Lect0. 11 Discounted Cash Flow Valuation-C
dcf估值模型实操要点
dcf估值模型实操要点DCF（Discounted Cash Flow）估值模型是一种常用的公司估值方法，基于未来现金流量的折现计算，以评估一个公司或项目的内在价值。
本文将介绍DCF估值模型的实操要点，以帮助读者更好地理解和应用该方法。
一、DCF估值模型概述DCF估值模型是基于现金流量的折现计算，其核心思想是将未来现金流量通过适当的折现率进行调整，得出企业的内在价值。
该模型的基本公式如下所示：内在价值= Σ（每期现金流量 / (1 + 折现率)^期数）二、确定未来现金流量在使用DCF估值模型之前，需要准确确定未来现金流量的预测值。
这需要综合考虑多个因素，包括市场趋势、行业竞争、公司业绩等。
可以通过分析财务报表、行业研究以及市场调查等手段来获取相关数据，并进行合理的预测和假设。
三、确定折现率折现率是DCF估值模型中的一个重要参数，用于调整未来现金流量的时间价值。
折现率的确定需要考虑到风险水平、市场利率、行业平均收益率等因素。
常用的方法包括权益资本成本（WACC）法和资本资产定价模型（CAPM）法等。
根据具体情况选择合适的折现率计算方法，并结合实际情况进行调整。
四、计算内在价值根据前述步骤中得出的未来现金流量和折现率，可以开始计算企业的内在价值。
采用DCF公式，将每期现金流量按相应折现率折现后求和，即可得到估值结果。
五、敏感性分析与风险评估DCF估值模型的结果可能会受到多个因素的影响，如现金流量的变动、折现率的调整等。
因此，在使用该模型进行估值时，应进行敏感性分析，评估结果对关键变量的敏感程度，以及模型的鲁棒性和可靠性。
在进行实际投资决策时，还应考虑可能的风险因素，并进行风险评估。
六、参考市场数据与专业意见在使用DCF估值模型时，可以参考市场数据和专业意见，以提高估值的准确性和可靠性。
例如，可以参考类似公司的市场估值情况，结合专业人士的观点和建议，对模型进行修正和调整，以更好地反映市场实际情况和投资者的预期。
le13 Discounted Cash Flow Applications(资产定价-上海交大,蔡明超)
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LOS a: Describe the components and the assumptions underlying the constant growth dividend discount model
three components of the constant growth model: • Next period’s dividend, D1. • The required rate of return, r. The required rate is typically computed using the CAPM where r = risk-free rate + beta(market rate ?risk-free rate). • The constant growth rate of dividends, g. Recall from previous discussions that g = retention return on equity (ROE).
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LOS e: Cal dollar-weighted and timeweighted rates of return on a portfolio.
Time-weighted return: 1. Break the evaluation period into two subperiods based on timing of cash flows. 2. Calculate the HPR for each holding period. 3. Take the geometric mean of the annual returns to find the annualized time-weighted rate of return over the measurement period.
折现现金流量估价(ppt 41页)
资将增长为$10,500。 $500 将是利息 ($10,000 × .05) $10,000 是本金偿还 ($10,000 × 1) $10,500 是总的应得金额。它可以计算如下： $10,500 = $10,000×(1.05)
在投资期末应得的总额被称作终值 (FV)。
第4章 折现现金流量估价
• Chapter 4
Discounted Cash Flow Valuation
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第4章 折现现金流量估价
4.1 单期投资的情形 4.2 多期投资的情形 4.3 复利计息期数 4.4 简化公式 4.5 如何评估公司的价值
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4.1 单期投资的情形
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4.1 单期投资的情形
在单期投资的情形下，终值的计算公式可以写为：
FV = C0×(1 + r) 其中，C0 是今天（时间0）的现金流量; r 是适用的利率
C0 = $10,000
C0×(1 + r)
$10,000 ´ 1.05
FV = $10,500
年0
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什么利率是满足的？
假设在12年后当你的孩子进入大学时大学的学费总额将达 $50,000。你现在有 $5,000 作投资。为了够支付你孩子大学 教育的费用，你在投资上必须挣得多少利率？
大约 21.15%.
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4.2 多期投资的情形
4.2.4 净现值 一系列现金流量的现值就是对各个现金流量现值
$5.92 = $1.10×(1.40)5
【推荐】财管术语：财务估价修正
财管术语：财务估价修正1.DCF（DiscountedCashFlow）估价模型（1）现金流量。
指流向股东和债权人的现金流量合计，即息前税后利润在满足再投资需求之后的剩余现金流量，又称公司自由现金流量（FCFF，FreeCashFlowtotheFirm）。
公司自由现金流量=息税前利润X（l-所得税税率）－（资本性支出-折旧）-非现金营运资本变动资本性支出即投资于（或购买）长期资产的支出；资本性支出一折旧一净资本支出；r反映融资组合成本与风险的折现率；N表示估价期限。
净资本支出及非现金营运资本的增加，代表着为产生当期及未来收益增长而进行的再投资，故可将这两项合并用“再投资率”表示，从而，公司自由现金流量=息税前利润×（1-所得税税率）×（1-再投资率）（2）预期增长率。
营业利润的预期增长取决于再投资率和再投资回报水平。
营业利润的预期增长=再投资率×资本收益率资本收益率=息税前利润×（1-所得税税率）/投入资本再投资率=（净资本支出+非现金营运资本变动）／[息税前利润×（1-所得税税率）]2.估价模型与会计信息DCF估价模型的基本输入变量有：息税前利润、所得税税率、资本性支出、营运资本、息税前利润的预期增长率、资本成本、资本收益率等。
将上述基本变量进一步展开，我们可以得到一系列会计项目，并将这些项目与会计信息复杂性联系起来考虑，估计其复杂程度。
降低会计信息复杂性，将有助于公司的真实价值被市场发现和认可，降低其在市场中运行的成本与风险。
例如，根据DCF模型，公司的预期增长应是再投资率与投资回报率的函数。
如果公司通过特别目的实体掩藏投资，则财务估价模型的输入变量之一预期增长将无法得到，则无法真实地评估公司价值。
为估计公司的加权平均资本成本，需要知道公司债务的成本。
如果公司通过制造复杂的会计信息来隐藏其债务，则将低估公司的违约风险，从而虚假地降低其资本成本。
Basics of Cash Flow Valuation
• Constant Growth Model • Variable Growth Model
Zero Growth Model
• Free cash flow is constant in perpetuity.
Calculating Free Cash Flow to the Firm (FCFF)
FCFF (enterprise cash flow) is cash flow available to repay lenders and/or pay common and preferred dividends and repurchase equity, after taxes and reinvestment requirements but before debt repayments.
FCFF = (Earnings before interest & taxes (1-tax rate) + Depreciation – ΔNet Working Capital1)2 – Gross Capital Expenditures3
1Excludes
cash in excess of normal operating requirements. 2Cash from operating activities. 3Cash from investing activities.
Basics of Cash Flow Valuation
Prantik Ray XLRI
Required Returns: Cost of Equity (COE)
现金流估值法和股利贴现模型
现金流估值法和股利贴现模型现金流估值法（DCF，Discounted Cash Flow）和股利贴现模型（Dividend Discount Model，简称DDM）是两种常用于估值企业或股票的财务模型。
它们都基于未来现金流的概念，但在具体的运用和计算方法上存在一些差异。
现金流估值法（DCF）：1.概述：DCF是一种基于未来现金流量的估值方法，它将未来的现金流量贴现至现值，以确定投资的内在价值。
2.计算过程：主要包括以下步骤：•预测未来现金流：通常使用财务模型对未来的现金流做出预测。
•确定贴现率（折现率）：该率考虑了时间价值的概念，通常使用加权平均资本成本（Weighted Average Cost of Capital，WACC）。
•贴现未来现金流：将未来现金流按照贴现率进行贴现，得到现值。
•求和：将所有未来现金流的现值相加，得到企业或资产的总价值。
3.适用情境：DCF适用于各种类型的资产，包括企业、项目等。
股利贴现模型（DDM）：1.概述：DDM是一种估值方法，主要用于估计股票的内在价值。
它基于预期未来的股利流，将未来的股利贴现至现值。
2.计算过程：主要包括以下步骤：•预测未来股利：对未来一系列的股利进行预测。
•确定折现率：通常使用资本资产定价模型（Capital Asset Pricing Model，CAPM）来确定股票的期望回报率。
•贴现未来股利：将未来股利按照折现率进行贴现，得到现值。
•求和：将所有未来股利的现值相加，得到股票的内在价值。
3.适用情境：DDM主要用于估值普通股，尤其是对于分红较为稳定的公司。
主要区别：1.对象不同：DCF可用于估值各种资产，而DDM主要用于估值股票。
2.估值依据：DCF基于企业的整体现金流，而DDM基于股利流。
3.适用性：DCF更灵活，适用于各种情境，而DDM更适用于那些分红相对稳定的公司。
总体而言，选择使用哪种方法通常取决于估值的具体目标和资产的特性。
财务管理 CHAPTER 6
CHAPTER 6Discounted Cash Flow ValuationI. DEFINITIONSANNUITYa 1. An annuity stream of cash flow payments is a set of:a. level cash flows occurring each time period for a fixed length of time.b. level cash flows occurring each time period forever.c. increasing cash flows occurring each time period for a fixed length of time.d. increasing cash flows occurring each time period forever.e. arbitrary cash flows occurring each time period for no more than 10 years.PRESENT VALUE FACTOR FOR ANNUITIESb 2. The present value factor for annuities is calculated as:a. (1 + present value factor) ÷ r.b. (1 – present value factor) ÷ r.c. present value factor + (1 ÷ r).d. (present value factor ⨯ r) + (1 ÷ r).e. r ⨯ (1 + present value factor).FUTURE VALUE FACTOR FOR ANNUITIESd 3. The future value factor for annuities is calculated as the:a. future value factor + r.b. (1 ÷ r) + (future value factor ⨯ r).c. (1 ÷ r) + future value factor.d. (future value factor –1) ÷ r.e. (future value factor + 1) ÷ r.ANNUITIES DUEe 4. Annuities where the payments occur at the end of each time period are called_____ , whereas _____ refer to annuity streams with payments occurring at thebeginning of each time period.a. ordinary annuities; early annuitiesb. late annuities; straight annuitiesc. straight annuities; late annuitiesd. annuities due; ordinary annuitiese. ordinary annuities; annuities duePERPETUITYc 5. An annuity stream where the payments occur forever is called a(n):a. annuity due.b. indemnity.c. perpetuity.d. amortized cash flow stream.e. amortization table.STATED INTEREST RATESa 6. The interest rate expressed in terms of the interest payment made each period iscalled the _____ rate.a. stated interestb. compound interestc. effective annuald. periodic intereste. daily interestEFFECTIVE ANNUALRATEc 7. The interest rate expressed as if it were compounded once per year is called the_____ rate.a. stated interestb. compound interestc. effective annuald. periodic intereste. daily interestANNUAL PERCENTAGE RATEb 8. The interest rate charged per period multiplied by the number of periods per year iscalled the _____ rate.a. effective annualb. annual percentagec. periodic interestd. compound intereste. daily interestPURE DISCOUNT LOANd 9. A loan where the borrower receives money today and repays a single lump sum atsome time in the future is called a(n) _____ loan.a. amortizedb. continuousc. balloond. pure discounte. interest-onlyINTEREST-ONLY LOANe 10. A loan where the borrower pays interest each period and repays the entire principalof the loan at some point in the future is called a(n) _____ loan.a. amortizedb. continuousc. balloond. pure discounte. interest-onlyAMORTIZED LOANa 11. A loan where the borrower pays interest each period, and repays some or all of theprincipal of the loan over time is called a(n) _____ loan.a. amortizedb. continuousc. balloond. pure discounte. interest-onlyBALLOON LOANc 12. A loan where the borrower pays interest each period, repays part of the principal ofthe loan over time, and repays the remainder of the principal at the end of the loan,is called a(n) _____ loan.a. amortizedb. continuousc. balloond. pure discounte. interest-onlyII. CONCEPTSORDINARY ANNUITY VERSUS ANNUITY DUEc 13. You are comparing two annuities which offer monthly payments for ten years. Bothannuities are identical with the exception of the payment dates. Annuity A pays on thefirst of each month while annuity B pays on the last day of each month. Which one ofthe following statements is correct concerning these two annuities?a. Both annuities are of equal value today.b. Annuity B is an annuity due.c. Annuity A has a higher future value than annuity B.d. Annuity B has a higher present value than annuity A.e. Both annuities have the same future value as of ten years from today.UNEVENCASH FLOWS ANDPRESENT VALUEb 14. You are comparing two investment options. The cost to invest in either option is thesame today. Both options will provide you with $20,000 of income. Option A pays fiveannual payments starting with $8,000 the first year followed by four annual payments of $3,000 each. Option B pays five annual payments of $4,000 each. Which one of thefollowing statements is correct given these two investment options?a. Both options are of equal value given that they both provide $20,000 of income.b. Option A is the better choice of the two given any positive rate of return.c. Option B has a higher present value than option A given a positive rate of return.d. Option B has a lower future value at year 5 than option A given a zero rate of return.e. Option A is preferable because it is an annuity due.UNEVENCASH FLOWS ANDFUTURE VALUEa 15. You are considering two projects with the following cash flows:Project A P roject BYear 1 $2,500 $4,000Year 2 3,000 3,500Year 3 3,500 3,000Year 4 4,000 2,500Which of the following statements are true concerning these two projects?I. Both projects have the same future value at the end of year 4, given a positive rate of return.II. Both projects have the same future value given a zero rate of return.III. Both projects have the same future value at any point in time, given a positive rate ofreturn.IV. Project A has a higher future value than project B, given a positive rate of return.a. II onlyb. IV onlyc. I and III onlyd. II and IV onlye. I, II, and III onlyPERPETUITY VERSUS ANNUITYd 16. A perpetuity differs from an annuity because:a. perpetuity payments vary with the rate of inflation.b. perpetuity payments vary with the market rate of interest.c. perpetuity payments are variable while annuity payments are constant.d. perpetuity payments never cease.e. annuity payments never cease.ANNUAL PERCENTAGE RATEe 17. Which one of the following statements concerning the annual percentage rate iscorrect?a. The annual percentage rate considers interest on interest.b. The rate of interest you actually pay on a loan is called the annual percentage rate.c. The effective annual rate is lower than the annual percentage rate when an interest rateis compounded quarterly.d. When firms advertise the annual percentage rate they are violating U.S. truth-in-lending laws.e. The annual percentage rate equals the effective annual rate when the rate on anaccount is designated as simple interest.INTEREST RATESb 18. Which one of the following statements concerning interest rates is correct?a. The stated rate is the same as the effective annual rate.b. An effective annual rate is the rate that applies if interest were charged annually.c. The annual percentage rate increases as the number of compounding periods per yearincreases.d. Banks prefer more frequent compounding on their savings accounts.e. For any positive rate of interest, the effective annual rate will always exceed the annualpercentage rate.EFFECTIVE ANNUAL RATEc 19. Which of the following statements concerning the effective annual rate are correct?I. When making financial decisions, you should compare effective annual rates ratherthan annual percentage rates.II. The more frequently interest is compounded, the higher the effective annual rate.III. A quoted rate of 6 percent compounded continuously has a higher effective annual ratethan if the rate were compounded daily.IV. When choosing which loan to accept, you should select the offer with the highest effective annual rate.a. I and II onlyb. I and IV onlyc. I, II, and III onlyd. II, III, and IV onlye. I, II, III,and IVCONTINUOUS COMPOUNDINGd 20. The highest effective annual rate that can be derived from an annual percentage rate of9 percent is computed as:a. .09e -1.b. e.09⨯ q.c. e ⨯ (1 + .09).d. e.09– 1.e. (1 + .09)q.PURE DISCOUNT LOANa 21. A pure discount loan is a(n):a. example of a present value problem.b. loan that is interest-free.c. loan that gives you a discount if you pay your payments on time.d. loan that requires all interest to be paid at the time the loan is made.e. loan that discounts the payments if you pay them in advance.INTEREST-ONLY LOANc 22. The principle amount of an interest-only loan is:a. never repaid.b. repaid in equal increments and included in each loan payment.c. repaid in full at the end of the loan period.d. repaid in equal annual payments even when the loan interest is repaid monthly.e. repaid in increasing increments and included in each loan payment.AMORTIZED LOANb 23. An amortized loan:a. requires the principle amount to be repaid in even increments over the life of the loan.b. may have equal or increasing amounts applied to the principle from each loanpayment.c. requires that all interest be repaid on a monthly basis while the principle is repaid atthe end of the loan term.d. requires that all payments be equal in amount and include both principle and interest.e. is the type of loan that describes most corporate bonds.III. PROBLEMSORDINARY ANNUITY AND PRESENT VALUEd 24. Your parents are giving you $100 a month for four years while you are in college. At a6 percent discount rate, what are these payments worth to you when you first startcollege?a. $3,797.40b. $4,167.09c. $4,198.79d. $4,258.03e. $4,279.32ORDINARY ANNUITYAND PRESENT VALUEb 25. You just won the lottery! As your prize you will receive $1,200 a month for 100months. If you can earn 8 percent on your money, what is this prize worth to youtoday?a. $87,003.69b. $87,380.23c. $87,962.77d. $88,104.26e. $90,723.76ORDINARY ANNUITYAND PRESENT VALUEb 26. Todd is able to pay $160 a month for five years for a car. If the interest rate is 4.9percent, how much can Todd afford to borrow to buy a car?a. $6,961.36b. $8,499.13c. $8,533.84d. $8,686.82e. $9,588.05ORDINARY ANNUITYAND PRESENT VALUEa 27. You are the beneficiary of a life insurance policy. The insurance company informsyou that you have two options for receiving the insurance proceeds. You canreceive a lump sum of $50,000 today or receive payments of $641 a month for tenyears. You can earn 6.5 percent on your money. Which option should you take andwhy?a. You should accept the payments because they are worth $56,451.91 today.b. You should accept the payments because they are worth $56,523.74 today.c. You should accept the payments because they are worth $56,737.08 today.d. You should accept the $50,000 because the payments are only worth $47,757.69today.e. You should accept the $50,000 because the payments are only worth $47,808.17today.ORDINARY ANNUITYAND PRESENT VALUEc 28. Your employer contributes $25 a week to your retirement plan. Assume that youwork for your employer for another twenty years and that the applicable discountrate is 5 percent. Given these assumptions, what is this employee benefit worth toyou today?a. $13,144.43b. $15,920.55c. $16,430.54d. $16,446.34e. $16,519.02ORDINARY ANNUITYAND PRESENT VALUEa 29. You have a sub-contracting job with a local manufacturing firm. Your agreementcalls for annual payments of $50,000 for the next five years. At a discount rate of12 percent, what is this job worth to you today?a. $180,238.81b. $201,867.47c. $210,618.19d. $223,162.58e. $224,267.10ANNUITY DUE AND PRESENT VALUEb 30. The Ajax Co. just decided to save $1,500 a month for the next five years as a safetynet for recessionary periods. The money will be set aside in a separate savingsaccount which pays 3.25 percent interest compounded monthly. They deposit thefirst $1,500 today. If the company had wanted to deposit an equivalent lump sumtoday, how much would they have had to deposit?a. $82,964.59b. $83,189.29c. $83,428.87d. $83,687.23e. $84,998.01ANNUITY DUE AND PRESENT VALUEb 31. You need some money today and the only friend you have that has any is your‘miserly’ friend. He agrees to loan you the money you need, if you make paymentsof $20 a month for the next six month. In keeping with his reputation, he requiresthat the first payment be paid today. He also charges you 1.5 percent interest permonth. How much money are you borrowing?a. $113.94b. $115.65c. $119.34d. $119.63e. $119.96ANNUITY DUE AND PRESENT VALUEc 32. You buy an annuity which will pay you $12,000 a year for ten years. The paymentsare paid on the first day of each year. What is the value of this annuity today at a 7percent discount rate?a. $84,282.98b. $87,138.04c. $90,182.79d. $96,191.91e. $116,916.21ORDINARY ANNUITY VERSUS ANNUITY DUEa 33. You are scheduled to receive annual payments of $10,000 for each of the next 25years. Your discount rate is 8.5 percent. What is the difference in the present valueif you receive these payments at the beginning of each year rather than at the end ofeach year?a. $8,699b. $9,217c. $9,706d. $10,000e. $10,850ORDINARY ANNUITY VERSUS ANNUITY DUEd 34. You are comparing two annuities with equal present values. The applicablediscount rate is 7.5 percent. One annuity pays $5,000 on the first day of each yearfor twenty years. How much does the second annuity pay each year for twentyyears if it pays at the end of each year?a. $4,651b. $5,075c. $5,000d. $5,375e. $5,405ORDINARY ANNUITY VERSUS ANNUITY DUEa 35. Martha receives $100 on the first of each month. Stewart receives $100 on the lastday of each month. Both Martha and Stewart will receive payments for five years.At an 8 percent discount rate, what is the difference in the present value of thesetwo sets of payments?a. $32.88b. $40.00c. $99.01d. $108.00e. $112.50ORDINARY ANNUITYAND FUTURE VALUEc 36. What is the future value of $1,000 a year for five years at a 6 percent rate ofinterest?a. $4,212.36b. $5,075.69c. $5,637.09d. $6,001.38e. $6,801.91ORDINARY ANNUITYAND FUTURE VALUEd 37. What is the future value of $2,400 a year for three years at an 8 percent rate ofinterest?a. $6,185.03b. $6,847.26c. $7,134.16d. $7,791.36e. $8,414.67ORDINARY ANNUITYAND FUTURE VALUEc 38. Janet plans on saving $3,000 a year and expects to earn 8.5 percent. How much willJanet have at the end of twenty-five years if she earns what she expects?a. $219,317.82b. $230,702.57c. $236,003.38d. $244,868.92e. $256,063.66ANNUITY DUE VERSUS ORDINARY ANNUITYb 39. Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 tohis savings on the last day of each year. They both earn a 9 percent rate of return.What is the difference in their savings account balances at the end of thirty years?a. $35,822.73b. $36,803.03c. $38,911.21d. $39,803.04e. $40,115.31ORDINARY ANNUITY PAYMENTSd 40. You borrow $5,600 to buy a car. The terms of the loan call for monthly paymentsfor four years at a 5.9 percent rate of interest. What is the amount of each payment?a. $103.22b. $103.73c. $130.62d. $131.26e. $133.04ORDINARY ANNUITY PAYMENTS AND COST OF INTERESTc 41. You borrow $149,000 to buy a house. The mortgage rate is 7.5 percent and the loanperiod is 30 years. Payments are made monthly. If you pay for the house accordingto the loan agreement, how much total interest will you pay?a. $138,086b. $218,161c. $226,059d. $287,086e. $375,059ORDINARY ANNUITY PAYMENTS AND FUTURE VALUEd 42. The Great Giant Corp. has a management contract with their newly hired president.The contract requires a lump sum payment of $25 million be paid to the president upon the completion of her first ten years of service. The company wants to set aside anequal amount of funds each year to cover this anticipated cash outflow. The companycan earn 6.5 percent on these funds. How much must the company set aside each year for this purpose?a. $1,775,042.93b. $1,798,346.17c. $1,801,033.67d. $1,852,617.25e. $1,938,018.22ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEe 43. You retire at age 60 and expect to live another 27 years. On the day you retire, youhave $464,900 in your retirement savings account. You are conservative and expectto earn 4.5 percent on your money during your retirement. How much can youwithdraw from your retirement savings each month if you plan to die on the dayyou spend your last penny?a. $2,001.96b. $2,092.05c. $2,398.17d. $2,472.00e. $2,481.27ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEc 44. The McDonald Group purchased a piece of property for $1.2 million. They paid adown payment of 20 percent in cash and financed the balance. The loan termsrequire monthly payments for 15 years at an annual percentage rate of 7.75 percentcompounded monthly. What is the amount of each mortgage payment?a. $7,440.01b. $8,978.26c. $9,036.25d. $9,399.18e. $9,413.67ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEd 45. You estimate that you will have $24,500 in student loans by the time you graduate.The interest rate is 6.5 percent. If you want to have this debt paid in full within fiveyears, how much must you pay each month?a. $471.30b. $473.65c. $476.79d. $479.37e. $480.40ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEb 46. You are buying a previously owned car today at a price of $6,890. You are paying$500 down in cash and financing the balance for 36 months at 7.9 percent. What isthe amount of each loan payment?a. $198.64b. $199.94c. $202.02d. $214.78e. $215.09ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEb 47. The Good Life Insurance Co. wants to sell you an annuity which will pay you $500per quarter for 25 years. You want to earn a minimum rate of return of 5.5 percent.What is the most you are willing to pay as a lump sum today to buy this annuity?a. $26,988.16b. $27,082.94c. $27,455.33d. $28,450.67e. $28,806.30ANNUITY DUE PAYMENTSAND PRESENT VALUEc 48. Your car dealer is willing to lease you a new car for $299 a month for 60 months.Payments are due on the first day of each month starting with the day you sign thelease contract. If your cost of money is 4.9 percent, what is the current value of thelease?a. $15,882.75b. $15,906.14c. $15,947.61d. $16,235.42e. $16,289.54ANNUITY DUE PAYMENTS AND PRESENT VALUEd 49. Your great-aunt left you an inheritance in the form of a trust. The trust agreementstates that you are to receive $2,500 on the first day of each year, startingimmediately and continuing for fifty years. What is the value of this inheritancetoday if the applicable discount rate is 6.35 percent?a. $36,811.30b. $37,557.52c. $39,204.04d. $39,942.42e. $40,006.09ANNUITY DUE PAYMENTS AND PRESENT VALUEe 50. You recently filed suit against a company. Today, you received three settlementoptions as follows:Option A: $10,000 on the first day of each year for 25 yearsOption B: $880 on the first day of each month for 25 yearsOption C: $119,830 as a lump sum payment todayYou can earn 7.5 percent on your investments. You do not care if you personallyreceive the funds or if they are paid to your heirs should you die within the next 25years. Which one of the following statements is correct given this information?a. Option C is clearly the best choice since you can earn 7.5 percent on the entirelump sum starting immediately.b. Option B is clearly the best choice since it offers the largest number of payments.c. Option A is clearly the best choice since it has by far the largest future value.d. Option B is clearly the best choice since it has by far the largest present value.e. You are relatively indifferent to the three options as they are all approximatelyequal in value to you.ANNUITY DUE PAYMENTSAND FUTURE VALUEa 51. Your firm wants to save $250,000 to buy some new equipment three years fromnow. The plan is to set aside an equal amount of money on the first day of eachyear starting today. The firm can earn a 4.7 percent rate of return. How much doesthe firm have to save each year to achieve their goal?a. $75,966.14b. $76,896.16c. $78,004.67d. $81.414.14e. $83,333.33ANNUITY DUE PAYMENTSAND FUTURE VALUEe 52. Today is January 1. Starting today, Sam is going to contribute $140 on the first ofeach month to his retirement account. His employer contributes an additional 50percent of the amount contributed by Sam. If both Sam and his employer continueto do this and Sam can earn a monthly rate of ½ of 1 percent, how much will hehave in his retirement account 35 years from now?a. $199,45.944.b. $200,456.74c. $249,981.21d. $299,189.16e. $300,685.11ORDINARY ANNUITY TIME PERIODS AND PRESENT VALUEc 53. You are considering an annuity which costs $100,000 today. The annuity pays$6,000 a year. The rate of return is 4.5 percent. What is the length of the annuitytime period?a. 24.96 yearsb. 29.48 yearsc. 31.49 yearsd. 33.08 yearse. 38.00 yearsORDINARY ANNUITY TIME PERIODS AND PRESENT VALUEd 54. Today, you signed loan papers agreeing to borrow $4,954.85 at 9 percentcompounded monthly. The loan payment is $143.84 a month. How many loanpayments must you make before the loan is paid in full?a. 29.89b. 36.00c. 38.88d. 40.00e. 41.03ORDINARY ANNUITY TIME PERIODS AND FUTURE VALUEa 55. Winston Enterprises would like to buy some additional land and build a newfactory. The anticipated total cost is $136 million. The owner of the firm is quiteconservative and will only do this when the company has sufficient funds to paycash for the entire expansion project. Management has decided to save $450,000 amonth for this purpose. The firm earns 6 percent compounded monthly on the fundsit saves. How long does the company have to wait before expanding its operations?a. 184.61 monthsb. 199.97 monthsc. 234.34 monthsd. 284.61 monthse. 299.97 monthsANNUITY DUE TIME PERIODS AND PRESENT VALUEb 56. Today, you are retiring. You have a total of $413,926 in your retirement savingsand have the funds invested such that you expect to earn an average of 3 percent,compounded monthly, on this money throughout your retirement years. You wantto withdraw $2,500 at the beginning of every month, starting today. How long willit be until you run out of money?a. 185.00 monthsb. 213.29 monthsc. 227.08 monthsd. 236.84 monthse. 249.69 monthsANNUITY DUE TIME PERIODSc 57. The Bad Guys Co. is notoriously known as a slow-payer. They currently need toborrow $25,000 and only one company will even deal with them. The terms of theloancall for daily payments of $30.76. The first payment is due today. The interest rateis 21 percent compounded daily. What is the time period of this loan?a. 2.88 yearsb. 2.94 yearsc. 3.00 yearsd. 3.13 yearse. 3.25 yearsORDINARY ANNUITY INTEREST RATEc 58. The Robertson Firm is considering a project which costs $123,900 to undertake.The project will yield cash flows of $4,894.35 monthly for 30 months. What is therate of return on this project?a. 12.53 percentb. 13.44 percentc. 13.59 percentd. 14.02 percente. 14.59 percentORDINARY ANNUITY INTEREST RATEa 59. Your insurance agent is trying to sell you an annuity that costs $100,000 today. Bybuying this annuity, your agent promises that you will receive payments of $384.40 amonth for the next 40 years. What is the rate of return on this investment?a. 3.45 percentb. 3.47 percentc. 3.50 percentd. 3.52 percente. 3.55 percentORDINARY ANNUITY INTEREST RATEe 60. You have been investing $120 a month for the last 15 years. Today, yourinvestment account is worth $47,341.19. What is your average rate of return onyour investments?a. 9.34 percentb. 9.37 percentc. 9.40 percentd. 9.42 percente. 9.46 percentORDINARY ANNUITY INTEREST RATEc 61. Brinker, Inc. has been investing $136,000 a year for the past 4 years into a businessventure. Today, Brinker sold that venture for $685,000. What is their rate of returnon this venture?a. 9.43 percentb. 11.06 percentc. 15.59 percentd. 16.67 percente. 18.71 percentANNUITY DUE INTEREST RATEb 62. Your mother helped you start saving $25 a month beginning on your 10th birthday.She always made you make your deposit on the first day of each month just to“start the month out right”. Today, you turn 21 and have $4,482.66 in your account.What is your rate of return on your savings?a. 5.25 percentb. 5.29 percentc. 5.33 percentd. 5.36 percente. 5.50 percentANNUITY DUE INTERESTRATEa 63. Today, you turn 21. Your birthday wish is that you will be a millionaire by your40th birthday. In an attempt to reach this goal, you decide to save $25 a day, everyday until you turn 40. You open an investment account and deposit your first $25today. What rate of return must you earn to achieve your goal?a. 15.07 percentb. 15.13 percentc. 15.17 percentd. 15.20 percente. 15.24 percentUNEVENCASH FLOWS ANDPRESENT VALUEb 64. Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co.can generate cash flows of $5,000, $9,000, and $15,000 over the next three years,respectively. After that time, they feel the business will be worthless. Marko hasdetermined that a 14 percent rate of return is applicable to this potential purchase.What is Marko willing to pay today to buy ABC Co.?a. $19,201.76b. $21,435.74c. $23,457.96d. $27,808.17e. $31,758.00UNEVEN CASH FLOWS ANDPRESENT VALUEa 65. You are considering two savings options. Both options offer a 4 percent rate ofreturn. The first option is to save $1,200, $1,500, and $2,000 a year over the nextthree years, respectively. The other option is to save one lump sum amount today. Ifyou want to have the same balance in your savings at the end of the three years,regardless of the savings method you select, how much do you need to save today ifyou select the lump sum option?a. $4,318.67b. $4,491.42c. $4,551.78d. $4,607.23e. $4,857.92b 66. You are considering two insurance settlement offers. The first offer includes annualpayments of $5,000, $7,500, and $10,000 over the next three years, respectively.The other offer is the payment of one lump sum amount today. You are trying todecide which offer to accept given the fact that your discount rate is 5 percent.What is the minimum amount that you will accept today if you are to select thelump sum offer?a. $19,877.67b. $20,203.00c. $21,213.15d. $23,387.50e. $24,556.88。
公司理财Discounted Cash Flow Valuation
CHAPTER 4Discounted Cash Flow Valuation Multiple Choice Questions:I. DEFINITIONSANNUITY1. An annuity stream of cash flow payments is a set of:a. level cash flows occurring each time period for a fixed length of time.b. level cash flows occurring each time period forever.c. increasing cash flows occurring each time period for a fixed length of time.d. increasing cash flows occurring each time period forever.e. arbitrary cash flows occurring each time period for no more than 10 years.ANNUITIES DUE2. Annuities where the payments occur at the end of each time period are called _____ , whereas_____ refer to annuity streams with payments occurring at the beginning of each time period.a. ordinary annuities; early annuitiesb. late annuities; straight annuitiesc. straight annuities; late annuitiesd. annuities due; ordinary annuitiese. ordinary annuities; annuities duePERPETUITY3. An annuity stream where the payments occur forever is called a(n):a. annuity due.b. indemnity.c. perpetuity.d. amortized cash flow stream.e. amortization table.II. CONCEPTSORDINARY ANNUITY VERSUS ANNUITY DUEc 4. You are comparing two annuities which offer monthly payments for ten years. Bothannuities are identical with the exception of the payment dates. Annuity A pays on thefirst of each month while annuity B pays on the last day of each month. Which one ofthe following statements is correct concerning these two annuities?a. Both annuities are of equal value today.b. Annuity B is an annuity due.c. Annuity A has a higher future value than annuity B.d. Annuity B has a higher present value than annuity A.e. Both annuities have the same future value as of ten years from today.UNEVEN CASH FLOWS AND PRESENT VALUEb 5. You are comparing two investment options. The cost to invest in either option is thesame today. Both options will provide you with $20,000 of income. Option A pays fiveannual payments starting with $8,000 the first year followed by four annual paymentsof $3,000 each. Option B pays five annual payments of $4,000 each. Which one of thefollowing statements is correct given these two investment options?a. Both options are of equal value given that they both provide $20,000 of income.b. Option A is the better choice of the two given any positive rate of return.c. Option B has a higher present value than option A given a positive rate of return.d. Option B has a lower future value at year 5 than option A given a zero rate of return.e. Option A is preferable because it is an annuity due.UNEVEN CASH FLOWS AND FUTURE VALUEa 6. You are considering two projects with the following cash flows:Project A Project BYear 1 $2,500 $4,000Year 2 3,000 3,500Year 3 3,500 3,000Year 4 4,000 2,500Which of the following statements are true concerning these two projects?I. Both projects have the same future value at the end of year 4, given a positive rate ofreturn.II. Both projects have the same future value given a zero rate of return.III. Both projects have the same future value at any point in time, given a positive rate of return.IV. Project A has a higher future value than project B, given a positive rate of return.a. II onlyb. IV onlyc. I and III onlyd. II and IV onlye. I, II, and III onlyPERPETUITY VERSUS ANNUITYd 7. A perpetuity differs from an annuity because:a. perpetuity payments vary with the rate of inflation.b. perpetuity payments vary with the market rate of interest.c. perpetuity payments are variable while annuity payments are constant.d. perpetuity payments never cease.e. annuity payments never ceaseTIME VALUEc 8. The time value of money concept can be defined asa. the relationship between the supply and demand of money.b. the relationship between money spent versus money received.c. the relationship between a dollar to be received in the future and a dollar today.d. the relationship of interest rate stated and amount paid.e. None of the above.CASH FLOWSd 9. Discounting cash flows involvesa. discounting only those cash flows that occur at least 10 years in the future.b. estimating only the cash flows that occur in the first 4 years of a project.c. multiplying expected future cash flows by the cost of capital.d. discounting all expected future cash flows to reflect the time value of money.e. taking the cash discount offered on trade merchandise.INTERESTa 10. Compound interesta. allows for the reinvestment of interest payments.b. does not allow for the reinvestment of interest payments.c. is the same as simple interest.d. provides a value that is less than simple interest.e. Both A and D.ANNUITYc 11. An annuitya. is a debt instrument that pays no interest.b. is a stream of payments that varies with current market interest.c. is a level stream of equal payments through time.d. has no value.e. None of the above.III. PROBLEMSPRESENT VALUE – SINGLE SUMa 12. Find the present value of $5,325 to be received in one period if the rate is 6.5%.a. $5,000.00b. $5,023.58c. $5,644.50d. $5,671.13e. None of the above.FUTURE VALUE – SINGLE SUMd 13. Bradley Snapp has deposited $7,000 in a guaranteed investment account with a promised rate of6% compounded annually. He plans to leave it there for 4 full years when he will make a down payment on a car after graduation. How much of a down payment will he be able to make?a. $1,960.00b. $2,175.57c. $8,960.00d. $8,837.34e. $9,175.57ORDINARY ANNUITY AND PRESENT VALUEb 14. You just won the lottery! As your prize you will receive $1,200 a month for 100 months. If youcan earn 8% on your money, what is this prize worth to you today?a. $87,003.69b. $87,380.23c. $87,962.77d. $88,104.26e. $90,723.76ORDINARY ANNUITY AND PRESENT VALUEa 15. You have a sub-contracting job with a local manufacturing firm. Your agreement calls forannual payments of $50,000 for the next five years. At a discount rate of 12 percent, what isthis job worth to you today?a. $180,238.81b. $201,867.47c. $210,618.19d. $223,162.58e. $224,267.10ORDINARY ANNUITY VERSUS ANNUITY DUEa 16. You are scheduled to receive annual payments of $10,000 for each of the next 25 years. Yourdiscount rate is 8.5 percent. What is the difference in the present value if you receive thesepayments at the beginning of each year rather than at the end of each year?a. $8,699b. $9,217c. $9,706d. $10,000e. $10,850ORDINARY ANNUITY AND FUTURE VALUEc 17. What is the future value of $1,000 a year for five years at a 6% rate of interest?a. $4,212.36b. $5,075.69c. $5,637.09d. $6,001.38e. $6,801.91ANNUITY DUE VERSUS ORDINARY ANNUITYb 18. Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 to his savings onthe last day of each year. They both earn a 9% rate of return. What is the difference in theirsavings account balances at the end of thirty years?a. $35,822.73b. $36,803.03c. $38,911.21d. $39,803.04e. $40,115.31PRESENT VALUE, PAY MENTS AND FUTURE VALUEb 19. The Bluebird Company has a $10,000 liability they must pay three years from today.The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit anadditional $2,500 a year for the next three years, starting one year from today. The accountpays a 3% rate of return. How much does the Bluebird Company need to deposit today?a. $1,867.74b. $2,079.89c. $3,108.09d. $4,276.34e. $4,642.28PERPETUITY PRESENT VALUEe 20. A 9% preferred stock pays an annual dividend of $4.50. What is one share of this stock worthtoday?a. $.41b. $4.50c. $5.00d. $45.00e. $50.00PRESENT VALUEb 21. Your grandmother invested one lump sum 17 years ago at 4.25% interest.Today, she gave you the proceeds of that investment which totaled $5,539.92. Howmuch did your grandmother originally invest?a. $2,700.00b. $2,730.30c. $2,750.00d. $2,768.40e. $2,774.90SOLUTIONS TO TEST BANK PROBLEMSChapter 412. Enter 1 6.5 5325N I/Y PV PMT FVSolve for -5,00013. $7,000 (1.06)4 = $8,837.3414. ⎪⎪⎭⎪⎪⎬⎫⎪⎪⎩⎪⎪⎨⎧⎥⎦⎤⎢⎣⎡+-⨯=1208.)1208.1/(11200,1$100APV = $1,200 ⨯ 72.816858 = $87,380.23 15.[]⎭⎬⎫⎩⎨⎧+-⨯=12.)12.1/(11000,50$5APV = $50,000 ⨯ 3.6047762 = $180,238.81 16.[]⎭⎬⎫⎩⎨⎧+-⨯=085.)085.1/(11000,10$25APV = $10,000 ⨯ 10.234191 = $102,341.91[]()085.1085.)085.1/(11000,10$25+⨯⎭⎬⎫⎩⎨⎧+-⨯=PV A due = $10,000 ⨯ 10.234191 ⨯ 1.085 = $111,040.97Difference = $111,040.97 - $102,341.91 = $8,699.06 = $8,699 (rounded)Note: The difference = .085 ⨯ $102,341.91 = $8,699.0617. 06.1)06.1(000,1$5-+⨯=AFV = $1,000 ⨯ 5.63709 = $5,637.0918. 09.1)09.1(000,3$30-+⨯=AFV = $3,000 ⨯ 136.3075385 = $408,922.62()09.109.1)09.1(000,3$30+⨯-+⨯=FV A due = $3,000 ⨯ 136.3075385 ⨯ 1.09 = $445,725.65 Difference = $445,725.65 - $408,922.62 = $36,803.03 Note: Difference = $408,922.62 ⨯ .09 = $36,803.03 19. [][][]500,2$)03.1(500,2$)03.1(500,2$)03.1(000,10$123+⨯+⨯+⨯=C ; C= $2,079.89 20. 09.50.4$=PV ; PV = $50.00 21. Present value = $5,539.92 ⨯ [1 ÷ (1 + .0425)17] = $2,730.30。
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息税前利润（1-税率） – (资本开支 – 折旧) – 非现金流动资本的变化
此外，FCFF还可以是：
息税前利润 (1-税率) × (1 – 再投资率)
FIN 580 CF – Prof. Pinteris
计算FCFF的主要元素 的主要元素 计算
从利润表中取得息税前利润，并进行加（减）调整
FIN 580 CF – Prof. Pinteris
计算企业股权价值
FCFE来自： FCFF – 偿贷 + 信贷发行 定义
净新增贷款 = 新贷发行 – 偿贷金额
FIN 580 CF – Prof. Pinteris
计算企业股权价值
计算净新增贷款余额： Δ 应付票据 + Δ 长期债务当期到期部分 + Δ 长期债务
现金流折现估值法
FIN 580 CF – Prof. Pinteris
现金流折现（ 现金流折现（DCF）估值要素 ）
FIN 580 CF – Prof. Pinteris
给予企业估值
使用DCF法意味着将公司自由现金流（FCFF）进行折现 FCFF包括如下现金流：
流向债权人 流向股东
预测FCFF之前，必须了解：
两阶段模型中，常见的变异包括：
稳定增长变为长期可持续增速 增速下滑变为长期可持续增速
三阶段模型只是两阶段模型的简单延伸
例如：稳定增长、增速下滑和长期可持续增速
FIN 580 CF – Prof. Pinteris
对马拉松石油公司进行估值 三阶段FCFF模型） 模型） （三阶段 模型
当前FCFF = 7.45亿美元 流通股份 = 3.0939亿股 股权BETA = 0.9 无风险回报率 = 5.04% 市场溢价回报率 = 5.5% 债务成本 = 7.1% 税率 = 34% D/V = 20% 债务 = 15.18亿美元 FCFF增速
当前投资更高的超额回报意味着更高的未来增速
竞争优势
高准入壁垒，高利润率（垄断环境） 管理层素质
FIN 580 CF – Prof. Pinteris
预计EBIT预期增速 预期增速 预计
营业利润的增速会由什么因素驱动？
可利用历史经验预期未来增速 但需了解驱动增速的因素
EBIT增速的驱动因素
EBIT增速 = 再投资率 x 资本回报率
盈利增速减缓或下降 利润率开始遭受压力 利润增速开始向经济增速看齐 资本需求减少 正FCFE和股息不断提高
成熟阶段
股权回报率接近股权成本 盈利增速、股息和股权回报率稳定在长期可持续增速水平
FIN 580 CF – Prof. Pinteris
自由现金流模型的变异
DCF模型的变异
两阶段模型 三阶段模型
现金与可转让证券 持有其他企业和子公司的少数权益
对各子公司进行估值并按比例计算价值
养老金资产
将资产盈余的税后部分加入估值中
FIN 580 CF – Prof. Pinteris
计算企业股权价值
通过用DCF法计算企业股权价值，我们可以：
使用DCF计算企业价值，并从中刨除企业债务的价值 使用DCF法将股权自由现金流（FCFE）按照公司的股权成本折现 （使用与前述FCFF同样的步骤）
计算终止价格
第t期的终止价格： TVt = (FCFFt(1+g))/(WACC-g) g = 预测器后FCFF增速
FIN 580 CF – Prof. Pinteris
预计FCFF增速 增速 预计
企业销售额、息税前利润（EBIT）和算得的FCFF的高增速 能维持多久？
企业规模（小企业高增长期会更久） 当前增速和超额回报
第一阶段
每年8.8%（1-4年）
第二阶段
第五年7.4% 第六年6% 第七年4.6%
第三阶段
第八年及以后3.2%
FIN 580 CF – Prof. Pinteris
FIN 580 CF – Prof. Pinteris
自由现金流模型的变异
企业估值分析中，通常会假设企业在生命周期经历三个阶 段：
增长阶段
市场扩张 高利润率 超高的增速 FCFE 负值 没有后很低的股息支付率
FIN 580 CF – Prof. Pinteris
自由现金流模型的变异
转ቤተ መጻሕፍቲ ባይዱ（到成熟）阶段
记为运营费用的财务费用（如：经营性租赁） 记为经营费用的资本开支（如：研发） 一次性或非经常性收入（减）和费用
FIN 580 CF – Prof. Pinteris
计算FCFF的主要元素 的主要元素 计算
税率的两个选择
实际税率：应缴税费/应税所得 边际税率（美国为35-40%）
如合理，预测期可采用实际税率
FIN 580 CF – Prof. Pinteris
预计EBIT预期增速 预期增速 预计
再投资率 (资本开支 – 折旧 + Δ 非现金流动资本) ÷ EBIT (1 – 税率) 资本回报 EBIT (1 – 税率) ÷ 已投资本
FIN 580 CF – Prof. Pinteris
预计EBIT预期增速 预期增速 预计
税收抵免 递延税项 报税与财报会计的不同
预测期外现金流使用边际税率
FIN 580 CF – Prof. Pinteris
计算FCFF的主要元素 的主要元素 计算
资本开支各期不同
如必要，可将各期平均后取标准值
将折旧费用从利润表中剔除 净流动资本并不稳定
通常与销售额相关联
FIN 580 CF – Prof. Pinteris
再投资率通常使用历史均值
再投资率随着企业不断成熟而下降 或者使用行业均值
计算资本回报
通常基于当前投资的资本回报
不一定适合作为未来投资的回报率
使用资本账面值（债务账面值+股权账面值）
通常调整账面值以反映无形资产（研发、商标）
FIN 580 CF – Prof. Pinteris
缺失项目
为计算企业价值，需再加入如上方法并未计算的资产价值
税负 再投资需要
FIN 580 CF – Prof. Pinteris
给予企业估值
预计5-10年FCFF流量 按合理增速的假设预计企业的终止价格 预计企业的资本成本
FIN 580 CF – Prof. Pinteris
给予企业估值
FIN 580 CF – Prof. Pinteris
计算FCFF 计算