CFA Lv2 权益

在CFA（特许金融分析师）二级考试中，权益（Equity）模块是核心组成部分之一，它不仅涵盖了公司估值的深层次理论，还涉及了多种估值方法和实际应用。本框架图旨在系统性地梳理CFA二级权益模块的关键知识点，帮助考生构建清晰的知识体系，并通过配套的习题巩固所学内容。

CFA Lv2 权益

• M1 Equity Valuation: Applications and Processes
  • Valuation definitions
    • Intrinsic value
      • E(IV) - P = (IV - P) + (E(IV) - IV)
        • 例题
          • tatement 2 “An active investment manager attempts to capture positive alpha. But mispricing of assets is not directly observable. It is therefore important that you understand the possible sources of perceived mispricing.” Based on Statement 2, which of the following sources of perceived mispricing do active investment managers attempt to identify? The difference between: A intrinsic value and market price. B estimated intrinsic value and market price. C intrinsic value and estimated intrinsic value
            • A is correct. The difference between the true (real) but unobservable intrinsic value and the observed market price contributes to the abnormal return or alpha, which is the concern of active investment managers.
              • 这题要注意，问的不是perceived mispricing是什么，而是perceived mispricing的哪部分是active investment managers 关注的
      • IV - P: true mispricing
      • E(IV) - IV: estimation error
      • E(IV) - P: Perceived mispricing
    • Going-concern value vs. liquidation value
      • Going-concern value
      • Liquidation value
        • Going-concern value > Liquidation value
      • Orderly Liquidation Value
        • adequate time
      • 例题
        • Statement 3 “For its distressed securities fund, Global-Guardian Capital screens its investable universe of securities for companies in financial distress.” Statement 4 “For its core equity fund, GlobalGuardian Capital selects financially sound companies that are expected to generate significant positive free cash flow from core business operations within a multiyear forecast horizon.” With respect to Statements 3 and 4, which of the following measures of value would the distressed securities fund’s analyst consider that a core equity fund analyst might ignore? A Fair value B Liquidation value C Fair market value
          • B is correct. The measure of value the distressed securities fund’s analyst would consider that the core equity fund analyst might ignore is liquidation value. The liquidation value of a company is its value if it were dissolved and its assets sold individually.
            • 送分题
    • Fair market value
    • Investment value
  • Valuation applications and process
    • Applications of equity valuation
      • Selecting stocks
      • Inferring market expectations
      • 其他战略放弃
        • 愿好运与你同在
    • Valuation process
      • Understanding the business
        • Industry and competitive analysis
          • Porter's five forces
            • 例题
              • Marshall discusses her current projects that entail analyzing publicly traded firms with White. Marshall is concerned about the effects of inflation on her revenue and cost assessments. White says to Marshall, "If the firm uses futures contracts to offset possible increases in future costs, the firm may not necessarily need to increase the price of its products." which following force is least likely affected by using futures contracts? A. Supplier bargaining power B. Customer bargaining power C. Threat of cheaper substitute products
                • B is correct. B is correct. Customer bargaining power is the Porter five force least likely affected by using futures contracts. Using futures contracts to control costs does not affect the bargaining power of customers. A is incorrect. Using futures contracts to control costs does mitigate supplier bargaining power. C is incorrect. Using futures contracts to control costs prevents final product prices from increasing, which mitigates the threat of cheaper substitute products.
                  • 客户的定价能力是外部影响，成本控制是内部因素。
        • Analysis of financial reports
        • Sources of information
        • Considerations in using accounting information
      • Forecasting company performance
      • Selecting the appropriate valuation model
        • Absolute valuation models
          • 例题
            • To estimate each firm's intrinsic value, Richardson applies appropriate discount rates to each firm's estimated free cash flows over a ten-year time horizon and to the estimated value of the firm at the end of the ten-year horizon. Which valuation model is Richardson applying in his analysis of the retailers? A Relative value B Absolute value C Sum-of-the-parts
              • B is correct. An absolute valuation model is a model that specifies an asset's intrinsic value. The most important type of absolute equity valuation models are present value models (also referred to as discounted cash flow models), and the model described by Richardson is of that type.
                • 送分题
        • Relative valuation models
        • Valuation of the total entity and its components
        • Issues in model selection and interpretation
        • Conglomerate discount
          • discount to sum-of-parts value
        • Situational adjustments
          • control premium
          • lack of marketability discount
          • illiquidity discount
          • blockage factor
            • block of shares be lower than market price
        • 例题
          • Michelle Lee, a junior technology analyst at GlobalGuardian, asks the director of research for advice as to which valuation model to use for VEGA, a fast growing semiconductor company that is rapidly gaining market share. The director of research states that “the valuation model selected must be consistent with the characteristics of the company being valued.” Lee tells the director of research that VEGA is not expected to be profitable for several more years. According to management guidance, when the company turns profitable, it will invest in new product development; as a result, it does not expect to initiate a dividend for an extended period of time. Lee also notes that she expects that certain larger competitors will become interested in acquiring VEGA because of its excellent growth prospects. The director of research advises Lee to consider that in her valuation. Which valuation model would the director of research most likely recommend Lee use to estimate the value of VEGA? A Free cash flow B Dividend discount C P/E relative valuation
            • A is correct. The broad criteria for model selection are that a valuation model be consistent with the characteristics of the company being valued — that it be appropriate given the availability and quality of the data and consistent with the purpose of the valuation. VEGA currently has negative earnings, making the use of P/E relative valuation difficult if not impossible. As VEGA does not pay a dividend and is not expected to for the foreseeable future, the application of a dividend discount model is problematic. However, the lack of a dividend would not be an obstacle to free cash flow valuation. Furthermore, the director of research has advised that the possibility that competitors may seek to acquire VEGA be taken in to account in valuing VEGA. The reading states that free cash flow valuation can be appropriate in such circumstances. Thus, the director of research would be most likely to recommend free cash flow valuation.
              • 需要深刻理解不同估值方法的优缺点
      • Converting forecasts to a valuation
      • Applying the valuation conclusions
  • Communicating valuation results
    • Effective research report
• M2 Discounted Dividend Valuation
  • PV Models Comparisons
    • DDM
      • Adv
        • less volatile
        • Less sensitive to short term fluctuations
        • Accoutns for reinvested earnings
      • Disadv
        • Firm may not pay dividends
        • Firm may pay less dividends for tax reasons
        • Dividends may not reflect control perspective
      • Appropriateness
        • dividend policy that has an understandable and consistent relationship to profitability
        • non-control perspective
          • 例题
            • D'Shaun Jackson, an individual do-it-yourself investor, is reviewing retail companies for potential addition to his portfolio. The first company he considers is Discount Days Ltd. (DDL) an up-andcoming regional competitor in the dollar store segment. Jackson’s analysis shows that the company is profitable and has strong positive operating cash flows. While the company is working to expand the number of stores in its network, investing cash flows are exceeding operating cash flows. To date, the company has not paid dividends, but Jackson believes it will likely start once it has finished its expansion plans. Jackson decides to use a dividend discount model to value the shares and estimates that DDL will start paying an annual dividend of $0.50 per share at the end of year 4 with a modest growth rate of 2% per year. He uses the capital asset pricing model to estimate a cost of equity of 7.25%. Which of the following factors would make the model Jackson selects to value DDL's shares the most appropriate model to use? A. Jackson has a noncontrol perspective. B. The company has intense capital demands for the next few years. C. The model considers Jackson’s opportunity cost of investing in the stock.
              • 答案：A 解析：A is correct. A dividend discount model (DDM) is most suitable when an investor takes a noncontrol perspective because he does not have the ability to meaningfully influence the timing or magnitude of a company’s cash flows and is therefore reliant on dividend policy. Because Jackson is looking for an investment for his personal portfolio, it is most likely that he has a noncontrol perspective. B is incorrect. If a company has intense capital demands — as DDL does based on its investment cash flows exceeding its operating ones — it may have negative free cash flow and be unable to pay dividends. In this situation, a residual income model would be the most appropriate model to use. C is incorrect. The residual income model considers the opportunity cost to an investor of investing in a stock, not a dividend discount model.
                • 送分题
        • Mature firms
    • FCF
      • Adv
        • different dividend and financing/leverage policies
        • FCF can be viewed as dividends paying capacity
        • Popular
      • Disadv
        • negative fcf
        • require long forecast periods, introducing greater model uncertainty
      • Appropriateness
        • no dividend payment history
        • FCF consistent with profitability
        • Controlling shareholder
    • RI
      • Adv
        • wide applicabilities
        • incorporates opportunity cost
      • Disadv
        • require detailed knowledge of accrual accounting
        • quality of accounting disclosure
      • Appropriateness
        • no dividend history
        • negative fcf
        • less horizon dependence
  • Gordon growth model
    • GGM
      • Assumption
        • 有dividend
        • 有g
        • r>g
          • 例题
            • Barton begins her analysis by looking at XRL. After doing some research, she concludes that a reasonable growth estimate for the company is the sustainable growth rate using the most recent year’s retention ratio and calculates a price for XRL using this information. She makes the following note: ● It will not be possible to use the Gordon growth model for the analysis of XRL. Using the data in Exhibit 1, Barton's note about the use of the Gordon growth model to value XRL is most likely: A. Correct because the required return on equity is less than the expected growth rate. B. incorrect because the sustainable growth rate is greater than the US economy's growth rate. C. incorrect because the required return on equity is greater than the US economy's growth rate.
              • A is correct A. Correct. The Gordon growth model cannot be used when r < g. In this case, r = 8.84%, and g = 13.84%. The calculations are as follows: Gordon growth model: P0 = D1/(r – g) where P0 = current price D1 = next period’s dividend r = required return on equity g = growth rate of dividends. The calculated expected growth rate of dividends is based on the sustainable growth rate model: g = b × ROE, where b = 1 – (DPS/EPS) = [1 – (1.77/3.15)] × 0.316 = 0.1384 where g = sustainable growth rate b = retention ratio DPS = dividends per share EPS = earnings per share The required return on equity is RF + βi[E(RM) – RF] = 0.0294 + (0.94 × 0.0628) = 0.0884 = 8.84%. B. Incorrect. The sustainable growth must be less than the economy's growth rate (3.7%) for the Gordon growth model to be appropriate, C. Incorrect. Although r must be greater than g, the appropriate growth rate is the company's growth rate in dividends rather than the economy's growth rate (3.7%).
                • 要注意考察知识点的灵活程度
      • V0 = D1 / (r-g)
        • 例题
          • ... At the beginning of 20X9, Daniel asks Rae to value the equity of Tasty Foods Company for its possible inclusion in the list of approved investments ... Rae notes that the company's EPS has been increasing at an average rate of 4.48% per year. The dividend payout ratio has remained fairly stable, and dividends have increased at an average rate of 5.30%. Rae uses the CAPM to compute the return on equity ... Rae's estimate for the required return on equity for Tasty Foods is 0.04+ 1.10(0.065) = 0.1115, or 11.15% Which of the following is closest to Rae's estimate of the stock’s value? A $10.08. B $10.54. C $10.62.
            • C is correct V0 = D1 / (r-g) = 0.59*1.053/(0.1115-0.053)=10.62
              • 这题的关键是，题目给了一堆数字，怎么挑出最合适的。因为说了dividend payout ratio has remained fairly stable，所以在暗示用DDM
      • Leading justified P/E
        • Justified P0/E1 = (1-b) / (r-g)
      • Trailing justified P/E
        • Justified P0/E0 = (1-b)(1+g) / (r-g)
      • 例题
        • 1 A free cash flow valuation model would not be appropriate to evaluate Company ABC if the firm becomes a takeover candidate. 2 A dividend discount model cannot be applied to Company XYZ if dividends are suspended for a few years. 3 A dividend discount model is suitable for evaluating the stock of Company JZY because of the historically consistent payout ratio. Which of the following statements made by Thomas is correct? A Statement 1 B Statement 2 C Statement 3
          • C is correct. A dividend discount model is especially useful when dividend policy bears an understandable and consistent relationship to the company's profitability. The relatively consistent dividend payout ratio suggests Company JZY would be a suitable candidate for a dividend discount model.
            • A说反了，有control的话，反而应该用FCF
            • 这里可能要注意B有点坑，没派D可以把D当成0来折现，而不是不适用DDM
      • 例题
        • Steve Lanes is a junior analyst at ABC Securities. He has been asked to prepare a research report for Sightseeing Corporation, a tourism company and give recommendation about its stock. Sightseeing is a small-cap publicly traded company that pays dividends regularly. Following is the 2015 year-end selected financial data of the company in $ millions: Net Income: 90 Dividends: 36 Total Assets: 1,015 Common Stock (70 million shares outstanding): 600 Retained earnings: 171 CAPM derived required rate of return: 10.5% Based on the Gordon growth model and the 2015 data collected by Lanes, Sightseeing’s intrinsic value per share as of 2015 is closest to: A. $15.72. B. $9.21. C. $10.33.
          • A is correct. Using the Gordon growth model, V0 = D0 (1 + g)/(r – g). g = b × ROE b = 1 – Payout ratio = 1 – (36 / 90) = 0.6 ROE = Net income / Shareholders' equity = 90 / (600 + 171) = 11.67% g = 0.6 × 11.67% = 7.00%. D0 = $36 million / 70 million shares = $0.5143/share V0 = 0.5143 (1 + 0.07) / (0.105 – 0.07) = $15.72.
            • GGM=D1/(r-g)
              • D1可以通过D0*(1+g)求出，所以还是缺少g
              • g可以通过ROE*(1-b)求出，所以下一步应该去找b和ROE
              • 题目给了D0，和NI，可以得到b=36/90=0.4
              • 我们有NI，可以通过NI/E得到ROE
              • E可以通过common stock + retained earning得到
              • 最后得到ROE=90/(600+171)=0.116732 -> g=0.116732*0.6=0.070039 -> GGM = (36*1.07)/(0.105-0.07)=1100.571429 -> P/S = 1100.57/70=15.722429
      • 例题
        • In her presentation, Thomas links justified price multiples to discounted cash flow models by assuming the Gordon growth model and the sustainable growth rate. She shows a numerical example on justified P/B using the following details: a firm’s ROE is 11.5%, its required rate of return is 9.5%, and its expected growth rate is 6.5%. Based on the information given, the justified P/B presented by Thomas is closest to: A. 1.21. B. 1.67. C. 1.78.
          • B is correct. Because candidates use the accurate formula for justified P/B. The figure is computed as: (ROE – g)/(r – g) = (0.115 – 0.065)/(0.095 – 0.065) = 0.5/0.3 = 1.67. According to the Gordon growth model, V0 = E1 × (1 – b)/(r – g). Defining ROE as E1/B0 so that E1 = B0 × ROE and substituting for E1 into the prior expression, we have V0 = B0 × ROE × (1 – b)/(r – g), giving V0/B0 = ROE × (1 – b)/(r – g). The sustainable growth rate expression is g = b × ROE. Substituting b = g/ROE into the expression just given for V0/B0, we have V0/B0 = (ROE – g)/(r – g). Because justified price is intrinsic value, V0.
            • Justified P/B = V/B = GGM/B GGM=D1/(r-g)
              • r和g都是现成的，所以这里要找D1/B
              • D1=E1(1-b)，需要找b
              • b=(ROE-g)/ROE
              • E1/B=ROE
              • 汇总: V/B = D1/(r-g)*B = E1(1-b)/(r-g)*B = ROE(1-b)/(r-g)=g/(r-g)=(ROE-g)/(r-g) =(0.115-0.065)/(0.095-0.065)=1.666667
              • 要注意，ROE是E1/B0，而不是E0/B0。
    • Present value of growth opportunities (PVGO)
      • V0 = E1/r + PVGO
        • 例题
          • Peters then asks the team to examine the growth opportunities of three Canadian stocks currently held in the portfolio. These stocks are listed in Exhibit 1. Peters believes that the stocks are fairly valued. Based on Exhibit 1, the stock with the largest present value of growth opportunities (PVGO) is: A ABTD. B BKKQ. C CPMN.
            • B is correct. BKKQ has the largest PVGO, calculated as follows: PVGO (ABTD) = P0 – E1/r = 80.00 – [7.30/0.105] = C$10.48 PVGO (BKKQ) = P0 – E1/r = 39.00 – [2.12/0.08] = C$12.50 PVGO (CPMN) = P0 – E1/r = 27.39 – [1.90/0.12] = C$11.56 where P0 is the current price per share, E1 is the forecasted earnings per share, and r is the required rate of return.
              • 送分题
        • 例题
          • Exhibit 2: PRBl's Data and Estimates for PVGO and H Models: Required return on equity: 12.40% Weighted average cost of capital (WACC): 10.60% Dividend payout ratio: 60% Most recent eamings per share: $5.33 Dividends and earnings growth rate over next 10 years (i.e.. Years 1 to 10): 15.00% Dividends and earnings growth rate after Year 10: 4.00% Current stock price: $70.00 Using the data in Exhibit 2, the estimate of PRBI's present value of growth opportunities (PVGO) is closest to: A.$20.57. B.$27.02. C.$40.34.
            • 答案：A 解析：A is correct. Using the PVGO and assuming that the company has no positive NPV projects: PVGO Model: V0 = E1/r + PVGO = $70 = [($5.33 × 1.15)/0.124] + PVGO $70 = $49.43 + PVGO PVGO = $70 – $49.43 = $20.57 B is incorrect. It uses E0 instead of E1. C is incorrect. It uses dividends instead of earnings.
              • 要注意PVGO是E1/r，不要被其他参数迷惑了。
              • 【PS】这题关键是要理解E1。E1这里说的是no-growth earnings level。但是题目给的多阶段growth，并且后面g会变化。但是我们只需要先算出E1，然后得到PVGO即可，在做PVGO的计算，不要考虑的太复杂。
              • 【PS2】基于对基本公式的理解，常见的考法有3种，按以下顺序分别求解：
              • 1. 题目给了E1，如果问PVGO，那只能假设是no growth，所以只要给了E1就直接拿来用，有E1的情况下，直接用E1算出PVGO；
              • 2. 假设没有E1，但是题目给了E0，因为PVGO的假设是E是no growth的，所以E0=E1，如果只有E0，也拿来直接用，代替E1来计算PVGO；
              • 3. 如果题目没给E1，只给了E0，又明确说了会增长，这里是有些矛盾的，但是为了算PVGO，我们只能用E0 * (1+g)得到E1，来代入公式。
              • 【PS3】要特别注意，这里是E1是no-growth earnings level，而不是estimated/expected earning in year 1。但是因为case题一般会一个case把多个知识点揉在一起考，所以真的case里遇到，假设no-growth算PVGO，再假设growth算DGM/GGM，不冲突，be water。（不懂变通的人都在学ACCA和CPA，懂变通的人才在学CFA，XD）
      • Leading P/E
        • P0/E1 = 1/r + PVGO/E1
          • 例题
            • Peters then asks the team to examine the growth opportunities of three Canadian stocks currently held in the portfolio. These stocks are listed in Exhibit 1. Peters believes that the stocks are fairly valued. Based on Exhibit 1, the growth component of the leading P/E is largest for: A ABTD. B BKKQ. C CPMN.
              • C is correct. The leading P/E is calculated as follows: P0/E1 = [1/r] + [PVGO/E1], where 1/r captures the no-growth component of P/E and PVGO/E1 captures the growth component of the P/E. PVGO is computed as follows: PVGO (ABTD) = P0 – E1/r = 80.00 – [7.30/0.105] = C$10.48 PVGO (BKKQ) = P0 – E1/r = 39.00 – [2.12/0.08] = C$12.50 PVGO (CPMN) = P0 – E1/r = 27.39 – [1.90/0.12] = C$11.56 where P0 is the current price per share, E1 is the forecasted earnings per share, and r is the required rate of return.The growth component of the P/E for each stock [PVGO/E1] is as follows: ABTD: 10.48/7.30 = 1.44× BKKQ: 12.50/2.12 = 5.90× CPMN: 11.56/1.90 = 6.08×
                • 注意这题的问法，the growth component of leading P/E，问的是PVGO/E1
                • 当然，你也可以先算出P/E，然后乘以PVGO%
      • 例题
        • A Canadian company in the consumer staples sector with a required rate of return of 7.35%. Recent media reports suggest that ABC might be a takeover candidate. Peters and her team estimate that if the incumbent Canadian prime minister's party retains its power, the company's current annual dividend of C$0.65 per share will grow 12% a year for the next four years and then stabilize at a 3.5% growth rate a year indefinitely. If a new government takes office in Canada, however, then the team estimates that ABC will likely not experience the elevated 12% short- run growth because of new regulatory and tax changes, and instead it will grow by 3.5% indefinitely Assume that a new government takes office in Canada. If Peters and her team use the Gordon growth model and assume that Company ABC stock is fairly valued, then which of the following would most likely be true? A The total return of ABC stock will be 10.85%. B The dividend yield of ABC stock will be 3.85%. C The stock price of ABC will grow at 7.35% annually.
          • B is correct. In the Gordon growth model, Total return = Dividend yield + Capital gains yield (i.e., constant growth rate). When a stock is fairly valued, the expected total return will equal the required return or discount rate (i.e., 7.35%). In the case of ABC, the total return is 7.35% and the capital gains yield is 3.5%. Therefore, the dividend yield is 7.35% – 3.5% = 3.85%.
            • 这题的破题点是stock is fairly valued，这里的潜台词是达到了均衡，expected total return等于required return
  • Multi-stage DDM
    • Principle
    • Two-stage
      • Two distinct phase
        • 例题
          • A Canadian company in the consumer staples sector with a required rate of return of 7.35%. Recent media reports suggest that ABC might be a takeover candidate. Peters and her team estimate that if the incumbent Canadian prime minister’s party retains its power, the company’s current annual dividend of C$0.65 per share will grow 12% a year for the next four years and then stabilize at a 3.5% growth rate a year indefinitely. If a new government takes office in Canada, however, then the team estimates that ABC will likely not experience the elevated 12% short- run growth because of new regulatory and tax changes, and instead it will grow by 3.5% indefinitely. Assuming the incumbent government retains office in Canada, Peters and her team estimate that the current value of Company ABC stock would be closest to: A C$22.18. B C$23.60. C C$25.30.
            • B is correct D1 = 0.65*1.12=0.728 D2 = 0.65*1.12^2=0.81536 D3 = 0.65*1.12^3=0.913203 D4 = 0.65*1.12^4=1.022788 P4 = 1.0228*1.035/(0.0735-0.035)=27.496052 V0 = 0.728/1.0735+0.8154/1.0735^2+0.9132/1.0735^3+(1.0228+27.4961)/1.0735^4=23.598475
              • DDM的基础计算题，必须熟练掌握
        • 例题
          • Jinsan Corp.'s current annual dividend of $1(Do) per share will grow 10% (gs) a year for the next four years (n) and then stabilize at a 3% (gL) growth rate a year indefinitely; the required rate of return is 5%, what is the current intrinsic value?
            • 解析： D1 = 1*1.1=1.1 D2 = 1*1.1^2=1.21 D3 = 1*1.1^3=1.331 V3 = 1.331*1.1/(0.05-0.03)=73.205 V0 = 1.1/1.05+1.21/1.05^2+(1.331+73.205)/1.05^3=66.532124 【拓展】深刻理解GGM的本质和前提条件，用V3代替D4和V4减少计算量。
      • H-model
        • V0 = D0 * ((1+gL)/(r-gL) + H*(gS-gL)/(r-gL))
        • 画图，GGM加个三角形
        • 例题
          • Steve Lanes is a junior analyst at ABC Securities. He has been asked to prepare a research report for Sightseeing Corporation, a tourism company and give recommendation about its stock. Sightseeing is a small-cap publicly traded company that pays dividends regularly. Following is the 2015 year-end selected financial data of the company in $ millions: Net Income: 90 Dividends: 36 Total Assets: 1,015 Common Stock (70 million shares outstanding): 600 Retained earnings: 171 CAPM derived required rate of return: 10.5% Lanes uses the Gordon growth model to calculate the intrinsic value of Sightseeing. Lanes' manager reviews the calculations and suggests that Sightseeing should use the H-model to account for the anticipated growth in revenues over the next six years. Lanes incorporates the following inputs into the H-model computations: A short-term growth rate of 18% and after six years, a 6% constant growth rate. An addition of a small-firm risk premium of 1.5% to the rate of return on the stock. Using Lanes’ estimates for growth and required return on the stock, the intrinsic value per share of Sightseeing’s stock as of 2015 based on H-model is closest to? A. $15.6. B. $12.2. C. $9.01.
            • B is correct. The H-model is: V0 = D0 (1 + gL) + D0H (gs – gL) / (r – gL) D0 = $36 million / 70 million = ?0.5143/share gS = Initial short-term dividend growth rate = 18% gL = Normal long-term dividend growth rate = 6% r = 10.5% + 1.5% = 12% H = 6 / 2 = 3. V0 = [0.5143(1.06) + 0.5143 x 3 (0.18 – 0.06)] / (0.12 – 0.06) = $12.17.
              • 这里的r不是10.5%，而是10.5%+1.5%=12%。
        • 例题
          • Using the data in Exhibit 2, the estimate of PRBI's stock according to the H-model is closest to: A.$64.76. B.$77.12. C.$60.60.
            • 答案：C 解析：C is correct. Using the H-model: D0 = $5.33 × 0.60 = $3.20 H = half of the life of high-growth period = 10/2 = 5 years V=(3.2*(1+4%))/(12.4%-4%)+(3.2*5*(15%-4%))/(12.4%-4%)=60.60 A is incorrect; it starts with D1 instead of D0. B is incorrect. It uses WACC instead of the required return on equity.
              • 熟练掌握H-model的计算
        • 例题
          • Jacques is the portfolio manager of AB pension and she recently consider adding PZ Inc. (New York Stock Exchange: PZ) to its portfolio. After carefully considering the characteristics of the company and its competitors, she believes the company's growth rate declines linearly from 12 percent in the first year to 6 percent in the eleventh. PZ's total dividends paid on 2017 was $0.22.She estimated that the required return is 9 percent. What is the intrinsic value of the stock? A. 10.19 B. 9.97 C. 8.97
            • 解析： 这题的关键点是理解6 percent in the eleventh，这里说明H-Model的第一阶段是10年，从第11年开始进入第二阶段。 套公式：(0.22*1.06+0.22*(0.12-0.06)*5)/(0.09-0.06)=9.97，选B。
              • 【PS】H-model的记忆方法，可以用画图法，下面是个长方形，普通GGM，D1/(r-g)。上面是个三角形，底乘以高除以二，D0*(rs-rl)*T/2/(r-g)。
              • 【PS2】要深刻理解H-model的g。这既是一个时间点的增长率，比如0到10年的增长率，也是一个时间段的增长率，比如第一年内的增长率。因为g说的增长率，是某一年这个整体时间段的增长率，在当年结束这个时间点确定。所以无论是从时间点的角度，说0-10年的增长率，还是第一年20%，到了第11年5%，说的都是同一件事，即第一阶段是0-10年，从11年开始是第二阶段。
    • Three stage
      • Three distinct model
      • High-growth + H-model
    • Spreadsheet modeling
  • Determine growth rate
    • Different phases
      • Growth
        • g(company) > g(economy)
      • Transition
        • g(company) > g(economy), declining
      • Mature
        • g(company) = g(economy)
      • 例题
        • Barton and Eckhart discuss the impact of a company's growth rate on its future stock price. Barton determines XRL's growth rate of earnings for the period from 4 Years Prior to the Most Recent Year and compares it with the current nominal growth rate of the US economy. She concludes that XRL is likely to be in the transition stage of growth. Barton's conclusion that XRL is in the transition phase is best described as: A. correct. B. incorrect, because the company is in the supernormal growth phase. C. incorrect, because the company is in the mature phase.
          • C is correct A. Incorrect. A company in the transition phase is characterized by earnings growth rates above the average nominal growth for the economy but with the growth rate declining. The growth rate is not above the economy's nominal growth rate, so the fact that it is declining (2.7% for Most Recent Year vs. 1 Year Prior) is not relevant. B. Incorrect. A company in the supernormal growth phase has growth higher than the economys nominal growth rate. C. Correct. Barton's statement is incorrect because the company is in the mature phase. The economy's nominal growth rate, from Exhibit 1, is Real growth rate + Inflation rate = 3.7% + 2% = 5.7%. XRL's compound growth rate over the four-year period is 5.7%, which is approximately equal to the economy’s growth rate and calculated as follows: g = (3.15/2.52)^0.25=5.7% where g is the compound growth rate in earnings, and EPS is earnings per share. A company in the mature phase typically has earnings growth at a rate comparable with the economy's growth rate.
            • 灵活的通过公司和经济的增长率之间的关系，判断公司所处的阶段
    • Calc
      • g=Retention rate * ROE
        • 例题
          • Armishaw shows his report to Anthony Stack, Fulsom-Wagner's senior portfolio manager and Armishaw's reporting official. In the H-model calculation, Stack notices that Armishaw assumes a sustainable growth rate of 5% following the period of high growth. Stack asks Armishaw if it is true that the sustainable growth model assumes the company will require 1. external debt financing; 2. external equity financing, 3. improving return on equity. Which of Stack's three assumptions regarding the sustainable growth rate model is most accurate? A.1 B.2 C.3
            • 答案：A 解析：A is correct. The sustainable growth rate model assumes that the growth will be financed with the issuance of debt and only internally generated equity will be used to maintain a target capital structure. No additional common equity will be issued. The ROE is assumed to be a constant during this period. B is incorrect. It is assumed in the sustainable growth model that all additional equity comes from internally generated funds, not new issues. C is incorrect. The ROE is constant during this period.
              • 要注意永续增长的前提，外部融债，内部融股
              • 【PS】DDM的理解非常重要。公式是P0=D1/(re-g)。其中有3个假设，D>0，D以g永续增长，Re>g。这里关键是对g的理解。g是sustainable growth rate，也就是说，这个是持续的，并且是稳定的。
              • 【PS2】从DDM的3个基本假设，可以进一步拓展，因为g=ROE*b。如果要使得g一直是一个常数，并且ROE和b没有直接关系，那么唯一的办法就是让ROE和b也是一个常数。这不是基本假设，但是是可以从基本假设中拓展出来得到的结论。
              • 【PS3】在ROE不变的情况下，我们可以进一步拓展，因为ROE=(NI/Sales) * (Sales/Asset) * (Asset/Equity)，如果ROE想要是一个常数，那么3个部分也需要是一个常数，可以得到一个拓展结论，NI/Sales是不变，Sales/Asset不变，Asset/Equity不变。因为Equity是以g稳定增长，要是的杠杆率不变，Asset也需要以g稳定增长，同理Sales和NI也需要以g稳定增长。这也可以成为拓展后的结论。当然，进一步拓展，Asset = Equity + Liability。因为Asset和Equity都以g稳定增长，所以Liability也会以g稳定增长，换而言之，对外的Debt也需要以g稳定增长。所以公司需要持续借债以保持Debt的稳定增长速度，这也可以作为一个拓展的结论。
              • 【PS4】我们可以接着拓展，因为V0=D1/(re-g)，V1=D2/(re-g)。D是以g稳定增长，所以V也会以g稳定增长，所以P也会以g稳定增长。所以可以得到一个进一步的拓展结论，公司的股价也会以g稳定增长。
              • 【PS5】经过上面的拓展，可以回到最初的起点，收益除了分红外，全部留存下来(internal equity financing)，而且要保持稳定增长，不能有外部的新的equity financing，而我们的debt需要持续增长，所以需要持续的外部融债（external debt financing），同时，所有东西，和g挂钩的，全部要维持不变，和equity挂钩的，全部以g稳定增长。没有墙头草这第三个选项。
      • PART model
        • g = Retention ratio * Net profit margin * Asset turnover * Leverage
• M3 Free Cash Flow Valuation
  • General ideas
    • Definition
      • FCFF
        • 例题
          • McCormick wants to identify the most appropriate approach to value Firm A, which consistently had positive FCFE during the past decade. Management is about to start an aggressive growth strategy primarily financed with debt. McCormick expects a highly fluctuating amounts of net borrowing for the next three years. McCormick also expects annual earnings growth rate to fluctuate between 25% and 35% during the next three years before it gradually declines to long-run sustainable rate of 2%. Which of the following is the most appropriate approach to use for valuing Firm A? A. Two-stage FCFE model B. Three-stage FCFE model C. Three-stage FCFF model
            • 正确答案：C C.Correct because earnings growth follows a three-stage model and FCFF is preferred over FCFE when capital structure is expected to change. Three-stage models are a straightforward extension of the two-stage models. A common model is a three-stage model with constant growth rates in Stages 1 and 3 and a declining growth rate in Stage 2. Since Firm A's earnings will go through a period of gradual decline between the high growth phase and stable growth phase, the overall growth regime is best characterized with three stages. Stage 1 (high growth stage): Next three years characterized 25%-35% annual growth Stage 2 (declining growth stage): Period where annual growth rate declines to stable growth level of 2% Stage 3 (stable growth stage): Time period where annual growth rate is stabilized at the long-term sustainable rate of 2%. In addition, reading also suggests that three-stage models are often considered to be good approximations for cash flow streams that, in reality, fluctuate from year to year. Consistently, McCormick's expectations suggest that Firm A's earnings are expected to fluctuate due to the management's aggressive growth strategy. Also, as discussed in the reading, "...if the company’s capital structure is relatively stable, using FCFE to value equity is more direct and simpler than using FCFF. The FCFF model is often chosen, however, in two other cases: [1] A levered company with negative FCFE and [2] A levered company with a changing capital structure." Vignette states that a highly fluctuating amounts of net borrowing is expected due to primarily debt-financed aggressive growth strategy. Therefore FCFF is more appropriate than FCFE.
              • 注意资本结构变化只能用FCFF
              • 注意gradually declines to，说明中间还有个逐步下降的阶段
      • FCFE
        • 例题
          • McCormick reviews his FCFE valuation model for Firm C. Firm C's management has just announced that they will issue new common stock during the next year. McCormick evaluates the potential effect of this change on next year's FCFE forecast. Given Firm C's announced change, next year's FCFE forecast will most likely: A. decrease B. remain unchanged C. increase
            • 正确答案：B B.Correct because because transactions between the company and its shareholders (through cash dividends, share repurchases, and share issuances) do not affect free cash flow. Transactions that involve exchanging cash flows between the firm and shareholders represent the use of FCFE whereas FCFE represents cash flows available to stockholders and is irrelevant to how firm uses its FCFE.
              • 注意公司和股东直接的交易，不影响FCFE。因为FCFE是看available，而dividend和repurchase是use，issurance是source，所以都不影响。
                • 股利
                • 回购
                • 发行
    • Stengths and limitations of FCF
      • 例题
        • Leigh responds to each of Smith's points as follows: 1 "I will use your estimates and calculate Emerald's long- term, sustainable dividend growth rate." 2 "There are two reasons why I used the FCFE model to value Holt's common stock instead of using a DDM. The first reason is that Holt's dividends have differed significantly from its capacity to pay dividends. The second reason is that Holt is a takeover target and once the company is taken over, the new owners will have discretion over the uses of free cash flow." Do the reasons provided by Leigh support his use of the FCFE model to value Holt's common stock instead of using a DDM? A Yes. B No, because Holt's dividend situation argues in favor of using the DDM. C No, because FCFE is not appropriate for investors taking a control perspective.
          • A is correct. Justifications for choosing the FCFE model over the DDM include the following: ■ The company pays dividends, but its dividends differ significantly from the company's capacity to pay dividends (the first reason given by Leigh). ■ The investor takes a control perspective (the second reason given by Leigh).
            • 要能正确辨析FCF和DDM模型的优缺点
    • FCFF vs FCFE
      • 例题
        • Wadgett's ambitious growth projections will likely require a substantial investment in manufacturing facilities. In order to finance the project, Wadgett expects to borrow substantially more than it has in the past and intends to retire the debt within the next 10 years. During a discussion of how this debt may influence the valuation, the analysts make the following statements: Statement 1 Because the capital structure seems very likely to change significantly, it would be best to use free cash flow to equity (FCFE) because the value to equity is more direct. Statement 2 I would select FCFF over FCFE. When we look forward, the required return on equity may be more sensitive to changes in financial leverage than just the changes in weighted average cost of capital (WACC). Statement 3 With either model, we should discount future cash flows by the required return on equity because we are considering buying the stock. In discussing Wadgett's growth projections and the influence they may have on the FCFE and FCFF valuation process, which of the analysts' statements is most accurate? A. Statement 1 B. Statement 3 C. Statement 2
          • 答案：C 解析：C is correct. FCFF is preferred over FCFE when a company is leveraged and expecting a change in capital structure. FCFF growth will reflect fundamentals more clearly because FCFE growth will reflect fluctuating amounts of net borrowing. Second, in a forward-looking context, the required return on equity might be expected to be more sensitive to changes in financial leverage than changes in the WACC. A is incorrect. Statement 1 suggests that FCFE should be used, but this choice is inappropriate given the already levered balance sheet and coming increase in debt capital. B is incorrect. Statement 3 suggests that the required return to equity should apply to both FCFE and FCFF, yet WACC is the proper discount rate to use in the FCFF method.
            • 要能熟练辨析FCF的区别
  • FCF Calc
    • FCFF
      • FCFF = NI + NCC + Int(1-t) - WCInv - FCInv
        • CFO = NI + NCC - WCInv
        • NI = (EBIT-Int)(1-t)
        • NI = (EBITDA-NCC)(1-t)
      • 例题
        • Based on Exhibits 1 and 2, Sienna’s FCFF in 2019 is: A €680million. B €1,200million. C €3,080million.
          • A is correct. Sienna’ s FCFF in 2019 is calculated as FCFF = EBIT(1 – Tax rate) + Dep – FCInv – WCInv. FCInv = Purchases of PP&E = 1,000 (outflow). WCInv = Increase in accounts receivable (outflow) + Increase in inventory (outflow) + Increase in accounts payable (inflow). WCInv = – 2,000 (outflow) + – 200 (outflow) + 1,000 (inflow) = – 1,200 (outflow). FCFF = 3,200(1 – 0.35) + 800 – 1,000 – 1,200. FCFF = € 680 million.
            • 送分题
      • 例题
        • She assumes that for the next 12 months, Thunder's revenues will increase by the longterm annual growth rate of 3%. She also makes the following assumptions to calculate the free cash flow to the firm for the next 12 months: ■ Gross profit margin is 45%. ■ Depreciation is 2% of revenues. ■ Selling, general, and administrative expenses are 24% of revenues. ■ Capital expenditures equal 125% of depreciation to support the current level of revenues. ■ Additional capital expenditures of 15% of incremental revenues are needed to fund future growth. ■ Working capital investment equals 8% of incremental revenues. ■ Marginal tax rate on EBIT is 35%. The free cash flow to the firm is closest to: A $23,031,000. B $25,441,000. C $36,091,000.
          • 解析： 确认基础公式：FCFF = NI + NCC + Int(1-T) - WC - FC。 NI + Int(1-T) = EBIT - T = 200*1.03*(0.45-0.24-0.02)*0.65=25.44 NCC = 200*1.03*0.02=4.12M WC = 0.08*0.03*200=0.48 FC = 1.25*0.02*1.03*200+0.15*0.03*200=6.05 FCFF = 25.44+4.12-0.48-6.05=23.03 M，选A。
            • 【PS1】在计算NI的时候要扣减NCC (Dep)，后面算FCFF的时候要加回，但是2个不能对冲，因为前面扣减的NCC还要扣税，加回的不扣税。
            • 【PS2】考试时候所有FCF的公式，都由基本公式出发：FCFF = NI + NCC + Int * (1-t) - WCInv - FCInv；FCFE = NI + NCC + NB - WCInv - FCInv
    • FCFE
      • FCFE = NI + NCC + NB - WCInv - FCInv
      • 例题
        • Holt's FCFE (in millions) for 2008 is closest to: A $175. B $250. C $364.
          • B is correct. FCFE = NI + NCC – FCInv – WCInv + Net borrowing. In this case: NI = $485 million. NCC = Depreciation expense = $270 million. FCInv = Net purchase of fixed assets = Increase in gross fixed assets =4.275-3,752 = $523 million. WCInv = Increase in accounts receivable + Increase in inventory - Increase in accounts payable -Increase in accrued liabilities =(770-711)+(846-780)-(476-443)-(149-114)= $57 million. Net borrowing = Increase in notes payable + Increase in long-term debt =(465-450)+(1,575-1,515)= $75 million. FCFE=485+270-523-57+75 = $250 million.
            • 记住FCFE的公式不难，找准数，比如NB, WCInv, FCInv才是关键。不能总指望天上掉馅饼全是简单的题，也需要为稍微复杂点但是正常的题目多做准备。
      • 例题
        • Chan Mei Yee is valuing McLaughlin Corporation common shares using a free cash flow approach. Yee gathered information about McLaughlin from several sources. She begins her analysis by determining free cash flow to the firm (FCFF) and free cash flow to equity (FCFE) for the 2012 fiscal year, using the financial statements in Exhibits 1 and 2. McLaughlin’s fiscal year ends 31 December. McLaughlin's FCFF ($ millions) for 2012 is closest to: A.$418. B.$485. C.$460.
          • 答案：B 解析：B is correct. WCInv = ((1290-32) - 2783) - ((1199-21)-2678) = -25 FCFF = NI + NCC + Int(1 – Tax rate) – FCInv – WCInv Net income (given) = $626; Non-cash charges (depreciation, given) = $243; Interest expense (given) = $186; Tax rate = 294/920 = 32%; Fixed capital investment (given) = $535 FCFF = 626 + 243 + 186(1 – 0.32) – 535 – (–25) = 485.48 = $485 million A is incorrect. It uses t not (1 – t). FCFF = 626 + 243 + 186(0.32) – 535 – (–25) = 418.2 = $418 million C is incorrect. It ignores working capital investment FCFF = 626 + 243 + 186(1 – 0.32) – 535 = 460.48 = $460 million
            • FCFF的计算公式必须熟练掌握
      • 例题
        • In regard to calculating Wadgett's FCFF, the comment that is most appropriate is the one dealing with: A. working capital adjustments. B. treatment of all non-cash charges. C. treatment of net borrowing.
          • 答案：A 解析：A is correct. Cash flow from operations (CFO) already reflects changes in working capital items, therefore Paschel's first comment is correct. EBITDA has the non-cash charges of depreciation and amortization added back, so Covey's statement is incorrect, not all non-cash charges will need to be added back. Net borrowing is added back for FCFE not FCFF, so Paschel's second statement is incorrect. B is incorrect. Depreciation has already been added back to EBITDA, though there may be other items that still need to be added back. C is incorrect. Adjusting for net borrowing is not necessary for FCFF (just FCFE).
            • 这题关键是对FCFF公式的理解。 FCFF和FCFE有近10个公式，建议只记忆2个基础公式，考试的时候，其他公式都可以从这2个现场推出来： FCFF = NI + NCC + Int(1-t) - WCInv - FCInv FCFF = NI + NCC + NB - WCInv - FCInv A说CFO出发，我们先得到NI + NCC - WCInv = CFO，所以FCFF = CFO + Int(1-t) - FCInv。所以不需要调整WCInv，A是对的。 B说从EBITDA出发，我们先得到(EBITDA - Int) * (1-t) = NI，所以FCFF = (EBITDA - NCC - Int) * (1-t) + NCC + Int(1-t) - WCInv - FCInv = EBITDA * (1-t) + NCC * t - WCInv - FCInv，所以不是加回所有的NCC。B是错的。 C说NB，那个只影响FCFE，B是错的。
              • 【PS】公式大家都知道是-WCInv，但是考试时候是用purchase还是sales，如果搞错。一个办法是从定义WC Investment出发，因为Investment是花钱，所以负的investment就是得到钱，所以-WCInv应该是负的sales或者purchase。另外一个办法是理解背后的含义。WC = CA - CL (注：B/S，需要扣减cash等)，所以WC是一种asset（B/S），而WCInv = Delta(WC) = WC1 - WC0。站在B/S的角度，你算出来的是WCInv。站在CF的角度，我们要看的是流入，比如CFO，CFI, CFF，都是从流入的角度看问题，所以从CF的方向去看，你算出来的是(-WCInv)。FCFF, FCFE都是从CF角度看问题，所以统计WC的变化的时候，就是(-WCInv)。所以你问今年的运营资本有多少，你看B/S，得到的结论是100万，你看C/F，得到的结论是-100万。但是说的是一个东西。FCInv和WCInv同理。考试时候比较简单，如果是标准的财报，把CF里的Changes in working capital下面的所有数字用数学求和，得到的本身就已经是-WCInv。
              • 【PS2】FCInv的计算方法是FCInv = Capital Expenditure - Proceeds，一般在CFI里找。和WCInv同理，我们考虑FC的办法是把CF/S的-FCInv加上去，而标准的财报里的CFI已经CapExp - Proceeds，直接把CFI的数字拿过来，本身就是-FCInv。
              • 【PS3】【可不看】理解公式后，考试可能不一定给数字让你计算，而可能为了提升难度让你自己算出要的数。最常见的考法就是不给你CF/S，给你B/S。如果真的遇到，建议随便三选一，插个旗子，下一题，回来再慢慢做。只给B/S，不给C/F，来求解FCF的方法见PS4 ~ PS5。
              • 【PS4】WCInv比较简单，唯一要注意的是，B/S里算出来的是WCInv，而CF/S里算出来的是-WCInv，要注意方向。具体原因上面已经解释。
              • 【PS4 Pro】FCInv分2种情况，1个是没有proceed，这时候FCInv = 【CF/S】Capital Expenditure = 【B/S】Delta(Net PP&E) + 【I/S】Depreciation = 【B/S】Net PP&E + 【B/S】Accumulate Depreciation。至于具体用Net PP&E还剩Gross PP&E，看题目给什么。
              • 【PS5】如果题目说了有proceeds，还不给你CF/S，快跑！下一题。如果一定要做的话，要分2种情况： 1. 如果题目给了Gross PP&E，【B/S】: Gross PP&E(t-1) + CapEx - Proceeds(BV0) = Gross PP&E(t)，我们得到CapEx。然后在【I/S】：Proceeds = Proceeds(BVt) + Gain。最后通过CapEx - Proceeds得到FCInv。 2. 如果题目给了Net PP&E，【B/S】: Net PP&E(t-1) + CapEx - Proceeds(BVt) - Dep = Net PP&E(t)，【I/S】：Proceeds = Proceeds(BVt) + Gain -> Net PP&E(t-1) + CapEx - Proceeds + Gain - Dep = Net PP&E(t) -> Net PP&E(t-1) + FCInv + Gain - Dep = Net PP&E(t) -> 得到FCInv。
              • 【Xbox】上面的知识点并未朝纲，只不过有点难度，考到概率可能不太高。要不多花点时间，认真学懂。要不直接战略性放弃，考到就蒙一个。千万不要学的一知半解死记公式。
              • 【Xbox 360】拓展说下NB的计算，最基本的就是NB = (LT Debt(t) - LT Debt(t-1)) + (ST Debt(t) - ST Debt(t-1))。注意这里是debt，不是liability。如果题目不给这些参数，给target debt ratio，也可以通过NB = (WCInv + FCInv - Dep) * Debt Ratio。
              • 【Xbox One】如果题目有说优先股，那么公式需要进一步调整成common stock作为equity。调整后的公式为 FCFF = ((NI(common) + Div(pre)) + NCC - WCInv) + Int * (1-T) - FCinv FCFE = FCFF - Int * (1-T) - Div(pre) + NB
              • 【Xbox Series】要注意，FCF不能NI和EBITDA代替（能的话请让CFA删除这部分内容，谢谢）。并且杠杆影响FCFE但是不影响FCFF（因为杠杆是内部D和E的博弈）。
    • NCC
      • Depreciation
      • Amortization and impairment of intangibles
      • Restructuring g/l
      • G/l on non-operating activities
      • Amortization of long-term bond discounts/premiums
    • WCInv
      • WCInv = CA - CL
      • CA exclude cash/cash equivalents
        • 剔除原因是非经营性资产
      • CL exclude notes payable and current portion of LT debt
        • 剔除的原因是因为来自融资服务
    • FCInv
      • No disposal
        • FCInv = CAPEX = GV(end) - GV(beg)
        • FCInv = BV(end) - BV(beg) + depreciation expense
      • Asset disposed
        • FCInv = CAPEX - proceeds from sales of LT assets
    • NB
      • NB = new debt issuances - debt repurchases
      • Affect FCFE only
  • FCF forecast
    • Calc historical FCF
    • Forecast components of FCF
    • Sales-based forecasting
      • 假设
        • (FCInv-Dep)/Delta(Sales)是常数
        • WCInv/Delta(Sales)是常数
        • DR=D/(D+E)不变
        • Net Borrowing = DR * (FCInv - Dep + WCInv)
        • NI/Delta(Sales)不变
      • FCFE = NI - (1-DR)(FCInv+WCInv-Dep)
        • 例题
          • Base case valuation 2013 FCFF will be $600 million. Beyond 2013, FCFF will grow in perpetuity at 4% annually. The market value and book value of McLaughlin’s long-term debt are approximately equal. Alternative valuation 2013 earnings per share (EPS) will be $1.80. EPS will grow forever at 6% annually. For 2013 and beyond: Net capital expenditures (fixed capital expenditures minus depreciation) will be 30% of EPS. Investments in working capital will be 10% of EPS. Of future investments, 60% will be financed with equity and 40% will be financed with debt. Using Yee's alternative valuation assumptions and the FCFE valuation approach, the year-end 2012 value per share of McLaughlin's common stock is closest to: A.$24.17. B.$18.00. C.$22.80.
            • 答案：C 解析：C is correct. First, it is necessary to estimate FCFE2013. FCFE = Net income – (1 – DR) × (FCInv – Depreciation) – (1 – DR) × (WCInv) Where DR = debt ratio, which is 40% FCInv = investment in fixed capital, which is 30% of EPS WCInv = investment in working capital, which is 10% of EPS On a per-share basis: FCFE1 (2013) = 1.80 – (1 – 0.40) × (0.30 ×1.80) – (1 – 0.40) × (0.10 ×1.80) = 1.80 – 0.324 – 0.108 = 1.368. FCFE will grow at the same rate as net income, 6% annually. The value per share is $22.80. A is incorrect. It uses FCFE1 × (1 + g) = 1.368 × (1.06)/(0.12 – 0.06) = 24.17. B is incorrect. It uses FCFF: (1.80 – 0.54 – 0.18 )/(0.12 – 0.06) = 18.00
              • FCFE的核心是NI扣除WC和FC投资的equity占用部分。 这里直接用EPS来代替NI 1.8-0.6*(1.8*0.4)=1.368 FCFE的增长率和NI的增长率保持一致，这个要理解 1.368/0.06=22.8 这里需要用到sales-based forecast的一个重要的公式：FCFE = NI - (WCInv + FCInv - Dep) * (1 - Debt Ratio) 所以FCFE1 = 1.8-(1.8*0.4)*0.6=1.368 FCFE应该用EPS Growth Rate折算。1.368/(0.12-0.06)=22.8，选C。
                • 【PS】这里的FCFE不是基本公式，而是基于sales-based forecasting method，公式也不是很复杂，建议记一下以防考到。
                • 【PS2】从FCFF估值，公司价值=FCFF/(WACC-g)，从FCFE估值，公司价值=FCFE/(re-g)
  • FCF valuation
    • Effects of financing decisions
    • Single-stage FCF valuation
      • Firm value0 = FCFF1 / (WACC - gFCFF)
      • Equity value0 = FCFE1 / (r - gFCFE)
    • Total firm value = firm value + value of the non-operating assets
    • Equity value = firm value - MV(debt)
• M4 Market-based Valuation: Price and Enterprise Value Multiples
  • General ideas
    • Types of multiples
      • Price multiples
      • Enterprise value multiples
    • Method of comparables
    • Method based on forecasted fundamentals
      • Method of Comparables
        • 可比法
      • Method based on forecasted fundamentals
        • 预期基本面法
  • Price multiples
    • P/E
      • Rationales and drawbacks
        • Drawbacks
          • Negative or very low earnings
          • Valatile or transitory earnings
      • Trailing and leading P/E
        • 例题
          • Risso gathers information on Centralino. Exhibit1 presents earnings and dividend data, and Exhibit 2 presents balance sheet data. Net sales were €3.182billion in 2019. Risso estimates a required return of 15% for Centralino and forecasts growth in dividends of 6% into perpetuity. Based on Exhibit 1 and Risso's estimates of return and dividend growth, Centralin's justified forward P/E based on the Gordon growth dividend discount model is closest to: A 5.4. B 5.7. C 8.3.
            • A is correct. The justifed forward P/E is calculated as follows: P0 / E1 = D1/E1 / (r-g) = (2.91 /6.00) / (0.15-0.06) = 5.4
              • 这题的关键是，如果用D1和E1，你不需要再用D0*(1+g)得到D1
        • 例题
          • Pinho directs Silveira to use a valuation metric that would allow for a meaningful ranking of relative value of the three companies' shares. Exhibit 1 provides selected financial information for the three companies Silveira reviews underlying trailing EPS for Adesivo. Adesivo has basic trailing EPS of BRL0.84. Silveira finds the following note in Adesivo's financial statements: "On a per share basis, Adesivo incurred in the last four quarters i. from a lawsuit, a nonrecurring gain of BRL0.04; and ii. from factory integration, a nonrecurring cost of BRL0.03 and a recurring cost of BRL0.01 in increased depreciation. Based on Exhibit 1 and the note to Adesivo's financial statements, the trailing P/E for Adesivo using underlying EPS is closest to: A. 17.7. B. 18.2. C. 18.4
            • 答案：C 解析：C is correct. The EPS figure that Silveira should use is diluted trailing EPS of BRL0.81, adjusted as follows: 1. Subtract the BRL0.04 nonrecurring legal gain. 2. Add BRL0.03 for the nonrecurring factory integration charge. No adjustment needs to be made for the BRL0.01 charge related to depreciation because it is a recurring charge. Therefore, underlying trailing EPS = BRL0.81 – BRL0.04 + BRL0.03 = BRL0.80 and trailing P/E using underlying trailing EPS = BRL14.72/BRL0.80 = 18.4
              • 注意题目里暗戳戳的还有句and notes，不要直接用表格里的D EPS。也不能用后面给的Basic EPS当基础。
      • Adjustments for P/E
        • Nonrecurring items
          • 例题
            • Gast recommends Hughes calculate the trailing and forward price/earnings multiples based on core earnings. Hughes uses the data in Exhibit 2 for his calculations for WPR. Following Gast's recommended approach, Western Plains Rail’s forward P/E multiple is closest to: A.14.2×. B.15.5×. C.14.5×.
              • A is correct Gast's recommended approach is to calculate the forward P/E based on core earnings: Next year's EPS growth: 8% x 1.15 = 9.20% Next year's EPS: $3 60 x (1 + 0.092)=S3.93 Add: expected restructuring charge$3.93x2%=$0.08 Equals Core EPS: $4.01 P/E multipie =$57.00/$4.01 =14.214
                • 注意Non-recurring charge要被加回，才是完整的normalized EPS。 先得到预计的EPS = 3.6*(1+0.08*1.15)=3.93，然后调回restructuring cost：3.93*1.02=4.01。最后计算P/E: 57/4.01=14.21。选A。
                  • 【PS】要注意1.15X是基于8%的增长，而不是1.08。
                  • 【PS2】重构费用在算earning的时候是被扣减的，但是这个不是可持续的，随意要加回再估值。
        • Business-cycle influences
          • Method of historical average EPS
          • Method of average ROE
            • Preferred
            • 例题
              • Risso also wants to calculate normalized EPS using the average return on equity method. She determines that the 2016–19 time period in Exhibit 1 represents a full business cycle for Centralino. Based on Exhibits 1 and 2, the normalized earnings per share for Centralino as calculated by Risso should be closest to: A €2.96. B €3.21. C €5.07.
                • A is correct. Method of average ROE: normalized EPS = average ROE from the most recent full business cycle X current book value per share. Average ROE = (0.1301 + 0.1371 + 0.1158 + 0.1421) / 4 = 0.131Book value of (common) equity = value of shareholders’ equity - value attributable to the preferred stock = 1,027 million - 80 million = 947 million. Current book value per share (BVPS) = 947 million / 41.94 million = 22.58. Normalized EPS = Average ROE x BVPS = 0.131 x €22.58 = 2.96
                  • 注意，千万不要傻乎乎的直接算EPS的熟悉平均。能拿来平均的只有比率，比如ROE
        • Dealing with low, zero or negative earnings
          • Normalized EPS
          • Earning yield, E/P
      • Valuation based on forecasted fundamentals
        • Justified P/E
          • P0/E1 = (1-b)/(r-g)
          • P0/E0 = (1+g)(1-b)/(r-g)
        • Cross-sectional regressions
      • Valuation based on comparables
        • Peer-company multiples
          • PEG ratio
            • 例题
              • Exhibit 2: Earnings Growth Rate Estimates over Five Years Company | Earnings Growth Rate Estimate (%) Adesivo: 16.67 Enviado: 21.91 Gesticular: 32.33 Based on Exhibits 1 and 2, which company's shares are the most attractively priced based on the five-year forward P/E-to-growth (PEG) ratio? A. Adesivo B. Enviado C. Gesticular
                • 答案：A 解析：A is correct. The forward PEG ratios for the three companies are calculated as follows: Forward P/E = Stock’s current price/Forecasted EPS. Forward PEG ratio = Forward P/E ÷ Expected earnings growth rate (in percentage terms). Adesivo forward P/E = BRL14.72/BRL0.91 = 16.18. Adesivo forward PEG ratio = 16.18/16.67 = 0.97. Enviado forward P/E = BRL72.20/BRL3.10 = 23.29. Enviado forward PEG ratio = 23.29/21.91 = 1.06. Gesticular forward P/E = BRL132.16/BRL2.85 = 46.37. Gesticular forward PEG ratio = 46.37/32.33 = 1.43. Adesivo has the lowest forward PEG ratio, 0.97, indicating that it is the most undervalued of the three equities based on the forward PEG ratio.
                  • 注意PEG是越小越好
            • 拓展题
              • Mark Cannan is updating research reports on two well-established consumer companies before first quarter 2021 earnings reports are released. His supervisor, Sharolyn Ritter, has asked Cannan to use market-based valuations when updating the reports. Delite Beverage is a manufacturer and distributor of soft drinks and recently acquired a major water bottling company in order to offer a broader product line. The acquisition will have a significant impact on Delite's future results. You Fix It is a US retail distributor of products for home improvement, primarily for those consumers who choose to do the work themselves. The home improvement industry is cyclical; the industry was adversely affected by the recent downturn in the economy, the level of foreclosures, and slow home sales. Although sales and earnings at You Fix It weakened, same store sales are beginning to improve as consumers undertake more home improvement projects. Poor performing stores were closed, resulting in significant restructuring charges in 2020. Before approving Cannan’s work, Ritter wants to discuss the calculations and choices of ratios used in the valuation of Delite and You Fix It. The data used by Cannan in his analysis are summarized in Exhibit 1. Exhibit 1: Select Financial Data for Delite 2010-Earnings per share (EPS): $3.44 2011 estimated-EPS: $3.50 Book value per share end of year: $62.05 Current share price: $65.50 Ritter provides Cannan with financial data on three close competitors as well as the overall beverage sector, which includes other competitors, in Exhibit 2. She asks Cannan to determine, based on the P/E-to-growth (PEG) ratio, whether Delite shares are overvalued, fairly valued, or undervalued. Exhibit-2.Beverage Sector Data: Company | Forward P/E | Earnings Growth Delite | - | 12.41% Fresh lced Tea Company | 16.59 | 9.52% Nonutter Soda | 15.64 | 11.94% Tasty Root -Beer | 44.10 | 20% Beverage sector average | 16.40 | 10.80% Based upon the information in Exhibits 1 and 2, Cannan would most likely conclude that Delite’s shares are: A. overvalued. B. undervalued. C. fairly valued.
                • 解析： 因为D收购Y会影响股价（significant impact on Delite’s future results），所以应该用leading earning（3.5）而不是trailing。P用market value（65.5）。PEG = (65.5/3.5)/12.41=1.508。行业PEG=16.4/10.8=1.518519。两者近似，所以选C。
                  • 【PS1】如果题目没特别说adjusted，默认用题目给出的price，而非自己计算的intrinsic value。
                  • 【PS2】price优先使用market price，没有market price才考虑book value。
                  • 【PS3】如果earning变动比较大，过去不等于未来，优先用未来earning，即forward/leading earning。
                  • 【PS4】PEG的公式为(P/E) / G，其中G要拿走百分号。
                  • 【PS4 Pro】无论PE还是PEG，都是越低越好。
                  • 【PS5】如果题目给出多个公司和行业平均，优先用行业平均，没有的话再用多个公司。如果是多个公司，优先用调和平均值，其次是几何和算数平均值。
                  • 【Xbox Series X】一般差异在0.02或者以内，都可以当成fairly valued处理。
        • Industry and sector multiples
        • Overall market multiples
        • Own historical P/E
      • Obtain terminal value
    • P/B
      • Rationales and drawbacks
        • Rationale
          • companies composed chiefly of liquid assets
          • companies that are not expected to cotinue as going concern
        • Drawbacks
          • not reflect intangible assets
          • cannot compare companies with difference in asset size
          • different accounting convention
          • inflation and technological change may cause big differences between BV and MV
        • 例题
          • Haugg wants to carry out a relative valuation of AT Banca, a publicly traded stock. For her initial valuation she determines AT Banca's P/B multiple using the data in Exhibit 1. Her approach is to consider AT Banca to be fairly valued if its P/B is within 10% of the benchmark peer company P/B which is currently 0.75. A drawback of the multiple that Haugg uses for her initial valuation of AT Banca is that: A. it is less stable than the P/E ratio B. it is not suitable when comparing multiples of financial companies C. share repurchases may distort comparisons with historical multiples
            • 正确答案：C A.Incorrect because P/B ratio is more stable than P/E ratio. Because book value per share is more stable than EPS, P/B may be more meaningful than P/E when EPS is abnormally high or low or is highly variable. B.Incorrect because P/B ratio is suitable for comparing multiples of financial companies. P/Bs are considered to be more comparable for companies with significant amounts of financial assets and also book value per share has been viewed as appropriate for valuing companies composed chiefly of liquid assets, such as finance, investment, insurance, and banking institutions. C.Correct because one of the possible drawbacks of P/Bs in practice is that share repurchases or issuances may distort historical comparisons.
              • 一般book value比earning更稳定，所以A说反了。
              • 金融公司更适合P/B，所以B也说反了。
                • 背后的原理是，金融公司有大量流动性资产，所以BV接近MV，适合用P/B
              • C的逻辑链是，回购影响Equity，进而影响common equity，最后影响book value per share。
      • Adjustments to P/B
      • Justified P/B
        • Justified P/B = (ROE - g) / (r-g)
          • 例题
            • At 31 December 2013, Kim provides the following forecasted fundamentals for DongSun: projected earnings per share (EPS) for 2013 are KRW4,000; expected long-term return on equity (ROE) is 15%; DongSun will retain 60% of its earnings over the long term; and after 2014, earnings and dividends will grow at 9% per year. Using the information in Exhibits 1 and 2, Kim’s forecasts, and the single-stage (constant growth) residual income approach, the justified price-to-book ratio (P/B) at 31 December 2013 for DongSun common stock is closest to: A.1.66. B.2.00. C.2.48.
              • 答案：B 解析：B is correct. The justified P/B using a single-stage (constant growth) residual income approach is given by P0/B0 = (ROE – g)/(r – g) = (0.15 – 0.09)/(0.12 – 0.09) = 2.00
                • 送分题
      • 例题
        • ... Centralino’s common share price is €50 and its preferred shares trade for €5.25 per share. Based on Exhibit 2, the price-to-book multiple for Centralino is closest to: A 2.0. B 2.2. C 2.5.
          • B is correct. Price to book is calculated as the current market price per share divided by book value per share. Book value per share is common shareholders' equity divided by the number of common shares outstanding. Common share holders' equity is calculated as total shareholders' equity minus the value of preferred stock. Thus, Common shareholders' equity = € 1,027 – € 80 = € 947 million. Book value per share = € 947 million/41.94 million = € 22.58. Price-to-book ratio (P/B) for Centralino = € 50/€ 22.58 = 2.2.
            • 这里的关键点在于，账上的equity是包括优先股，应该从账上减去优先股，而不是在price加上优先股再和账上equity做比较
            • 【PS1】preferred stock因为是定期付股息，性质有点类似debt，所以虽然是stock，但是算BV(equity)的时候需要把拿掉。
    • P/S
      • Rationales and drawbacks
        • Rationale
          • sales always positive
          • sales more stable
          • useful for mature, cyclical and zero-income stock
        • Drawbacks
          • logical mismatch
            • price reflects effect of debt financing, sales is prefinancing
          • not reflect differences in cost structure
          • Different revenue recognition
      • Justified P/S = E0/S0 * (1-b)(1+g)/(r-g)
      • 例题
        • ... Centralino’s common share price is €50 and its preferred shares trade for €5.25 per share. Risso gathers information on Centralino. Exhibit1 presents earnings and dividend data, and Exhibit 2 presents balance sheet data. Net sales were €3.182billion in 2019. Risso estimates a required return of 15% for Centralino and forecasts growth in dividends of 6% into perpetuity. Based on Exhibit 2, the multiple of enterprise value to sales for Centralino as of 31 December 2019 is closest to: A 0.67. B 0.74. C 0.77.
          • C is correct. Enterprise value (EV) is calculated as follows: EV = Market value of common equity + Market value of preferred stock + Market value of debt – Cash, cash equivalents, and short-term investments = (€ 50 × 41.94 million) + (€ 5.25 × 16.00 million) + € 367 million – € 102 million = € 2,446 million (or € 2.446 billion). So, EV/sales = € 2.446 billion/€ 3.182 billion = 0.77.
            • 这里的关键点在于，enterprice value需要扣减掉流动资产和流动负责。
            • 有market value就用MV，没有的话就用book value
      • 例题
        • Bourne considers a price-to-sales ratio (P/S) approach to analyze SA Telecom. He plans to calculate the firm's justified P/S using the information in Exhibit 1. Based on the data in Exhibit 1, Bourne's estimate of the justified price-to-sales ratio for SA Telecom is closest to: A.0.50. B.0.52. C.0.72.
          • B is correct. P0/S0 = (E0/S0) * (1-b) * (1+g) / (r-g) E0/S0 = the business’s long-term profit margin = 8.0% b = retention ratio = 0.30 (1 – b) = the projected payout ratio = 0.70 g = the long-run earnings growth rate = 4.8% r = required rate of return = 16% 0.08*0.7*1.048/(0.16-0.048)=0.524
            • Justified P/S = V/S = D1/(r-g)/S = E1*(1-b)/(r-g)/S = E0*(1+g)*(1-b)/(r-g)/S = 0.08*1.048*0.7/(0.16-0.048)=0.524，选B。
              • 【PS】注意是从dividend的角度估值，随意要通过earning转换为D。
              • 【PS2】分母的r-g的r是equity的required rate of return而不是WACC。
    • P/CF
      • Rationales and drawbacks
        • Rationales
          • difficult to manipulate CF
          • CF is more stable
        • 例题
          • Alexandra Haugg is an analyst covering the financial sector. She has been asked to carry out a peer comparison amongst leading international banks. Haugg notes that these banks report under different accounting standards and considers which multiple would be most appropriate for her peer comparison. Which of the following multiples would be most appropriate for Haugg's peer comparison of international banks? A. P/E B. EV/EBITDA C. price to cash flow from operations (P/CFO)
            • 正确答案：C A.Incorrect because P/E will generally be more affected by different accounting standards than P/CFO (and is also more prone to manipulation). Using price to cash flow rather than P/E addresses the issue of differences in accounting conservatism between companies (differences in the quality of earnings). Additionally, there are many ways in which earnings can be manipulated (discretionary accounting decisions about expenses, aggressive accounting decisions, inflating revenues, etc.). Thus cross-border comparison is more appropriate with P/CFO than with P/E. B.Incorrect because EV/EBITDA is generally more affected by different accounting standards than P/CFO. Multiples based on such concepts as EBITDA, which start from accounting earnings, will generally be the most affected (by accounting standards or accounting decisions). C.Correct because Haugg's valuation comparison is done from a cross-border perspective and P/CFO is least impacted by various accounting standards. From the perspective of international differences of accounting standards: P/CFO and P/FCFE will generally be least affected by accounting differences. P/B, P/E, and multiples based on such concepts as EBITDA, which start from accounting earnings, will generally be the most affected.
              • 这题的破题点是比较对象是跨国公司，所以会计准则不同，会计处理方法不同，都会影响比较的结果。 在财报中，越是没经过修饰的，收到不同会计准则、会计处理的影响就越小。所以从CFO到EBITDA到NI，CFO经过加工的最少，受到的影响也最小。
      • Justified P/CF
        • V0/FCFE0 = (1+g)/(r-g)
    • Dividend yield
      • Rationales and drawbacks
        • Drawbacks
          • dividend displacement of earnings
      • Trailing vs leading
      • Justified dividend yield
        • D0/P0 = (r-g)/(1+g)
  • Enterprise value multiples
    • EV/EBITDA
      • Rationales and drawbacks
      • Valuation
        • EV = MV(common stock) + MV(debt) + MV(preferred stock) - Cash and Cash investments
          • 1级：Debt只考虑短期和长期 2级：Debt只考虑长期借款
        • 例题
          • Smirnoff suggests that Rivera should adjust BTP's multiples to reflect a 25% discount for additional risks because of its small size and thin trading. Rivera agrees with Smirnoff and collects the data needed, which are shown in Exhibit 2. Using the data in Exhibit 2 and the adjustment suggested by Smirnoff, BTP's EV/EBITDA multiple is closest to: A.3.36. B.2.31. C.2.02.
            • C is correct. EV = Market value of equity + Debt – Cash = 250 + 150 – 50 = 350 EBITDA= Net Income + Interest + Taxes + Depreciation + Amortization = 20 + 5 + 10 + 80 + 15 = 130 EV/EBITDA = 2.69 Adjustment per Smirnoff's suggestion: 2.69 × (1 – 0.25) = 2.02 A is incorrect. It incorrectly applies the 25% discount per Smirnoff's suggestion. Adjustment per Smirnoff's suggestion: 2.69 × (1 + 0.25) = 3.36 B is incorrect. It ignores cash.
              • 送分题
        • 例题
          • Silveira also analyzes the three companies using the enterprising value EV-to-EBITDA multiple. Silveira notes that the EBITDA for Gesticular for the most recent year is BRL560 million and gathers other selected information on Gesticular, which is presented in Exhibit 3. Based on Exhibit 3, Gesticular's EV/EBITDA multiple is closest to: A. 11.4. B. 13.7. C. 14.6.
            • 答案：B 解析：B is correct. The EV for Gesticular is calculated as follows: EV = Market value of debt + Market value of common equity + Market value of preferred equity – Cash and short-term investments. EV = BRL1,733 million + BRL6,766 million + BRL275 million – BRL581 million – BRL495 million = BRL7,698 million. EV/EBITDA = BRL7,698 million/BRL560 million = 13.7.
              • 送分题
  • Others
    • Momentum indicators
      • Unexpected earnings
        • UE =EPS - E(EPS)
        • 例题
          • Thomas points out that positive earnings surprises may be associated with persistent positive abnormal returns and describes popular momentum indicators used in valuation. While demonstrating the calculation of standardized unexpected earnings (SUE), she states “In SUE, the magnitude of unexpected earnings is scaled by a variability measure.” In response to a question on what measure can be used for the calculation, she mentions the following possible measures: Measure 1: The standard deviation of analysts’ earnings forecasts. Measure 2: The standard deviation in past industry average earnings surprise. Measure 3: The standard deviation in past unexpected earnings over some period. Which of the following measures mentioned by Thomas is most likely to be used in calculating standardized unexpected earnings? A. Measure 1 B. Measure 2 C. Measure 3
            • C is correct A is incorrect because Measure 1 (The standard deviation of analysts’ earnings forecasts) is used for scaled earnings surprise, not for standardized unexpected earnings. When used directly as a valuation indicator, earnings surprise is generally scaled by a measure reflecting the variability or range in analysts’ EPS estimates. The principle is that the less disagreement among analysts’ forecasts, the more meaningful the EPS forecast error of a given size in relation to the mean. A way to accomplish such scaling is to divide unexpected earnings by the standard deviation of analysts’ earnings forecasts, which we refer to as the scaled earnings surprise. B is incorrect because Measure 3 (The standard deviation in past unexpected earnings over some period), not Measure 2 (The standard deviation in past industry average earnings surprise), is used for standardized unexpected earnings. In SUE, the magnitude of unexpected earnings is scaled by a measure of the size of historical forecast errors or surprises. C is correct because Measure 3 (The standard deviation in past unexpected earnings over some period) is used for standardized unexpected earnings. The numerator is the unexpected earnings at time t and the denominator is the standard deviation of past unexpected earnings over some period prior to time t. In SUE, the magnitude of unexpected earnings is scaled by a measure of the size of historical forecast errors or surprises. The principle is that the smaller (larger) the historical size of forecast errors, the more (less) meaningful a given size of EPS forecast error.
              • 切记unexpected earning是公司自己的事，不要拿行业指标做对比
      • Standardlized unexpected earnings
        • SUE = (EPS - E(EPS)) / SD(EPS - E(EPS))
    • Central tendency measure
      • Arithmetic mean
      • Harmonic mean
      • Weighted harmonic mean
      • Mediam
• M5 Residual Income Valuation
  • Definition of residual income
    • Concepts of residual income
      • 例题
        • Targaryen's senior equity analyst, Steve Toussaint, and a junior analyst, Mace Windsor, are valuing the common stock of Sailor Company Inc. using a residual income valuation approach. Toussaint makes the following comments about Sailor's expected performance over the next four-years: Comment I: Free cash flows generated may be negative. Comment II: No significant amounts of pension adjustments or foreign currency translation adjustments to be reported in the other comprehensive income. Could of Toussaint's comments be reasons why the RI model should be used for Sailor Company Inc.? A. No. B. Yes, but only comment I. C. Yes, both comment I and comment II.
          • C is correct A residual income model is applied when a company’s expected free cash flows are negative within the forecast period; significant departures from clean surplus accounting do not exist; great uncertainty exists in forecasting terminal values using other valuation approaches, and inputs of the RI model such as book value and ROE are predictable. Hence Toussaint's both comments could be reasons to use RI model for valuation.
            • RI模型的假设是clean surplus relation: 长期只有retained earning对equity有影响。所以OCI要保持稳定。C2是对的。
    • Calculation of residual income
      • RI = NI - (Equity capital * Cost of Equity)
        • 例题
          • Strozzi selects the residual income method to value the equity of Siroe, a utility company. All relevant financial data about Siroe are presented in Exhibit 2. Siroe's residual income is closest to: A. –$6.45 million B. $2.33 million C. $12.30 milllion
            • B is correct Because both net income and the equity charge have been correctly calculated to arrive at residual income. Total assets = $450 million, and the debt ratio is 60%. Therefore, debt = $270 million and equity = $180 million. The pre-tax interest rate is 5%, so interest is $13.5 million. We are given EBIT of $42 million. The calculation of net income is as follows (in $ millions): EBIT: 42.000 Less: Interest expense: 13.500 Pretax income: 28.500 Less: Income tax expense (35%): 9.975 Net income: 18.525 The equity charge is equity capital × cost of equity capital. We are given the cost of equity in Exhibit 2, i.e. 9%. So equity charge = 180 × 9% = 16.2. Therefore, residual income = 18.525 – 16.2 = 2.325 or approximately $2.33 million. Note: There is a second way to get to residual income: EBIT × (1 – Tax rate) – Equity charge – Debt charge. In this case: EBIT: 42.000 Less: Taxes on EBIT: 35% × 42.000 = 14.700 Less: Equity charge: 16.200 Less: Debt charge: 450 × 60% × 5% × (1 – 35%) = 8.775 Residual income = 2.325 or approximately $2.33 million.
              • 送分题。基础的计算，理清了逻辑后，就是送的
        • 例题
          • Strozzi also values Rinaldo using the residual income model. She notes that last year Rinaldo made a one-time revision to its revaluation surplus due to an increase in the total market value of its fixed assets. This revision was included in other comprehensive income but not in net income. Which revision should Strozzi make when calculating last year's residual income for Rinaldo? A. Increase net income B. Increase the book value of equity C. Decrease the book value of equity
            • A is correct A.Correct because this action would adjust for a violation of the clean surplus relationship. The fact that the revision to the revaluation surplus increases Rinaldo's assets, and consequently equity, but not net profit, constitutes a violation of the clean surplus relationship. Using an ROE forecast or a net income forecast that ignores violations of clean surplus accounting will distort estimates of residual income. Strozzi should avoid such a distortion by using total comprehensive income (net income plus other comprehensive income) for her residual income calculation. This means increasing net income when calculating last year's residual income for Rinaldo. B.Incorrect because the change to the balance sheet has already been made and no adjustment is necessary. The assets will already have been increased by the amount of the revision to the revaluation surplus. This change will be reflected in the book value of equity. In all of these cases in which items bypass the income statement, the book value of equity is stated accurately because it includes 'accumulated other comprehensive income,' but net income is not stated properly from the perspective of residual income valuation. C.Incorrect because the change to the balance sheet has already been made and no adjustment is necessary. In all of these cases in which items bypass the income statement, the book value of equity is stated accurately. An unprepared candidate may conclude that a one-time adjustment to equity caused by the revision should be reversed for the purpose of the calculation.
              • 题目中把one-time revision to its revaluation surplus放在OCI里的做法是没问题的。但是我们现在是用RI模型来估值，RI是看NI-Equity Charge，这里没包含一次性的修正，所以需要在NI里做对应的调整。
      • RI = EBIT(1-t) - Total Capital * WACC%
    • Uses of residual income in equity valuation
      • 例题
        • Mangoba Nkomo, CFA, a senior equity analyst with Robertson-Butler Investments, South Africa, has been assigned a recent graduate, Manga Mahlangu, to assist in valuations. Mahlangu is interested in pursuing a career in equity analysis. In their first meeting, Nkomo and Mahlangu discuss the concept of residual income and its commercial applications. Nkomo asks Mahlangu to determine the market value added for a hypothetical South African firm using the data provided in Exhibit 1. Based on the information in Exhibit 1, the market value added of the hypothetical firm is closest to: A R65million. B R113million. C R168million.
          • C is correct. Market value added equals the market value of firm minus total accounting book value of total capital. Market value added = Market value of company – Accounting book value of total capital Market value of firm = Market value of debt + Market value of equity Market value of firm = R55 million + (30,000,000 × R25.43) Market value of firm = R55 million + R762.9 million = R817.9 million Market value added = R817.9 million – R650 million = R167.9 million, or approximately R168 million.
            • 这里要注意，market price是common stock，一般要加上preferred stock和debt才是enterprise value。然后book value是所有capital的book value
      • 例题
        • Stack tells Armishaw that he prefers the use of a residual income model to value the company over other available methods. He provides three justifications for his preference: 1. The model explicitly incorporates the cost of debt capital. 2. The model can be used when cash flows are unpredictable. 3. There is less of an impact arising from the uncertainty in forecasting terminal value. The least appropriate justification that Stack makes in support of the use of the residual income model is Statement: A.3. B.1. C.2.
          • B is correct. The residual income model uses accounting income estimates and assumes that the cost of debt capital is properly reflected by interest expense, but because of changing market conditions interest expense may not be a good proxy for the company's cost of debt capital. C is incorrect. This is a strength of the residual income model. A is incorrect. This is a strength of the residual income model.
            • RI可以反应debt cost，但是不能反应最新的市场状态。
            • S1错在，我们计算RI的时候，用的是利润表的Int，但是这个不能反应真实的债务成本，因为Int是基于发债时候确定的利率，不能反应现在市场最新的利率。S2是对的，FCF用不了的时候RI可以用。S3也是对的，DDM和FCF里TV都是大头，而RI里BV是大头。
              • 【PS】S1也不能说不反应债务成本，不过和S2，S3比，明显对的没有其他2个选项那么多。而且都用了explicitly，明显就是给你个台阶。
    • Commercial implementations
      • EVA = NOPAT - Total Capital * WACC%
        • R&D expenses are capitalized
        • Deferred taxes are eliminated
        • Inventory LIFO reserve is added back
        • EVA = EBIT * (1-T) - Capital * WACC
          • 股东的剩余收益叫做Residual Income (RI)
          • 整个公司的剩余收益叫做Economic value added (EVA)
        • 例题
          • Windsor is also assigned a task to vale PDD, a small E-commence company. PDD has total assets of $3 million financed 60 percent with debt and 40 percent with equity capital. The cost of debt is 8 percent before taxes. The cost of equity capital is 13 percent. The company has earnings before interest and taxes (EBIT) of $500,000 and a tax rate of 30 percent. What is the EVA for PDD? A. $256,800 B. $93,200 C. $48,800
            • B is correct WACC = 0.6×8%×(1-30%)+ 0.4×13%=8.56% $WACC = 8.56% ×$3,000,000 = $256,800 EVA = $500,000× (1-30%)-$256,800 = $93,200
      • MVA = Market value of firm - Invested capital
  • Valuations using residual income
    • General model
      • V0 = B0 + Sum(PV(RI))
        • 例题
          • Stark asks Parker to compare residual income models to dividend discount models and free cash flow models. Parker recognizes that valuation models based on discounting dividends or discounting free cash flows are as theoretically sound as the residual income model. While investigating the relationship of the residual income model to other valuation models, Parker makes the following statements. Statement 1: Residual income valuations recognize value later than different present value approaches. Statement 2: In theory, residual income valuations are mutually consistent with other present value approaches Are Parker's statements comparing residual income models with different present value approaches both correct? A. Yes B. No, only statement 1 is correct C. No, only Statement 2 is correct
            • C is correct A.Incorrect because residual income models recognize value earlier, not later, than different present value approaches, making Statement 1 incorrect. Residual income models and the dividend discount model are, in theory, mutually consistent, making Statement 2 correct. B.Incorrect because residual income models recognize value earlier, not later, than different present value approaches, making Statement 1 incorrect, while residual income models and the dividend discount model are, in theory, mutually consistent, making Statement 2 correct. In other words, residual income models tend to assign a relatively small portion of a security’s total present value to the earnings that occur in later years. The derivation of value from the earlier portion of a forecast horizon is one reason residual income valuation can be a useful analytical tool. The dividend discount and residual income models are in theory mutually consistent. Because of the real-world uncertainty in forecasting distant cash flows, however, the earlier recognition of value in a residual income approach relative to other present value approaches is a practical advantage. C.Correct because because residual income models and the dividend discount model are, in theory, mutually consistent, making Statement 2 correct , while residual income models recognize value earlier, not later, than different present value approaches, making Statement 1 incorrect.
              • 这里S1的说法背后的原理是，RI是从BV0出发，大头都在BV0，所以确认价值比较早。而其他模型大头在TV，所以确认价值比较晚。
        • 例题
          • For the residual income valuation, Windsor gathers the following information shown in Exhibit 1.
          • Based on Exhibit 1 and the residual income valuation model, the value per share (€) of Sailor Company Inc. is closest to: A. 36. B. 40. C. 39.
            • C is correct Based on the relationship RIt = Et – r×Bt-1 = (ROEt – r) × Bt-1. Besides calculating the current rate of abnormal earnings, (ROEt –r), one must calculate the beginning of yearbook values, Bt-1. As the table shows, Bt = Bt-1 + Et – Dt. Using the information of Exhibit 1:
            • As after year 4, residual income is expected to be zero，the terminal value after year 4 should be zero. Use the equation: V0 = B0 +∑RIt / (1 +r)t Where V0 is calculated by using the CF editor of the Financial Calculator: CF0 = 25; CF1 = 6.25, CF2 = 4.76, CF3 = 3.77, CF4 = 2.16, I = 10, NPV CPT = 38.92.
              • 计算是核心内容，必须牢牢掌握
              • 建议自己手算次
      • Difference between RI and DCF
        • RI: less sensitive to terminal value estimate
        • DCF: terminal value is most of the value estimate
    • Fundamental determinants
      • ROE > Required return
        • RI > 0
        • Justified market-to-book > 1
      • ROE = Required return
        • Justified market value = book value
        • Market-to-book ratio = 1
    • Single-stage residual income model
      • V0 = B0 + B0(ROE-r)/(r-g) = B0(ROE-g)/(r-g)
      • Justified P/B = (ROE-g)/(r-g)
        • 例题
          • Satisfied with Mahlangu's response, Nkomo requests that Mahlangu use the single-stage residual income model to determine the intrinsic value of the equity of Jackson Breweries, a brewery and bottling company, using data provided in Exhibit 2. Based on the information in Exhibit 2, the intrinsic value per share of the equity of Jackson Breweries is closest to: A R97.67. B R130.22. C R186.03.
            • B is correct. With a single-stage residual income (Rl) model, the intrinsic value,V0 is calculated assuming a constant return on equity (ROE) and a constantearnings growth (g). V0= B0 * (ROE-g)/(r-g) = 55.81*(0.13-0.095)/(0.11-0.095)=130.223333
              • 送分题
              • 核心公式，必须牢记
        • 例题
          • At the conclusion of their meeting, Beckworth asks Castovan to value SSX using RI models. Selected financial information on SSX is presented in Exhibit1. Exhibit1 SSXFinancial(SSX) Selected Financial Data Total assets (millions): 4,000.00 Capital structure: 60% debt/40% equity EBIT (millions): 700.00 Tax rate: 35.00% Return on equity (ROE): 23.37% Pretax cost of debt*: 5.20% Cost of equity: 15.00% Market price per share: 48.80 Price-to-book ratio: 2.10 * Interest expense is tax-deductible. Based on Exhibit 1 and the single-stage residual income model, the implied growth rate of earnings for SSX is closest to: A 5.8%. B 7.4%. C 11.0%
            • 解析： 确定核心公式：V = B + (ROE - r) / (r - g) * B = 48.8/2.1+48.8/2.1*(0.2337-0.15)/(0.15-g) = 48.8 -> g=7.4，选B。
              • 【PS1】RI的核心公式，必会。
              • 【PS2】如果multiple stage，公式为折算之前的RI，最后的PVt(continuing RI) = RI(t+1) / (1+re -w)，其中w为presistence factor。1-w为RI的衰减率。w=1代表不衰减，RI为常数。
    • Multistage residual income model
      • Premium over book value
        • V0 = B0 + Sum(PV(EPS-r*B(t-1))) + PV(Pt-Bt)
          • 例题
            • Scenario 2 Estimate the value of Amersheen shares using a multistage residual income model with the data provided in Exhibit3, but assume that at the end of 2024, share price is expected to equal book value per share. Under Scenario 2, the intrinsic value per share of the equity of Amersheen is closest to: A R13.29. B R15.57. C R16.31.
              • • 送分题
                • share price is expected to equal book value per share说明最后一期没有RI
                • 一定要自己算几次！
      • Persistence factor
        • V0 = B0 + PV(RI) + RI(t+1)/(1+r-w)
          • g=w-1
        • w
          • High
            • Low dividend payout
            • High historical RI persistence in the industry
          • Low
            • Extremely high ROE
            • Large special items
            • Large accounting accruals
        • Possible assumptions
          • w=0
            • no competitive advantage, pure competition
          • W=1
            • Perpetual competitive advantage
            • 例题
              • For the multistage model, Castovan forecasts TTCI's ROE to be higher than its long-term ROE for the first three years. Forecasted earnings per share and dividends per share for TTCI are presented in Exhibit3. Starting in Year 4, Castovan forecasts TTCI's ROE to revert to the constant long-term ROE of 12% annually. The terminal value is based on an assumption that residual income per share will be constant from Year 3 into perpetuity.
              • Based on Exhibits 2 and 3 and the multistage RI model, Castovan should estimate the intrinsic value of TTCI to be closest to: A €54.88. B €83.01. C €85.71.
                • • 基础题，必须掌握
                  • 要注意RI不变，说明w=1，可以直接用永续年金的方法计算
                  • 第3年开始持续不变，所以可以折算到TV(2)
          • 0<w<1
            • 例题
              • For the multistage model, Castovan forecasts TTCI's ROE to be higher than its long-term ROE for the first three years. Forecasted earnings per share and dividends per share for TTCI are presented in Exhibit3. Starting in Year 4, Castovan forecasts TTCI’s ROE to revert to the constant long-term ROE of 12% annually. The terminal value is based on an assumption that residual income per share will be constant from Year 3 into perpetuity. Beckworth questions Castovan's assumption regarding the implied persistence factor used in the multistage RI valuation. She tells Castovan that she believes that a persistence factor of 0.10 is appropriate for TTCI. The persistence factor suggested by Beckworth will lead to a multistage value estimate of TTCI's shares that is: A less than Castovan's multistage value estimate. B equal to Castovan's multistage value estimate. C greater than Castovan's multistage value estimate.
                • A is correct. In Castovan's multistage valuation, she assumes that TTCI's residual income will remain constant in perpetuity after Year 3. This perpetuity assumption implies a persistence factor of 1 in the calculation of the terminal value. A persistence factor of 0.10 indicates that TTCI's residual income is forecasted to decline at an average rate of 90% per year. This assumption would lead to a lower valuation than Castovan's multistage value estimate, which assumes that residual income will remain constant in perpetuity after Year 3.
                  • 定性理解w的含义和作用
            • 例题
              • Armishaw next presents Exhibit 2, which contains the basis for his estimates for the share price (as of 15 January 2014) if he assumes a terminal value in 2023 arising from treating 2023's residual income as a perpetuity. Stack questions Armishaw's assumption in his 2014 valuation (Exhibit 2) that a perpetuity would best describe the terminal value of the stream and suggests that residual income should fade over time. Stack further suggests that a persistence factor of 0.50 might be appropriate Using the information in Exhibit 2, comparing Armishaw's approach to terminal value to Stack's approach, Stack's assumption leads to a 2024 value that is approximately: A.$6.50 lower than Armishaw's approach. B.$6.74 lower than Armishaw's approach. C.$26.30 higher than Armishaw's approach.
                • • 注意应该用RI1，而不是RI0做分子
                  • 时间点是2014，而算出来TV的差值的时间点是2024
                  • 先算2024的RI: 5.32*(1+0.2*0.6)=5.96。再算2024的差别5.32/0.15-5.96/(1+0.15-0.5)=26.30。折回10年前26.30/(1+0.15)^10=6.50，选A。
                    • 【PS】下一年的RI不要直接那ROE评估，要抠掉D。
                    • 【PS2】记住RI的公式是PV(t-1) = RI(t) / (1+r-w)
                    • 【PS3】这题题目有点问题，23年年底已经结束了第一阶段，24年进入第二阶段，但是没24年的ROE，所以强行用23年的ROE代替。
                    • 【PS4】要注意所在时点是14年年初，而结束第一阶段时间点是23年年底。折的时候，14年年初到23年年底是10年，而不是9年。
          • Decline to mature industry level
  • Accounting issues
    • Violations of clean surplus relationship
      • 例题
        • Strozzi also values Rinaldo using the residual income model. She notes that last year Rinaldo made a one-time revision to its revaluation surplus due to an increase in the total market value of its fixed assets. This revision was included in other comprehensive income but not in net income. Which revision should Strozzi make when calculating last year's residual income for Rinaldo? A. Increase net income B. Increase the book value of equity C. Decrease the book value of equity
          • A is correct A.Correct because this action would adjust for a violation of the clean surplus relationship. The fact that the revision to the revaluation surplus increases Rinaldo's assets, and consequently equity, but not net profit, constitutes a violation of the clean surplus relationship. Using an ROE forecast or a net income forecast that ignores violations of clean surplus accounting will distort estimates of residual income. Strozzi should avoid such a distortion by using total comprehensive income (net income plus other comprehensive income) for her residual income calculation. This means increasing net income when calculating last year's residual income for Rinaldo. B.Incorrect because the change to the balance sheet has already been made and no adjustment is necessary. The assets will already have been increased by the amount of the revision to the revaluation surplus. This change will be reflected in the book value of equity. In all of these cases in which items bypass the income statement, the book value of equity is stated accurately because it includes 'accumulated other comprehensive income,' but net income is not stated properly from the perspective of residual income valuation. C.Incorrect because the change to the balance sheet has already been made and no adjustment is necessary. In all of these cases in which items bypass the income statement, the book value of equity is stated accurately. An unprepared candidate may conclude that a one-time adjustment to equity caused by the revision should be reversed for the purpose of the calculation.
            • 注意clean surplus是RI模型的前提，考法会很灵活。
    • Balance sheet adjustments
    • Nonrecurring items
    • Aggressive accounting practices
    • International accounting differences
  • Model comparison
    • Advantages of DDM / FCF / RI
    • Disadvantages of DDM / FCF / RI
    • Appropriateness of using DDM / FCF / RI
• M6 Private Company Valuation
  • Basics of private company valuation
    • Private vs public companies
      • 例题
        • Alan Chin, CEO of Thunder Corporation, has asked his chief financial officer, Constance Ebinosa, to prepare a valuation of Thunder for the purpose of selling the company to a private investment partnership. Thunder is a profitable US-domiciled manufacturer of generic household products with $200 million in annual sales. Customers consist of several grocery store chains in the United States. Competitors include large companies such as Procter & Gamble, The Clorox Company, and Unilever. Thunder has been in business for 15 years and is privately owned by the original shareholders, none of whom are employed by the company. Thunder's senior management has been in charge of the company's operations for most of the past 15 years and expects to remain in that capacity after any sale. The least likely factor that would be a source of differences in valuing Thunder compared with valuing a publicly traded company is: A access to public debt markets. B agency problems. C the size of the company.
          • B is correct. Thunder's size and its probable lack of access to public debt markets are potential factors affecting its valuation compared with a public company. Given that the separation of ownership and control at Thunder is similar to that at public companies, however, agency problems are not a distinguishing factor in its valuation
            • 要能是吧public和private的对比
      • 例题
        • Aaron opens his presentation by stating there are key differences between public and private company valuations. He add that the characteristics of private companies and the absence of universally recognized valuation methods have lead to the development of diverse valuation practices. He notes that some companies grow through acquisitions and that the prices paid in such transactions need to be evaluated. He mentions there are many additional concerns he looks to address as he begins an evaluation and lists the following: Agency issues, quality of financial statements, and concentration of control. With regard to private versus public company valuation, do Aaron's concerns include both company specific and stock specific factors? A. Yes B. No regarding stock specific factors C. No regarding company specific factors
          • 答案：A 解析：A is correct because Aaron's concerns includes agency issues, quality of financial statements and concentration of control. Agency issues and quality of financial statements are company specific factors. Concentration of control can be viewed as both a stock specific factor and a company-specific factor. Therefore Aaron's comment address both stock specific and company specific factors.
            • 要注意，集中控制问题既是公司因素，也是股票因素
    • Uses of private business valuation
      • Ebinosa also explains that several approaches are available for valuing private companies. She mentions that one possibility is to use an assetbased approach because Thunder has a relatively large and efficient factory and warehouse for its products. A real estate appraiser can readily determine the value of these facilities. A second method would be the market approach and using an average of the price-to-earnings multiples for Procter & Gamble and Clorox. A third possibility is a discounted free cash flow approach. The latter would focus on a continuation of Thunder's trend of slow profitable growth during the past 10 years Ebinosa can best value Thunder using the: A excess earnings approach. B asset-based approach. C discounted free cash flow approach.
        • C is correct. The excess earnings method would rarely be applied to value a company's equity, particularly when it is not needed to value intangibles. The asset-based approach is less appropriate because it is infrequently used to estimate the business enterprise value of operating companies. By contrast, the free cash flow method is broadly applicable and readily applied in this case.
          • 家里没矿/地不用B，A很少用，选C，最常用。
          • 【PS1】一般而言，有很多无形资产会选excess earning。有形资产为主，并且可以确定资产的市场价值，用asset-based。制造业选DCF。如果啥都没说，大部分选DCF。
    • Private company valuation areas of focus
    • Normalized earnings adjustments
      • 例题
        • Jim Hester, MVA's merger and acquisition (M&A) analyst is evaluating Fargo Durum Farms, Inc. (FDF) for a potential acquisition. FDF owns 1,500 acres of fertile land, farm buildings, machinery, residential quarters, livestock, cattle feed, seeds, grain, significant amounts of intangible assets, and so on. Selected data from FDF's income statement for the year ended December 2012 and additional estimates compiled by Hester are presented in Exhibits 1 and 2. Using the company's data and Hester's assessments and estimates in Exhibits 1 and 2, FDF's normalized operating income after taxes for 2012 is closest to: A.$367,500. B.$325,500. C.$402,500.
          • • 这题最坑的地方在于，CoGS ratio shall be higher at 45%，注意这里说的是CoGS ratio，也就是CoGS/Revnue。而不是说现在的CoGS变成1.45倍。
  • Income approach
    • Discount rate estimation
      • Factors to consider
      • Discount rate model
        • CAPM
          • 例题
            • Chin knows that if an income approach is used, the choice of discount rate may have a large influence on the estimated value. He makes two statements regarding discount rate estimates: 1 If the CAPM method is used to estimate the discount rate with a beta estimate based on public companies with operations and revenues similar to Thunder, then a small stock premium should be added to the estimate. 2 The weighted average cost of capital of the private investment partnership should be used to value Thunder. Regarding the two statements about discount rate estimates, Chin is: A correct with respect to adding the small stock premium and correct with respect to the weighted average cost of capital. B correct with respect to adding the small stock premium and incorrect with respect to the weighted average cost of capital. C incorrect with respect to adding the small stock premium and incorrect with respect to the weighted average cost of capital.
              • C is correct. CAPM 单因子模型， 只有一个因子 market factor； 多因子模型 Expanded CAPM 或 Building-up 中有多个因子， 比如 small size premium The correct weighted average cost of capital should reflect the risk of Thunder's cash flows, not the risk of the acquirer's cash flows.
                • 要注意private investment partnership不是target company，不要中招
        • Expanded CAPM
        • Build-up approach
          • 例题
            • Ebinosa decides to calculate a value of Thunder's equity using the capitalized cash flow method and decides to use the build-up method to estimate Thunder's required return on equity. She makes the following assumptions: ■ Growth of FCFE is at a constant annual rate of 3%. ■ Free cash flow to equity for the year ahead is $2.5million. ■ Risk-free rate is 4.5%. ■ Equity risk premium is 5.0%. ■ Size premium is 2.0%. The indicated value of Thunder's equity using the build-up method and the capitalized cash flow method (CCM) based on free cash flow to equity is closest to: A $29.41million. B $38.46million. C $125.00million.
              • A is correct. The return on equity is the sum of the risk-free rate, equity risk premium, and the size premium for a total of 4.5+ 5.0+ 2.0= 11.5%. The value of the firm using the CCM is V = FCFE1/(r – g) = 2.5/(0.115 – 0.03) = $29.41million.
                • Build up的考法不一定很难。说不定题目很仁慈，直接把所有条件都给你。
    • Free cash flow method
    • Capitalized cash flow method
    • Excess earnings method
      • V(intangible) = RI(0) * (1+g) / (r(intangible) - g)
        • RI(0) = NI(0) - r(wc) * WC - r(fa) * FA
      • V(firm) = V(intangible) + WC + FA
  • Market approach
    • Guideline public company method
      • Adv
        • large pool of guideline companies
      • Disadv
        • comparability and subjectivity
      • Control premium
    • Guideline transactions method
      • Basics
        • controlling interest
      • Control premium
      • 例题
        • Olsen justifies her choice of the GTM approach in the following three statements: 1. The GTM approach works well for valuing FDF because it uses a multiple that specifically relates to sale of entire companies. Statement of Financial Accounting Standard (SFAS) No. 157 presents a fair value hierarchy that gives the highest priority to market-based evidence. 2. Most appraisers readily accept the valuation from the GTM approach because of the reliability of transactions data. 3. The market approach to determine the value of equity is appropriate even for companies with highly leveraged financial conditions or significant volatility expected in future financial performance. Satisfied with Olsen's valuation and her methodological choice, the Mahoney brothers move ahead with their competing offer for FDF. Which of Olsen's three statements justifying her choice of the GTM approach is most accurate? A.3 B.2 C.1
          • 答案：C 解析： C is correct The GTM approach uses a multiple that specifically relates to the sale of entire companies, and SFAS No. 157 also presents a fair value hierarchy that gives the highest priority to market-based evidence. Additionally, in the United States, tax courts assessing private company valuations have generally stated a preference for valuation based on market transactions although they often accept valuations based on the income approach. A is incorrect because the market approach to determine the value of equity of firms that are highly levered or with high volatility expected in future financial performance is frequently not appropriate. B is incorrect because many appraisers challenge the reliability of the transactions data because information may be limited and is generally not readily confirmed.
            • 需要看FV可以用GTM
            • 但是交易的价格可能不靠谱
            • 如果股权杠杆或者财务表现变动大，不能用GTM
    • Prior transaction method
      • Minority equity interest
  • Discounts and premiums
    • Lack of control discount
      • DLOC = 1 - 1/(1+control premium)
      • DLOC Expected?
        • GTM: Yes
        • GPCM: No
        • CCM/FCF: depends
    • Lack of marketability
    • Total discount = 1 - (1-DLOC)(1-DLOM)
      • 例题
        • Schmidt also requests that Beckett value a 15% interest in Food Garden, another grocery retailer. Based on a recent transaction involving a change in control, Beckett estimates the total equity value of Food Garden to be $100,000,000. In arriving at a value for the 15% interest, Beckett concludes that a discount for lack of control (DLOC) of 20% and a discount for lack of marketability (DLOM) of 35% are applicable. Beckett should estimate the value of the 15% equity interest in Food Garden to be: A $6,750,000. B $7,800,000. C $12,750,000
          • B is correct. 15%的股权： 100 MN x 15% = 15MN 折价调整后： 15MN x (1-20%) x (1-35%) = 7.8MN Total discount = 1 - (1-DLOC)*(1-DLOM) 总折价率 = 1 - (1-20%) x (1-35%) = 0.48 折价调整后： 15MN x (1-总折价率) = 15MN x (1-0.48) = 7.8MN
            • 送分题
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