公司理财罗斯第9 版Chap004

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罗斯公司理财第九版第四章课后答案

23题：This question is asking for the present value of an annuity, but the interest rate changes during the life of the annuity. We need to find the present value of the cash flows for the last eight years first. The PV of these cash flows is:PVA2 = $1,500 [{1 – 1 / [1 + (.09/12)]⌒96} / (.09/12)] = $102,387.66Note that this is the PV of this annuity exactly seven years from today. Now, we can discount this lump sum to today. The value of this cash flow today is:PV = $102,387.66 / [1 + (.13/12)]⌒84 = $41,415.70Now, we need to find the PV of the annuity for the first seven years. The value of these cash flows today is:PVA1 = $1,500 [{1 – 1 / [1 + (.13/12)]⌒84} / (.13/12)] = $82,453.99The value of the cash flows today is the sum of these two cash flows, so:PV = $82,453.99 + 41,415.70 = $123,869.9924题The monthly interest rate is the annual interest rate divided by 12, or:Monthly interest rate = .104 / 12 Monthly interest rate = .00867Now we can set the present value of the lease payments equal to the cost of the equipment, or $3,500. The lease payments are in the form of an annuity due, so:PV Adue = (1 + r) C({1 – [1/(1 + r)]⌒t } / r )$3,500 = (1 + .00867) C({1 – [1/(1 + .00867)]⌒24 } / .00867 ) C = $160.7625题Here, we need to compare to options. In order to do so, we must get the value of the two cash flow streams to the same time, so we will find the value of each today. We must also make sure to use the aftertax cash flows, since it is more relevant. For Option A, the aftertax cash flows are:Aftertax cash flows = Pretax cash flows(1 – tax rate)Aftertax cash flows = $175,000(1 – .28)Aftertax cash flows = $126,000The aftertax cash flows from Option A are in the form of an annuity due, so the present value of the cash flow today is:PV Adue = (1 + r) C({1 – [1/(1 + r)]⌒t } / r )PV Adue = (1 + .10)$126,000({1 – [1/(1 + .10)]⌒31 } / .10 )PV Adue = $1,313,791.22For Option B, the aftertax cash flows are:Aftertax cash flows = Pretax cash flows(1 – tax rate)Aftertax cash flows = $125,000(1 – .28)Aftertax cash flows = $90,000The aftertax cash flows from Option B are an ordinary annuity, plus the cash flow today, so the present value:PV = C({1 – [1/(1 + r)]⌒t } / r ) + CF0PV = $90,000{1 – [1/(1 + .10)]⌒30 } / .10 ) + $530,000PV = $1,378,422.3026题The cash flows for this problem occur monthly, and the interest rate given is the EAR. Since the cash flows occur monthly, we must get the effective monthly rate. One way to do this is to find the APR based on monthly compounding, and then divide by 12. So, the pre-retirement APR is: EAR = .11 = [1 + (APR / 12)]⌒12– 1; APR = 12[(1.11)1/12 – 1] = 10.48%And the post-retirement APR is:EAR = .08 = [1 + (APR / 12)]⌒12 – 1; APR = 12[(1.08)1/12 – 1] = 7.72%First, we will calculate how much he needs at retirement. The amount needed at retirement is the PV of the monthly spending plus the PV of the inheritance. The PV of these two cash flows is:PV A = $20,000{1 – [1 / (1 + .0772/12)⌒12*20]} / (.0772/12) = $2,441,554.61PV = $1,000,000 / (1 + .08)20 = $214,548.21So, at retirement, he needs: $2,441,554.61 + 214,548.21 = $2,656.102.81He will be saving $1,900 per month for the next 10 years until he purchases the cabin. The value of his savings after 10 years will be:FV A = $1,900[{[ 1 + (.1048/12)]⌒12*10– 1} / (.1048/12)] = $400,121.62After he purchases the cabin, the amount he will have left is: $400,121.62 – 320,000 = $80,121.62 He still has 20 years until retirement. When he is ready to retire, this amount will have grown to: FV = $80,121.62[1 + (.1048/12)]⌒12*20 = $646,965.50So, when he is ready to retire, based on his current savings, he will be short:$2,656,102.81 – 645,965.50 = $2,010,137.31This amount is the FV of the monthly savings he must make between years 10 and 30. So, finding the annuity payment using the FVA equation, we find his monthly savings will need to be: FVA = $2,010,137.31 = C[{[ 1 + (.1048/12)]⌒12*20 – 1} / (.1048/12)]C = $2,486.1227题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 $1. 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 = $1 + $520{1 – [1 / (1 + .08/12)⌒12*3]} / (.08/12) = $16,595.14The 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 = $26,000 / [1 + (.08/12)]⌒12*3 = $20,468.62The PV of the decision to purchase is:$38,000 – 20,468.62 = $17,531.38In this case, it is cheaper to lease the car than buy it since the PV of the leasing cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the tw o options the same. In other words, the PV of the decision to buy should be:$38,000 – PV of resale price = $16,595.14PV of resale price = $21,404.86The resale price that would make the PV of the lease versus buy decision is the FV of this value, so:Breakeven resale price = $21,404.86[1 + (.08/12)]⌒12*3 = $27,189.2528题First, we will find the APR and EAR for the loan with the refundable fee. Remember, we need to use the actual cash flows of the loan to find the interest rate. With the $2,100 application fee, you will need to borrow $202,100 to have $200,000 after deducting the fee. Solving for the payment under these circumstances, we get:PV A = $202,100 = C {[1 – 1/(1.00567)⌒360]/.00567} where .00567 = .068/12 C = $1,317.54 We can now use this amount in the PV A equation with the original amount we wished to borrow, $200,000. Solving for r, we find:PV A = $200,000 = $1,317.54[{1 – [1 / (1 + r)]⌒360}/ r]Solving for r with a spreadsheet, on a financial calculator, or by trial and error, gives:r = 0.5752% per monthAPR = 12(0.5752%) = 6.90% EAR = (1 + .005752)⌒12– 1 = .0713 or 7.13%With the nonrefundable fee, the APR of the loan is simply the quoted APR since the fee is not considered part of the loan. So:APR = 6.80% EAR = [1 + (0.068/12)]⌒12– 1 = .0702 or 7.02%29题Here, we need to find the interest rate that makes us indifferent between an annuity and a perpetuity. To solve this problem, we need to find the PV of the two options and set them equal to each other. The PV of the perpetuity is:PV = $20,000 / rAnd the PV of the annuity is:PVA = $35,000[{1 – [1 / (1 + r)]⌒10 } / r ]Setting them equal and solving for r, we get:$20,000 / r = $35,000[{1 – [1 / (1 + r)]⌒10 } / r ]$20,000 / $35,000 = 1 – [1 / (1 + r)]⌒10 .057141/10 = 1 / (1 + r)r = 1 / .5714⌒1/10 – 1 r = .0576 or 5.76%30题。

Cha04 罗斯公司理财第九版原版书课后习题

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。

罗斯《公司理财》第9版笔记和课后习题(含考研真题)详解[视频详解](折现现金流量估价)【圣才出品】

罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]第4章折现现金流量估价[视频讲解]4.1复习笔记当前的1美元与未来的1美元的价值是不同的，因为当前1美元用于投资，在未来可以得到更多，而且未来的1美元具有不确定性。

这种区别正是“货币的时间价值”。

货币的时间价值概念是金融投资和融资的基石之一，资本预算、项目决策、融资管理和兼并等领域均有涉及。

因此有必要理解和掌握相关的现值、终值、年金和永续年金的概念和计算公式。

1．现值与净现值现值是未来资金在当前的价值，是把未来的现金流按照一定的贴现率贴现到当前的价值。

以单期为例，一期后的现金流的现值：其中，C1是一期后的现金流，r是适当贴现率。

在多期的情况下，求解PV的公式可写为：其中，C T是在T期的现金流，r是适当贴现率。

净现值的计算公式为：NPV=-成本+PV。

也就是说，净现值NPV是这项投资未来现金流的现值减去成本的现值所得的结果。

一种定量的财务决策方法是净现值分析法。

产生N期现金流的投资项目的净现值为：NPV=其中，-C0是初始现金流，由于它代表了一笔投资，即现金流出，因而是负值。

2．终值一笔投资在多期以后终值的一般计算公式可以写为：FV=C0×（1+r）T其中，C0是期初投资的金额，r是利息率，T是资金投资持续的期数。

一项投资每年按复利计息m次的年末终值为：其中：C0是投资者的初始投资；r是名义年利率。

当m趋近于无限大时，则是连续复利计息，这时T年后的终值可以表示为：C0×e rT。

连续复利在高级金融中有广泛的应用。

3．名义利率和实际利率名义年利率是不考虑年内复利计息的，不同的银行或金融机构有不同的称谓，比较通用的是年百分比利率（APR）；实际利率（EAR）是指在年内考虑复利计息的，然后折算成一年的利率。

名义利率和实际利率之间的差别在于名义利率只有给出计息间隔期下才有意义。

4．年金年金是指一系列稳定有规律的，持续一段固定时期的现金收付活动，即在一定期间内，每隔相同时期（一年、半年或一季等）收入或支出相等金额的款项。

ROSS公司理财第九版第4章课后案例作业

所需成本现值=65000+3000+
（
+
=140952.90
所得报酬的现值= =1669675.47 因此，Ben 选择到 Wilton 大学去读 MBA 的净现值为 1528722.57 美元。（3）Ben 选择到 Mount Perry 大学去读 MBA
学费/年
保险费
书费等
食宿费
签约费
薪酬/年
第4章
折现现金流量估价习题参考答案
小案例
有关取得 MBA 学位的决定 P89
Ben Bates 6 年前大学毕业并获得理财学学士学位，尽管对目前的工作很满意，但他的目标是成为一名投资银行家。他认为一个 MBA 学位将使他达到该目标。经过考试，其可选学校有 Wilton 大学和 Mount Perry 大学。尽管两所学校均鼓励通过实习拿到学分，但实习是没有薪酬的。除了实习，两所学校都不允许学生在 MBA 期间工作。 Ben 目前在 Dewey and Louis 投资管理公司工作。他每年的薪酬为 60000 美元，并且预期薪酬会以每年 3%的比例增长直到其退休。他目前是 28 岁，估计还可以工作 35 年。他目前的工作还包括一个完全支付的健康保险计划，并且其目前平均税率为 26%。Ben 的储蓄账户有足够的钱来完成 MBA 学业。 Wilton 大学 Ritter 商学院是该国顶尖的商学院之一。要获取该学院的 MBA 学位，需要在学校里全脱产学习 2 年。每学年的学费为 65000 美元，这些学费需要在该年年初支付。书与其他用品花费估计每年需要 3000 美元。Ben 估计从该学校毕业后，他将找到一份新的工作，其每年可以给他带来 110000 美元的薪酬，并且还有 20000 美元的签约酬金，该工作的薪酬将以每年 4%的增长率增长。由于薪酬较高，其平均首付税率将增至 31%。 Mount Perry 大学 Bradley 商学院从 16 年前开始设 MBA 课程。与 Ritter 学院相比，Bradley 学院显得很小而且不出名。Bradley 商学院提供了一个速成的、1 年期的课程。在被录取入学时要叫学费 80000 美元。书与其他用品花费估计需要 4500 美元。 Ben 估计毕业后，他将找到一份新的工作，其每年可以给他带来 92000 美元的薪酬，并且还有 18000 美元的签约薪酬，该工作的薪酬将以每年 3.5%的增长率增长。其平均税率将增至 29%。两所大学均提供了一份健康保险计划，其花费为每年 3000 美元，在每年年初支付。Ben 估计在任一所大学的食宿花费每年需 2000 美元。适当的折现率是 6.5%。源自学费/年保险费书费等

公司理财第九版罗斯课后案例答案 Case Solutions Corporate Finance

公司理财第九版罗斯课后案例答案 Case Solutions CorporateFinance1. 案例一：公司资金需求分析问题：一家公司需要资金支持其新项目。

通过分析现金流量，推断该公司是否需要向外部借款或筹集其他资金。

解答：为了确定公司是否需要外部资金，我们需要分析公司的现金流量状况。

首先，我们需要计算公司的净现金流量（净收入加上非现金项目）。

然后，我们需要将净现金流量与项目的投资现金流量进行对比。

假设公司预计在项目开始时投资100万美元，并在项目运营期为5年。

预计该项目每年将产生50万美元的净现金流量。

现在，我们需要进行以下计算：净现金流量 = 年度现金流量 - 年度投资现金流量年度投资现金流量 = 100万美元年度现金流量 = 50万美元净现金流量 = 50万美元 - 100万美元 = -50万美元根据计算结果，公司的净现金流量为负数（即净现金流出），意味着公司每年都会亏损50万美元。

因此，公司需要从外部筹集资金以支持项目的运营。

2. 案例二：公司股权融资问题：一家公司正在考虑通过股权融资来筹集资金。

根据公司的财务数据和资本结构分析，我们需要确定公司最佳的股权融资方案。

解答：为了确定最佳的股权融资方案，我们需要参考公司的财务数据和资本结构分析。

首先，我们需要计算公司的资本结构比例，即股本占总资本的比例。

然后，我们将不同的股权融资方案与资本结构比例进行对比，选择最佳的方案。

假设公司当前的资本结构比例为60%的股本和40%的债务，在当前的资本结构下，公司的加权平均资本成本（WACC）为10%。

现在，我们需要进行以下计算：•方案一：以新股发行筹集1000万美元，并将其用于项目投资。

在这种方案下，公司的资本结构比例将发生变化。

假设公司的股本增加至80%，债务比例减少至20%。

根据资本结构比例的变化，WACC也将发生变化。

新的WACC可以通过以下公式计算得出：新的WACC = (股本比例 * 股本成本) + (债务比例 * 债务成本)假设公司的股本成本为12%，债务成本为8%：新的WACC = (0.8 * 12%) + (0.2 * 8%) = 9.6%•方案二：以新股发行筹集5000万美元，并将其用于项目投资。

罗斯《公司理财》第9版英文原书课后部分章节答案

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。

罗斯《公司理财》第9版笔记和课后习题(含考研真题)详解-第4篇资本结构与股利政策【圣才出品】

第4篇资本结构与股利政策第14章有效资本市场和行为学挑战[视频讲解]14.2 课后习题详解一、概念题1．泡沫理论（bubble theory）答：泡沫理论是描述经济的虚假繁荣（即泡沫经济）和价格的虚假上涨（即经济泡沫）的一种金融理论。

这一理论认为，泡沫的具体表现是证券的价格有时大大高于其真实价值，经济及金融市场过热，形成虚假繁荣，最终价格跌到原有的水平，从而给投资者造成大量损失。

17世纪荷兰的“郁金香狂潮”和18世纪英国的“南海泡沫”就是历史上两起最有名的泡沫事件。

泡沫经济常常误导资源配置，造成资源的极大浪费，并引起社会分配严重不公，损害经济长期增长。

2．半强型效率（semi strong-form efficiency）答：半强型效率是指现行证券价格反映了全部已公开的信息，或者说全部已公开的信息对证券价格的变动没有任何影响，这种是证券市场效率的中等程度。

3．有效市场假说（efficient-market hypothesis）答：有效市场假说是资本市场研究的一种理论假设，指在一个有效的资本市场中，有关投资品的全部信息都能够迅速、完整和准确地被投资者所获得，投资者可以据此准确判断该投资品的价值并作出正确的决策。

反过来说，任何时刻的投资品价格都已充分反映了投资者当时所能得到的一切相关信息，该价格全面反映了该投资品的内在价值。

有效市场假说的主要内容有：投资品价格迅速反映未预期的信息；投资品价格随机变动；投资者无法获得超额利润。

有效资本市场成立的充分条件：信息公开的有效性；信息从公开到被接收的有效性；市场价格的独立性；信息接收者对所获得信息作出判断的有效性;信息的接收者依照其判断实施投资的有效性。

在现实中，这一理论假设存在种种约束，表现在：信息公开的数量、规模和时间的制约；信息传递的时效性；投资者对信息的判断存在个体差异；投资者实施投资决策的有效性受到限制。

有效市场理论中的市场效率不是指市场的运作效率（如市场中的信息运输、交易指令的执行、交割、清算、记录等功能的质量、速度和成本水平），而是指市场的信息效率，即资本市场中投资品的价格对信息的敏感程度和反应速度。

罗斯公司理财英文习题答案chap004

Chapter 4: Net Present Value4.1 a. $1,000 1.0510 = $1,628.89b. $1,000 1.0710 = $1,967.15c. $1,000 1.0520 = $2,653.30d. Interest compounds on the I nterest already earned. Therefore, the interest earned in part c, $1,653.30, is more than double the amount earned in part a, $628.89.4.2 a. $1,000 / 1.17 = $513.16b. $2,000 / 1.1 = $1,818.18c. $500 / 1.18 = $233.254.3 You can make your decision by computing either the present value of the$2,000 that you can receive in ten years, or the future value of the$1,000 that you can receive now.Present value: $2,000 / 1.0810 = $926.39Future value: $1,000 1.0810 = $2,158.93Either calculation indicates you should take the $1,000 now.4.4 Since this bond has no interim coupon payments, its present value issimply the present value of the $1,000 that will be received in 25 years.Note: As will be discussed in the next chapter, the present value of the payments associated with a bond is the price of that bond.PV = $1,000 /1.125 = $92.304.5 PV = $1,500,000 / 1.0827 = $187,780.234.6 a. At a discount rate of zero, the future value and present valueare always the same. Remember, FV = PV (1 + r) t. If r = 0, then the formula reduces to FV = PV. Therefore, thevalues of the options are $10,000 and $20,000, respectively. Youshould choose the second option.b. Option one: $10,000 / 1.1 = $9,090.91Option two: $20,000 / 1.15 = $12,418.43Choose the second option.c. Option one: $10,000 / 1.2 = $8,333.33Option two: $20,000 / 1.25 = $8,037.55Choose the first option.d. You are indifferent at the rate that equates the PVs of the twoalternatives. You know that rate must fall between 10% and 20%because the option you would choose differs at these rates. Letr be the discount rate that makes you indifferent between theoptions.$10,000 / (1 + r) = $20,000 / (1 + r)5(1 + r)4 = $20,000 / $10,000 = 21 + r = 1.18921r = 0.18921 = 18.921%4.7 PV of Joneses’ offer = $150,000 / (1.1)3 = $112,697.22Since the PV of Joneses’ offer is less than Smiths’ offer, $115,000,you should choose Smiths’ offer.4.8 a. P0 = $1,000 / 1.0820 = $214.55b. P10 = P0 (1.08)10 = $463.20c. P15 = P0 (1.08)15 = $680.594.9 The $1,000 that you place in the account at the end of the first yearwill earn interest for six years. The $1,000 that you place in theaccount at the end of the second year will earn interest for five years, etc. Thus, the account will have a balance of$1,000 (1.12)6 + $1,000 (1.12)5 + $1,000 (1.12)4 + $1,000 (1.12)3= $6,714.614.10 PV = $5,000,000 / 1.1210 = $1,609,866.184.11 a. The cost of investment is $900,000.PV of cash inflows = $120,000 / 1.12 + $250,000 / 1.122 + $800,000 / 1.123= $875,865.52Since the PV of cash inflows is less than the cost of investment,you should not make the investment.b. NPV = -$900,000 + $875,865.52= -$24,134.48c. NPV = -$900,000 + $120,000 / 1.11 + $250,000 / 1.112 + $800,000/ 1.113= $-4,033.18Since the NPV is still negative, you should not make the investment.4.12 NPV = -($340,000 + $10,000) + ($100,000 - $10,000) / 1.1+ $90,000 / 1.12 + $90,000 / 1.13 + $90,000 / 1.14 + $100,000 /1.15= -$2,619.98Since the NPV is negative, you should not buy it.If the relevant cost of capital is 9 percent,NPV = -$350,000 + $90,000 / 1.09 + $90,000 / 1.092 + $90,000 /1.093+ $90,000 / 1.094 + $100,000 / 1.095= $6,567.93Since the NPV is positive, you should buy it.4.13 a. Profit = PV of revenue - Cost = NPVNPV = $90,000 / 1.15 - $60,000 = -$4,117.08No, the firm will not make a profit.b. Find r that makes zero NPV.$90,000 / (1+r)5 - $60,000 = $0(1+r)5 = 1.5r = 0.08447 = 8.447%4.14 The future value of the decision to own your car for one year is the sumof the trade-in value and the benefit from owning the car. Therefore,the PV of the decision to own the car for one year is$3,000 / 1.12 + $1,000 / 1.12 = $3,571.43Since the PV of the roommate’s offer, $3,500, is lower than the aunt’s offer, you should accept aunt’s offer.4.15 a. $1.000 (1.08)3 = $1,259.71b. $1,000 [1 + (0.08 / 2)]2 3 = $1,000 (1.04)6 = $1,265.32c. $1,000 [1 + (0.08 / 12)]12 3 = $1,000 (1.00667)36 = $1,270.24d. $1,000 e0.08 3 = $1,271.25e. The future value increases because of the compounding. Theaccount is earning interest on interest. Essentially, theinterest is added to the account balance at the end of everycompounding period. During the next period, the account earnsinterest on the new balance. When the compounding period shortens, the balance that earns interest is rising faster.4.16 a. $1,000 e0.12 5 = $1,822.12b. $1,000 e0.1 3 = $1,349.86c. $1,000 e0.05 10 = $1,648.72d. $1,000 e0.07 8 = $1,750.674.17 PV = $5,000 / [1+ (0.1 / 4)]4 12 = $1,528.364.18 Effective annual interest rate of Bank America= [1 + (0.041 / 4)]4 - 1 = 0.0416 = 4.16%Effective annual interest rate of Bank USA= [1 + (0.0405 / 12)]12 - 1 = 0.0413 = 4.13%You should deposit your money in Bank America.4.19 The price of the consol bond is the present value of the coupon payments.Apply the perpetuity formula to find the present value. PV = $120 / 0.15 = $8004.20 Quarterly interest rate = 12% / 4 = 3% = 0.03Therefore, the price of the security = $10 / 0.03 = $333.334.21 The price at the end of 19 quarters (or 4.75 years) from today = $1 /(0.15 4) = $26.67The current price = $26.67 / [1+ (.15 / 4)]19 = $13.254.22 a. $1,000 / 0.1 = $10,000b. $500 / 0.1 = $5,000 is the value one year from now of theperpetual stream. Thus, the value of the perpetuity is $5,000 /1.1 = $4,545.45.c. $2,420 / 0.1 = $24,200 is the value two years from now of theperpetual stream. Thus, the value of the perpetuity is $24,200 / 1.12 = $20,000.4.23 The value at t = 8 is $120 / 0.1 = $1,200.Thus, the value at t = 5 is $1,200 / 1.13 = $901.58.4.24 P = $3 (1.05) / (0.12 - 0.05) = $45.004.25 P = $1 / (0.1 - 0.04) = $16.674.26 The first cash flow will be generated 2 years from today.The value at the end of 1 year from today = $200,000 / (0.1 - 0.05) =$4,000,000.Thus, PV = $4,000,000 / 1.1 = $3,636,363.64.4.27A zero NPV-$100,000 + $50,000 / r = 0-r = 0.54.28 Apply the NPV technique. Since the inflows are an annuity you can usethe present value of an annuity factor.NPV = -$6,200 + $1,200 81.0= -$6,200 + $1,200 (5.3349)= $201.88Yes, you should buy the asset.4.29 Use an annuity factor to compute the value two years from today of thetwenty payments. Remember, the annuity formula gives you the value ofthe stream one year before the first payment. Hence, the annuity factorwill give you the value at the end of year two of the stream of payments.AValue at the end of year two = $2,000 2008.0= $2,000 (9.8181)= $19,636.20The present value is simply that amount discounted back two years.PV = $19,636.20 / 1.082 = $16,834.884.30 The value of annuity at the end of year fiveA = $500 (5.84737) = $2,923.69= $500 15.015The present value = $2,923.69 / 1.125 = $1,658.984.31 The easiest way to do this problem is to use the annuity factor. Theannuity factor must be equal to $12,800 / $2,000 = 6.4; remember PV =C A t r.The annuity factors are in the appendix to the text. To use the factortable to solve this problem, scan across the row labeled 10 years untilyou find 6.4. It is close to the factor for 9%, 6.4177. Thus, the rateyou will receive on this note is slightly more than 9%.You can find a more precise answer by interpolating between nine and tenpercent.10% 6.1446a rbc 6.4 d9% 6.4177By interpolating, you are presuming that the ratio of a to b is equal tothe ratio of c to d.(9 - r ) / (9 - 10) = (6.4177 - 6.4 ) / (6.4177 - 6.1446)r = 9.0648%The exact value could be obtained by solving the annuity formula for theinterest rate. Sophisticated calculators can compute the rate directlyas 9.0626%.4.32 a. The annuity amount can be computed by first calculating the PV ofthe $25,000 which you need in five years. That amount is$17,824.65 [= $25,000 / 1.075]. Next compute the annuity which has the same present value.$17,824.65 = C 507.0A$17,824.65 = C (4.1002)C = $4,347.26Thus, putting $4,347.26 into the 7% account each year will provide $25,000 five years from today.b. The lump sum payment must be the present value of the $25,000, i.e., $25,000 / 1.075 = $17,824.65 The formula for future value of any annuity can be used to solvethe problem (see footnote 14 of the text).4.33 The amount of loan is $120,000 0.85 = $102,000.2010.0C A = $102,000The amount of equal installments is C = $102,000 / 2010.0A = $102,000 / 8.513564 = $11,980.884.34 The present value of salary is $5,000 3601.0A = $150,537.53The present value of bonus is $10,000 31268.0A = $23,740.42 (EAR = 12.68% is used since bonuses are paid annually.) The present value of the contract = $150,537.53 + $23,740.42 =$174,277.944.35 The amount of loan is $15,000 0.8 = $12,000.C 480067.0A = $12,000The amount of monthly installments is C = $12,000 / 480067.0A = $12,000 / 40.96191 = $292.964.36 Option one: This cash flow is an annuity due. To value it, you must usethe after-tax amounts. The after-tax payment is $160,000 (1 - 0.28) = $115,200. Value all except the first payment using the standard annuity formula, then add back the first payment of $115,200 to obtain the value of this option.Value = $115,200 + $115,200 3010.0A= $115,200 + $115,200 (9.4269)= $1,201,178.88Option two: This option is valued similarly. You are able to have$446,000 now; this is already on an after-tax basis. You will receive an annuity of $101,055 for each of the next thirty years. Those paymentsare taxable when you receive them, so your after-tax payment is $72,759.60 [= $101,055 (1 - 0.28)].Value = $446,000 + $72,759.60 30.010= $446,000 + $72,759.60 (9.4269)= $1,131,897.47Since option one has a higher PV, you should choose it.4.37 The amount of loan is $9,000. The monthly payment C is given by solvingthe equation:C 60008.0A = $9,000C = $9,000 / 47.5042 = $189.46 In October 2000, Susan Chao has 35 (= 12 5 - 25) monthly payments left, including the one due in October 2000.Therefore, the balance of the loan on November 1, 2000 = $189.46 + $189.46 34008.0A= $189.46 + $189.46 (29.6651)= $5,809.81Thus, the total amount of payoff = 1.01 ($5,809.81) = $5,867.914.38 Let r be the rate of interest you must earn.$10,000(1 + r)12 = $80,000(1 + r)12 = 8r = 0.18921 = 18.921%4.39 First compute the present value of all the payments you must make foryour children’s education. The value as of on e year beforematriculation of one child’s education is$21,000 415.0A = $21,000 (2.8550) = $59,955.This is the value of the elder child’s education fourteen years from now.It is the value of the younger child’s education sixteen yea rs fromtoday. The present value of these isPV = $59,955 / 1.1514 + $59,955 / 1.1516= $14,880.44You want to make fifteen equal payments into an account that yields 15% so that the present value of the equal payments is $14,880.44.Payment = $14,880.44 / 1515.0A = $14,880.44 / 5.8474 = $2,544.804.40 The NPV of the policy isNPV = -$750 306.0A - $800 306.0A / 1.063 + $250,000 / [(1.066)(1.0759)] = -$2,004.76 - $1,795.45 + $3,254.33= -$545.88Therefore, you should not buy the policy.4.41 The NPV of the lease offer isNPV = $120,000 - $15,000 - $15,000 908.0A - $25,000 / 1.0810= $105,000 - $93,703.32 - $11,579.84= -$283.16Therefore, you should not accept the offer.4.42 This problem applies the growing annuity formula. The first payment is$50,000(1.04)2(0.02) = $1,081.60.PV = $1,081.60 [1 / (0.08 - 0.04) - {1 / (0.08 - 0.04)}{1.04 / 1.08}40]= $21,064.28This is the present value of the payments, so the value forty years from today is$21,064.28 (1.0840) = $457,611.464.43 Use the discount factors to discount the individual cash flows. Thencompute the NPV of the project. Notice that the four $1,000 cash flowsform an annuity. You can still use the factor tables to compute their PV. Essentially, they form cash flows that are a six year annuity less a two year annuity. Thus, the appropriate annuity factor to use with them is2.6198 (= 4.3553 - 1.7355). Year Cash Flow Factor PV1 $7000.9091 $636.372 9000.8264 743.763 1,0004 1,000 2.6198 2,619.805 1,0006 1,0007 1,250 0.5132 641.508 1,375 0.4665 641.44Total $5,282.87NPV = -$5,000 + $5,282.87= $282.87Purchase the machine.4.44 Weekly inflation rate = 0.039 / 52 = 0.00075Weekly interest rate = 0.104 / 52 = 0.002PV = $5 [1 / (0.002 - 0.00075)] {1 – [(1 + 0.00075) / (1 + 0.002)]5230}= $3,429.384.45 Engineer:NPV = -$12,000 405.0A + $20,000 / 1.055 + $25,000 / 1.056 - $15,000 /1.057- $15,000 / 1.058 + $40,000 2505.0A / 1.058= $352,533.35Accountant:NPV = -$13,000 405.0A + $31,000 3005.0A / 1.054= $345,958.81Become an engineer.After your brother announces that the appropriate discount rate is 6%,you can recalculate the NPVs. Calculate them the same way as above except using the 6% discount rate.Engineer NPV = $292,419.47Accountant NPV = $292,947.04Your brother made a poor decision. At a 6% rate, he should studyaccounting.4.46 Since Goose receives his first payment on July 1 and all payments in oneyear intervals from July 1, the easiest approach to this problem is to discount the cash flows to July 1 then use the six month discount rate (0.044) to discount them the additional six months.PV = $875,000 / (1.044) + $650,000 / (1.044)(1.09) + $800,000 / (1.044)(1.092)+ $1,000,000 / (1.044)(1.093) + $1,000,000/(1.044)(1.094) + $300,000/ (1.044)(1.095)+ $240,000 1709.0A / (1.044)(1.095) + $125,000 1009.0A / (1.044)(1.0922)= $5,051,150Remember that the use of annuity factors to discount the deferredpayments yields the value of the annuity stream one period prior to the first payment. Thus, the annuity factor applied to the first set of deferred payments gives the value of those payments on July 1 of 1989. Discounting by 9% for five years brings the value to July 1, 1984. The use of the six month discount rate (4.4%) brings the value of thepayments to January 1, 1984. Similarly, the annuity factor applied to the second set of deferred payments yields the value of those payments in 2006. Discounting for 22 years at 9% and for six months at4.4% provides the value at January 1, 1984.The equivalent five-year, annual salary is the annuity that solves:$5,051,150 = C 509.0AC = $5,051,150/3.8897C = $1,298,596The student must be aware of possible rounding errors in this problem. The difference between 4.4% semiannual and 9.0% and for six months at4.4% provides the value at January 1, 1984.4.47 PV = $10,000 + ($35,000 + $3,500) [1 / (0.12 - 0.04)] [1 - (1.04 /1.12) 25 ]= $415,783.604.48 NPV = -$40,000 + $10,000 [1 / (0.10 - 0.07)] [1 - (1.07 / 1.10)5 ]= $3,041.91Revise the textbook.4.49The amount of the loan is $400,000 (0.8) = $320,000A= $ 2,348.10 The monthly payment is C = $320,000 / 360..0067Thirty years of payments $ 2,348.10 (360) = $ 845,316.00Eight years of payments $2,348.10 (96) = $225,417.60The difference is the balloon payment of $619,898.404.50The lease payment is an annuity in advanceA = $4,000C + C 2301.0C (1 + 20.4558) = $4,000C = $186.424.51The effective annual interest rate is[ 1 + (0.08 / 4) ] 4 – 1 = 0.0824The present value of the ten-year annuity isA = $5,974.24PV = 900 100824.0Four remaining discount periodsPV = $5,974.24 / (1.0824) 4 = $4,352.434.52The present value of Ernie’s retirement incomeA / (1.07) 30 = $417,511.54PV = $300,000 2007.0The present value of the cabinPV = $350,000 / (1.07) 10 = $177,922.25The present value of his savingsA = $280,943.26PV = $40,000 10.007In present value terms he must save an additional $313,490.53 In future value termsFV = $313,490.53 (1.07) 10 = $616,683.32He must saveA = $58,210.54C = $616.683.32 / 2007.0。

精编版罗斯《公司理财》中文版第九版课件资料

由于资金在不同时点的价值不同，所以资金时间价值的表现形式就有两种：现值和终值。
现值是指未来一定时间的特定货币按一定利率折算到现在的价值。
终值是指现在一定数额的资金按一定的利率计算的一定时间后的价值。
2.1资金时间价值观念
复利终值与现值
复利终值，是指一次性的收、付款项经过若干期的使用后，所获得的包括本金和利息在内的未来价值。
因为永续年金无终止时间，所以不存在终值问题，永续年金推倒公式如下：
2.1资金时间价值观念
资金时间价值计算中的几个特殊问题
不等额系列款项现值的计算：为求得不等额的系列付款的现值之和，可以先计算每次付款的复利现值，然后加总。
年金与不等额的系列付款混合情况下的现值：如果在一组不等额的系列款项中，有部分是连续发生的等额付款，则可分段计算其年金现值及复利现值，然后加总。
式中：是第j种证券的预期报酬率；是第j种证券在全部投资额中的比重；m是组合中证券种类总数。
2.2风险与收益权衡观念
组合投资的风险及度量。证券组合的风险不仅仅取决于组合内各种证券的风险，还取决于各个证券之间的关系。投资组合报酬率概率分布的标准差的计算公式为：
式中：m是组合内证券种类总数；是第j种证券在投资总额中占的比例；是第k种证券在投资总额中占的比例；是第j种证券与第k种证券报酬率的协方差。
1.4公司理财的原则与职能
公司理财原则
资金合理配置原则财务收支平衡原则成本－效益原则风险与收益均衡原则利益关系协调原则
1.4公司理财的原则与职能
公司理财职能
财务预测财务决策财务预算财务控制财务分析
1.5公司理财环境
公司理财的宏观环境
经济环境

罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]（股票估值）【圣才出品】

罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]（股票估值）【圣才出品】罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]第9章股票估值9.1复习笔记1．不同类型股票的估值（1）零增长股利股利不变时，一股股票的价格由下式给出：在这里假定Div1=Div2=…=Div。

（2）固定增长率股利如果股利以恒定的速率增长，那么一股股票的价格就为：式中，g是增长率；Div是第一期期末的股利。

（3）变动增长率股利2．股利折现模型中的参数估计（1）对增长率g的估计有效估计增长率的方法是：g=留存收益比率×留存收益收益率（ROE）只要公司保持其股利支付率不变，g就可以表示公司的股利增长率以及盈利增长率。

（2）对折现率R的估计对于折现率R的估计为：R=Div/P0+g该式表明总收益率R由两部分组成。

其中，第一部分被称为股利收益率，是预期的现金股利与当前的价格之比。

3．增长机会每股股价可以写做：该式表明，每股股价可以看做两部分的加和。

第一部分（EPS/R）是当公司满足于现状，而将其盈利全部发放给投资者时的价值；第二部分是当公司将盈利留存并用于投资新项目时的新增价值。

当公司投资于正NPVGO的增长机会时，公司价值增加。

反之，当公司选择负NPVGO 的投资机会时，公司价值降低。

但是，不管项目的NPV是正的还是负的，盈利和股利都是增长的。

不应该折现利润来获得每股价格，因为有部分盈利被用于再投资了。

只有股利被分到股东手中，也只有股利可以加以折现以获得股票价格。

4．市盈率即股票的市盈率是三个因素的函数：（1）增长机会。

拥有强劲增长机会的公司具有高市盈率。

（2）风险。

低风险股票具有高市盈率。

（3）会计方法。

采用保守会计方法的公司具有高市盈率。

5．股票市场交易商：持有一项存货，然后准备在任何时点进行买卖。

经纪人：将买者和卖者撮合在一起，但并不持有存货。

9.2课后习题详解一、概念题1．股利支付率（payout ratio）答：股利支付率一般指公司发放给普通股股东的现金股利占总利润的比例。

罗斯《公司理财》中文版第九版课件-精品文档307页

名义利率和实际利率的换算：将名义利率调整为次利率，再转换为实际利率，然后按实际利率计算资金时间价值；不计算实际利率，而是调整有关指标。
。
2.1资金时间价值观念
利率（折现率）的确定：
对于复利来说，若已知P，F，n，可不用查表而直接计算出i；
但对普通年金问题，首先要根据等额的款项A、相应的终值FA或现值PA，计算出相应系数（FA/A, i, n）或（PA/A, i, n），然后，根据该系数和已知的基数n去查相应的系数表，或用插值法计算所要求的利率。
由于资金在不同时点的价值不同，所以资金时间价值的表现形式就有两种：现值和终值。
现值是指未来一定时间的特定货币按一定利率折算到现在的价值。
终值是指现在一定数额的资金按一定的利率计算的一定时间后的价值。
2.1资金时间价值观念
复利终值与现值
复利终值，是指一次性的收、付款项经过若干期的使用后，所获得的包括本金和利息在内的未来价值。
所有者和经营者财务目标的协调所有者和债权人财务目标的协调
1.3公司理财的主要内容
公司理财活动由筹资、投资、分配三个环节组成，即筹集公司经营所需资金、将资金投放到有利可赢的投资项目上、将获得的收益按照一定的程序向股东分配。
1.3公司理财的主要内容
1 -11
筹资管理
筹资管理可以看成公司理财中首要的、基本的环节。筹资决策的关键在于决定各种资金来源在总资金中所占的比重，即注重资本结构的合理安排，以使筹资风险、筹资成本与期望资金收益相匹配。
1.2公司理财目标与价值理论
企业价值理论企业价值计量理论企业价值其理论计算公式如下：
n
V NCF（ i 1i）t
如果各t1年的现金流量相等，则上式可简化为：

金融学考研【金融学经典教材解读】《公司理财(原书第9版)》罗斯等编著

金融学考研【金融学经典教材解读】《公司理财（原书第9版）》罗斯等编著教材介绍：吴世农沈艺峰王志强等译《公司理财（原书第9版）》分8篇，共31章，涵盖了公司财务管理的所有问题，包括资产定价、投资决策、融资工具和筹资决策、资本结构和股利分配政策、长期财务规划和短期财务管理、收购兼并、国际理财和财务困境等，并且新增了股票和债券的内容。

《公司理财（原书第9版）》篇章结构十分精妙、逻辑严密、内容新颖、资料翔实、易教易学，既适合作为商学院mba、财务管理和金融管理本科生、研究生的教科书，又适合作为财务和投资专业人士、大学相关教师和研究人员的必读名著或参考书。

网友使用心得：A、绝对是公司类财务书籍的经典！不同于国内的大学教材，这本书很适合自学者自学。

作者通过提问的方式来阐述知识，并通过大量的案例来阐述原理。

试比国内大学教材的死沉单调，这本书更有利于学通、学透。

但是也有少许的翻译错误，个别地方甚至出现数据错误。

如果要买这本书，我建议和英文版的一起看。

B、非常好的一本书，对于公司的财务状况、融资架构、资本运走讲解的很到位，特别适合从事投资、私募等方面的人研读。

C、无论是作为学生还是专业人士，都可以从中学到最新的西方公司财务管理的理念和新的观念。

很有启发的一本书。

D、这个考研考金融的不可错过啊！很多学校都指定了这本书，比如上财，公司理财就占了60%的比重，这本书不可忽视。

E、作为考研专业课用书来说，这本公司金融既通俗又详细，完全不用担心看不懂的问题，很棒的书。

【金融学经典教材解读】现代货币银行学教程（第四版）胡庆康编著教材介绍：本书是“复旦博学·金融学系列”之一。

全书共分九章，对货币和货币制度、金融市场运行机制、金融中介机构体系、中央银行及其调控机制、商业银行、金融深化与金融创新理论、货币供给与货币需求理论、通货膨胀与通货紧缩理论等方面作了详细的分析。

与第三版相比，第四版作了如下改进：(1)第三章中增加了本轮金融危机发展过程中的相关金融衍生产品的内容。

罗斯《公司理财》第9版精要版英文原书课后部分章节答案

CH5 11，13，18，19，2011.To find the PV of a lump sum, we use:PV = FV / (1 + r)tPV = $1,000,000 / (1.10)80 = $488.1913.To answer this question, we can use either the FV or the PV formula. Both will give the sameanswer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving for r, we get:r = (FV / PV)1 / t– 1r = ($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)tFV = $1,260,000(1.0840)33 = $18,056,409.9418.To find the FV of a lump sum, we use:FV = PV(1 + r)tFV = $4,000(1.11)45 = $438,120.97FV = $4,000(1.11)35 = $154,299.40Better 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)tFV = $20,000(1.084)6 = $32,449.3320.To answer this question, we can use either the FV or the PV formula. Both will give the sameanswer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving for t, we get:t = ln(FV / PV) / ln(1 + r)t = ln($75,000 / $10,000) / ln(1.11) = 19.31So, the money must be invested for 19.31 years. However, you will not receive the money for another two years. Fro m now, you’ll wait:2 years + 19.31 years = 21.31 yearsCH6 16，24，27，42，5816.For this problem, we simply need to find the FV of a lump sum using the equation:FV = PV(1 + r)tIt 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 = $8,505.9324.This problem requires us to find the FVA. The equation to find the FVA is:FVA = C{[(1 + r)t– 1] / r}FVA = $300[{[1 + (.10/12) ]360 – 1} / (.10/12)] = $678,146.3827.The cash flows are annual and the compounding period is quarterly, so we need to calculate theEAR 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– 1EAR = [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 / 1.11462 + $1,360 / 1.11464 = $2,320.3642.The amount of principal paid on the loan is the PV of the monthly payments you make. So, thepresent value of the $1,150 monthly payments is:PVA = $1,150[(1 – {1 / [1 + (.0635/12)]}360) / (.0635/12)] = $184,817.42The 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 = $55,182.58This 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 = $368,936.5458.To answer this question, we should find the PV of both options, and compare them. Since we arepurchasing 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 thesame as the interest rate of the loan. The PV of leasing is:PV = $99 + $450{1 – [1 / (1 + .07/12)12(3)]} / (.07/12) = $14,672.91The 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) = $18,654.82The PV of the decision to purchase is:$32,000 – 18,654.82 = $13,345.18In 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 = $14,672.91PV of resale price = $17,327.09The resale price that would make the PV of the lease versus buy decision is the FV of this value, so:Breakeven resale price = $17,327.09[1 + (.07/12)]12(3) = $21,363.01CH7 3，18，21，22，313.The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice thisproblem 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] = $918.89We 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 remainder of the solutions key.18.The bond price equation for this bond is:P0 = $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 the semiannual 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 haspassed 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 = $12.33And we calculate the clean price as:Clean price = Dirty price – Accrued interest = $968 – 12.33 = $955.6721. Accrued interest is the coupon payment for the period times the fraction of the period that haspassed 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 = $22.67And we calculate the dirty price as:Dirty price = Clean price + Accrued interest = $1,073 + 22.67 = $1,095.6722.To find the number of years to maturity for the bond, we need to find the price of the bond. Sincewe 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/P0P0 = $80/.0755 = $1,059.60Now that we have the price of the bond, the bond price equation is:P = $1,059.60 = $80[(1 – (1/1.072)t ) / .072 ] + $1,000/1.072tWe can solve this equation for t as follows:$1,059.60(1.072)t = $1,111.11(1.072)t– 1,111.11 + 1,000111.11 = 51.51(1.072)t2.1570 = 1.072tt = log 2.1570 / log 1.072 = 11.06 11 yearsThe bond has 11 years to maturity.31.The price of any bond (or financial instrument) is the PV of the future cash flows. Even thoughBond 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(PVIFA3.5%,16)(PVIF3.5%,12) + $1,400(PVIFA3.5%,12)(PVIF3.5%,28) + $20,000(PVIF3.5%,40)P M= $19,018.78Notice that for the coupon payments of $1,400, 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(PVIF3.5%,40) = $5,051.45CH8 4，18，20，22，24ing the constant growth model, we find the price of the stock today is:P0 = D1 / (R– g) = $3.04 / (.11 – .038) = $42.2218.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 Year 19, one year before the first dividend payment. Doing so, we get:P19 = $20.00 / .064P19 = $312.50The price of the stock today is the PV of the stock price in the future, so the price today will be: P0 = $312.50 / (1.064)19P0 = $96.1520.We can use the two-stage dividend growth model for this problem, which is:P0 = [D0(1 + g1)/(R –g1)]{1 – [(1 + g1)/(1 + R)]T}+ [(1 + g1)/(1 + R)]T[D0(1 + g2)/(R –g2)]P0= [$1.25(1.28)/(.13 – .28)][1 – (1.28/1.13)8] + [(1.28)/(1.13)]8[$1.25(1.06)/(.13 – .06)]P0= $69.5522.We are asked to find the dividend yield and capital gains yield for each of the stocks. All of thestocks 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: P0 = D0(1 + g) / (R–g) = $4.50(1.10)/(.19 – .10) = $55.00Dividend yield = D1/P0 = $4.50(1.10)/$55.00 = .09 or 9%Capital gains yield = .19 – .09 = .10 or 10%X: P0 = D0(1 + g) / (R–g) = $4.50/(.19 – 0) = $23.68Dividend yield = D1/P0 = $4.50/$23.68 = .19 or 19%Capital gains yield = .19 – .19 = 0%Y: P0 = D0(1 + g) / (R–g) = $4.50(1 – .05)/(.19 + .05) = $17.81Dividend yield = D1/P0 = $4.50(0.95)/$17.81 = .24 or 24%Capital gains yield = .19 – .24 = –.05 or –5%Z: P2 = D2(1 + g) / (R–g) = D0(1 + g1)2(1 + g2)/(R–g2) = $4.50(1.20)2(1.12)/(.19 – .12) = $103.68P0 = $4.50 (1.20) / (1.19) + $4.50 (1.20)2/ (1.19)2 + $103.68 / (1.19)2 = $82.33Dividend yield = D1/P0 = $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 forthe first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be:P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, so:P0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.112 + $2.45(1.20)(1.15)(1.10)/1.113 + $65.08/1.113 P0 = $55.70CH9 3，4，6，9，153.Project A has cash flows of $19,000 in Year 1, so the cash flows are short by $21,000 ofrecapturing the initial investment, so the payback for Project A is:Payback = 1 + ($21,000 / $25,000) = 1.84 yearsProject B has cash flows of:Cash flows = $14,000 + 17,000 + 24,000 = $55,000during 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 yearsUsing 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 valuetoday of the project cash flows for the first four years is:Value today of Year 1 cash flow = $4,200/1.14 = $3,684.21Value today of Year 2 cash flow = $5,300/1.142 = $4,078.18Value today of Year 3 cash flow = $6,100/1.143 = $4,117.33Value today of Year 4 cash flow = $7,400/1.144 = $4,381.39To find the 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 yearsFor 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 yearsNotice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 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 Year 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 years6.Our definition of AAR is the average net income divided by the average book value. The averagenet income for this project is:Average net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325And the average book value is:Average book value = ($15,000,000 + 0) / 2 = $7,500,000So, the AAR for this project is:AAR = Average net income / Average 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 cashinflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = –$138,000 + $28,500(PVIFA8%, 9) = $40,036.31At 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(PVIFA20%, 9) = –$23,117.45At 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 cashoutflows. The equation for the profitability index at a required return of 10 percent is:PI = [$7,300/1.1 + $6,900/1.12 + $5,700/1.13] / $14,000 = 1.187The equation for the profitability index at a required return of 15 percent is:PI = [$7,300/1.15 + $6,900/1.152 + $5,700/1.153] / $14,000 = 1.094The equation for the profitability index at a required return of 22 percent is:PI = [$7,300/1.22 + $6,900/1.222 + $5,700/1.223] / $14,000 = 0.983We 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 is less than one.CH10 9，13，14，17，18ing the tax shield approach to calculating OCF (Remember the approach is irrelevant; the finalanswer will be the same no matter which of the four methods you use.), we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = ($2,650,000 – 840,000)(1 – 0.35) + 0.35($3,900,000/3)OCF = $1,631,50013.First we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation = $560,000/5Annual depreciation = $112,000Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:Aftertax salvage value = MV + (BV – MV)t cVery often the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:Aftertax salvage value = MV + (0 – MV)t cAftertax salvage value = MV(1 – t c)We will use this equation to find the aftertax salvage value since we know the book value is zero.So, the aftertax salvage value is:Aftertax salvage value = $85,000(1 – 0.34)Aftertax salvage value = $56,100Using the tax shield approach, we find the OCF for the project is:OCF = $165,000(1 – 0.34) + 0.34($112,000)OCF = $146,980Now we can find the project NPV. Notice we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.NPV = –$560,000 – 29,000 + $146,980(PVIFA10%,5) + [($56,100 + 29,000) / 1.105]NPV = $21,010.2414.First we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation charge = $720,000/5Annual depreciation charge = $144,000The aftertax salvage value of the equipment is:Aftertax salvage value = $75,000(1 – 0.35)Aftertax salvage value = $48,750Using the tax shield approach, the OCF is:OCF = $260,000(1 – 0.35) + 0.35($144,000)OCF = $219,400Now we can find the project IRR. There is an unusual feature that is a part of this project.Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the aftertax salvage value at the end of the project. The IRR of the project is:NPV = 0 = –$720,000 + 110,000 + $219,400(PVIFA IRR%,5) + [($48,750 – 110,000) / (1+IRR)5]IRR = 21.65%17.We will need the aftertax salvage value of the equipment to compute the EAC. Even though theequipment for each product has a different initial cost, both have the same salvage value. The aftertax salvage value for both is:Both cases: aftertax salvage value = $40,000(1 – 0.35) = $26,000To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is:OCF = –$67,000(1 – 0.35) + 0.35($290,000/3) = –9,716.67NPV = –$290,000 – $9,716.67(PVIFA10%,3) + ($26,000/1.103) = –$294,629.73EAC = –$294,629.73 / (PVIFA10%,3) = –$118,474.97And the OCF and NPV for Techron II is:OCF = –$35,000(1 – 0.35) + 0.35($510,000/5) = $12,950NPV = –$510,000 + $12,950(PVIFA10%,5) + ($26,000/1.105) = –$444,765.36EAC = –$444,765.36 / (PVIFA10%,5) = –$117,327.98The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.18.To find the bid price, we need to calculate all other cash flows for the project, and then solve forthe bid price. The aftertax salvage value of the equipment is:Aftertax salvage value = $70,000(1 – 0.35) = $45,500Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the NPV of the project is:NPV = 0 = –$940,000 – 75,000 + OCF(PVIFA12%,5) + [($75,000 + 45,500) / 1.125]Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:OCF = $946,625.06 / PVIFA12%,5 = $262,603.01The easiest way to calculate the bid price is the tax shield approach, so:OCF = $262,603.01 = [(P – v)Q – FC ](1 – t c) + t c D$262,603.01 = [(P – $9.25)(185,000) – $305,000 ](1 – 0.35) + 0.35($940,000/5)P = $12.54CH14 6、9、20、23、246. The pretax cost of debt is the YTM of the company’s bonds, so:P0 = $1,070 = $35(PVIFA R%,30) + $1,000(PVIF R%,30)R = 3.137%YTM = 2 × 3.137% = 6.27%And the aftertax cost of debt is:R D = .0627(1 – .35) = .0408 or 4.08%9. ing the equation to calculate the WACC, we find:WACC = .60(.14) + .05(.06) + .35(.08)(1 – .35) = .1052 or 10.52%b.Since interest is tax deductible and dividends are not, we must look at the after-tax cost ofdebt, which is:.08(1 – .35) = .0520 or 5.20%Hence, on an after-tax basis, debt is cheaper than the preferred stock.ing the debt-equity ratio to calculate the WACC, we find:WACC = (.90/1.90)(.048) + (1/1.90)(.13) = .0912 or 9.12%Since the project is riskier than the company, we need to adjust the project discount rate for the additional risk. Using the subjective risk factor given, we find:Project discount rate = 9.12% + 2.00% = 11.12%We would accept the project if the NPV is positive. The NPV is the PV of the cash outflows plus the PV of the cash inflows. Since we have the costs, we just need to find the PV of inflows. The cash inflows are a growing perpetuity. If you remember, the equation for the PV of a growing perpetuity is the same as the dividend growth equation, so:PV of future CF = $2,700,000/(.1112 – .04) = $37,943,787The project should only be undertaken if its cost is less than $37,943,787 since costs less than this amount will result in a positive NPV.23. ing the dividend discount model, the cost of equity is:R E = [(0.80)(1.05)/$61] + .05R E = .0638 or 6.38%ing the CAPM, the cost of equity is:R E = .055 + 1.50(.1200 – .0550)R E = .1525 or 15.25%c.When using the dividend growth model or the CAPM, you must remember that both areestimates for the cost of equity. Additionally, and perhaps more importantly, each methodof estimating the cost of equity depends upon different assumptions.Challenge24.We can use the debt-equity ratio to calculate the weights of equity and debt. The debt of thecompany has a weight for long-term debt and a weight for accounts payable. We can use the weight given for accounts payable to calculate the weight of accounts payable and the weight of long-term debt. The weight of each will be:Accounts payable weight = .20/1.20 = .17Long-term debt weight = 1/1.20 = .83Since the accounts payable has the same cost as the overall WACC, we can write the equation for the WACC as:WACC = (1/1.7)(.14) + (0.7/1.7)[(.20/1.2)WACC + (1/1.2)(.08)(1 – .35)]Solving for WACC, we find:WACC = .0824 + .4118[(.20/1.2)WACC + .0433]WACC = .0824 + (.0686)WACC + .0178(.9314)WACC = .1002WACC = .1076 or 10.76%We will use basically the same equation to calculate the weighted average flotation cost, except we will use the flotation cost for each form of financing. Doing so, we get:Flotation costs = (1/1.7)(.08) + (0.7/1.7)[(.20/1.2)(0) + (1/1.2)(.04)] = .0608 or 6.08%The total amount we need to raise to fund the new equipment will be:Amount raised cost = $45,000,000/(1 – .0608)Amount raised = $47,912,317Since the cash flows go to perpetuity, we can calculate the present value using the equation for the PV of a perpetuity. The NPV is:NPV = –$47,912,317 + ($6,200,000/.1076)NPV = $9,719,777CH16 1，4，12，14，171. a. A table outlining the income statement for the three possible states of the economy isshown below. The EPS is the net income divided by the 5,000 shares outstanding. The lastrow shows the percentage change in EPS the company will experience in a recession or anexpansion economy.Recession Normal ExpansionEBIT $14,000 $28,000 $36,400Interest 0 0 0NI $14,000 $28,000 $36,400EPS $ 2.80 $ 5.60 $ 7.28%∆EPS –50 –––+30b.If the company undergoes the proposed recapitalization, it will repurchase:Share price = Equity / Shares outstandingShare price = $250,000/5,000Share price = $50Shares repurchased = Debt issued / Share priceShares repurchased =$90,000/$50Shares repurchased = 1,800The interest payment each year under all three scenarios will be:Interest payment = $90,000(.07) = $6,300The last row shows the percentage change in EPS the company will experience in arecession or an expansion economy under the proposed recapitalization.Recession Normal ExpansionEBIT $14,000 $28,000 $36,400Interest 6,300 6,300 6,300NI $7,700 $21,700 $30,100EPS $2.41 $ 6.78 $9.41%∆EPS –64.52 –––+38.714. a.Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax.The EPS under this capitalization will be:EPS = $350,000/160,000 sharesEPS = $2.19Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so:NI = $500,000 – .08($2,800,000)NI = $126,000And the EPS will be:EPS = $126,000/80,000 sharesEPS = $1.58Plan I has the higher EPS when EBIT is $350,000.b.Under Plan I, the net income is $500,000 and the EPS is:EPS = $500,000/160,000 sharesEPS = $3.13Under Plan II, the net income is:NI = $500,000 – .08($2,800,000)NI = $276,000And the EPS is:EPS = $276,000/80,000 sharesEPS = $3.45Plan II has the higher EPS when EBIT is $500,000.c.To find the breakeven EBIT for two different capital structures, we simply set the equationsfor EPS equal to each other and solve for EBIT. The breakeven EBIT is:EBIT/160,000 = [EBIT – .08($2,800,000)]/80,000EBIT = $448,00012. a.With the information provided, we can use the equation for calculating WACC to find thecost of equity. The equation for WACC is:WACC = (E/V)R E + (D/V)R D(1 – t C)The company has a debt-equity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the weight of equity is 1/2.5, soWACC = .10 = (1/2.5)R E + (1.5/2.5)(.07)(1 – .35)R E = .1818 or 18.18%b.To find the unlevered cost of equity we need to use M&M Proposition II with taxes, so:R E = R U + (R U– R D)(D/E)(1 – t C).1818 = R U + (R U– .07)(1.5)(1 – .35)R U = .1266 or 12.66%c.To find the cost of equity under different capital structures, we can again use M&MProposition II with taxes. With a debt-equity ratio of 2, the cost of equity is:R E = R U + (R U– R D)(D/E)(1 – t C)R E = .1266 + (.1266 – .07)(2)(1 – .35)R E = .2001 or 20.01%With a debt-equity ratio of 1.0, the cost of equity is:R E = .1266 + (.1266 – .07)(1)(1 – .35)R E = .1634 or 16.34%And with a debt-equity ratio of 0, the cost of equity is:R E = .1266 + (.1266 – .07)(0)(1 – .35)R E = R U = .1266 or 12.66%14. a.The value of the unlevered firm is:V U = EBIT(1 – t C)/R UV U = $92,000(1 – .35)/.15V U = $398,666.67b.The value of the levered firm is:V U = V U + t C DV U = $398,666.67 + .35($60,000)V U = $419,666.6717.With no debt, we are finding the value of an unlevered firm, so:V U = EBIT(1 – t C)/R UV U = $14,000(1 – .35)/.16V U = $56,875With debt, we simply need to use the equation for the value of a levered firm. With 50 percent debt, one-half of the firm value is debt, so the value of the levered firm is:V L = V U + t C(D/V)V UV L = $56,875 + .35(.50)($56,875)V L = $66,828.13And with 100 percent debt, the value of the firm is:V L = V U + t C(D/V)V UV L = $56,875 + .35(1.0)($56,875)V L = $76,781.25c.The net cash flows is the present value of the average daily collections times the daily interest rate, minus the transaction cost per day, so:Net cash flow per day = $1,276,275(.0002) – $0.50(385)Net cash flow per day = $62.76The net cash flow per check is the net cash flow per day divided by the number of checksreceived per day, or:Net cash flow per check = $62.76/385Net cash flow per check = $0.16Alternatively, we could find the net cash flow per check as the number of days the system reduces collection time times the average check amount times the daily interest rate, minusthe transaction cost per check. Doing so, we confirm our previous answer as:Net cash flow per check = 3($1,105)(.0002) – $0.50Net cash flow per check = $0.16 per checkThis makes the total costs:Total costs = $18,900,000 + 56,320,000 = $75,220,000The flotation costs as a percentage of the amount raised is the total cost divided by the amount raised, so:Flotation cost percentage = $75,220,000/$180,780,000 = .4161 or 41.61%8.The number of rights needed per new share is:Number of rights needed = 120,000 old shares/25,000 new shares = 4.8 rights per new share.Using P RO as the rights-on price, and P S as the subscription price, we can express the price per share of the stock ex-rights as:P X = [NP RO + P S]/(N + 1)a.P X = [4.8($94) + $94]/(4.80 + 1) = $94.00; No change.b. P X = [4.8($94) + $90]/(4.80 + 1) = $93.31; Price drops by $0.69 per share.。

公司理财(罗斯)第4章

感谢您的观看
投资风险和回报的权衡
风险与回报的关系
高风险往往伴随着高回报，投资者需要在风险和回报之间进行权衡。
风险分散
通过多元化投资，分散单一项目的风险，降低整体投资组合的风险水平。
风险控制
采取措施降低投资风险，如对冲策略、限制杠杆等。
风险偏好
根据投资者对风险的容忍程度，选择适合的投资项目和策略。
04 资本结构和融资决策
公司理财(罗斯)第4章
目录
• 公司理财的目标和原则 • 财务报表和财务分析 • 资本预算和投资决策 • 资本结构和融资决策 • 营运资本管理
01 公司理财的目标和原则
公司理财的定义和目标
公司理财定义
公司理财是对公司财务的管理，包括对公司财务活动进行计划、组织、指挥、协调、控制和监督等一系列的管理活动。
05 营运资本管理
营运资本的定义和构成
营运资本的定义
指公司用于日常经营活动的流动资金，包括短期资产和短期负债。
营运资本的构成
由流动资产和流动负债组成，其中流动资产包括现金、存货、应收账款等，流动负债包括应付账款、短期借款等。
营运资本管理的目标和原则
营运资本管理的目标
确保公司有足够的营运资本来支持日常经营，同时保持较低的资本成本和风险。
偿债能力指标
包括流动比率、速动比率、资产负债率等，用于评估公司的偿债能力。
盈利能力指标
包括销售利润率、资产收益率、权益净利率等，用于评估公司的盈利能力。
营运能力指标
包括存货周转率、应收账款周转率、总资产周转率等，用于评估公司的资产管理和运用效率。
成长性指标
包括营业收入增长率、净利润增长率、总资产增长率等，用于评估公司的成长潜力。

罗斯公司理财第九版课后习题第四章答案

1.当你增加时间的长度时，终值会发生什么变化，现值会发生什么变化？答：当增加时间长度时根据公司PV=C/(1+r)^t得到现值会减少（dwindle，diminish），而终值FV=C*(1+r)^t会增加。

2.如果利率增加，年金的终值会有什么变化？现值会有什么变化？答：当利率增加时，终值增大，现值FV=C(1/r-1/(r*(1+r)^t))得现值会减小分析这两道题都考察了对终值和现值的概念的理解:终值：一笔资金经过一个时期或者多个时期的以后的价值，如果考察终值就是在现在或将来我得到一笔资金C那么这笔资金在更远的未来将会价值多少，如果考察现值则是将来我得到一笔钱那么它现在的价值是多少（在某个固定的折现率下）3.假设有两名运动员签署了一份10年8000万的合同，一份是每年支付800万，一份是8000万分十次，支付金额每年递增5%，哪种情况最好答：计算过程如下图：u由上图的应该选第一种4.贷款法是否应该要求贷款者报告实际利率而不是名义利率？为什么？答：他们应该报告实际利率，名义利率的优势只是在于它们方便计算，可是在计算机技术发达的今天，计算已经不再是一个问题5.有津贴的斯坦福联邦贷款是为大学生提供帮助的一种普遍来源，直到偿还贷款才开始付息。

谁将收到更多的津贴，新生还是高年级的学生？请解释答：新生将获得跟多的津贴，因为新生使用无息贷款的时间比高年级学生长。

详细数据如下：由此可见新生的津贴=22235-20000=2235；而高年级的学生为1089根据下面的信息回答接下去的5个题：6.由计算得到如果500美金若在30年后要变成10000则实际年利率是10.5%,我想应该是GMAC的决策者认为公司的投资收益率大于10.5%7.如果公司可以在30年内的任意时间内以10000元的价格购买该债券的话，将会使得该债券更具有吸引力8.1）这500元不能影响我后面30年的正常生活，也就是我说我是否有500元的多余资金；2）该公司是否能够保证在30年后我能收到10000元3）当前我认为的投资收益率是否高于10.5%，若高于10.5%则不应该考虑投资该债券我的回答是：是取决的承诺偿还的人9.财政部的发行该种债券的价格较高因为财政部在所有的债券发行者中信用最好10.价格会超过之前的500美元，因为如果随着时间的推移，该债券的价值就越接近10000美元，如果在2010年的看价格有可能会更高，但不能确定，因为GMAC有财务恶化的可能或者资本市场上的投资收益率提高。

公司理财罗斯第九版课后答案

公司理财罗斯第九版课后答案【篇一：罗斯公司理财第九版课后习题答案中文版】形式的公司中,股东是公司的所有者。

股东选举公司的董事会,董事会任命该公司的管理层。

企业的所有权和控制权分离的组织形式是导致的代理关系存在的主要原因。

管理者可能追求自身或别人的利益最大化,而不是股东的利益最大化。

在这种环境下,他们可能因为目标不一致而存在代理问题2.非营利公司经常追求社会或政治任务等各种目标。

非营利公司财务管理的目标是获取并有效使用资金以最大限度地实现组织的社会使命。

3.这句话是不正确的。

管理者实施财务管理的目标就是最大化现有股票的每股价值，当前的股票价值反映了短期和长期的风险、时间以及未来现金流量。

4.有两种结论。

一种极端,在市场经济中所有的东西都被定价。

因此所有目标都有一个最优水平，包括避免不道德或非法的行为，股票价值最大化。

另一种极端,我们可以认为这是非经济现象,最好的处理方式是通过政治手段。

一个经典的思考问题给出了这种争论的答案:公司估计提高某种产品安全性的成本是30美元万。

然而,该公司认为提高产品的安全性只会节省20美元万。

请问公司应该怎么做呢?”5.财务管理的目标都是相同的,但实现目标的最好方式可能是不同的,因为不同的国家有不同的社会、政治环境和经济制度。

7.其他国家的代理问题并不严重,主要取决于其他国家的私人投资者占比重较小。

较少的私人投资者能减少不同的企业目标。

高比重的机构所有权导致高学历的股东和管理层讨论决策风险项目。

此外,机构投资者比私人投资者可以根据自己的资源和经验更好地对管理层实施有效的监督机制。

8.大型金融机构成为股票的主要持有者可能减少美国公司的代理问题，形成更有效率的公司控制权市场。

但也不一定能。

如果共同基金或者退休基金的管理层并不关心的投资者的利益，代理问题可能仍然存在,甚至有可能增加基金和投资者之间的代理问题。

9.就像市场需求其他劳动力一样，市场也需求首席执行官，首席执行官的薪酬是由市场决定的。

公司理财-罗斯 (第9版) 第4章折现现金流量估价

£15 £15 2 £15 3
…
0
1
15 PV 150 .10
永续增长年金
能始终以某固定的增长率保持增长的一系列现金流。

C 0 1
C×(1+g) C ×(1+g)2 2 3
…
C C (1 g ) C (1 g ) PV 2 3 (1 r ) (1 r ) (1 r )
如果你打算按揭买车，你每月能承担的月供额为 400美元，则在利率为7%，贷款期为36个月的条件下，你所能购买的最高车价不能超过多少？ $400 0 1 $400 2

$400
$400

3 36
$400 1 PV $12,954.59 1 36 .07 / 12 (1 .07 12)
年金一系列稳定有规律的、持续一段固定时期的现金收
付活动。 C 1 C 2 C C

0 3 T
C C C C PV 2 3 (1 r ) (1 r ) (1 r ) (1 r )T
C 1 PV 1 T r (1 r )
年金: 例
为了能在1年后偿还10 000美元的债务，债务人在今天就需要存起来的钱，就是现值（Present Value，PV）。
请注意， 10 000美元 =9 523.81美元×1.05
净现值

某个项目的净现值（Net Present Value，NPV）等于该项目的预期现金流量的现值与项目投资成本之差。假定某项投资承诺将在一年后归还10 000美元，现在需要的出资金额为9 500美元。你的资金利息率为5%。这项投资可行吗？
10 000×1.05 = 10 500美元该投资在期末的本息合计金额被称为终值（Future Value，FV），或复利值。