Dividend Discount Model

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dcf估值模型

DCF估值模型股利折现模型（DDM，Dividend Discount Model），是最为基础的估值模型。

指通过预测上市公司的未来盈利能力，按一定的收益率计算出整个上市公司的价值。

即通过将公司未来现金各年的股利按投资回报率进行折现、加总后得到的公司价值。

折现现金流模型（DCF，Discount Cash Flow），是最严谨的对企业和股票估值的方法，DCF估值法与DDM的本质区别是，DCF 估值法用自由现金流替代股利。

其中的现金流量可以采用股利现金流量（FCFE，Free cash flow for the equity）——公司在经营过程中产生，在满足了再投资需求之后剩余的、不影响公司持续发展前提下的可供“股东”分配的现金；也可以采用公司自由现金流量(FCFF,Free cash flow for the film)——公司在经营过程中产生，在满足了再投资需求之后剩余的、不影响公司持续发展前提下的可供“企业资本供应者和各种利益要求人（股东、债权人）”分配的现金。

现金流折现估值模型DCF(Discounted cash flow)属于绝对估值法。

具体做法是：假设企业会快速成长若干年，然后平稳成长若干年（也有人算成永续成长），把未来所有赚的自由现金流（通常要预测15-30年，应该是企业的寿命吧），用折现率（WACC）折合成现在的价值。

这样，股票目前的价值就出来了：If 估值>当前股价，→当前股价被低估。

可以买入。

If 估值<当前股价，→当前股价被高估。

需回避或卖出。

股票的价值等于它未来现金流的折现值，不多也不少。

公司的价值取决于公司未来（在其寿命剩余期内）所创造的现金流折现的净值（注意：是净值。

所以要拿自由现金流来折现，而不是其他什么包含负债税息的收入来折现）。

企业的价值=前十年的自由现金流总和+永续经营价值为什么是前10年？因为通常很难估算企业十年后的现金流。

永续经营价值，就是第10年后直到无限远的价值。

收益定价模型

收益定价模型
收益定价模型（Earnings Pricing Model）是一种用于确定股票
或其他金融资产价格的模型。

该模型尝试通过分析公司的盈利能力来估计资产的合理价格。

常见的收益定价模型有以下几种：
1. 资本资产定价模型（Capital Asset Pricing Model，CAPM）：基于风险和预期回报之间的线性关系，通过考虑资产相对于市场的风险来确定合理的期望收益率，并进而确定资产价格。

2. 股利贴现模型（Dividend Discount Model，DDM）：基于公
司未来的股利或现金流量来确定股票的合理价格。

该模型将未来收益现值化，然后将其与当前股票价格进行比较。

3. 增长定价模型（Growth Pricing Model）：适用于快速增长
的公司，该模型基于预计未来增长率来确定股票的合理价格。

通常使用过去的增长数据和预测的未来增长来估计。

4. 相对估值模型（Relative Valuation Model）：将公司或资产
与类似公司或资产进行比较，通过比较相似公司的估值指标（如市盈率、市净率等）来确定合理的价格。

该模型基于市场上其他类似公司的估值水平。

这些模型都有其各自的局限性和假设，投资者在使用时需要结合具体情况进行综合分析。

同时，还需要注意到市场上价格由
多种因素影响，例如市场情绪、供需关系等，因此通过单一模型得出的价格可能并不一定准确。

Dividend Discount Model

Financial Market RevisionDividend Discount Models1.The intrinsic value, denoted V0, of a share of stock is defined as the present value of all cash paymentsto the investor in the stock, including dividends as well as the proceeds from the ultimate sale of the stock, discounted at the appropriate risk-adjusted interest rate, k. Whenever the intrinsic value, or the investor’s own estimate of what the stock is really worth, exceeds the market price, the stock is considered undervalued and a good investment.2.Dividend Discount Model: Stock valuation model that solves for the value of a common stock as thepresent value of future dividends expected to be received.3.The dividend discount model holds that the price of a share of stock should equal the present value of allfuture dividends per share, discounted at an interest rate commensurate with the risk of the stock.4.The constant growth dividend discount model is best suited for firms that are expected to exhibit stablegrowth rates over the foreseeable future. In reality, however, firms progress through lifecycles. In early years, attractive investment opportunities are ample and the firm responds with high plowback ratios and rapid dividend growth. Eventually, however, growth rates level off to more sustainable values. Three-stage growth models are well-suited to such a pattern. These models allow for an initial period of rapid growth, a final period of steady dividend growth, and a middle, or transition, period in which the dividend growth rate declines from its initial high rate to the lower sustainable rate.5.Problems of dividend-based valuations:∙investors tend to have very different expectations from each other (Modigliani and Miller’s theories can hardly cope with the present-day wide difference in attitude between institutional and individual investors);∙most investors look for a return based on two components: dividend and capital appreciation leading to capital gain on sale of the shares;∙The mechanistic aspect of all such models. It should be noted that d0 is, of course, much dependent on EPS, and the factors mentioned above in regard to earnings-based valuations must be taken into account.∙Dividend-based valuations are suitable for valuing small shareholdings rather than for valuing a controlling interest.Past paper questions:Question 1:a)Discuss how you would value the share price of a newly formed internet company which will grow at anon constant rate for the first n years and then grow at a constant rate g forever.b) A company forecasts that its dividends for the next five years will be £1, £2, £3, £4 and £5. After that,growth will decline to a steady 5% annually. If the company’s share price is currently trading at £55, what is the rate of return obtained by buying the company stock?c)Explain the limitations of the approach you have used to calculate the stock return.Question 2:a)Explain, how you would value the stock of a newly started technology company which is expected togrow at non constant rate for the first n years of its existence and thereafter expected to grow at a constant rate forever.b)Assume the technology company pays a constant dividend of £2 per share during the first five years,during the next five years it pays dividends of £3, £4, £5, £6 and £7 respectively. Thereafter the company has a steady growth of 7% per year till perpetuity. Assuming the expected return from the stock is 13%, what is the value of the stock?c)Under, what circumstances would the approach in part b) be invalid?Question 3:At year end 2001, the consensus among City analysts was that Innovation plc’s earnings and dividends would grow at 25% for four years, after which growth would fall to a market average of 8%. Selected data are as follows:a)Calculate the intrinsic value of Innovation’s firm value per share at year-end 2001. What is the firmvalue, assuming no growth opportunities? What is the present value of the firm’s growth opportunities?The risk free rate of return on Treasury bills is 4.8%. The market risk premium is 6% and Innovation’s share beta is 1.2.b)Calculate Innovation’s price-earnings ratio and the price-book ratio (i.e. the ratio of the market value tobook value) as of 31 December 2002.c)What are the advantages and disadvantages of each of the three valuation methods used in (a), and (b)?d)State whether Innovation’s share is overvalued or undervalued as of 31 December 2002. Support yourconclusion using your answers to previous questions and any data provided. The past 10-year average FTSE All Share index relative price-earnings and price-book ratios for Innovation were 0.4 and 1.12, respectively.a. Dividend Discount ModelThe oldest discounted cash flow models in practice tend to be dividend discount models. While many analysts have turned away from dividend discount models on the premise that they yield estimates of value that are far too conservative, many of the fundamental principles that come through with dividend discount models apply when we look at other discounted cash flow models.Basis for Dividend Discount ModelsWhen investors buy stock in publicly traded companies, they generally expect to get two types of cashflows - dividends during the holding period and an expected price at the end of the holding period. Since this expected price is itself determined by future dividends, the value of a stock is the present value of dividends through infinity.Value per share of stock = !"=t=1ttet)k + (1) E(DPSwhere,E(DPSt) = Expected dividends per share in period tke= Cost of equityThe rationale for the model lies in the present value rule - the value of any asset is the present value of expected future cash flows discounted at a rate appropriate to the riskiness of the cash flows. There are two basic inputs to the model - expected dividends and the cost on equity. To obtain the expected dividends, we make assumptions about expected future growth rates in earnings and payout ratios. The required rate of return on a stock is determined by its riskiness, measured differently in different models - the market beta in the CAPM, and the factor betas in the arbitrage and multi-factor models. The model is flexible enough to allow for time-varying discount rates, where the time variation is caused by expected changes in interest rates or risk across time.While explicit mention of dividend discount models did not show up in research until the last few decades, investors and analysts have long linked equity values to dividends. Perhaps the first book to explicitly connect the present value concept with dividends was The Theory of Investment Value by John Burr Williams (1938), where he stated the following:“A stock is worth the present value of all the dividends ever to be paid upon it, no more, no less... Present earnings, outlook, financial condition, and capitalization should bear upon the price of a stock only as they assist buyers and sellers in estimating future dividends.”Williams also laid the basis for forecasting pro forma financial statements and drew a distinction between valuing mature and growth companies.11 While much of his work has become shrouded with myth, Ben Graham (1934) also made the connection between dividends and stock values, but not through a discounted valuation model. He chose to develop instead a series of screening measures that including low PE, high dividend yields, reasonable growth and low risk that highlighted stocks that would be under valued using a dividend discount model.12Variations on the Dividend Discount ModelSince projections of dollar dividends cannot be made in perpetuity and publicly traded firms, at least in theory, can last forever, several versions of the dividend discount model have been developed based upon different assumptions about future growth. We will begin with the simplest – a model designed to value stock in a stable-growth firm that pays out what it can afford to in dividends. The value of the stock can then be written as a function of its expected dividends in the next time period, the cost of equity and the expected growth rate in dividends.Value of Stock =Expected Dividends next period(Cost of equity - Expected growth rate in perpetuityThough this model has made the transition into every valuation textbook, its origins are relatively recent and can be traced to early work by David Durand and Myron Gordon. It was Durand (1957) who noted that valuing a stock with dividends growing at a constant rate forever was a variation of The Petersburg Paradox, a seminal problem in utility theory for which a solution was provided by Bernoulli in the eighteenth century.13 It was Gordon, though, who popularized the model in subsequent articles and a book, thus11 Williams, J.B., 1938, Theory of Investment Value, Fraser Publishing company (reprint).12 Dodd, D. and B. Graham, 1934, Security Analysis, McGraw Hill, New York; Graham, B., 1949, The Intelligent Investor, Collins (reprint).13 Durand, D., 1957, Growth Stocks and the St. Petersburg Paradox, Journal of Finance, v12, 348-363.giving it the title of the Gordon growth model.14While the Gordon growth model is a simple approach to valuing equity, its use is limited to firms that are growing at stable rates that can be sustained forever. There are two insights worth keeping in mind when estimating a 'stable' growth rate. First, since the growth rate in the firm's dividends is expected to last forever, it cannot exceed the growth rate of the economy in which the firm operates. The second is that the firm's other measures of performance (including earnings) can also be expected to grow at the same rate as dividends. To see why, consider the consequences in the long term of a firm whose earnings grow 3% a year forever, while its dividends grow at 4%. Over time, the dividends will exceed earnings. On the other hand, if a firm's earnings grow at a faster rate than dividends in the long term, the payout ratio, in the long term, will converge towards zero, which is also not a steady state. Thus, though the model's requirement is for the expected growth rate in dividends, analysts should be able to substitute in the expected growth rate in earnings and get precisely the same result, if the firm is truly in steady state.In response to the demand for more flexibility when faced with higher growth companies, a number of variations on the dividend discount model were developed over time in practice. The simplest extension is a two-stage growth model allows for an initial phase where the growth rate is not a stable growth rate and a subsequent steady state where the growth rate is stable and is expected to remain so for the long term. While, in most cases, the growth rate during the initial phase will be higher than the stable growth rate, the model can be adapted to value companies that are expected to post low or even negative growth rates for a few years and then revert back to stable growth. The value of equity can be written as the present value of expected dividends during the non-stable growth phase and the present value of the price at the end of the high growth phase, usually computed using the Gordon growth model:P 0=E(DPSt)(1+ Cost of Equity)tt=1t=n"+P n(1+ Cost of Equity)nwhere Pn=E(DPSn+1)(Cost of Equity - g)where E(DPSt) is the expected dividends per share in period t and g is the stable growth rate after n years. More complicated variants of this model allow for more than two14 Gordon, M.J., 1962, The Investment, Financing and Valuation of the Corporation, Homewood, Illinois:stages of growth, with a concurrent increase in the number of inputs that have to be estimated to value a company, but no real change in the underlying principle that the value of a stock is the present value of the expected dividends.15To allow for computational simplicity with higher growth models, some researchers added constraints on other aspects of firm behavior including risk and dividend payout to derive “simpler” high growth models. For instance, the H model is a two-stage model for growth, but unlike the classical two-stage model, the growth rate in the initial growth phase is not constant but declines linearly over time to reach the stable growth rate in steady state. This model was presented in Fuller and Hsia (1984) and is based upon the assumption that the earnings growth rate starts at a high initial rate (g a) and declines linearly over the extraordinary growth period (which is assumed to last 2H periods) to a stable growth rate (g n).16 It also assumes that the dividend payout and cost of equity are constant over time and are not affected by the shifting growth rates. Figure 1 graphs the expected growth over time in the H Model.Figure 1: Expected Growth in the H ModelExtraordinary growth phase: 2H years Infinite growth phaseRichard D. Irwin, Inc.15 The development of multi-stage dividend discount models can be attributed more to practitioners than academic researchers. For instance, Sanford Bernstein, an investment firm founded in 1967, has used a proprietary two-stage dividend discount model to analyze stocks for decades. An extensive categorization of multi-stage models is provided in Damodaran, A., 1994, Damodaran on Valuation, John Wiley, New York.16Fuller, R.J. and C. Hsia, 1984, A Simplified Common Stock Valuation Model, Financial Analysts Journal, v40, 49-56.The value of expected dividends in the H Model can be written as:P 0=DPS* (1+gn)(r-gn)+DPS*H*(ga-gn)(r-gn)where DPSis the current dividend per share and growth is expected to decline linearlyover the next 2H years to a stable growth rate of gn. This model avoids the problems associated with the growth rate dropping precipitously from the high growth to the stable growth phase, but it does so at a cost. First, the decline in the growth rate is expected to follow the strict structure laid out in the model -- it drops in linear increments each year based upon the initial growth rate, the stable growth rate and the length of the extraordinary growth period. While small deviations from this assumption do not affect the value significantly, large deviations can cause problems. Second, the assumption that the payout ratio is constant through both phases of growth exposes the analyst to an inconsistency -- as growth rates decline the payout ratio usually increases. The allowance for a gradual decrease in growth rates over time may make this a useful model for firms which are growing rapidly right now, but where the growth is expected to decline gradually over time as the firms get larger and the differential advantage they have over their competitors declines. The assumption that the payout ratio is constant, however, makes this an inappropriate model to use for any firm that has low or no dividends currently. Thus, the model, by requiring a combination of high growth and high payout, may be quite limited in its applicability 17.Applicability of the Dividend Discount ModelWhile many analysts have abandoned the dividend discount model, arguing that its focus on dividends is too narrow, the model does have its proponents. The dividend discount model's primary attraction is its simplicity and its intuitive logic. After all, dividends represent the only cash flow from the firm that is tangible to investors. Estimates of free cash flows to equity and the firm remain estimates and conservative investors can reasonably argue that they cannot lay claim on these cash flows. The second advantage of using the dividend discount model is that we need fewer17 Proponents of the model would argue that using a steady state payout ratio for firms that pay little or no dividends is likely to cause only small errors in the valuation.assumptions to get to forecasted dividends than to forecasted free cashflows. To get to the latter, we have to make assumptions about capital expenditures, depreciation and working capital. To get to the former, we can begin with dividends paid last year and estimate a growth rate in these dividends. Finally, it can be argued that managers set their dividends at levels that they can sustain even with volatile earnings. Unlike cash flows that ebb and flow with a company’s earnings and reinvestments, dividends remain stable for most firms. Thus, valuations based upon dividends will be less volatile over time than cash flow based valuations.The dividend discount model’s strict adherence to dividends as cash flows does expose it to a serious problem. Many firms choose to hold back cash that they can pay out to stockholders. As a consequence, the free cash flows to equity at these firms exceed dividends and large cash balances build up. While stockholders may not have a direct claim on the cash balances, they do own a share of these cash balances and their equity values should reflect them. In the dividend discount model, we essentially abandon equity claims on cash balances and under value companies with large and increasing cash balances. At the other end of the spectrum, there are also firms that pay far more in dividends than they have available in cash flows, often funding the difference with new debt or equity issues. With these firms, using the dividend discount model can generate value estimates that are too optimistic because we are assuming that firms can continue to draw on external funding to meet the dividend deficits in perpetuity.Notwithstanding its limitations, the dividend discount model can be useful in three scenarios.•It establishes a baseline or floor value for firms that have cash flows to equity that exceed dividends. For these firms, the dividend discount model will yield a conservative estimate of value, on the assumption that the cash not paid out by managers will be wasted n poor investments or acquisitions.•It yields realistic estimates of value per share for firms that do pay out their free cash flow to equity as dividends, at least on average over time. There are firms, especially in mature businesses, with stable earnings, that try to calibrate their dividends to available cashflows. At least until very recently, regulated utility companies in the United States, such as phone and power, were good examples of such firms.•In sectors where cash flow estimation is difficult or impossible, dividends are the only cash flows that can be estimated with any degree of precision. There are two reasons why dividend discount model remain widely used to value financial service companies. The first is that estimating capital expenditures and working capital for a bank, an investment bank or an insurance company is difficult to do.18 The second is that retained earnings and book equity have real consequences for financial service companies since their regulatory capital ratios are computed on the basis of book value of equity.In summary, then, the dividend discount model has far more applicability than its critics concede. Even the conventional wisdom that the dividend discount model cannot be used to value a stock that pays low or no dividends is wrong. If the dividend payout ratio is adjusted to reflect changes in the expected growth rate, a reasonable value can be obtained even for non-dividend paying firms. Thus, a high-growth firm, paying no dividends currently, can still be valued based upon dividends that it is expected to pay out when the growth rate declines. In practice, Michaud and Davis (1981) note that the dividend discount model is biased towards finding stocks with high dividend yields and low P/E ratios to be under valued.19 They argue that the anti-growth bias of the dividend discount model can be traced to the use of fixed and often arbitrary risk premiums and costs of equity, and suggest that the bias can be reduced or even eliminated with the use of market implied risk premiums and returns.How well does the dividend discount model work?The true measure of a valuation model is how well it works in (i) explaining differences in the pricing of assets at any point in time and across time and (ii) how quickly differences between model and market prices get resolved.Researchers have come to mixed conclusions on the first question, especially at it relates to the aggregate equity market. Shiller (1981) presents evidence that the volatility18 This is true for any firm whose primary asset is human capital. Accounting conventions have generally treated expenditure on human capital (training, recruiting etc.) as operating expenditures. Working capital is meaningless for a bank, at least in its conventional form since current assets and liabilities comprise much of what is on the balance sheet.19Michaud, R.O. and P.L. Davis, 1981, Valuation Model Bias and the Scale Structure of Dividend Discount Returns, Journal of Finance, v37, 563-573.in stock prices is far too high to be explained by variance in dividends over time; in other words, market prices vary far more than the present value of dividends.20 In attempts to explain the excess market volatility, Poterba and Summers (1988) argue that risk premiums can change over time21 and Fama and French (1988) note that dividend yields are much more variable than dividends.22 Looking at a much longer time period (1871-2003), Foerster and Sapp (2005) find that the dividend discount model does a reasonably good job of explaining variations in the S&P 500 index, though there are systematic differences over time in how investors value future dividends.23To answer the second question, Sorensen and Williamson (1985) valued 150 stocks from the S&P 400 in December 1980, using the dividend discount model.24 They used the difference between the market price at that time and the model value to form five portfolios based upon the degree of under or over valuation. They made fairly broad assumptions in using the dividend discount model:(a) The average of the earnings per share between 1976 and 1980 was used as thecurrent earnings per share.(b) The cost of equity was estimated using the CAPM.(c) The extraordinary growth period was assumed to be five years for all stocksand the I/B/E/S consensus analyst forecast of earnings growth was used as the growth rate for this period.(d) The stable growth rate, after the extraordinary growth period, was assumed tobe 8% for all stocks.(e) The payout ratio was assumed to be 45% for all stocks.The returns on these five portfolios were estimated for the following two years (January 1981-January 1983) and excess returns were estimated relative to the S&P 500 Index using the betas estimated at the first stage. Figure 2 illustrates the excess returns earned20Shiller, R., 1981, Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends? American Economic Review, v71, 421-436.21Poterba, J., and L. Summers, 1988, Mean reversion in stock prices: evidence and implications, Journal of Financial Economics, v22, 27-59.22Fama, E. and K. French, 1988, Dividend Yields and Expected Stock Returns, Journal of Financial Economics 22, 3-25.23Foerster, S.R. and S.G. Sapp, 2005, Dividends and Stock Valuation: A Study of the Nineteenth to the Twenty-first Century, Working Paper, University of Western Ontario.24Sorensen, E.H. and D.A. Williamson, 1985, Some Evidence on the Value of the Dividend Discount17 by the portfolio that was undervalued by the dividend discount model relative to both the market and the overvalued portfolio.The undervalued portfolio had a positive excess return of 16% per annum between 1981and 1983, while the overvalued portfolio had a negative excess return of almost 20% per annum during the same time period. In the long term, undervalued (overvalued) stocksfrom the dividend discount model outperform (under perform) the market index on a risk-adjusted basis. However, this result should be taken with a grain of salt, given that the dividend discount model tends to find stocks with high dividend yields and low PE ratiosto be under valued, and there is well established empirical evidence showing that stockswith those characteristics generate excess returns, relative to established risk and return models in finance. In other words, it is unclear how much of the superior performance attributed to the dividend discount model could have been replicated with a far simpler strategy of buying low PE stocks with high dividend yields.Model, Financial Analysts Journal, v41, 60-69.。

股利折现模型名词解释

股利折现模型什么是股利折现模型？股利折现模型（Dividend Discount Model，简称DDM）是一种股票估值模型，它基于股票未来的股利流和投资者的期望收益进行计算。

这个模型假设投资者购买股票是为了获取股利收益，并且将股利从未来现金流中折现到现在的价值。

股利折现模型的原理股利折现模型使用时间价值的概念，即未来的一笔现金流价值低于现在同等金额的现金流。

这是因为投资者有机会将现金投资以获取回报。

股利折现模型认为股利是股票投资的主要回报，因此将未来股利进行折现。

这一模型的核心就是计算未来股利的现值。

为了计算现值，需要使用折现率（Discount Rate）。

折现率是投资者要求的收益率，它通常与股票的风险有关。

如果折现率高，那么股票的现值就会相应下降。

股利折现模型的公式股利折现模型的公式可以表示为：[ P_0 = + + + + ]其中，(P_0)代表股票的现值，(D_1, D_2, D_3, , D_n)代表未来每期的股利，(r)代表折现率，(n)代表预计的股利支付期数。

股利折现模型的使用方法计算股票的现值可以帮助投资者判断股票是被低估还是高估。

如果计算出的现值大于当前股票的市场价格，那么股票可能是被低估的，投资者可以考虑购买。

相反，如果现值小于市场价格，那么股票可能是被高估的，投资者应该谨慎购买或者寻找其他投资机会。

股利折现模型也可以用来评估股票的风险。

折现率反映了投资者对风险的要求。

如果一个公司的股利稳定且增长可预测，那么折现率可能会较低。

相反，如果一个公司的股利不稳定或者增长不可预测，那么折现率可能会较高。

股利折现模型的局限性股利折现模型是一种相对简单的估值模型，它忽略了许多现实世界中的复杂因素。

例如，该模型假设公司会稳定地支付股利，并且投资者可以无限期持有股票。

然而，在现实世界中，公司的股利支付可能会受到各种因素的影响，如经济衰退、行业竞争和管理层决策等。

此外，投资者通常不会无限期持有股票，他们可能会根据市场条件和个人需求来调整投资组合。

股利折现模型法公式

股利折现模型法公式股利折现模型法（DividendDiscountModel，简称DDM）是一种基于定价股票的金融投资的折现模型。

该模型的基本原理是根据股利本金的实际购买价格来预测股票的价格，并了解股票风险、投资赚钱效果和投资回报率。

DDM是一种经典投资理论，能够指导投资者在价格发现过程中选择和评估股票投资。

股利折现模型法的基本原理是，对某只股票的价值可以通过计算其未来流动收入的折现值来估算。

计算公式为：股票价格 =息（D）/折现率（K）+ 1/（1 + K）的n次幂。

其中，D表示股息，K表示折现率，n表示股息支付的年度增长率（通常是常用的公允程度）。

首先，投资者要对未来股利（D）做出预测。

他们要考虑到股份公司的股利政策、收入水平和现金流量，以及分配给股东的现金流量，以确定一个可行的预测。

其次，投资者需要确定一个合理的折现率（K）。

为了确定一个合理的折现率，投资者应考虑当前的市场利率、投资的风险和股份的特征（如定期股息）。

最后，投资者要根据股利的历史记录来估计股息的年度增长率。

DDM的优点是它能够根据具体的财务数据来预测股票的未来价格。

它还可以在投资者和分析师之间提供适当的沟通，并允许投资者和分析师更好地理解影响股票价格的变量。

此外，DDM可以帮助投资者在股票价格发现过程中确定一个合理的投资策略。

但DDM也有缺点，主要在于其假设的基础上。

虽然现代版的DDM 已经允许投资者考虑更多的变量，但它仍然假设股息可以持续增长，这在实际中很难实现。

DDM也忽视了股票价格受其他因素影响的事实，例如经济状况、行业发展、公司战略等。

总之，股利折现模型法是用于评估和定价股票的一种有效投资模型。

它可以用来帮助投资者发现股票价格，辅助投资者在投资决策中进行合理的权衡，并且提供一种评估投资赢利情况的方法。

但是，投资者也应考虑到DDM的局限性，因为它可能忽略一些重要的变量，而这些变量可能会影响股票定价决策。

金融市场的股票估值模型

金融市场的股票估值模型股票估值是金融市场中一项重要的任务，它是投资者判断一只股票是否被低估或高估的关键指标之一。

股票的估值模型是一种用于计算股票价值的方法和工具。

通过对公司的财务指标、市场状况以及其他相关因素进行分析和计算，股票估值模型可以帮助投资者做出更明智的决策。

在金融市场中，有许多股票估值模型可供投资者选择使用。

以下是几种常见的股票估值模型：1. 价格收益比模型（P/E Ratio Model）价格收益比模型是一种简单而广泛使用的股票估值模型。

它通过将公司的市值除以其每股盈利来计算股票的价格收益比。

价格收益比是投资者购买每一单位盈利所需支付的金额。

一般来说，价格收益比越低，意味着股票可能被低估，而越高则可能被高估。

2. 相对估值模型（Relative Valuation Model）相对估值模型是通过将目标股票与其同行业或同类股票进行比较来确定股票价值的模型。

它通常使用一些相对指标，如市盈率、市净率、市销率等，来比较不同公司之间的估值。

这种模型适用于同行业或同类股票估值的比较，可以帮助投资者判断股票是否被高估或低估。

3. 股利贴现模型（Dividend Discount Model）股利贴现模型是一种基于公司未来股利支付来估计股票价值的模型。

它假设公司未来的股利会增长，并根据股利增长率和折现率来计算股票的价值。

这种模型适用于那些持续支付股利的公司，能够提供相对准确的估值。

4. 自由现金流模型（Free Cash Flow Model）自由现金流模型是一种以公司自由现金流量作为估值依据的模型。

自由现金流是指公司在经营活动中所产生的现金净流入，用于支付股东分红和进行公司发展等活动。

这种模型可以帮助投资者了解公司的盈利能力及潜在增长，并据此估计股票的价值。

需要注意的是，股票估值模型只是一种辅助工具，不能独自决定投资决策。

股票市场的走势受众多因素的影响，包括宏观经济状况、行业前景、公司管理层能力、竞争等等。

多阶段股利贴现模型

多阶段股利贴现模型1. 引言多阶段股利贴现模型（Multi-Stage Dividend Discount Model，简称MSDDM）是估算公司股票价值的一种方法。

该模型的基本原理是将预期未来的股息以一定的折现率进行现值计算，以衡量股票的合理价格。

相对于简单的单阶段股利贴现模型（Single-Stage Dividend Discount Model，简称SSDDM），MSDDM更加适用于具有不断增长的股息和阶段性的盈利发展的公司。

2. 基本公式在多阶段股利贴现模型中，我们需要根据公司的盈利预测和股息政策，将预期未来的股息分为不同的阶段进行估算。

假设公司的盈利和股息在不同的阶段呈现出不同的增长率，我们可以使用以下公式来计算每个阶段的股息现值：PV=∑D n (1+r)nNn=1其中，PV表示股息的现值，D n表示第n个阶段的预期股息，r表示折现率，N表示总阶段数。

3. 模型应用多阶段股利贴现模型主要适用于对盈利增长稳定的公司进行估值，特别是对于科技、新兴产业等具有高风险和高增长的企业。

在应用该模型时，我们需要进行以下步骤：3.1 确定阶段数根据公司的盈利预测和业务发展情况，我们需要确定适当的阶段数。

通常情况下，2到3个阶段是较为常见的选择。

每个阶段的长度应根据具体情况而定，可以是几年或者更长时间。

3.2 估算每个阶段的股息增长率根据公司的盈利预测和行业分析，我们需要估算每个阶段的股息增长率。

对于不同阶段的增长率，应基于合理的分析和假设进行估计。

通常情况下，第一阶段的增长率会较高，后续阶段的增长率会逐渐下降。

3.3 确定折现率折现率是多阶段股利贴现模型中的一个重要参数。

在确定折现率时，需要考虑市场利率、公司风险和行业风险等因素。

一般而言，较高的风险对应着较高的折现率。

3.4 计算现值根据各个阶段的股息和折现率，可以利用基本公式进行计算，得出每个阶段的股息现值。

将所有阶段的股息现值相加，即可得到公司股票的合理价格。

绝对估值法DDM、DCF模型和RNAV简介

绝对估值法DDM、DCF模型及RNAV简介绝对估值法（折现方法）1.DDM模型（Dividend discount model /股利折现模型)2.DCF /Discount Cash Flow /折现现金流模型）（1）FCFE （ Free cash flow for the equity equity /股权自由现金流模型)模型（2）FCFF模型（ Free cash flow for the firm firm /公司自由现金流模型）DDM模型V代表普通股的内在价值， Dt为普通股第t期支付的股息或红利，r为贴现率对股息增长率的不同假定，股息贴现模型可以分为：零增长模型、不变增长模型（高顿增长模型）、二阶段股利增长模型（H 模型）、三阶段股利增长模型和多元增长模型等形式。

最为基础的模型；红利折现是内在价值最严格的定义； DCF法大量借鉴了DDM的一些逻辑和计算方法（基于同样的假设/相同的限制）。

1. DDM DDM模型模型法（Dividend discount model / Dividend discount model / 股利折现模型股利折现模型)DDM模型2. DDM 模型的适用分红多且稳定的公司，非周期性行业；3. DDM 模型的不适用分红很少或者不稳定公司，周期性行业；DDM模型在大陆基本不适用；大陆股市的行业结构及上市公司资金饥渴决定，分红比例不高，分红的比例与数量不具有稳定性，难以对股利增长率做出预测。

DCF 模型2.DCF /Discount Cash Flow /折现现金流模型） DCF估值法为最严谨的对企业和股票估值的方法，原则上该模型适用于任何类型的公司。

自由现金流替代股利，更科学、不易受人为影响。

当全部股权自由现金流用于股息支付时， FCFE模型与DDM模型并无区别；但总体而言，股息不等同于股权自由现金流，时高时低，原因有四：稳定性要求（不确定未来是否有能力支付高股息）；未来投资的需要（预计未来资本支出/融资的不便与昂贵）；税收因素（累进制的个人所得税较高时）；信号特征（股息上升/前景看好；股息下降/前景看淡）DCF模型的优缺点优点：比其他常用的建议评价模型涵盖更完整的评价模型，框架最严谨但相对较复杂的评价模型。

Model(股利折现模型)

6-4 Simplifying the Dividend Discount Model(股利折現模型)■ simplifying case 1: the dividend discount model with no growth●assumption: A company pays out all its earnings to its common shareholders. It does not raise any money either. [The company does not have good investment opportunities in the future.]implication: Such a company could not grow because it could not reinvest.Stockholders might enjoy a generous immediate dividend, butthey could forecast no increase in future dividends.The company ’s stock would offer a perpetual stream of equalcash payments, i.e., DIV 1 = DIV 2 = … = DIV t = …, whereDIV t denotes dividends per share(每股股利) at year t.● today ’s price of the stock: r DIV r DIV r DIV r DIV P t 112110...)1(...)1(1=+++++++= <= Please see valuing perpetuities in chapter 4.●Since the company pays out all its earnings as dividends, earnings and dividends are the same, i.e., EPS 1 = DIV 1, where EPS 1 is the next year ’s earnings per share(每股盈餘) of the stock.=> the value of a no-growth stock: r EPS P 10=. ● estimating the expected rate of return: 01P EPS r = ■ simplifying case 2: the constant-growth dividend discount model● assumption: Forecast dividends grow at a constant rate into the indefinite future.=> future dividends: ,...,)1(),1(,213121g DIV DIV g DIV DIV DIV +=+=...,)1(11-+=t t g DIV DIVa note:DIV tDIV 0t● the value of a constant-growth stock: ...)1(...)1()1(1332210+++++++++=t t r DIV r DIV r DIV r DIV P ...)1()1(...)1()1()1()1(111321211++++++++++++=-t t r g DIV r g DIV r g DIV r DIV ...)1()1(...)1()1()1()1(1)1()[11(13312211++++++++++++++=t t r g DIV r g DIV r g DIV r g DIV g ...])11(...11()11(11)[(1(321++++++++++++++=t rg r g r g r g g DIV r g if gr g g DIV <-++=)1)(1(1 r g if g r DIV <-=1. ● Example 6-3: DIV 1 = $3.0, g = 8%, r = 12%75$04.03$08.012.03$10==-=-=g r DIV P● estimating the expected rate of return: g P DIV r g r DIV P +=⇒-=0110= dividend yield (股利收益率) + growth rate Example above: r = 3/75 + 8% = 4% + 8% = 12%a note: 下學期的內容有一個重點是討論r 如何決定。

评估企业价值的金融模型比较

评估企业价值的金融模型比较在现代金融学中，评估企业价值是一个重要的任务。

对于投资者、分析师和决策者来说，了解企业的价值情况对于做出明智的决策至关重要。

为了准确评估企业的价值，金融模型被广泛应用。

本文将对几种主要的金融模型进行比较，以探讨其优劣和适用情况。

一、股票评估模型股票评估模型是金融领域中最常用的一种模型。

其基本理论是通过计算企业未来现金流的折现值来评估企业的价值。

典型的股票评估模型包括股息折现模型（Dividend Discount Model，简称DDM）和自由现金流折现模型（Free Cash Flow Discount Model，简称FCFDM）。

DDM模型基于预期的股息流，通过折现股息流得出企业的价值。

这种模型适合那些有稳定股息历史的企业。

然而，DDM模型没有考虑企业的成长，且对未来股息预测的不确定性较高。

相比之下，FCFDM模型更加全面。

它考虑了企业的自由现金流，即企业能够用于分配给股东和债权人的现金流。

这种模型更注重企业的财务状况和未来的成长潜力，因此在评估成长型企业时更为适用。

二、财务比率模型财务比率模型是另一种常用的金融模型。

这种模型通过计算一系列财务比率来评估企业的价值。

常用的财务比率包括市盈率（Price Earnings Ratio，简称PER）、市净率（Price to Book Ratio，简称PBR）和市销率（Price to Sales Ratio，简称PSR）等等。

市盈率是用企业市值除以净利润，它是股票价格相对于企业盈利能力的一个关键指标。

市净率则是用股票价格除以每股净资产，它衡量了股票的账面价值。

市销率则是用股票价格除以每股销售收入，它反映了市场对企业营收的评估。

财务比率模型相对简单易行，但是它往往只能提供一个相对粗略的企业价值估计。

对于特定行业和企业，财务比率模型可能会受到行业因素、会计政策等因素的影响。

三、实物资产模型实物资产模型是另一种评估企业价值的方法。

固定增长的股利折现模型_证券投资学_[共2页]

209 股票价值评估第十二章式（12-3）说明股票价格等于无限期内所有预期股利的现值之和。

该式被称为股利折现模型（dividend discount model ，DDM ）。

式（12-3）很容易让人认为股利折现模型只重视股利，而忽视了资本利得也是投资股票的一个动机，这种观点并不正确。

事实上，式（12-1）已经说明了资本利得（反映在预期售价中）是股票价值的一部分。

股利折现模型说明股票未来的售价取决于投资者对股利的预期。

式（12-3）仅出现股利并不说明投资者忽视了资本利得，而是因为资本利得是由股票售出时投资者对未来股利的预期决定的。

这就是为什么式（12-2）中的股票价格可以写成股利现值与任何时间出售的股票售价的现值之和。

P H 是在时间点H 上对所有H 时期后预期股利的折现值之和。

然后将这个值折现到现在，即时间0。

股利折现模型说明了股票价格最终取决于股票持有者不断取得的现金流收入，即股利。

如果投资者从未预期可以获得股息收入，那么该模型将意味着股票没有任何价值。

但实际中不发放股息的股票仍有市场价值，为使股息折现模型与这一现实相一致，就必须假设投资者在未来某天会获得一些现金支付，即使仅是清算的股息。

三、固定增长的股利折现模型式（12-3）对股票进行估价时的作用并不大，因为它要求预测未来无限期内的股利。

为使股利折现模型更具实用性，引进一些简化的假设是很有必要的。

在这个问题上，一个很常见的假设是股利增长率g 是固定的。

假设g =0.05，最近支付的股利是D 0=3.81，那么预期未来的股利为：D 1=D 0(1+g )=3.81×1.05=4.00D 2=D 0(1+g )2=3.81×1.052=4.20D 3=D 0(1+g )3=3.81×1.053=4.41把这些股利的预测值代入式（12-3），可得出内在价值为：23000023(1)(1)(1)1(1)(1)D g D g D g V k k k +++=++++++" 该式可化简为：010(1)D g D V k g k g+==−- （12-4）注意，式（12-4）中是用D 1而非D 0除以k -g 来计算内在价值的。

DCF现金流量估值模型知识讲解

D C F现金流量估值模型股利折现模型（DDM，Dividend Discount Model），是最为基础的估值模型。

指通过预测上市公司的未来盈利能力，按一定的收益率计算出整个上市公司的价值。

即通过将公司未来现金各年的股利按投资回报率进行折现、加总后得到的公司价值，折现现金流模型（DCF，Discount Cash Flow），是最严谨的对企业和股票估值的方法，DCF估值法与DDM的本质区别是，DCF估值法用自由现金流替代股利。

现金流折现估值模型 DCF(Discounted cash flow)属于绝对估值法。

这样，股票目前的价值就出来了：If 估值>当前股价，→当前股价被低估。

可以买入。

If 估值<当前股价，→当前股价被高估。

需回避或卖出。

股票的价值等于它未来现金流的折现值，不多也不少。

公司的价值取决于公司未来（在其寿命剩余期内）所创造的现金流折现的净值（注意：是净值。

所以要拿自由现金流来折现，而不是其他什么包含负债税息的收入来折现）。

企业的价值=前十年的自由现金流总和+永续经营价值为什么是前10年？因为通常很难估算企业十年后的现金流。

永续经营价值，就是第10年后直到无限远的价值。

DDM（股利贴现模型）

DDM（股利贴现模型）一、什么是DDM模型？股利贴现模型（Dividend Discount Model），简称DDM，是其中一种最基本的股票内在价值评价模型。

威廉姆斯（Williams）和戈登（Gordon）1938年提出了公司（股票）价值评估的股利贴现模型（DDM），为定量分析虚拟资本、资产和公司价值奠定了理论基础，也为证券投资的基本分析提供了强有力的理论根据。

二、指导思想：模型的方法论意义大于精确计算的意义。

DDM的含义：（如果我们回归到投资的初心，我们之所以愿意成为一个公司的股东，本质上是因为看好这个公司的发展，希望每年都能获得公司给他的分红。

）三、DDM模型推导及演变如下图所示：转化为股利不变的增长模型可得：在传统的股票市场中，其中：V－代表普通股的内在价值Dt－每期股利D0－是当前股利r－是贴现率g－表示股利的不变增长率从DDM出发，影响股票内在价值的因素主要有三个：分子端是股利，与企业盈利有关；分母端的贴现率由两方面组成：一个是无风险利率，与央行有关；还有一个是风险溢价，代表你愿意为买股票多付的成本，由情绪决定。

DDM模型是一种资产定价模型，其核心观点是（以股票为例）：股票现在的价格应当是未来股息的贴现值。

通俗点就是，未来能分多少钱，换算到现在值多少钱，就是股票当前的价格。

公式中净资产*ROE=利润，d表示分红率，分子端即为股息，而决定股息大小的最主要因素为ROE，也就是企业盈利能力。

分母端主要为两个部分，其一为无风险利率，指的是将资金投资于某一项没有任何风险的投资对象的利息率；其二为风险溢价rm，rm=β* 风险评价/风险偏好，而影响风险溢价最主要的因素在于风险偏好。

因此，该模型的影响因素主要归结为：其一，分子端的企业盈利能力，也就是ROE；其二，分母端的无风险利率rf；其三，分母端的风险偏好，主要通过影响风险溢价rm进而影响股价。

再简单粗暴一点的粗略框架：四、从DDM出发，我们赚的是什么钱？第一是赚企业盈利增长的钱。

ddm模型计算例题

ddm模型计算例题
DDM模型是一种常用的股票估值模型，用于计算股票的内在价值。

它基于股息贴现模型（Dividend Discount Model），通过估算未来股息流的现值来确定股票的合理价值。

下面我将以一个例题来说明如何使用DDM模型进行计算。

假设我们有一家公司，每年支付股息1元，且预计未来股息每年以5%的增长率增加。

假设我们的折现率为10%。

我们希望计算该公司的股票内在价值。

首先，我们需要计算未来股息流的现值。

根据DDM模型，未来股息流的现值可以通过以下公式计算：
PV = D1 / (r g)。

其中，PV表示未来股息流的现值，D1表示未来一年的股息，r 表示折现率，g表示股息增长率。

在这个例子中，D1 = 1 (1 + 5%) = 1.05元，r = 10%，g =
5%。

将这些值代入公式，我们可以计算得到未来股息流的现值：
PV = 1.05 / (0.10 0.05) = 21元。

因此，根据DDM模型，该公司的股票内在价值为21元。

需要注意的是，DDM模型的计算结果仅仅是一个估计值，可能
受到多种因素的影响。

股息增长率、折现率以及其他未考虑的因素
都可能对计算结果产生影响。

因此，在使用DDM模型进行股票估值时，需要谨慎考虑各种因素，并结合其他分析方法进行综合评估。

以上是对DDM模型计算例题的详细解答，希望能对你有所帮助。

如果还有其他问题，请随时提问。

戈登模型的详细推导过程

戈登模型的详细推导过程戈登模型是一种用于估计股票的内在价值的模型，它在股票投资领域中被广泛应用。

本文将详细介绍戈登模型的推导过程，包括其基本假设和公式推导。

我也会分享一些关于戈登模型的观点和理解。

1. 引言戈登模型是由美国经济学家戈登·雪隆（Myron J. Gordon）在1962年提出的，用于估计股票的内在价值。

它基于股息贴现模型（Dividend Discount Model，简称DDM），通过将未来股息贴现到现在，计算股票的合理价格。

2. 基本假设戈登模型的推导基于以下几个基本假设：- 公司将持续支付股息，且股息具有稳定的增长率。

- 投资者要求一定的风险溢价，即所谓的股息折现率。

- 公司的市场价值可以通过对未来股息进行贴现得到。

3. 推导过程为了推导戈登模型，我们需要考虑以下几个关键参数：- D：当前的股息支付- r：股息折现率- g：股息增长率根据戈登模型，股票的内在价值（V0）可以通过以下公式计算：V0 = D / (r - g)为了推导这个公式，我们首先假设股息增长率等于股息折现率（g = r）。

在这种情况下，公式可以简化为：V0 = D / r这个公式表示，股票的内在价值等于当前股息除以股息折现率。

投资者要求的股息折现率越高，公司的内在价值就越低。

若假设股息增长率小于股息折现率（g < r），则公式可以进一步简化为：V0 = D / (r - g)这个公式表示，股票的内在价值等于当前股息除以股息折现率减去股息增长率。

这意味着如果公司的股息增长率低于投资者要求的股息折现率，股票的内在价值会降低。

4. 观点和理解戈登模型的推导过程相对简单，但它在股票估值中有一定的局限性。

模型假设股息增长率保持不变，这在实际情况中不太可能。

公司的盈利状况和市场环境都会对股息增长率产生影响。

投资者在使用戈登模型时应谨慎考虑。

戈登模型只适用于有稳定股息的公司，而不适用于不支付股息或股息波动较大的公司。

5.权益总复习笔记

Discounted Cash Flow ModelsDDM（dividend discount model）缺陷①如果我知道N期后的Price，我不需要进行估值解决：所以假设这家公司是持续经营的（going concern）→消除最后一项②不可能知道N期后，具体的公司分红金额→引入GGM（Gorden growth model）GGM（Gorden groth model）前提（assumption）①假设我的dividend是按照公司的增长（g）来计算的，而且g永远不变②r（要求回报率）＞g（增长速度），r永远不变为了解决g永远不变的问题→引入Two-stage DDM models定性判断：当r上升，V0下降；g上升，V0上升计算：g=ROE×（1-dividend）；CAPM=Rf+β（Re-Rf）；D1=EPS0×payout ratio [二级内容]Clean surplus：△Equity=△REPrefered stock valuation优先股股利由于每年是约定好的，g=0，r永远不变（年金公式）Two-stage DDM models注意点①D0不需要折现②terminal value需要折现；高速增长的最后一期也需要折现Multiplier modelsPrice multiplesP/E:分子P=market value或者D1/（r-g）当分子选用D1/(r-g)→Justified P/E ratio当分子选用market value→P/E ratioP/E:分母E=E0或者E1（E：EPS）当分母选用E0→Traling price multiples当分母选用E1→Leading price multiplesP/E的本质：P是投资股票投入的成本；E是公司的盈利的能力→不考虑价格变动的情况，收投资回收P/E越大→成本越高，收回投资时间越长；P/E越小→成本越小，收回投资时间越短；越短越好Justified P/E ratio traling price multiplesP0/E0=D1×E0/(r-g)=（1-b）/r-g；b：留存收益比率Justified P/E ratio Leading price multiplesP0/E1=D1×E1/(r-g)=（1-b）（1+g）/r-g；b：留存收益比率定性：①r和P/E是一个反向关系（reversely）②由于g会影响b，所以g和P/E的关系是模糊的（ambiguous）③如果考题中出现g和b是independent关系，那么g和P/E的关系是正相关（positive）优点①可以横向比较（cross-sectional）和纵向比较（time series）②使用最广泛的指标之一缺点①DCF比较的基准是market value，而P/E的比较基准是time series和cross sectional，可能会产②根据不同的会计政策会导致P/E=P/（EPS）的不同③对于周期性公司→波动性更大→P/E波动也大，参考意义降低Enterprise value multipelsEnterprise value=（market value of common stock + market value of preferred stock + market value of debt）–cash and cash equivalents由于market value在市场上很难观测到，可以使用book value替代。

资产定价计算公式

资产定价计算公式
资产定价的计算公式可能因不同类型的资产（例如股票、债券、衍生品等）而有所不同。

1.对于股票，常见的定价模型有股利折现模型（Dividend Discount
Model, DDM），例如戈登增长模型(Gordon Growth Model)。

其计算公式为：股票价格=预期股利/（折现率-成长率）。

2.对于债券，其定价通常使用现金流折现模型(Discounted Cash Flow,
DCF)，通过计算未来现金流的现值来确定债券价格。

3.对于衍生品，如期权，布莱克-斯科尔斯期权定价模型(Black-Scholes
Options Pricing Model)是常见的定价方法。

其计算公式为：期权价格=标的资产价格* N(d1) -行权价* e^(-r * t) * N(d2)，其中，d1 =（ln （S/K）+（r+（σ^2）/2）*t）/（σ* √t），d2 = d1 -σ* √t，S为标的资产价格，K为行权价，r为无风险利率，t为时间，σ为标的资产的波动率。

此外，对于某些特定的资产类别或投资策略，还存在其他一些资产定价模型和公式。

例如，资本资产定价模型(CAPM)是用来评估风险和预期收益之间关系的模型。

需要注意的是，这些公式和模型只是提供了一个参考框架，实际应用中还需要根据具体情况进行调整和优化。

同时，资产定价并非一个简单的计算过程，它涉及到许多复杂的因素和不确定性，因此在实际操作中需要综合考虑各种因素进行决策。