = 11.06 11 years The bond has 11 years to maturity.31. The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is: P M = $1,100(PVIFA 3.5%,16 )(PVIF 3.5%,12 ) + $1,400(PVIFA3.5%,12 )(PVIF 3.5%,28 ) + $20,000(PVIF 3.5%,40 ) P M = $19,018.78 Notice that for the coupon payments of $1,400, we found the PV A for the coupon payments, and then discounted the lump sum back to today. Bond N is a zero coupon bond with a $20,000 par value, therefore, the price of the bond is the PV of the par, or: P N = $20,000(PVIF3.5%,40 ) = $5,051.45 CH8 4，18，20，22，244. Using the constant growth model, we find the price of the stock today is: P 0 = D 1 / (R – g) = $3.04 / (.11 – .038) = $42.22 5 / 17 18. The price of a share of preferred stock is the dividend payment divided by the required return. We know the dividend payment in Year 20, so we can find the price of the stock in Y ear 19, one year before the first dividend payment. Doing so, we get: P 19 = $20.00 / .064 P 19 = $312.50 The price of the stock today is the PV of the stock price in the future, so the price today will be: P 0 = $312.50 / (1.064) 19 P 0 = $96.15 20. We can use the two-stage dividend growth model for this problem, which is: P 0 = [D 0 (1 + g 1 )/(R – g 1 )]{1 – [(1 + g 1 )/(1 + R)] T }+ [(1 + g 1 )/(1 + R)] T [D 0 (1 + g 2 )/(R –g 2 )] P0 = [$1.25(1.28)/(.13 –.28)][1 –(1.28/1.13) 8 ] + [(1.28)/(1.13)] 8 [$1.25(1.06)/(.13 – .06)] P 0 = $69.55 22. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield. W: P 0 = D 0 (1 + g) / (R – g) = $4.50(1.10)/(.19 – .10) = $55.00 Dividend yield = D 1 /P 0 = $4.50(1.10)/$55.00 = .09 or 9% Capital gains yield = .19 – .09 = .10 or 10% X: P 0 = D 0 (1 + g) / (R – g) = $4.50/(.19 – 0) = $23.68 Dividend yield = D 1 /P 0 = $4.50/$23.68 = .19 or 19% Capital gains yield = .19 – .19 = 0% Y: P 0 = D 0 (1 + g) / (R – g) = $4.50(1 – .05)/(.19 + .05) = $17.81 Dividend yield = D 1 /P 0 = $4.50(0.95)/$17.81 = .24 or 24% Capital gains yield = .19 – .24 = –.05 or –5% Z: P 2 = D 2 (1 + g) / (R – g) = D 0 (1 + g 1 ) 2 (1 +g 2 )/(R – g 2 ) = $4.50(1.20) 2 (1.12)/(.19 – .12) = $103.68 P 0 = $4.50 (1.20) / (1.19) + $4.50(1.20) 2 / (1.19) 2 + $103.68 / (1.19) 2 = $82.33 Dividend yield = D 1 /P 0 = $4.50(1.20)/$82.33 = .066 or 6.6% Capital gains yield = .19 – .066 = .124 or 12.4% In all cases, the required return is 19%, but the return is distributed differently between current income and capital gains. High growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time. 24. Here we have a stock with supernormal growth, but the dividend growth changes every year for the first four years. We can find the price of the stock in Y ear 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Y ear 3 will be the dividend in Y ear 4, divided by the required return minus the constant dividend growth rate. So, the price in Y ear 3 will be: 6 / 17 P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08 The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Y ear 3, so: P 0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.11 2 + $2.45(1.20)(1.15)(1.10)/1.11 3 + $65.08/1.11 3 P 0 = $55.70 CH9 3，4，6，9，15 3. Project A has cash flows of $19,000 in Y ear 1, so the cash flows are short by $21,000 of recapturing the initial investment, so the payback for Project A is: Payback = 1 + ($21,000 / $25,000) = 1.84 years Project B has cash flows of: Cash flows = $14,000 + 17,000 + 24,000 = $55,000 during this first three years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project B is: B: Payback = 3 + ($5,000 / $270,000) = 3.019 years Using the payback criterion and a cutoff of 3 years, accept project A and reject project B. 4. When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: V alue today of Y ear 1 cash flow = $4,200/1.14 = $3,684.21 V alue today of Y ear 2 cash flow = $5,300/1.14 2 = $4,078.18 V alue today of Y ear 3 cash flow = $6,100/1.14 3 = $4,117.33 V alue today of Y ear 4 cash flow = $7,400/1.14 4 = $4,381.39 To findthe discounted payback, we use these values to find the payback period. The discounted first year cash flow is $3,684.21, so the discounted payback for a $7,000 initial cost is: Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 years For an initial cost of $10,000, the discounted payback is: Discounted payback = 2 + ($10,000 –3,684.21 –4,078.18)/$4,117.33 = 2.54 years Notice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Y ear 1 and Y ear 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Y ear 3 to get the fractional portion of the discounted payback. If the initial cost is $13,000, the discounted payback is: Discounted payback = 3 + ($13,000 – 3,684.21 – 4,078.18 – 4,117.33) / $4,381.39 = 3.26 years 7 / 17 6. Our definition of AAR is the average net income divided by the average book value. The average net income for this project is: A verage net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325 And the average book value is: A verage book value = ($15,000,000 + 0) / 2 = $7,500,000 So, the AAR for this project is: AAR = A verage net income / A verage book value = $1,836,325 / $7,500,000 = .2448 or 24.48% 9. The NPV of a project is the PV of the outflows minus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = –$138,000 + $28,500(PVIFA 8%, 9 ) = $40,036.31 At an 8 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 20 percent required return is: NPV = –$138,000 + $28,500(PVIFA 20%, 9 ) = –$23,117.45 At a 20 percent required return, the NPV is negative, so we would reject the project. We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = –$138,000 + $28,500(PVIFA IRR, 9 ) IRR = 14.59% 15. The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The equation for the profitability index at a required return of 10 percent is: PI = [$7,300/1.1 + $6,900/1.1 2 + $5,700/1.1 3 ] / $14,000 = 1.187 The equation for the profitability index at a required return of 15 percent is: PI = [$7,300/1.15 + $6,900/1.15 2 + $5,700/1.15 3 ] / $14,000 = 1.094 The equation for the profitability index at a required return of 22 percent is: PI = [$7,300/1.22 + $6,900/1.22 2 + $5,700/1.22 3 ] / $14,000 = 0.983 8 / 17 We would accept the project if the required return were 10 percent or 15 percent since the PI is greater than one. We would reject the project if the required return were 22 percent since the PI。

CHAPTER 9RISK ANALYSIS, REAL OPTIONS, AND CAPITAL BUDGETINGAnswers to Concepts Review and Critical Thinking Questions1.Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows.The danger is greatest with a new product because the cash flows are probably harder to predict.2.With a sensitivity analysis, one variable is examined over a broad range of values. With a scenarioanalysis, all variables are examined for a limited range of values.3.It is true that if average revenue is less than average cost, the firm is losing money. This much of thestatement is therefore correct. At the margin, however, accepting a project with marginal revenue in excess of its marginal cost clearly acts to increase operating cash flow.4.From the shareholder perspective, the financial break-even point is the most important. A project canexceed the accounting and cash break-even points but still be below the financial break-even point.This causes a reduction in shareholder (your) wealth.5.The project will reach the cash break-even first, the accounting break-even next and finally thefinancial break-even. For a project with an initial investment and sales after, this ordering will always apply. The cash break-even is achieved first since it excludes depreciation. The accounting break-even is next since it includes depreciation. Finally, the financial break-even, which includes the time value of money, is achieved.6.Traditional NPV analysis is often too conservative because it ignores profitable options such as theability to expand the project if it is profitable, or abandon the project if it is unprofitable. The option to alter a project when it has already been accepted has a value, which increases the NPV of the project.7.The type of option most likely to affect the decision is the option to expand. If the country justliberalized its markets, there is likely the potential for growth. First entry into a market, whether an entirely new market, or with a new product, can give a company name recognition and market share.This may make it more difficult for competitors entering the market.8.Sensitivity analysis can determine how the financial break-even point changes when some factors(such as fixed costs, variable costs, or revenue) change.9.There are two sources of value with this decision to wait. Potentially, the price of the timber canpotentially increase, and the amount of timber will almost definitely increase, barring a natural catastrophe or forest fire. The option to wait for a logging company is quite valuable, and companies in the industry have models to estimate the future growth of a forest depending on its age.10.When the additional analysis has a negative NPV. Since the additional analysis is likely to occuralmost immediately, this means when the benefits of the additional analysis outweigh the costs. The benefits of the additional analysis are the reduction in the possibility of making a bad decision. Of course, the additional benefits are often difficult, if not impossible, to measure, so much of this decision is based on experience.Solutions to Questions and ProblemsNOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1.a. To calculate the accounting breakeven, we first need to find the depreciation for each year. Thedepreciation is:Depreciation = $896,000/8Depreciation = $112,000 per yearAnd the accounting breakeven is:Q A = ($900,000 + 112,000)/($38 – 25)Q A = 77,846 unitsb.We will use the tax shield approach to calculate the OCF. The OCF is:OCF base = [(P – v)Q – FC](1 – t c) + t c DOCF base = [($38 – 25)(100,000) – $900,000](0.65) + 0.35($112,000)OCF base = $299,200Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is:NPV base = –$896,000 + $299,200(PVIFA15%,8)NPV base = $446,606.60To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 105,000 units. The NPV at this sales level is:OCF new = [($38 – 25)(105,000) – $900,000](0.65) + 0.35($112,000)OCF new = $341,450And the NPV is:NPV new = –$896,000 + $341,450(PVIFA15%,8)NPV new = $636,195.93So, the change in NPV for every unit change in sales is:∆NPV/∆S = ($636,195.93 – 446,606.60)/(105,000 – 100,000)∆NPV/∆S = +$37.918If sales were to drop by 100 units, then NPV would drop by:NPV drop = $37.918(100) = $3,791.80You may wonder why we chose 105,000 units. Because it doesn’t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same.c.To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at avariable cost of $24. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use.So, using the tax shield approach, the OCF at a variable cost of $24 is:OCF new = [($38 – 24)(100,000) – 900,000](0.65) + 0.35($112,000)OCF new = $364,200So, the change in OCF for a $1 change in variable costs is:∆OCF/∆v = ($299,200 – 364,200)/($25 – 24)∆OCF/∆v = –$65,000If variable costs decrease by $5 then, OCF would increase byOCF increase = $65,000*5 = $325,0002.We will use the tax shield approach to calculate the OCF for the best- and worst-case scenarios. Forthe best-case scenario, the price and quantity increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. Doing so, we get:OCF best = {[($38)(1.1) – ($25)(0.9)](100K)(1.1) – $900K(0.9)}(0.65) + 0.35($112K)OCF best = $892,650The best-case NPV is:NPV best = –$896,000 + $892,650(PVIFA15%,8)NPV best = $3,109,607.54For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. Doing so, we get: OCF worst = {[($38)(0.9) – ($25)(1.1)](100K)(0.9) – $900K(1.1)}(0.65) + 0.35($112K)OCF worst = –212,350The worst-case NPV is:NPV worst = –$896,000 – $212,350(PVIFA15%,8)NPV worst = –$1,848,882.723.We can use the accounting breakeven equation:Q A = (FC + D)/(P – v)to solve for the unknown variable in each case. Doing so, we find:(1): Q A = 130,200 = (€850,000 + D)/(€41 – 30)D = €582,200(2): Q A = 135,000 = (€3.2M + 1.15M)/(P –€56)P = €88.22(3): Q A = 5,478 = (€160,000 + 105,000)/(€105 – v)v = €56.624.When calculating the financial breakeven point, we express the initial investment as an equivalentannual cost (EAC). Dividing the in initial investment by the seven-year annuity factor, discounted at12 percent, the EAC of the initial investment is:EAC = Initial Investment / PVIFA12%,5EAC = £200,000 / 3.60478EAC = £55,481.95Note, this calculation solves for the annuity payment with the initial investment as the present value of the annuity, in other words:PVA = C({1 – [1/(1 + R)]t } / R)£200,000 = C{[1 – (1/1.12)5 ] / .12}C = £55,481.95The annual depreciation is the cost of the equipment divided by the economic life, or:Annual depreciation = £200,000 / 5Annual depreciation = £40,000Now we can calculate the financial breakeven point. The financial breakeven point for this project is: Q F = [EAC + FC(1 – t C) – Depreciation(t C)] / [(P – VC)(1 – t C)]Q F = [£55,481.95 + £350,000(.75) – £40,000(0.25)] / [(£25 – 5) (.25)]Q F = 20,532.13 or about 20,532 units5.If we purchase the machine today, the NPV is the cost plus the present value of the increased cashflows, so:NPV0 = –฿1,500,000 + ฿280,000(PVIFA12%,10)NPV0 = ฿82,062.45We should not purchase the machine today. We would want to purchase the machine when the NPV is the highest. So, we need to calculate the NPV each year. The NPV each year will be the cost plus the present value of the increased cash savings. We must be careful however. In order to make the correct decision, the NPV for each year must be taken to a common date. We will discount all of the NPVs to today. Doing so, we get:Year 1: NPV1 = [–฿1,375,000 + ฿280,000(PVIFA12%,9)] / 1.12NPV1 = ฿104,383.88Year 2: NPV2 = [–฿1,250,000 + ฿280,000(PVIFA12%,8)] / 1.122NPV2 = ฿112,355.82Year 3: NPV3 = [–฿1,125,000 + ฿280,000(PVIFA12%,7)] / 1.123NPV3 = ฿108,796.91Year 4: NPV4 = [–฿1,000,000 + ฿280,000(PVIFA12%,6)] / 1.124NPV4 = ฿96,086.55Year 5: NPV5 = [–฿1,000,000 + ฿280,000(PVIFA12%,5)] / 1.125NPV5 = ฿5,298.26Year 6: NPV6 = [–฿1,000,000 + ฿280,000(PVIFA12%,4)] / 1.126NPV6 = –฿75,762.72The company should purchase the machine two years from now when the NPV is the highest.6.We need to calculate the NPV of the two options, go directly to market now, or utilize test marketingfirst. The NPV of going directly to market now is:NPV = C Success (Prob. of Success) + C Failure (Prob. of Failure)NPV = $20,000,000(0.45) + $5,000,000(0.55)NPV = $11,750,000Now we can calculate the NPV of test marketing first. Test marketing requires a $2 million cashoutlay. Choosing the test marketing option will also delay the launch of the product by one year.Thus, the expected payoff is delayed by one year and must be discounted back to year 0.NPV= C0 + {[C Success (Prob. of Success)] + [C Failure (Prob. of Failure)]} / (1 + R)tNPV = –$2,000,000 + {[$20,000,000 (0.75)] + [$5,000,000 (0.25)]} / 1.15NPV = $12,130,434.78The company should not go directly to market with the product since that option has lower expected payoff.7.We need to calculate the NPV of each option, and choose the option with the highest NPV. So, theNPV of going directly to market is:NPV = C Success (Prob. of Success)NPV = Rs.1,200,000 (0.55)NPV = Rs.660,000The NPV of the focus group is:NPV = C0 + C Success (Prob. of Success)NPV = –Rs.120,000 + Rs.1,200,000 (0.70)NPV = Rs.720,000And the NPV of using the consulting firm is:NPV = C0 + C Success (Prob. of Success)NPV = –Rs.400,000 + Rs.1,200,000 (0.90)NPV = Rs.680,000The firm should conduct a focus group since that option has the highest NPV.8.The company should analyze both options, and choose the option with the greatest NPV. So, if thecompany goes to market immediately, the NPV is:NPV = C Success (Prob. of Success) + C Failure (Prob. of Failure)NPV = ₦30,000,000(.55) + ₦3,000,000(.45)NPV = ₦17,850,000.00Customer segment research requires a ₦1 million cash outlay. Choosing the research option will also delay the launch of the product by one year. Thus, the expected payoff is delayed by one year and must be discounted back to year 0. So, the NPV of the customer segment research is:NPV= C0 + {[C Success (Prob. of Success)] + [C Failure (Prob. of Failure)]} / (1 + R)tNPV = –₦1,000,000 + {[₦30,000,000 (0.70)] + [₦3,000,000 (0.30)]} / 1.15NPV = ₦18,043,478.26Graphically, the decision tree for the project is:₦3 million at t = 0The company should undertake the market segment research since it has the largest NPV.9. a.The accounting breakeven is the aftertax sum of the fixed costs and depreciation charge dividedby the aftertax contribution margin (selling price minus variable cost). So, the accounting breakeven level of sales is:Q A = [(FC + Depreciation)(1 – t C)] / [(P – VC)(1 – t C)]Q A = [($340,000 + $20,000) (1 – 0.35)] / [($2.00 – 0.72) (1 – 0.35)]Q A = 281,250.00b.When calculating the financial breakeven point, we express the initial investment as anequivalent annual cost (EAC). Dividing the in initial investment by the seven-year annuity factor, discounted at 15 percent, the EAC of the initial investment is:EAC = Initial Investment / PVIFA15%,7EAC = $140,000 / 4.1604EAC = $33,650.45Note, this calculation solves for the annuity payment with the initial investment as the presentvalue of the annuity, in other words:PVA = C({1 – [1/(1 + R)]t } / R)$140,000 = C{[1 – (1/1.15)7 ] / .15}C = $33,650.45Now we can calculate the financial breakeven point. The financial breakeven point for this project is:Q F = [EAC + FC(1 – t C) – Depreciation(t C)] / [(P – VC)(1 – t C)]Q F = [$33,650.45 + $340,000(.65) – $20,000(.35)] / [($2 – 0.72) (.65)]Q F = 297,656.79 or about 297,657 units10.When calculating the financial breakeven point, we express the initial investment as an equivalentannual cost (EAC). Dividing the in initial investment by the five-year annuity factor, discounted at 8 percent, the EAC of the initial investment is:EAC = Initial Investment / PVIFA8%,5EAC = ¥300,000 / 3.60478EAC = ¥75,136.94Note, this calculation solves for the annuity payment with the initial investment as the present value of the annuity, in other words:PVA = C({1 – [1/(1 + R)]t } / R)¥300,000 = C{[1 – (1/1.08)5 ] / .08}C = ¥75,136.94The annual depreciation is the cost of the equipment divided by the economic life, or:Annual depreciation = ¥300,000 / 5Annual depreciation = ¥60,000Now we can calculate the financial breakeven point. The financial breakeven point for this project is: Q F = [EAC + FC(1 – t C) – Depreciation(t C)] / [(P – VC)(1 – t C)]Q F = [¥75,136.94 + ¥100,000(.66) – ¥60,000(0.34)] / [(¥60 – 8) (.34)]Q F = 3,517.98 or about 3,518 unitsIntermediate11.a. At the accounting breakeven, the IRR is zero percent since the project recovers the initialinvestment. The payback period is N years, the length of the project since the initial investmentis exactly recovered over the project life. The NPV at the accounting breakeven is:NPV = I [(1/N)(PVIFA R%,N) – 1]b. At the cash breakeven level, the IRR is –100 percent, the payback period is negative, and theNPV is negative and equal to the initial cash outlay.c. The definition of the financial breakeven is where the NPV of the project is zero. If this is true,then the IRR of the project is equal to the required return. It is impossible to state the paybackperiod, except to say that the payback period must be less than the length of the project. Sincethe discounted cash flows are equal to the initial investment, the undiscounted cash flows aregreater than the initial investment, so the payback must be less than the project life.ing the tax shield approach, the OCF at 110,000 units will be:OCF = [(P – v)Q – FC](1 – t C) + t C(D)OCF = [($28 – 19)(110,000) – 150,000](0.66) + 0.34($420,000/4)OCF = $590,100We will calculate the OCF at 111,000 units. The choice of the second level of quantity sold is arbitrary and irrelevant. No matter what level of units sold we choose, we will still get the same sensitivity. So, the OCF at this level of sales is:OCF = [($28 – 19)(111,000) – 150,000](0.66) + 0.34($420,000/4)OCF = $596,040The sensitivity of the OCF to changes in the quantity sold is:Sensitivity = ∆OCF/∆Q = ($596,040 – 590,100)/(111,000 – 110,000)∆OCF/∆Q = +$5.94OCF will increase by $5.94 for every additional unit sold.13.a. The base-case, best-case, and worst-case values are shown below. Remember that in the best-case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease,and costs increase.Scenario Unit sales Variable cost Fixed costsBase 190 元15,000 元225,000Best 209 元13,500 元202,500Worst 171 元16,500 元247,500Using the tax shield approach, the OCF and NPV for the base case estimate is:OCF base = [(元21,000 – 15,000)(190) –元225,000](0.65) + 0.35(元720,000/4)OCF base = 元657,750NPV base = –元720,000 + 元657,750(PVIFA15%,4)NPV base = 元1,157,862.02The OCF and NPV for the worst case estimate are:OCF worst = [(元21,000 – 16,500)(171) –元247,500](0.65) + 0.35(元720,000/4)OCF worst = 元402,300NPV worst = –元720,000 + 元402,300(PVIFA15%,4)NPV worst = +元428,557.80And the OCF and NPV for the best case estimate are:OCF best = [(元21,000 – 13,500)(209) –元202,500](0.65) + 0.35(元720,000/4)OCF best = 元950,250NPV best = –元720,000 + 元950,250(PVIFA15%,4)NPV best = 元1,992,943.19b. To calculate the sensitivity of the NPV to changes in fixed costs we choose another level offixed costs. We will use fixed costs of 元230,000. The OCF using this level of fixed costs and the other base case values with the tax shield approach, we get:OCF = [(元21,000 – 15,000)(190) –元230,000](0.65) + 0.35(元720,000/4)OCF = 元654,500And the NPV is:NPV = –元720,000 + 元654,500(PVIFA15%,4)NPV = 元1,148,583.34The sensitivity of NPV to changes in fixed costs is:∆NPV/∆FC = (元1,157,862.02 – 1,148,583.34)/(元225,000 – 230,000)∆NPV/∆FC = –元1.856For every dollar FC increase, NPV falls by 元1.86.c. The accounting breakeven is:Q A= (FC + D)/(P – v)Q A = [元225,000 + (元720,000/4)]/(元21,000 – 15,000)Q A = 68At the accounting breakeven, the DOL is:DOL = 1 + FC/OCFDOL = 1 + (元225,000/元180,000) = 2.25For each 1% increase in unit sales, OCF will increase by 2.25%.14.The marketing study and the research and development are both sunk costs and should be ignored.We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €700 ⨯ 55,000 = €38,500,000Exp. clubs €1,100 ⨯ (–13,000) = –14,300,000Cheap clubs €400 ⨯ 10,000 = 4,000,000€28,200,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs –€320 ⨯ 55,000 = –€17,600,000Exp. clubs –€600 ⨯ (–13,000) = 7,800,000Cheap clubs –€180 ⨯ 10,000 = –1,800,000–€11,600,000The pro forma income statement will be:Sales €28,200,000Variable costs 11,600,000Costs 7,500,000Depreciation 2,600,000EBT 6,500,000Taxes 2,600,000Net income € 3,900,000Using the bottom up OCF calculation, we get:OCF = NI + Depreciation = €3,900,000 + 2,600,000OCF = €6,500,000So, the payback period is:Payback period = 2 + €6.15M/€6.5MPayback period = 2.946 yearsThe NPV is:NPV = –€18.2M – .95M + €6.5M(PVIFA14%,7) + €0.95M/1.147NPV = €9,103,636.91And the IRR is:IRR = –€18.2M – .95M + €6.5M(PVIFA IRR%,7) + €0.95M/IRR7IRR = 28.24%15.The upper and lower bounds for the variables are:Base Case Lower Bound Upper Bound Unit sales (new) 55,000 49,500 60,500Price (new) €700 €630 €770VC (new) €320 €288 €352Fixed costs €7,500,000 €6,750,000 €8,250,000Sales lost (expensive) 13,000 11,700 14,300Sales gained (cheap) 10,000 9,000 11,000 Best-caseWe will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €770 ⨯ 60,500 = €46,585,000Exp. clubs €1,100 ⨯ (–11,700) = – 12,870,000Cheap clubs €400 ⨯ 11,000 = 4,400,000€38,115,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs €288 ⨯ 60,500 = €17,424,000Exp. clubs €600 ⨯ (–11,700) = – 7,020,000Cheap clubs €180 ⨯ 11,000 = 1,980,000€12,384,000Sales €38,115,000Variable costs 12,384,000Costs 6,750,000Depreciation 2,600,000EBT 16,381,000Taxes 6,552,400Net income €9,828,600Using the bottom up OCF calculation, we get:OCF = Net income + Depreciation = €9,828,600 + 2,600,000OCF = €12,428,600And the best-case NPV is:NPV = –€18.2M – .95M + €12,428,600(PVIFA14%,7) + .95M/1.147NPV = €34,527,280.98Worst-caseWe will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €630 ⨯ 49,500 = €31,185,000Exp. clubs €1,100 ⨯ (– 14,300) = – 15,730,000Cheap clubs €400 ⨯ 9,000 = 3,600,000€19,055,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs €352 ⨯ 49,500 = €17,424,000Exp. clubs €600 ⨯ (– 14,300) = – 8,580,000Cheap clubs €180 ⨯ 9,000 = 1,620,000€10,464,000Sales €19,055,000Variable costs 10,464,000Costs 8,250,000Depreciation 2,600,000EBT – 2,259,000Taxes 903,600 *assumes a tax creditNet income –€1,355,400Using the bottom up OCF calculation, we get:OCF = NI + Depreciation = –€1,355,400 + 2,600,000OCF = €1,244,600And the worst-case NPV is:NPV = –€18.2M – .95M + €1,244,600(PVIFA14%,7) + .95M/1.147NPV = –€13,433,120.3416.To calculate the sensitivity of the NPV to changes in the price of the new club, we simply need tochange the price of the new club. We will choose €750, but the choice is irrelevant as the sensitivity will be the same no matter what price we choose.We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €750 ⨯ 55,000 = €41,250,000Exp. clubs €1,100 ⨯ (– 13,000) = –14,300,000Cheap clubs €400 ⨯ 10,000 = 4,000,000€30,950,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs €320 ⨯ 55,000 = €17,600,000Exp. clubs €600 ⨯ (–13,000) = –7,800,000Cheap clubs €180 ⨯ 10,000 = 1,800,000€11,600,000Sales €30,950,000Variable costs 11,600,000Costs 7,500,000Depreciation 2,600,000EBT 9,250,000Taxes 3,700,000Net income € 5,550,000Using the bottom up OCF calculation, we get:OCF = NI + Depreciation = €5,550,000 + 2,600,000OCF = €8,150,000And the NPV is:NPV = –€18.2M – 0.95M + €8.15M(PVIFA14%,7) + .95M/1.147NPV = €16,179,339.89So, the sensitivity of the NPV to changes in the price of the new club is:∆NPV/∆P = (€16,179,339.89 – 9,103,636.91)/(€750 – 700)∆NPV/∆P = €141,514.06For every euro increase (decrease) in the price of the clubs, the NPV increases (decreases) by €141,514.06.To calculate the sensitivity of the NPV to changes in the quantity sold of the new club, we simply need to change the quantity sold. We will choose 60,000 units, but the choice is irrelevant as the sensitivity will be the same no matter what quantity we choose.We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be:SalesNew clubs €700 ⨯ 60,000 = €42,000,000Exp. clubs €1,100 ⨯ (– 13,000) = –14,300,000Cheap clubs €400 ⨯ 10,000 = 4,000,000€31,700,000For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will save these variable costs, which is an inflow. So:Var. costsNew clubs €320 ⨯ 60,000 = €19,200,000Exp. clubs €600 ⨯ (–13,000) = –7,800,000Cheap clubs €180 ⨯ 10,000 = 1,800,000€13,200,000The pro forma income statement will be:Sales €31,700,000Variable costs 13,200,000Costs 7,500,000Depreciation 2,600,000EBT 8,400,000Taxes 3,360,000Net income € 5,040,000Using the bottom up OCF calculation, we get:OCF = NI + Depreciation = €5,040,000 + 2,600,000OCF = €7,640,000The NPV at this quantity is:NPV = –€18.2M –€0.95M + €7.64(PVIFA14%,7) + €0.95M/1.147NPV = €13,992,304.43So, the sensitivity of the NPV to changes in the quantity sold is:∆NPV/∆Q = (€13,992,304.43 – 9,103,636.91)/(60,000 – 55,000)∆NPV/∆Q = €977.73For an increase (decrease) of one set of clubs sold per year, the NPV increases (decreases) by€977.73.17.a. The base-case NPV is:NPV = –£1,750,000 + £420,000(PVIFA16%,10)NPV = £279,955.54b.We would abandon the project if the cash flow from selling the equipment is greater than thepresent value of the future cash flows. We need to find the sale quantity where the two are equal, so:£1,500,000 = (£60)Q(PVIFA16%,9)Q = £1,500,000/[£60(4.6065)]Q = 5,427.11Abandon the project if Q < 5,428 units, because the NPV of abandoning the project is greater than the NPV of the future cash flows.c.The £1,500,000 is the market value of the project. If you continue with the project in one year,you forego the £1,500,000 that could have been used for something else.18. a.If the project is a success, present value of the future cash flows will be:PV future CFs = £60(9,000)(PVIFA16%,9)PV future CFs = £2,487,533.69From the previous question, if the quantity sold is 4,000, we would abandon the project, and the cash flow would be £1,500,000. Since the project has an equal likelihood of success or failure in one year, the expected value of the project in one year is the average of the success and failure cash flows, plus the cash flow in one year, so:Expected value of project at year 1 = [(£2,487,533.69 + £1,500,000)/2] + £420,000Expected value of project at year 1 = £2,413,766.85The NPV is the present value of the expected value in one year plus the cost of the equipment, so:NPV = –£1,750,000 + (£2,413,766.85)/1.16NPV = £330,833.49b. If we couldn’t abandon the project, the present value of the fut ure cash flows when the quantityis 4,000 will be:PV future CFs = £60(4,000)(PVIFA16%,9)PV future CFs = £1,105,570.53The gain from the option to abandon is the abandonment value minus the present value of the cash flows if we cannot abandon the project, so:Gain from option to abandon = £1,500,000 – 1,105,570.53Gain from option to abandon = £394,429.47We need to find the value of the option to abandon times the likelihood of abandonment. So, the value of the option to abandon today is:Option value = (.50)(£394,429.47)/1.16Option value = £170,012.70。

公司理财习题答案第九章Chapter 9: Capital Market Theory: An Overview9.1 a. Capital gains = $38 - $37 = $1 per shareb. Total dollar returns = Dividends + Capital Gains = $1,000 + ($1*500) = $1,500On a per share basis, this calculation is $2 + $1 = $3 per share c. On a per share basis, $3/$37 = 0.0811 = 8.11%On a total dollar basis, $1,500/(500*$37) = 0.0811 = 8.11%d. No, you do not need to sell the shares to include the capital gains in the computation of the returns. The capital gain is included whether or not you realize the gain. Since you could realize the gain if you choose, you shouldinclude it.9.2 Purchase Price = $10,400/200 = $52.00 a. Total dollar return = $600 + 200($54.25 - $52) =$1,050 b. Capital gain = 200($54.25-52) = $450 c. Percentage Return = $1050/$10400 = 10.10% d. Dividend Yield = $600/(200*52) = 5.77%9.3 ()[]2.40$31$42/42$8.60/$420.204820.48%+-=-=-=-9.4 The expected holding period return is:()[]$5.50$54.75$52/$520.1586515.865%+-== 9.5 You can find the nominal returns, I, on each of the securities in the text. The inflationrate, π, for the period is also in the text. It is 3.2%. The real return, r, is (1+I)/(1+π)-1. An approximation for the real rate is r = i - π. Notice that the approximation is good when the nominal interest rate is close to the inflation rate.Nominal Real Approximationa. Common Stocks 12.2% 8.7% 9.2%b. L/T Corp. Bonds 5.7% 2.4% 2.5%c. L/T Govt. Bonds 5.2% 1.9% 2.0%d. U.S. T-Bills3.7%0.5%0.5%9.6 E(R) = T-Bill rate + Average Excess Return = 6.2% + (12.4% -3.9%) = 14.7% 9.7 Suppose the two companies’ stock price 2 years ago were P 02 years ago 1 year ago TodayKoke P 0 1.1P 0 1.1*0.9*P 0= 0.99P 0 Pepsee P 0 0.9P 0 0.9*1.1*P 0= 0.99 P 0Both stocks have the same prices, but their prices are lower than 2 years ago.9.8 Five-year Holding Period Return = (1-0.0491)⨯(1+0.2141)⨯(1+0.2251)⨯(1+0.0627)⨯(1+0.3216)-1 = 98.64% 9.9 Risk Premium = 6.1 - 3.8 = 2.3%Expected Return on the market long term corporate bonds = 4.36% + 2.3% = 6.96%9.10 159.07199.0301.0164.0047.0438.001.0026.0R .a =+++++--=b. R R R - ()R R -2-0.026 -0.1850.03423 -0.010 -0.169 0.02856 0.438 0.279 0.07784 0.047 -0.112 0.01254 0.164 0.005 0.00003 0.301 0.142 0.02016 0.199 0.0400.00160Total 0.17496 ()σσ2=-====0.17496/710.029160.029160.170817.08%Note, because the data are historical data, the appropriate denominator in the calculation of the variance is N-1. 9.11 a. Common Treasury Realized Stocks BillsRisk Premium-7 32.4% 11.2% 21.2% -6 -4.9 14.7 -19.6 -5 21.4 10.5 10.9 -4 22.5 8.8 13.7 -3 6.3 9.9 -3.6 -2 32.2 7.7 24.5Last18.56.212.3b.The average risk premium is 8.49%.49.873.125.246.37.139.106.192.21=++-++-c.Yes, it is possible for the observed risk premium to be negative. This can happen in any single year. The average risk premium over many years should bepositive.公司理财习题答案第九章9.12 a.b.Standard deviation = 03311.0001096.0= 9.13a.b.Standard deviation = 0000984.= 0.03137 = 3.137%9.14 a. R 0.120.230.400.180.250.150.150.090.080.030.153 =15.3%m =⨯+⨯+⨯+⨯+⨯=b.()R 0.120.120.400.090.250.050.150.010.080.020.0628 = 6.28%T =⨯+⨯+⨯+⨯+⨯-=9.15 a.()()R 0.040.060.090.04/40.0575R 0.050.070.100.14/40.09p Q =+++==+++=b.R R p p -()R R p p -2-0.0175 0.00031 -0.0025 0.00001 +0.0325 0.00106 -0.0175 0.000310.00169Variance of R p ==0001694000042./.Standard Deviation of 02049.000042.0R p==()R R R R Q QQ Q--2-0.04 0.0016 -0.02 0.0004 0.01 0.0001 0.05 0.0025 0.0046Variance of R Q ==000464000115./.Standard Deviation of R Q ==000115003391..9.16 S R = Average Return on the Small Company Stocks.mR= Average Return on the Market Index. 2S S = Variance in the Returns of the Small Company Stocks.S S = Standard Deviation in the Returns of the Small Company Stocks. 2m S = Variance in the Returns of the Market Index.m S = Standard Deviation in the Returns of the Market Index.a. S R = 1542.05005.0350.0339.0477.0=--+mR=1604.05004.0328.0580.0648.0402.0=++-+公司理财习题答案第九章b. Small Company StocksMarket IndexR R s s - ()R R s s -2R R m m - ()R R m m -20.3228 0.104199840.2416 0.058370560.1848 0.03415104 0.4876 0.23775376 -0.5042 0.25421764 -0.7404 0.54819216 0.1558 0.02427364 0.1676 0.02808976 -0.1592 0.02534464 -0.1564 0.02446096Total =0.896867200.473520.2242168m s 0.332490.1105467s s 0.2242168/40.896867202ms0.1105467/40.442186802ss========Note, because the data are historical returns, the appropriate denominator in the calculation of the variance is N-1.9.17Let R cs = The Returns on Common Stocks (in %) Let R ss = The Returns on Small Stocks (in %)Let R cb = The Returns on Long-term Corporate Bonds (in %) Let R gb = The Returns on Long- term Government Bonds (in %) Let R tb = The Returns on Treasury Bills (in %) Let – over a variable denote its average valueBecause these data are historical data, the proper divisor for computing the variance is N-1. Thus, the variance of the returns of each security is the sum of the squared deviations divided by six.Var ( Rcs ) = 0.018372 SD ( Rcs) = 0.1355Var ( Rss ) = 0.029734 SD ( Rss) = 0.1724Var ( Rcb ) = 0.029522 SD ( Rcb) = 0.1718Var ( Rgb ) = 0.02868 SD ( Rgb) = 0.16935Var ( Rtb ) = 0.00075 SD ( Rtb) = 0.027479.18 a. The average return on small company stocks isRs=(6.85-9.30+22.87+10.18-21.56+44.63)%/6 = 8.95% The average return on T-bills is:()R 6.16 5.47 6.358.377.81 5.60/6 6.63%T=+++++=公司理财习题答案第九章b.c. Returns on T-bills are lower than small stock returns but their variance is muchsmaller.9.19 The range with 95% probability is: []σσ,22-+M ean M ean⇒[ 17.5-2⨯ 8.5, 17.5+2⨯8.5]⇒[ 0.5%, 34.5%]9.20 a. Expected Return on the Market:= 0.25(-8.2%)+0.5(12.3%)+0.25(25.8%)= 10.55%Expected Return on T-Bills: = 3.5%b. Expected Premium = 0.25(-8.2-3.5)+0.5(12.3-3.5)+0.25(25.8-3.5) = 7.05%。

【最新整理，下载后即可编辑】Case SolutionsFundamentals of Corporate FinanceRoss, Westerfield, and Jordan9th editionCHAPTER 1THE McGEE CAKE COMPANY1.The advantages to a LLC are: 1) Reduction of personal liability. A soleproprietor has unlimited liability, which can include the potential loss of all personal assets. 2) Taxes. Forming an LLC may mean that more expenses can be considered business expenses and be deducted from the company’s income. 3) Improved credibility. The business may have increased credibility in the business world compared to a sole proprietorship. 4) Ability to attract investment. Corporations, even LLCs, can raise capital through the sale of equity. 5) Continuous life. Sole proprietorships have a limited life, while corporations have a potentially perpetual life. 6) Transfer of ownership. It is easier to transfer ownership in a corporation through the sale of stock.The biggest disadvantage is the potential cost, although the cost of forminga LLC can be relatively small. There are also other potential costs, includingmore expansive record-keeping.2.Forming a corporation has the same advantages as forming a LLC, but thecosts are likely to be higher.3.As a small company, changing to a LLC is probably the most advantageousdecision at the current time. If the company grows, and Doc and Lyn are willing to sell more equity ownership, the company can reorganize as a corporation at a later date. Additionally, forming a LLC is likely to be less expensive than forming a corporation.CHAPTER 2CASH FLOWS AND FINANCIAL STATEMENTS AT SUNSET BOARDS Below are the financial statements that you are asked to prepare.1.The income statement for each year will look like this:Income statement2008 2009Sales $247,259 $301,392Cost of goods sold 126,038 159,143Selling & administrative 24,787 32,352Depreciation 35,581 40,217EBIT $60,853 $69,680Interest 7,735 8,866EBT $53,118 $60,814Taxes 10,624 12,163Net income $42,494 $48,651Dividends $21,247 $24,326Addition to retainedearnings 21,247 24,3262.The balance sheet for each year will be:Balance sheet as of Dec. 31, 2008C-26 CASE SOLUTIONSCash $18,187 Accounts payable $32,143 Accountsreceivable 12,887 Notes payable 14,651 Inventory 27,119 Current liabilities $46,794 Current assets $58,193Long-term debt $79,235 Net fixed assets $156,975 Owners' equity 89,139Total assets $215,168 Total liab. &equity $215,168In the first year, equity is not given. Therefore, we must calculate equity as a plug variable. Since total liabilities & equity is equal to total assets, equity can be calculated as:Equity = $215,168 – 46,794 – 79,235Equity = $89,139CHAPTER 2 C-5Balance sheet as of Dec. 31, 2009Cash $27,478 Accounts payable $36,404 Accountsreceivable 16,717 Notes payable 15,997 Inventory 37,216 Current liabilities $52,401 Current assets $81,411Long-term debt $91,195 Net fixed assets $191,250 Owners' equity 129,065Total assets $272,661 Total liab. &equity $272,661The owner’s equity for 2009 is the beginning of year owner’s equity, plus the addition to retained earnings, plus the new equity, so:Equity = $89,139 + 24,326 + 15,600Equity = $129,065ing the OCF equation:OCF = EBIT + Depreciation – TaxesThe OCF for each year is:OCF2008 = $60,853 + 35,581 – 10,624OCF2008 = $85,180OCF2009 = $69,680 + 40,217 – 12,163OCF2009 = $97,734C-26 CASE SOLUTIONS4.To calculate the cash flow from assets, we need to find the capital spendingand change in net working capital. The capital spending for the year was: Capital spendingEnding net fixed assets $191,250– Beginning net fixedassets 156,975+ Depreciation 40,217Net capital spending $74,492And the change in net working capital was:Change in net working capitalEnding NWC $29,010– Beginning NWC 11,399Change in NWC $17,611CHAPTER 2 C-5 So, the cash flow from assets was:Cash flow from assetsOperating cash flow $97,734– Net capital spending 74,492– Change in NWC 17,611Cash flow from assets $ 5,6315.The cash flow to creditors was:Cash flow to creditorsInterest paid $8,866– Net new borrowing 11,960Cash flow to creditors –$3,0946.The cash flow to stockholders was:Cash flow tostockholdersDividends paid $24,326– Net new equityraised 15,600Cash flow tostockholders $8,726Answers to questions1.The firm had positive earnings in an accounting sense (NI > 0) and hadpositive cash flow from operations. The firm invested $17,611 in new netC-26 CASE SOLUTIONSworking capital and $74,492 in new fixed assets. The firm gave $5,631 to its stakeholders. It raised $3,094 from bondholders, and paid $8,726 to stockholders.2.The expansion plans may be a little risky. The company does have a positivecash flow, but a large portion of the operating cash flow is already going to capital spending. The company has had to raise capital from creditors and stockholders for its current operations. So, the expansion plans may be too aggressive at this time. On the other hand, companies do need capital to grow. Before investing or loaning the company money, you would want to know where the current capital spending is going, and why the company is spending so much in this area already.CHAPTER 3RATIOS ANALYSIS AT S&S AIR1.The calculations for the ratios listed are:Current ratio = $2,186,520 / $2,919,000Current ratio = 0.75 timesQuick ratio = ($2,186,250 – 1,037,120) / $2,919,000Quick ratio = 0.39 timesCash ratio = $441,000 / $2,919,000Cash ratio = 0.15 timesTotal asset turnover = $30,499,420 / $18,308,920Total asset turnover = 1.67 timesInventory turnover = $22,224,580 / $1,037,120Inventory turnover = 21.43 timesReceivables turnover = $30,499,420 / $708,400Receivables turnover = 43.05 timesTotal debt ratio = ($18,308,920 – 10,069,920) / $18,308,920 Total debt ratio = 0.45 timesDebt-equity ratio = ($2,919,000 + 5,320,000) / $10,069,920C-26 CASE SOLUTIONSDebt-equity ratio = 0.82 timesEquity multiplier = $18,308,920 / $10,069,920Equity multiplier = 1.82 timesTimes interest earned = $3,040,660 / $478,240Times interest earned = 6.36 timesCash coverage = ($3,040,660 + 1,366,680) / $478,420 Cash coverage = 9.22 timesProfit margin = $1,537,452 / $30,499,420Profit margin = 5.04%Return on assets = $1,537,452 / $18,308,920Return on assets = 8.40%Return on equity = $1,537,452 / $10,069,920Return on equity = 15.27%CHAPTER 3 C-11 2. Boeing is probably not a good aspirant company. Even though bothcompanies manufacture airplanes, S&S Air manufactures small airplanes, while Boeing manufactures large, commercial aircraft. These are two different markets. Additionally, Boeing is heavily involved in the defense industry, as well as Boeing Capital, which finances airplanes.Bombardier is a Canadian company that builds business jets, short-range airliners and fire-fighting amphibious aircraft and also provides defense-related services. It is the third largest commercial aircraft manufacturer in the world. Embraer is a Brazilian manufacturer than manufactures commercial, military, and corporate airplanes. Additionally, the Brazilian government is a part owner of the company. Bombardier and Embraer are probably not good aspirant companies because of the diverse range of products and manufacture of larger aircraft.Cirrus is the world's second largest manufacturer of single-engine, piston-powered aircraft. Its SR22 is the world's best selling plane in its class. The company is noted for its innovative small aircraft and is a good aspirant company.Cessna is a well known manufacturer of small airplanes. The company produces business jets, freight- and passenger-hauling utility Caravans, personal and small-business single engine pistons. It may be a good aspirant company, however, its products could be considered too broad and diversified since S&S Air produces only small personal airplanes.3. S&S is below the median industry ratios for the current and cash ratios.This implies the company has less liquidity than the industry in general.However, both ratios are above the lower quartile, so there are companiesC-26 CASE SOLUTIONSin the industry with lower liquidity ratios than S&S Air. The company may have more predictable cash flows, or more access to short-term borrowing.If you created an Inventory to Current liabilities ratio, S&S Air would havea ratio that is lower than the industry median. The current ratio is below theindustry median, while the quick ratio is above the industry median. This implies that S&S Air has less inventory to current liabilities than the industry median. S&S Air has less inventory than the industry median, but more accounts receivable than the industry since the cash ratio is lower than the industry median.The turnover ratios are all higher than the industry median; in fact, all three turnover ratios are above the upper quartile. This may mean that S&S Air is more efficient than the industry.The financial leverage ratios are all below the industry median, but above the lower quartile. S&S Air generally has less debt than comparable companies, but still within the normal range.The profit margin, ROA, and ROE are all slightly below the industry median, however, not dramatically lower. The company may want to examine its costs structure to determine if costs can be reduced, or price can be increased.Overall, S&S Air’s performance seems good, although the liquidity ratios indicate that a closer look may be needed in this area.CHAPTER 3 C-11 Below is a list of possible reasons it may be good or bad that each ratio is higher or lower than the industry. Note that the list is not exhaustive, but merely one possible explanation for each ratio.Ratio Good BadCurrent ratio Better at managingcurrent accounts. May be having liquidity problems.Quick ratio Better at managingcurrent accounts. May be having liquidity problems.Cash ratio Better at managingcurrent accounts. May be having liquidity problems.Total asset turnover Better at utilizing assets. Assets may be older anddepreciated, requiringextensive investmentsoon.Inventory turnover Better at inventorymanagement, possibly dueto better procedures.Could be experiencinginventory shortages.Receivables turnover Better at collectingreceivables.May have credit termsthat are too strict.Decreasing receivablesturnover may increasesales.Total debt ratio Less debt than industrymedian means thecompany is less likely toexperience creditproblems. Increasing the amount of debt can increase shareholder returns. Especially notice that it will increase ROE.Debt-equity Less debt than industry Increasing the amount ofC-26 CASE SOLUTIONSratio median means thecompany is less likely toexperience creditproblems. debt can increase shareholder returns. Especially notice that it will increase ROE.Equity multiplier Less debt than industrymedian means thecompany is less likely toexperience creditproblems.Increasing the amount ofdebt can increaseshareholder returns.Especially notice that itwill increase ROE.TIE Higher quality materialscould be increasing costs. The company may have more difficulty meeting interest payments in a downturn.Cash coverage Less debt than industrymedian means thecompany is less likely toexperience creditproblems. Increasing the amount of debt can increase shareholder returns. Especially notice that it will increase ROE.Profit margin The PM is slightly belowthe industry median. Itcould be a result of higherquality materials or bettermanufacturing. Company may be having trouble controlling costs.ROA Company may have newerassets than the industry. Company may have newer assets than the industry.ROE Lower profit margin maybe a result of higherquality. Profit margin and EM are lower than industry, which results in the lower ROE.CHAPTER 4PLANNING FOR GROWTH AT S&S AIR1.To calculate the internal growth rate, we first need to find the ROA and theretention ratio, so:ROA = NI / TAROA = $1,537,452 / $18,309,920ROA = .0840 or 8.40%b = Addition to RE / NIb = $977,452 / $1,537,452b = 0.64Now we can use the internal growth rate equation to get:Internal growth rate = (ROA × b) / [1 – (ROA × b)]Internal growth rate = [0.0840(.64)] / [1 – 0.0840(.64)]Internal growth rate = .0564 or 5.64%To find the sustainable growth rate, we need the ROE, which is:ROE = NI / TEROE = $1,537,452 / $10,069,920ROE = .1527 or 15.27%C-26 CASE SOLUTIONSUsing the retention ratio we previously calculated, the sustainable growth rate is:Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]Sustainable growth rate = [0.1527(.64)] / [1 – 0.1527(.64)]Sustainable growth rate = .1075 or 10.75%The internal growth rate is the growth rate the company can achieve with no outside financing of any sort. The sustainable growth rate is the growth rate the company can achieve by raising outside debt based on its retained earnings and current capital structure.CHAPTER 4 C-21 2.Pro forma financial statements for next year at a 12 percent growth rate are:Income statementSales $ 34,159,35COGS 24,891,530 Other expenses 4,331,600 Depreciation 1,366,680EBIT $ 3,569,541Interest 478,240Taxable income $ 3,091,301Taxes (40%) 1,236,520Net income $ 1,854,78Dividends $ 675,583C-26 CASE SOLUTIONSAdd to RE 1,179,197Balance sheetAssets Liabilities & EquityCurrent Assets Current LiabilitiesCash $ 493,92AccountsPayable $ 995,680Accounts rec. 793,408 Notes Payable 2,030,000 Inventory 1,161,574 Total CL $ 3,025,680 Total CA $ 2,448,902Long-term debt $ 5,320,000ShareholderEquityCommon stock $ 350,000Fixed assets Retainedearnings 10,899,117Net PP&E $ 18,057,088 Total Equity $ 11,249,117Total Assets $ 20,505,990 Total L&E $ 19,594,787CHAPTER 4 C-21 So, the EFN is:EFN = Total assets – Total liabilities and equityEFN = $20,505,990 – 19,594,797EFN = $911,193The company can grow at this rate by changing the way it operates. For example, if profit margin increases, say by reducing costs, the ROE increases, it will increase the sustainable growth rate. In general, as long as the company increases the profit margin, total asset turnover, or equity multiplier, the higher growth rate is possible. Note however, that changing any one of these will have the effect of changing the pro forma financial statements.C-26 CASE SOLUTIONS3.Now we are assuming the company can only build in amounts of $5 million.We will assume that the company will go ahead with the fixed asset acquisition. To estimate the new depreciation charge, we will find the current depreciation as a percentage of fixed assets, then, apply this percentage to the new fixed assets. The depreciation as a percentage of assets this year was:Depreciation percentage = $1,366,680 / $16,122,400Depreciation percentage = .0848 or 8.48%The new level of fixed assets with the $5 million purchase will be:New fixed assets = $16,122,400 + 5,000,000 = $21,122,400So, the pro forma depreciation will be:Pro forma depreciation = .0848($21,122,400)Pro forma depreciation = $1,790,525We will use this amount in the pro forma income statement. So, the pro forma income statement will be:Income statementSales $ 34,159,35COGS 24,891,530 Other expensesCHAPTER 4 C-214,331,600Depreciation 1,790,525EBIT $ 3,145,696Interest 478,240Taxable income $ 2,667,456Taxes (40%) 1,066,982Net income $ 1,600,473Dividends $ 582,955Add to RE 1,017,519C-26 CASE SOLUTIONSThe pro forma balance sheet will remain the same except for the fixed asset and equity accounts. The fixed asset account will increase by $5 million, rather than the growth rate of sales.Balance sheetAssets Liabilities & EquityCurrent Assets Current LiabilitiesCash $ 493,92AccountsPayable $ 995,680Accounts rec. 793,408 Notes Payable 2,030,000 Inventory 1,161,574 Total CL $ 3,025,680 Total CA $ 2,448,902Long-term debt $ 5,320,000ShareholderEquityCommon stock $ 350,000Fixed assets Retainedearnings 10,737,439Net PP&E $ 21,122,400 Total Equity $ 11,087,439Total Assets $ 23,571,302 Total L&E $ 19,433,119CHAPTER 4 C-21 So, the EFN is:EFN = Total assets – Total liabilities and equityEFN = $23,581,302 – 19,433,119EFN = $4,138,184Since the fixed assets have increased at a faster percentage than sales, the capacity utilization for next year will decrease.CHAPTER 6THE MBA DECISION1. Age is obviously an important factor. The younger an individual is, the moretime there is for the (hopefully) increased salary to offset the cost of the decision to return to school for an MBA. The cost includes both the explicit costs such as tuition, as well as the opportunity cost of the lost salary.2. Perhaps the most important nonquantifiable factors would be whether ornot he is married and if he has any children. With a spouse and/or children, he may be less inclined to return for an MBA since his family may be less amenable to the time and money constraints imposed by classes. Other factors would include his willingness and desire to pursue an MBA, job satisfaction, and how important the prestige of a job is to him, regardless of the salary.3.He has three choices: remain at his current job, pursue a Wilton MBA, orpursue a Mt. Perry MBA. In this analysis, room and board costs are irrelevant since presumably they will be the same whether he attends college or keeps his current job. We need to find the aftertax value of each, so:Remain at current job:Aftertax salary = $55,000(1 – .26) = $40,700CHAPTER 6 C-27 His salary will grow at 3 percent per year, so the present value of his aftertax salary is:PV = C {1 – [(1 + g)/(1 + r)]t} / (r–g)]PV = $40,700{[1 – [(1 +.065)/(1 + .03)]38} / (.065 – .03)PV = $836,227.34Wilton MBA:Costs:Total direct costs = $63,000 + 2,500 + 3,000 = $68,500PV of direct costs = $68,500 + 68,500 / (1.065) = $132,819.25PV of indirect costs (lost salary) = $40,700 / (1.065) + $40,700(1 + .03) / (1 + .065)2 = $75,176.00Salary:PV of aftertax bonus paid in 2 years = $15,000(1 –.31) / 1.0652= $9,125.17Aftertax salary = $98,000(1 – .31) = $67,620C-26 CASE SOLUTIONSHis salary will grow at 4 percent per year. We must also remember that he will now only work for 36 years, so the present value of his aftertax salary is: PV = C {1 – [(1 + g)/(1 + r)]t} / (r–g)]PV = $67,620{[1 – [(1 +.065)/(1 + .04)]36} / (.065 – .04)PV = $1,554,663.22Since the first salary payment will be received three years from today, so we need to discount this for two years to find the value today, which will be: PV = $1,544,663.22 / 1.0652PV = $1,370,683.26So, the total value of a Wilton MBA is:Value = –$75,160 – 132,819.25 + 9,125.17 + 1,370,683.26 =$1,171,813.18Mount Perry MBA:Costs:Total direct costs = $78,000 + 3,500 + 3,000 = $86,500. Note, this is also the PV of the direct costs since they are all paid today.PV of indirect costs (lost salary) = $40,700 / (1.065) = $38,215.96Salary:CHAPTER 6 C-27 PV of aftertax bonus paid in 1 year = $10,000(1 – .29) / 1.065 = $6,666.67 Aftertax salary = $81,000(1 – .29) = $57,510His salary will grow at 3.5 percent per year. We must also remember that he will now only work for 37 years, so the present value of his aftertax salary is: PV = C {1 – [(1 + g)/(1 + r)]t} / (r–g)]PV = $57,510{[1 – [(1 +.065)/(1 + .035)]37} / (.065 – .035)PV = $1,250,991.81Since the first salary payment will be received two years from today, so we need to discount this for one year to find the value today, which will be:PV = $1,250,991.81 / 1.065PV = $1,174,640.20So, the total value of a Mount Perry MBA is:Value = –$86,500 – 38,215.96 + 6,666.67 + 1,174,640.20 = $1,056,590.90C-26 CASE SOLUTIONS4.He is somewhat correct. Calculating the future value of each decision willresult in the option with the highest present value having the highest future value. Thus, a future value analysis will result in the same decision. However, his statement that a future value analysis is the correct method is wrong since a present value analysis will give the correct answer as well.5. To find the salary offer he would need to make the Wilton MBA asfinancially attractive as the as the current job, we need to take the PV of his current job, add the costs of attending Wilton, and the PV of the bonus on an aftertax basis. So, the necessary PV to make the Wilton MBA the same as his current job will be:PV = $836,227.34 + 132,819.25 + 75,176.00 – 9,125.17 = $1,035,097.42This PV will make his current job exactly equal to the Wilton MBA on a financial basis. Since his salary will still be a growing annuity, the aftertax salary needed is:PV = C {1 – [(1 + g)/(1 + r)]t} / (r–g)]$1,035,097.42 = C {[1 – [(1 +.065)/(1 + .04)]36} / (.065 – .04)C = $45,021.51This is the aftertax salary. So, the pretax salary must be:Pretax salary = $45,021.51 / (1 – .31) = $65,248.576.The cost (interest rate) of the decision depends on the riskiness of the use offunds, not the source of the funds. Therefore, whether he can pay cash orCHAPTER 6 C-27 must borrow is irrelevant. This is an important concept which will be discussed further in capital budgeting and the cost of capital in later chapters.CHAPTER 7FINANCING S&S AIR’S EXPANSION PLANS WITH A BOND ISSUEA rule of thumb with bond provisions is to determine who benefits by theprovision. If the company benefits, the bond will have a higher coupon rate.If the bondholders benefit, the bond will have a lower coupon rate.1. A bond with collateral will have a lower coupon rate. Bondholders have theclaim on the collateral, even in bankruptcy. Collateral provides an asset that bondholders can claim, which lowers their risk in default. The downside of collateral is that the company generally cannot sell the asset used as collateral, and they will generally have to keep the asset in good working order.2.The more senior the bond is, the lower the coupon rate. Senior bonds getfull payment in bankruptcy proceedings before subordinated bonds receive any payment. A potential problem may arise in that the bond covenant may restrict the company from issuing any future bonds senior to the current bonds.3. A sinking fund will reduce the coupon rate because it is a partial guaranteeto bondholders. The problem with a sinking fund is that the company must make the interim payments into a sinking fund or face default. This means the company must be able to generate these cash flows.4. A provision with a specific call date and prices would increase the couponrate. The call provision would only be used when it is to the company’s advantage, thus the bondholder’s disadvantage. The downside is theCHAPTER 7 C-29 higher coupon rate. The company benefits by being able to refinance at a lower rate if interest rates fall significantly, that is, enough to offset the call provision cost.5. A deferred call would reduce the coupon rate relative to a call provision witha deferred call. The bond will still have a higher rate relative to a plain vanillabond. The deferred call means that the company cannot call the bond for a specified period. This offers the bondholders protection for this period. The disadvantage of a deferred call is that the company cannot call the bond during the call protection period. Interest rates could potentially fall to the point where it would be beneficial for the company to call the bond, yet the company is unable to do so.6. A make-whole call provision should lower the coupon rate in comparison toa call provision with specific dates since the make-whole call repays thebondholder the present value of the future cash flows. However, a make-whole call provision should not affect the coupon rate in comparison to a plain vanilla bond. Since the bondholders are made whole, they should be indifferent between a plain vanilla bond and a make-whole bond. If a bond with a make-whole provision is called, bondholders receive the market value of the bond, which they can reinvest in another bond with similar characteristics. If we compare this to a bond with a specific call price, investors rarely receive the full market value of the future cash flows.CASE 3 C-30 7. A positive covenant would reduce the coupon rate. The presence of positivecovenants protects bondholders by forcing the company to undertake actions that benefit bondholders. Examples of positive covenants would be: the company must maintain audited financial statements; the company must maintain a minimum specified level of working capital or a minimum specified current ratio; the company must maintain any collateral in good working order. The negative side of positive covenants is that the company is restricted in its actions. The positive covenant may force the company into actions in the future that it would rather not undertake.8. A negative covenant would reduce the coupon rate. The presence ofnegative covenants protects bondholders from actions by the company that would harm the bondholders. Remember, the goal of a corporation is to maximize shareholder wealth. This says nothing about bondholders.Examples of negative covenants would be: the company cannot increase dividends, or at least increase beyond a specified level; the company cannot issue new bonds senior to the current bond issue; the company cannot sell any collateral. The downside of negative covenants is the restriction of the company’s actions.9.Even though the company is not public, a conversion feature would likelylower the coupon rate. The conversion feature would permit bondholders to benefit if the company does well and also goes public. The downside is that the company may be selling equity at a discounted price.10. The downside of a floating-rate coupon is that if interest rates rise, thecompany has to pay a higher interest rate. However, if interest rates fall, the company pays a lower interest rate.CHAPTER 8STOCK VALUATION AT RAGAN, INC.1.The total dividends paid by the company were $126,000. Since there are100,000 shares outstanding, the total earnings for the company were: Total earnings = 100,000($4.54) = $454,000This means the payout ratio was:Payout ratio = $126,000/$454,000 = 0.28So, the retention ratio was:Retention ratio = 1 – .28 = 0.72Using the retention ratio, the company’s growth rate is:g = ROE × b = 0.25*(.72) = .1806 or 18.06%The dividend per share paid this year was:= $63,000 / 50,000D= $1.26DNow we can find the stock price, which is:C-84 CASE SOLUTIONSP 0 = D 1 / (R – g )P 0 = $1.26(1.1806) / (.20 – .1806)P 0 = $76.752.Since Expert HVAC had a write off which affected its earnings per share, we need to recalculate the industry EPS. So, the industry EPS is:Industry EPS = ($0.79 + 1.38 + 1.06) / 3 = $1.08Using this industry EPS, the industry payout ratio is:Industry payout ratio = $0.40/$1.08 = .3715 or 37.15%So, the industry retention ratio isIndustry retention ratio = 1 – .3715 = .6285 or 62.85%。

Company Stock One option in the 401(k) plan is stock in East Coast Yachts. The company is currently privately held. However, when you interviewed with the owner, Larissa Warren, she informed you the company was expected to go public in the next three to four years. Until then, a company stock price is simply set each year by the board of directors.Bledsoe S&P 500 Index Fund This mutual fund tracks the S&P 500. Stocks in the fund are weighted exactly the same as the S&P 500. This means the fund return is approximately the return on the S&P 500, minus expenses. Because an index fund purchases assets based on the composition of the index it is following, the fund manager is not required to research stocks and make investment decisions. The result is that the fund expenses are usually low. The Bledsoe S&P 500 Index Fund charges expenses of .15 percent of assets per year.Bledsoe Small-Cap Fund This fund primarily invests in small-capitalization stocks. As such, the returns of the fund are more volatile. The fund can also invest 10 percent of its assets in companies based outside the United States. This fund charges 1.70 percent in expenses.Bledsoe Large-Company Stock Fund This fund invests primarily in large-capitalization stocks of companies based in the United States. The fund is managed by Evan Bledsoe and has outperformed the market in six of the last eight years. The fund charges 1.50 percent in expenses.Bledsoe Bond Fund This fund invests in long-term corporate bonds issued by U.S.–domiciled companies. The fund is restricted to investments in bonds with an investment-grade credit rating. This fund charges 1.40 percent in expenses.Bledsoe Money Market Fund This fund invests in short-term, high–credit quality debt instruments, which include Treasury bills. As such, the return on the money market fund is only slightly higher than the return on Treasury bills. Because of the credit quality and short-term nature of the investments, there is only a very slight risk of negative return. The fund charges .60 percent in expenses.1. What advantages do the mutual funds offer compared to the company stock?2. Assume that you invest 5 percent of your salary and receive the full 5 percent match from EastCoast Yachts. What EAR do you earn from the match? What conclusions do you draw about matching plans?3. Assume you decide you should invest at least part of your money in large-capitalization stocksof companies based in the United States. What are the advantages and disadvantages of choosing the Bledsoe Large-Company Stock Fund compared to the Bledsoe S&P 500 Index Fund?4. The returns on the Bledsoe Small-Cap Fund are the most volatile of all the mutual funds offeredin the 401(k) plan. Why would you ever want to invest in this fund? When you examine the expenses of the mutual funds, you will notice that this fund also has the highest expenses. Does this affect your decision to invest in this fund?5. A measure of risk-adjusted performance that is often used is the Sharpe ratio. The Sharpe ratiois calculated as the risk premium of an asset divided by its standard deviation. The standard deviations and returns of the funds over the past 10 years are listed here. Calculate the Sharpe ratio for each of these funds. Assume that the expected return and standard deviation of the company stock will be 16 percent and 70 percent, respectively. Calculate the Sharpe ratio for the company stock. How appropriate is the Sharpe ratio for these assets? When would you use the Sharpe ratio?6. What portfolio allocation would you choose? Why? Explain your thinking carefully.。

Cha02罗斯公司理财第九版原版书课后习题reported in the financing activity section of the accounting statement of cash flows. When Tyco received payments from customers, the cash inflows were reported as operating cash flows. Another method used by Tyco was to have acquired companies prepay operating expenses. In other words, the company acquired by Tyco would pay vendors for items not yet received. In one case, the payments totaled more than $50 million. When the acquired company was consolidated with Tyco, the prepayments reduced Tyco’s cash outflows, thus increasing the operating cash flows.Dynegy, the energy giant, was accused of engaging in a number of complex “round-trip trades.” The round-trip trades essentially involved the sale of natural resources to a counterparty, with the repurchase of the resources from the same party at the same price. In essence, Dynegy would sell an asset for $100, and immediately repurchase it from the buyer for $100. The problem arose with the treatment of the cash flows from the sale. Dynegy treated the cash from the sale of the asset as an operating cash flow, but classified the repurchase as an investing cash outflow. The total cash flows of the contracts traded by Dynegy in these round-trip trades totaled $300 million.Adelphia Communications was another company that apparently manipulated cash flows. In Adelphia’s case, the company capitalized the labor required to install cable. In other words, the company classified this labor expense as a fixed asset. While this practice is fairly common in the telecommunications industry, Adelphia capitalized a higher percentage of labor than is common. The effect of this classification was that the labor wastreated as an investment cash flow, which increased the operating cash flow.In each of these examples, the companies were trying to boost operating cash flows by shifting cash flows to a different heading. The important thing to notice is that these movements don’t affect the total cash flow of the firm, which is why we recommend focusing on this number, not just operating cash flow.Summary and ConclusionsBesides introducing you to corporate accounting, the purpose of this chapter has been to teach you how to determine cash flow from the accounting statements of a typical company.1. Cash flow is generated by the firm and paid to creditors and shareholders. It can be classifiedas:1. Cash flow from operations.2. Cash flow from changes in fixed assets.3. Cash flow from changes in working capital.2. Calculations of cash flow are not difficult, but they require care and particular attention to detailin properly accounting for noncash expenses such as depreciation and deferred taxes. It is especially important that you do not confuse cash flow with changes in net working capital and net income.Concept Questions1. Liquidity True or false: All assets are liquid at some price. Explain.2. Accounting and Cash Flows Why might the revenue and cost figures shown on a standardincome statement not represent the actual cash inflows andoutflows that occurred during a period?3. Accounting Statement of Cash Flows Looking at the accounting statement of cash flows,what does the bottom line number mean? How useful is this number for analyzing a company? 4. Cash Flows How do financial cash flows and the accounting statement of cash flows differ?Which is more useful for analyzing a company?5. Book Values versus Market Values Under standard accounting rules, it is possible for astoc kholders’ equity of Information Control Corp. one yearago:During the past year, Information Control issued 10 million shares of new stock at a total price of $43 million, and issued $10 million in new long-term debt. The company generated $9 million in net income and paid $2 million in dividends. Construct the current balance sheet reflecting the changes that occurred at Information Control Corp. during the year.8. Cash Flow to Creditors The 2009 balance sheet of Anna’s Tennis Shop, Inc., showed long-term debt of $1.34 million, and the 2010 balance sheet showed long-term debt of $1.39 million.The 2010 income statement showed an interest expense of $118,000. What was the firm’s cash flow to creditors during 2010?9. Cash Flow to Stockholders The 2009 balance sheet of Anna’s Tennis Shop, Inc., showed$430,000 in the common stock account and $2.6 million in the additional paid-in surplus account.The 2010 balance sheet showed $450,000 and $3.05 million in the same two accounts, respectively. If the company paid out $385,000 in cash dividends during 2010, what was the cash flow to stockholders for the year?10. Calculating Cash Flows Given the information for Anna’s Tennis Shop, Inc., in the previoustwo problems, suppose you also know that the firm’s net capital spending for 2010 was $875,000 and that the firmreduced its net working capital investment by $69,000. What was the firm’s 2010 operating cash flow, or OCF?INTERMEDIATE (Questions 11–24)11. Cash Flows Ritter Corporation’s accountants prepared the following financial statements foryear-end 2010:1. Explain the change in cash during 2010.2. Determine the change in net working capital in 2010.3. Determine the cash flow generated by the firm’s assets during 2010.12. Financial Cash Flows The Stancil Corporation provided the following current information:Determine the cash flows from the firm and the cash flows to investors of the firm.13. Building an Income Statement During the year, the Senbet Discount Tire Company hadgross sales of $1.2 million. The firm’s cost of goods sold and selling expenses were $450,000 and $225,000, respectively. Senbet also had notes payable of $900,000. These notes carried an interest rate of 9 percent. Depreciation was $110,000. Senbet’s tax rate was 35 percent.1. What was Senbet’s net income?2. What was Senbet’s operating cash flow?14. Calculating Total Cash Flows Schwert Corp. shows the following information on its 2010income statement: sales = $167,000; costs = $91,000; other expenses = $5,400; depreciation expense = $8,000; interest expense = $11,000; taxes = $18,060; dividends = $9,500. In addition, you’re told that the firm issued $7,250 in new equity during 2010 and redeemed $7,100 in outstanding long-term debt.1. What is the 2010 operating cash flow?2. What is the 2010 cash flow to creditors?3. What is the 2010 cash flow to stockholders?4. If net fixed assets increased by $22,400 during the year, what was the addition to networking capital (NWC)?15. Using Income Statements Given the followingi nformation for O’Hara Marine Co., calculatethe depreciation expense: sales = $43,000; costs = $27,500; addition to retained earnings = $5,300; dividends paid = $1,530;interest expense = $1,900; tax rate = 35 percent.1. What is owners’ equity for 2009 and 2010?2. What is the change in net working capital for 2010?3. In 2010, Weston Enterprises purchased $1,800 in new fixed assets. How much in fixedassets did Weston Enterprises sell? What is the cash flow from assets for the year? (The tax rate is 35 percent.)4. During 2010, Weston Enterprises raised $360 in new long-term debt. How much long-termdebt must Weston Enterprises have paid off during the year? What is the cash flow to creditors?Use the following information for Ingersoll, Inc., for Problems 23 and 24 (assume the tax rate is34 percent):23. Financial Statements Draw up an income statement and balance sheet for this company for2009 and 2010.24. Calculating Cash Flow For 2010, calculate the cash flow from assets, cash flow to creditors,and cash flow to stockholders.CHALLENGE (Questions 25–27)25. Cash Flows You are researching Time Manufacturing and have found the following accountingstatement of cash flows for the most recent year. You also know that the company paid $82 million in current taxes and had an interest expense of $43 million. Use the accounting statement of cash flows to construct the financial statement of cash flows.Nick has also provided the following information: During the year the company raised $118,000 in new long-term debt and retired $98,000 in long-term debt. The company also sold $11,000 in new stock and repurchased $40,000 in stock. The company purchased $786,000 in fixed assets and sold $139,000 in fixed assets.Angus has asked you to prepare the financial statement of cash flows and the accounting statement of cash flows. He has also asked you to answer the following questions:1. How would you describe Warf Computers’ cash flows?2. Which cash flow statement more accurately describes the cash flows at the company?3. In light of your previous answers, comment on Nick’s expansion plans.。

公司理财第九版课后习题答案第二章CHAPTER 2FINANCIAL STATEMENTS AND CASH FLOWAnswe rs to Concepts Review and Critical Thinking Questions1. True. Every asset can be converted to cash at some price. However, when we are referring to a liquidasset, the added assumption that the asset can be quickly converted to cash at or near market value is important.2. The recognition and matching principles in financial accounting call for revenues, and the costsassociated with producing those revenues, to be ―booked‖when the revenue process isessentiallycomplete, not necessarily when the cash is collected or bills are paid. Note that this way is notnecessarily correct; it‘s the way accountants have chosen to do it.3. The bottom line number shows the change in the ca sh balanc e on the balance sheet. As such, it is nota use ful number for analyzing a company.4. The major difference is the treatment of interest expense. The accounting statement of cash flowstreats interest as an operating ca sh flow, while the financial ca sh flows treat interest as a financing cash flow. The logic of the accounting statement of cash flows is that since interest appears on the income statement, which shows the operations for the period, it is an operating cash flow. In reality, interest is a financing expense, which results from the company‘s choice of debt and equity. We will have more to say about this in a laterchapter. When compa ring the two c ash flow statements, the financial statement of cash flows is a more appropriate measure of the company‘s performa ncebecause of its treatment of interest.5. Market values can never be negative. Imagine a share of stock selling for –$20. This would meanthat if you placed an order for 100 shares, you would get the stock along with a check for $2,000.How ma ny shares do you want to buy? More generally, because of corpora te andindividualbankruptcy laws, net worth for a person or a corporation cannot be negative, implying that liabilities cannot exceed assets in market value.6. For a successful c ompany that is rapidly expanding, for example, capital outlays will be large,possibly leading to negative c ash flow from assets. In general, what matters is whether the money is spent wisely, not whe ther cash flow from assets is positive or negative.7. It‘s probably not a good sign for an e stablished company to have negative cash flow from operations,but it would be fairly ordinary for a start-up, so it depends.would have this effect. Negative net c apital spending would mea n more long-lived assets wereliquidated than purchased.49.10. If a company raises more money from selling stock than it pays in dividends in a particular period,its cash flow to stockholders will be negative. If a companyborrows more than it pays in interest and principal, its cash flow to creditors will be negative.The adjustments discussed were purely accounting changes; they had no cash flow or market value consequences unless the new accounting information caused stockholders to revalue the derivatives.Solutions to Questions and Proble msNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiplesteps. Due to space and readability constraints, when these intermediate steps are included in thissolutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1. To find owners‘ equity, we must construct a balance sheet as follows:Balance SheetCA $ 5,300 CL $ 3,900NFA 26,000 LTD 14,200OE ??TA $31,300 TL & OE $31,300We know that total liabilities and owners‘ equity (TL & OE) must equal total assets of $31,300. We also know that TL & OE is equal to current liabilities plus long-term debt plus owner‘s equity, soowner‘s equity is:OE = $31,300 –14,200 – 3,900 = $13,200NWC = CA – CL = $5,300 – 3,900 = $1,4002. The income statement for the company is:Income StatementSales $493,000Costs 210,000Depreciation 35,000EBIT $248,000Interest 19,000EBT $229,000Taxes 80,150Net income $148,8503.4.5.6. One equation for net income is:Net income = Dividends + Addition to retained earningsRearranging, we get:Addition to retained earnings = Net income – Divide ndsAddition to retained earnings = $148,850 – 50,000Addition to retained earnings = $98,850To find the book value of current assets, we use: NWC = CA – CL. Rearranging to solve for current assets, we get:CA = NWC + CL = $800,000 + 2,100,000 = $2,900,000The market value of current assets and net fixed assets is given, so:Book value CA= $2,900,000 Market value CA= $2,800,000Book value NFA = $5,000,000 Market value NFA= $6,300,000 Book value assets = $7,900,000 Market value assets= $9,100,000Taxes = 0.15($50K) + 0.25($25K) + 0.34($25K) + 0.39($246K – 100K)Taxes = $79,190The average tax ra te is the total tax paid divided by net income, so:Average tax rate = $79,190 / $246,000Average tax rate = 32.19%The marginal tax rate is the tax rate on the next $1 of earnings, so the marginal tax ra te = 39%.To calculate OCF, we first need the income state ment:Income StatementSales $14,900Costs 5,800Depreciation 1,300EBIT $7,800Interest 780Taxable income $7,020Taxes 2,808Net income $4,212OCF = EBIT + Depreciation – TaxesOCF = $7,800 + 1,300 – 2,808OCF = $6,292Net capital spending = $1,730,000 – 1,650,000 + 284,000Net capital spending = $364,0007. The long-term debt account will increase by $10 million, the amount of the new long-term debt issue.Since the company sold 10 million new shares of stock with a $1 par value, the common stockaccount will increase by $10 million. The capital surplus account will increase by $33 million, thevalue of the new stoc k sold above its par value. Since the company had a net income of $9million,and pa id $2 million in dividends, the addition to retained earnings was $7 million, which willinc rease the accumulated retained earnings account. So, the new long-term debt a nd stockholders‘ equity portion of the balance sheet will be:Long-term debt $82,000,000Total long-term debt $82,000,000Shareholders equityPreferred stock $9,000,000Common stock ($1 par value) 30,000,000Ac cumulated retained earnings 104,000,000Capital surplus 76,000,000Total equity $ 219,000,000Total Liabilities & Equity $ 301,000,0008.9. Cash flow to creditors = Interest paid – Net new borrowingCash flow to creditors = $118,000 – ($1,390,000 – 1,340,000) Cash flow to creditors = $118,000 – 50,000Cash flow to creditors = $68,000Cash flow to stockholders = Dividends paid – Net new equity Cash flow to stockholders = $385,000 – [(Common+ APIS) –(Common+ APIS)]end end beg beg10. Cash flow to stockholders = $385,000 –[($450,000 + 3,050,000) – ($430,000 + 2,600,000)] Cash flow to stockholders = $385,000 – ($3,500,000 – 3,030,000)Cash flow to stockholders = –$85,000Note, APIS is the additional paid-in surplus.Cash flow from assets= Cash flow to creditors + Cash flow to stockholders= $68,000 – 85,000= –$17,000Cash flow from assets= –$17,000 = OCF – Change in NWC –Net capital spending–$17,000 = OCF – (–$69,000) – 875,000Operating cash flowOperating cash flow= –$17,000 – 69,000 + 875,000= $789,000Cash flow to creditors = $118,000 – (LTD– LTD)11. a. IntermediateThe accounting statement of cash flows explains the change in cash during the year. Theaccounting statement of cash flows will be:Statement of cash flowsOperationsNet income $105Depreciation 90Changes in other current assets (55)Accounts payable (10)Total cash flow from operations $170Investing activitiesAcquisition of fixed assets $(140)Total cash flow from investing activities $(140)Financing activitiesProc eeds of long-term debt $30Dividends (45)Total cash flow from financing activities ($15)Change in cash (on balance sheet) $15b.Change in NWC= NWC e nd– NWC beg= (CA end–CL en d ) – (CA beg–CL be g)c.= [($50 + 155) – 85] – [($35 + 140) – 95)= $120 – 80= $40To find the cash flow generated by the firm‘s assets, we need the operating cash flow, and thecapital spending. So, calculating each of these, we find:Operating cash flowNet income $105Depreciation 90Operating cash flow $195Note that we can calculate OCF in this manner since there a re no taxes.Capital spendingEnding fixed assets Beginning fixed assets DepreciationCapital spending $340 (290)90 $140Now we c an calculate the cash flow gene rated by the firm‘s assets, which is: Cash flow from assetsOperating cash flow Capital spending Change in NWC Cash flow from assets $195 (140) (40) $1512. With the information provided, the cash flows from the firm are the capital spending and the changein net working capital, so:Cash flows from the firmCapital spending $(15,000)Additions to NWC (1,500)Cash flows from the firm $(16,500)And the cash flows to the investors of the firm are:Cash flows to investors of the firmSale of long-term debt (19,000)Sale of common stock (3,000)Dividends paid 19,500Cash flows to investors of the firm $(2,500)13. a.b. The interest expense for the company is the amount of debt times the interest rate on the debt. So, the income statement for the company is:Income StatementSales $1,200,000Cost of goods sold 450,000Selling costs 225,000Depreciation 110,000EBIT $415,000Interest 81,000Taxable income $334,000Taxes 116,900Net income $217,100And the opera ting cash flow is:OCF = EBIT + Depreciation – TaxesOCF = $415,000 + 110,000 – 116,900OCF = $408,10014. To find the OCF, we first calculate net income.Income StatementSales $167,000Costs 91,000Depreciation 8,000Other expe nses 5,400EBIT $62,600Interest 11,000Taxable income $51,600Taxes18,060Net income $33,540Dividends $9,500Additions to RE $24,040a.OCF = EBIT + Depreciation – TaxesOCF = $62,600 + 8,000 – 18,060OCF = $52,540b.CFC = Interest – Net new LTDCFC = $11,000 – (–$7,100)CFC = $18,100Note that the net new long-term debt is negative because the compa ny repaid part of its long-term debt.c.CFS = Dividends – Net new equityCFS = $9,500 – 7,250CFS = $2,250d.We know that CFA = CFC + CFS, so:CFA = $18,100 + 2,250 = $20,350CFA is also equal to OCF – Net capital spending – Change in NWC. We already know OCF.Net capital spending is equal to:Net capital spending = Increase in NFA + De preciationNet capital spending = $22,400 + 8,000Net capital spending = $30,400Now we c an use:CFA = OCF – Net capital spending – Change in NWC$20,350 = $52,540 – 30,400 – Change in NWC.Solving for the change in NWC gives $1,790, me aning the company increased its NWC by$1,790.15. The solution to this question works the income statement backwards. Starting at the bottom:Net income = Dividends + Addition to ret. earningsNet income = $1,530 + 5,300Net income = $6,830Now, looking at the income statement:EBT –(EBT × Tax rate) = Net incomeRecognize that EBT × tax rate is simply the calculation for ta xes. Solving this for EBT yields: EBT = NI / (1– Tax rate) EBT = $6,830 / (1 – 0.65)EBT = $10,507.69Now we can calculate:EBIT = EBT + InterestEBIT = $10,507.69 + 1,900EBIT = $12,407.69The last step is to use:EBIT = Sales – Costs – Depreciation$12,407.69 = $43,000 – 27,500 – DepreciationDepreciation = $3,092.31Solving for depreciation, we find that depreciation = $3,092.3116. The balance sheet for the company looks like this:Balance SheetCash $183,000 Accounts payableAc counts receivable 138,000 Notes payableInventory 297,000 Current liabilitiesCurrent assets $618,000 Long-term debtTotal liabilities Tangible net fixed assets 3,200,000Intangible net fixed assets 695,000 Common stockAccumulated ret. earnings Total assets $4,513,000 Total liab. & owners‘ equity Total liabilities and owners‘ equity is: TL & OE = T otal debt + Common stock + Accumulated retained earnings Solving for this equation for equity gives us: Common stock = $4,513,000 – 1,960,000 – 2,160,000Common stock = $393,000$465,000145,000 $610,000 1,550,000 $2,160,0001,960,000 $4,513,00017.18.19. The market value of shareholders‘ equity canno t be negative. A negative market value in this casewould imply that the company would pay you to own the stock. The market value of sha reholders‘ equity can be stated as: Shareholders‘ equity = Max [(TA –TL), 0]. So, if TA is $9,700, equity isequal to $800, and if TA is $6,800, e quity is equal to $0. We should note here that while the market value of equity cannot be negative, the book value of shareholders‘ equity can be negative.a.Taxes Growth= 0.15($50K) + 0.25($25K) + 0.34($3K) = $14,770Taxes Income= 0.15($50K) + 0.25($25K) + 0.34($25K) + 0.39($235K) + 0.34($7.465M)= $2,652,000b. Each firm has a marginal tax rate of 34% on the next$10,000 of taxa ble income, despite theirdifferent average ta x rates, so both firms will pay an additional $3,400 in taxes.Income State mentSales $740,000COGS 610,000A&S expenses 100,000Depreciation 140,000EBIT ($115,000)Interest 70,000Taxable income ($185,000)Taxes (35%) 0/doc/5b4332add1f34693daef3eb1.html income ($185,000)b.OCF = EBIT + Depreciation – TaxesOCF = ($115,000) + 140,000 – 0OCF = $25,00020.21. c. Net income was negative because of the tax deductibility of depreciation and interest expense.However, the actual cash flow from operations wa s positive because de preciation is a non-cashexpense and interest is a financing expense, not an operating expense.A firm can still pay out dividends if net income is negative; it just has to be sure there is sufficientcash flow to make the dividend payments.Change in NWC = Net ca pital spending = Net new equity = 0. (Given)Cash flow from assets = OCF – Change in NWC – Net capitalspendingCash flow from assets = $25,000 – 0 – 0 = $25,000Cash flow to stockholders = Divide nds – Net new equityCash flow to stockholders = $30,000 – 0 = $30,000Cash flow to creditors = Cash flow from assets – Cash flow to stockholdersCash flow to creditors = $25,000 – 30,000Cash flow to creditors = –$5,000Cash flow to creditors is also:Cash flow to creditors = Interest – Net new LTDSo:Net new LTD = Interest – Cash flow to creditorsNet new LTD = $70,000 – (–5,000)Net new LTD = $75,000a. The income statement is:Income StatementSales $15,300Cost of good sold 10,900Depreciation 2,100EBIT $ 2,300Interest 520Taxable income $ 1,780Taxes712Net income $1,068b.OCF= EBIT + Depreciation – TaxesOCF = $2,300 + 2,100 – 712OCF = $3,688c. Change in NWC=NWC end– NWC beg= (CA end–CL en d ) – (CA beg–CL be g)22.= ($3,950 – 1,950) – ($3,400 – 1,900)= $2,000 – 1,500 = $500Ne t capital spending= NFA end– NFA beg+ Depreciation= $12,900 – 11,800 + 2,100= $3,200CFA= OCF – Change in NWC – Net capital spending= $3,688 – 500 – 3,200= –$12The cash flow from assets can be positive or ne gative, since it represents whether the firm raisedfunds or distributed funds on a net basis. In this problem, even though net income and OCF arepositive, the firm invested heavily in both fixed assets and net working capital; it had to raise a net $12 in funds from its stockholders and creditors to make these investments.d. Ca sh flow to creditors= Interest – Net new LTD= $520 – 0= $520Ca sh flow to stoc kholders = Cash flow from assets – Cash flow to creditors= –$12 – 520= –$532We can also calculate the cash flow to stockholders as:Ca sh flow to stoc kholders = Dividends – Ne t new equity Solving for net new equity, we get:Net new equity= $500 – (–532)= $1,032The firm had positive earnings in an accounting sense (NI > 0) and had positive cash flow fromoperations. The firm invested $500 in new net working capital and $3,200 in new fixed assets. The firm had to raise $12 from its stakeholders to support this new inve stment. It accomplished this by raising $1,032 in the form of new equity. After paying out $500 of this in the form of dividends to shareholders and $520 in the form of interest to creditors, $12 was left to meet the firm‘s ca sh flow needs for investment.a. Total assets 2009= $780 + 3,480 = $4,260Total liabilities 2009= $318 + 1,800 = $2,118Owners‘ equity 2009 = $4,260 – 2,118 = $2,142Total assets 2010= $846 + 4,080 = $4,926Total liabilities 2010= $348 + 2,064 = $2,412Owners‘ equity 2010= $4,926 – 2,412 = $2,51414b. NWC 2009NWC 2010Change in NWC = CA09 – CL09 = $780 – 318 = $462= CA10 – CL10 = $846 – 348 = $498= NWC10 – NWC09 = $498 – 462 = $36c.d. We can calculate net capital spe nding as:Net capital spending = Net fixed assets 2010 –Net fixed assets 2009 + Deprec iationNet capital spending = $4,080 – 3,480 + 960Net capital spending = $1,560So, the company had a net capital spending cash flow of$1,560. We also know that net capital spending is:Net capital spending = Fixed assets bought –Fixed assets sold$1,560= $1,800 – Fixed assets soldFixed assets sold= $1,800 – 1,560 = $240To c alculate the cash flow from assets, we must first calculate the operating cash flow. Theoperating cash flow is calculated as follows (you can also prepare a traditional incomestatement):EBIT = Sales – Costs – DepreciationEBIT = $10,320 – 4,980 – 960EBIT = $4,380EBT = EBIT – InterestEBT = $4,380 – 259EBT = $4,121Taxes = EBT ? .35Taxes = $4,121 ? .35Taxes = $1,442OCF = EBIT + Depreciation – TaxesOCF = $4,380 + 960 – 1,442OCF = $3,898Ca sh flow from a ssets = OCF – Change in NWC – Net capital spending.Ca sh flow from a ssets = $3,898 – 36 – 1,560Ca sh flow from a ssets = $2,302Net new borrowing = LTD10 – LTD09Net new borrowing = $2,064 – 1,800Net new borrowing = $264Ca sh flow to creditors = Interest – Net ne w LTDCa sh flow to creditors = $259 – 264Ca sh flow to creditors = –$5Net new borrowing = $264 = Debt issue d – Debt retired Debt retired = $360 – 264 = $9623.CashAccounts receivable InventoryCurrent assetsNet fixed assets Total assetsCashAccounts receivable InventoryCurrent assetsNet fixed assets Total assets Balance sheet as of Dec. 31, 2009 $2,739 Accounts payable3,626 Notes payable6,447 Current liabilities$12,812Long-term debt$22,970 Owners' equity$35,782 Total liab. & equityBalance sheet as of Dec. 31, 2010$2,802Accounts payable4,085 Notes payable6,625Current liabilities$13,512Long-term debt$23,518Owners' equity$37,030Total liab. & equity$2,877529$3,406$9,173$23,203$35,782$2,790497$3,287$10,702$23,041$37,03024.2009 Income StatementSales $5,223.00COGS 1,797.00Othe r expenses 426.00Depreciation 750.00EBIT $2,250.00Interest 350.00EBT $1,900.00Taxes646.00Net income $1,254.00Dividends $637.00Additions to RE 617.00OCF = EBIT + Depreciation – TaxesOCF = $2,459 + 751 – 699.38OCF = $2,510.62Change in NWC = NWC end– NWC beg= (CA – CL)end 2010 Income StatementSales $5,606.00COGS 2,040.00Other expense s 356.00Depreciation 751.00EBIT $2,459.00Interest 402.00EBT $2,057.00Taxes699.38Net income $1,357.62Dividends $701.00Additions to RE 656.62– (CA – CL)begChange in NWC = ($13,512 – 3,287) – ($12,812 – 3,406)Change in NWC = $819Net capital spending = $23,518 – 22,970 + 751Net capital spending = $1,299Net capital spending = NFA– NFA+ Depreciation25. Cash flow from assets = OCF –Change in NWC –Net capital spendingCash flow from assets = $2,510.62 – 819 – 1,299Cash flow from assets = $396.62Cash flow to creditors = Interest – Net new LTDNet new LTD = LTD end– LTD begCash flow to creditors = $402 – ($10,702 – 9,173)Cash flow to creditors = –$1,127Common stock + Retained earnings = Total owners‘ equity Net new equity = (OE – RE)end– (OE – RE)begRE end= RE beg+ Additions to RENet new equity = $23,041 – 23,203 – 656.62 = –$818.62Cash flow to stockholders = Dividends – Net new equityCash flow to stockholders = $701 – (–$818.62)Cash flow to stockholders = $1,519.62As a check, ca sh flow from assets is $396.62.Cash flow from assets = Cash flow from creditors + Cash flow to stockholdersCash flow from assets = –$1,127 + 1,519.62Cash flow from assets = $392.62ChallengeWe will begin by calculating the operating cash flow. First, we need the EBIT, which c an becalculated as:EBIT = Net income + Current taxes + Deferred taxes + Inte restEBIT = $144 + 82 + 16 + 43EBIT = $380Now we can calculate the operating cash flow as:Operating cash flowEarnings before interest and taxes $285Depreciation 78Current taxes (82)Operating cash flow $281Net new equity = Common stock– Common stockNet new equity = OE– OE+ RE– RE∴ Net new equity= OE– OE+ RE– (RE+ Additions to RE)= OE– OE– Additions to REThe cash flow from assets is found in the investing activities portion of the accounting statement of cash flows, so: Cash flow from assetsAcquisition of fixed a ssets $148Sale of fixed assets (19)Capital spending $129The net working capital cash flows are all found in theoperations cash flow section of theaccounting statement of cash flows. However, instead of c alculating the net working capital cashflows as the change in net working capital, we must calculate each item individually. Doing so, wefind:Net working capital cash flowCash $42Accounts receivable 15Inventories (18)Accounts payable (14)Accrued expenses 7Notes payable (5)Other (2)NWC cash flow $25Except for the interest expense and note s payable, the ca sh flow to creditors is found in the financing activities of the accounting statement of cash flows. The inte rest expense from the income statementis given, so:Cash flow to creditorsInterest $43Retirement of debt 135Debt service $178Proceeds from sale of long-term debt (97)Total $81And we can find the cash flow to stockholders in the financing se ction of the accounting stateme nt of cash flows. The cash flow to stockholders was:Cash flow to stockholdersDividends $ 72Repurchase of stock 11Cash to stockholders $ 83Proceeds from new stock issue(37)Total $ 4626. Net capital spending= (NFA– NFA + Depreciation) + (Depreciation + AD) – AD= (NFA+ AD) – (NFA+ ADbeg) =FAbeg– FAend end beg beg end beg27. a.b.c. The tax bubble causes average tax rates to catch up to marginal tax rates, thus eliminating the tax advantage of low marginal rates for high inc ome corporations.Assuming a taxable income of $335,000, the taxes will be:Taxes = 0.15($50K) + 0.25($25K) + 0.34($25K) + 0.39($235K) = $113.9KAverage tax rate = $113.9K / $335K = 34%The marginal tax rate on the next dollar of income is 34 percent.For corporate taxable income levels of $335K to $10M, average tax rates are equal to marginal tax rates.Taxes = 0.34($10M) + 0.35($5M) + 0.38($3.333M) = $6,416,667Average tax rate = $6,416,667 / $18,333,334 = 35%The marginal tax rate on the ne xt dollar of income is 35 percent. For corporate taxable income levels over $18,333,334, ave rage tax rates are again e qual to marginal tax rates.Taxes= 0.34($200K) = $68K = 0.15($50K) + 0.25($25K) + 0.34($25K) + X($100K);X($100K)= $68K – 22.25K = $45.75KX= $45.75K / $100KX= 45.75%=NFA– NFAend= (NFAbeg– NFA)+ AD– AD。