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| In [[financial markets]], '''stock valuation''' is the method of calculating theoretical values of companies and their [[stock]]s. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged ''[[Undervalued stock|undervalued]]'' (with respect to their theoretical value) are bought, while stocks that are judged ''overvalued'' are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall.
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| In the view of [[fundamental analysis]], stock valuation based on fundamentals aims to give an estimate of their [[Intrinsic value (finance)|intrinsic value]] of the stock, based on predictions of the future cash flows and profitability of the business. Fundamental analysis may be replaced or augmented by market criteria – what the market will pay for the stock, without any necessary notion of intrinsic value. These can be combined as "predictions of future cash flows/profits (fundamental)", together with "what will the market pay for these profits?" These can be seen as "supply and demand" sides – what underlies the supply (of stock), and what drives the (market) demand for stock?
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| In the view of others, such as [[John Maynard Keynes]], stock valuation is not a ''prediction'' but a ''[[#Keynes's view|convention]],'' which serves to facilitate investment and ensure that stocks are [[liquidity|liquid]], despite being underpinned by an illiquid business and its illiquid investments, such as factories.
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| == Fundamental criteria (fair value) ==
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| The most theoretically sound '''stock valuation method''', called income valuation or the [[discounted cash flow]] ('''DCF''') method, involves '''discounting of the profits''' (dividends, earnings, or cash flows) the stock will bring to the stockholder in the foreseeable future, and a final value on disposal.<ref>William F. Sharpe, "Investments", Prentice-Hall, 1978, pp. 300 et.seq.</ref> The discounted rate normally includes a [[risk premium]] which is commonly based on the [[capital asset pricing model]].
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| In July 2010, a Delaware court ruled on appropriate inputs to use in discounted cash flow analysis in a dispute between shareholders and a company over the proper fair value of the stock. In this case the shareholders' model provided value of $139 per share and the company's model provided $89 per share. Contested inputs included the terminal growth rate, the [[equity premium puzzle|equity risk premium]], and beta.<ref>[http://blogs.law.harvard.edu/corpgov/2010/07/16/delaware-provides-guidance-regarding-discounted-cash-flow-analysis/ Delaware Provides Guidance Regarding Discounted Cash Flow Analysis]. Harvard Law School Forum on Corporate Governance and Financial Regulation.</ref>
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| === Stock Valuation Methods ===
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| Stocks have two types of valuations. One is a value created using some type of cash flow, sales or fundamental earnings analysis. The other value is dictated by how much an investor is willing to pay for a particular share of stock and by how much other investors are willing to sell a stock for (in other words, by supply and demand). Both of these values change over time as investors change the way they analyze stocks and as they become more or less confident in the future of stocks.
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| The fundamental valuation is the valuation that people use to justify stock prices. The most common example of this type of valuation methodology is P/E ratio, which stands for Price to Earnings Ratio. This form of valuation is based on historic ratios and statistics and aims to assign value to a stock based on measurable attributes. This form of valuation is typically what drives long-term stock prices.
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| The other way stocks are valued is based on supply and demand. The more people that want to buy the stock, the higher its price will be. And conversely, the more people that want to sell the stock, the lower the price will be. This form of valuation is very hard to understand or predict, and it often drives the short-term stock market trends.
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| There are many different ways to value stocks. The key is to take each approach into account while formulating an overall opinion of the stock. If the valuation of a company is lower or higher than other similar stocks, then the next step would be to determine the reasons.
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| ==== Earnings Per Share (EPS) ====
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| EPS is the net income available to common shareholders of the company divided by the number of shares outstanding. Usually there will be two types of EPS listed: a GAAP (Generally Accepted Accounting Principles) EPS and a Pro Forma EPS, which means that the income has been adjusted to exclude any one time items as well as some non-cash items like amortization of goodwill or stock option expenses. The most important thing to look for in the EPS figure is the overall quality of earnings. Make sure the company is not trying to manipulate their EPS numbers to make it look like they are more profitable. Also, look at the growth in EPS over the past several quarters / years to understand how volatile their EPS is, and to see if they are an underachiever or an overachiever. In other words, have they consistently beaten expectations or are they constantly restating and lowering their forecasts?
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| The EPS number that most analysts use is the pro forma EPS. To compute this number, use the net income that excludes any one-time gains or losses and excludes any non-cash expenses like stock options or amortization of goodwill. Then divide this number by the number of fully diluted shares outstanding. Historical EPS figures and forecasts for the next 1–2 years can be found by visiting free financial sites such as Yahoo Finance (enter the ticker and then click on "estimates").
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| Through fundamental investment research, one can determine their own EPS forecasts and apply other valuation techniques below.
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| ==== Price to Earnings (P/E) ====
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| Now that you have several EPS figures (historical and forecasts), you'll be able to look at the most common valuation technique used by analysts, the price to earnings ratio, or P/E. To compute this figure, take the stock price and divide it by the annual EPS figure. For example, if the stock is trading at $10 and the EPS is $0.50, the P/E is 20 times. To get a good feeling of what P/E multiple a stock trades at, be sure to look at the historical and forward ratios.
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| Historical P/Es are computed by taking the current price divided by the sum of the EPS for the last four quarters, or for the previous year. You should also look at the historical trends of the P/E by viewing a chart of its historical P/E over the last several years (you can find on most finance sites like Yahoo Finance). Specifically you want to find out what range the P/E has traded in so that you can determine if the current P/E is high or low versus its historical average.
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| Forward P/Es reflect the future growth of the company into the figure. Forward P/Es are computed by taking the current stock price divided by the sum of the EPS estimates for the next four quarters, or for the EPS estimate for next calendar or fiscal year or two.
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| P/Es change constantly. If there is a large price change in a stock you are watching, or if the earnings (EPS) estimates change, the ratio is recomputed.
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| ==== Growth Rate ====
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| Valuations rely very heavily on the expected growth rate of a company. One must look at the historical growth rate of both sales and income to get a feeling for the type of future growth expected. However, companies are constantly changing, as well as the economy, so solely using historical growth rates to predict the future is not an acceptable form of valuation. Instead, they are used as guidelines for what future growth could look like if similar circumstances are encountered by the company. Calculating the future growth rate requires personal investment research. This may take form in listening to the company's quarterly conference call or reading a press release or other company article that discusses the company's growth guidance. However, although companies are in the best position to forecast their own growth, they are far from accurate, and unforeseen events could cause rapid changes in the economy and in the company's industry.
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| And for any valuation technique, it's important to look at a range of forecast values. For example, if the company being valued has been growing earnings between 5 and 10% each year for the last 5 years, but believes that it will grow 15 - 20% this year, a more conservative growth rate of 10 - 15% would be appropriate in valuations. Another example would be for a company that has been going through restructuring. They may have been growing earnings at 10 - 15% over the past several quarters / years because of cost cutting, but their sales growth could be only 0 - 5%. This would signal that their earnings growth will probably slow when the cost cutting has fully taken effect. Therefore, forecasting an earnings growth closer to the 0 - 5% rate would be more appropriate rather than the 15 - 20%. Nonetheless, the growth rate method of valuations relies heavily on gut feel to make a forecast. This is why analysts often make inaccurate forecasts, and also why familiarity with a company is essential before making a forecast.
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| ==== Price Earnings to Growth (PEG) Ratio ====
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| This valuation technique has really become popular over the past decade or so. It is better than just looking at a P/E because it takes three factors into account; the price, earnings, and earnings growth rates. To compute the PEG ratio, divide the Forward P/E by the expected earnings growth rate (you can also use historical P/E and historical growth rate to see where it's traded in the past). This will yield a ratio that is usually expressed as a percentage. The theory goes that as the percentage rises over 100% the stock becomes more and more overvalued, and as the PEG ratio falls below 100% the stock becomes more and more undervalued. The theory is based on a belief that P/E ratios should approximate the long-term growth rate of a company's earnings. Whether or not this is true will never be proven and the theory is therefore just a rule of thumb to use in the overall valuation process.
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| Here's an example of how to use the PEG ratio. Say you are comparing two stocks that you are thinking about buying. Stock A is trading at a forward P/E of 15 and expected to grow at 20%. Stock B is trading at a forward P/E of 30 and expected to grow at 25%. The PEG ratio for Stock A is 75% (15/20) and for Stock B is 120% (30/25). According to the PEG ratio, Stock A is a better purchase because it has a lower PEG ratio, or in other words, you can purchase its future earnings growth for a lower relative price than that of Stock B.
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| ==== Sum of Perpetuities Method ====
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| The PEG ratio is a special case in the [[Sum of Perpetuities Method]] (SPM) <ref name=SPM>{{cite journal|last=Brown|first=Christian|coauthors=Abraham, Fred|title=Sum of Perpetuities Method for Valuing Stock Prices|journal=Journal of Economics|date=October 2012|volume=38|issue=1|pages=59–72|url=http://business.uni.edu/economics/joe.htm|accessdate=20 October 2012}}</ref> equation. A generalized version of the Walter model (1956),<ref name=Walter>{{cite journal|last=Walter|first=James|title=Dividend Policies and Common Stock Prices|journal=Journal of Finance|date=March 1956|volume=11|issue=1|pages=29–41|url=http://www.jstor.org/stable/2976527|accessdate=20 October 2012}}</ref> SPM considers the effects of dividends, earnings growth, as well as the risk profile of a firm on a stock's value. Derived from the compound interest formula using the present value of a [[perpetuity]] equation, SPM is an alternative to the [[Gordon Growth Model]]. The variables are:
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| *<math>P</math> is the value of the stock or business
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| *<math>E</math> is a company's [[earnings]]
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| *<math>G</math> is the company's constant growth rate
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| *<math>K</math> is the company's risk adjusted [[interest rate|discount rate]]
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| *<math>D</math> is the company's dividend payment
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| ::<math>P = (\frac{E*G}{K^2}) + (\frac{D}{K})</math>
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| In a special case where <math>K</math> is equal to 10%, and the company does not pay dividends, SPM reduces to the PEG ratio.
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| Additional models represent the sum of perpetuities in terms of earnings, growth rate, the risk-adjusted discount rate, and accounting book value. <ref>Yee, Kenton K., Earnings Quality and the Equity Risk Premium: A Benchmark Model, Contemporary Accounting Research, Vol. 23, No. 3, pp. 833-877, Fall 2006 | URL= http://papers.ssrn.com/sol3/papers.cfm?abstract_id=921914 </ref>
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| ==== Nerbrand Z ====
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| Given that investments are subject to revisions of future expectations the Nerbrand Z utilises uncertainty of consensus estimates to assess how much earnings forecasts can be revised in standard deviation terms before P/E rations return to normalised levels. This calculation is best done with I/B/E/S consensus estimates. The market tend to focus on the 12 month forward P/E level but this ratio is dependent on earnings estimates which are never homogenous. Hence there is a standard deviation of 12 month forward earnings estimates.
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| [[The Nerbrand z]] is therefore expressed as
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| :<math>Z = \frac{\frac{P}{H[P/E]} - E12}{stdev(E12)} </math>
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| where
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| H[P/E] = normalised P/E, e.g. a 5 year historical average of 12 month forward P/E ratios.
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| E12 = mean 12 month forward earnings estimates
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| stdev(E12) = standard deviation of 12 month forward earnings estimates.
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| A negative number indicates that earnings can be downgraded before valuations normalise. As such, a negative number indicate a valuation adjusted earnings buffer. For example, if the 12 month forward mean EPS forecast is $10, the price of the equity is $100, the historical average P/E ratio is 15, the standard deviation of EPS forecast is 2 then the Nerbrand Z is -1.67. That is, 12 month forward consensus earnings estimates could be downgraded by 1.67 standard deviation before P/E ratio would go back to 15.
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| ==== Return on Invested Capital (ROIC) ====
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| This valuation technique measures how much money the company makes each year per dollar of invested capital. Invested Capital is the amount of money invested in the company by both stockholders and debtors. The ratio is expressed as a percent and you should look for a percent that approximates the level of growth that you expect. In its simplest definition, this ratio measures the investment return that management is able to get for its capital. The higher the number, the better the return.
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| To compute the ratio, take the pro forma net income (same one used in the EPS figure mentioned above) and divide it by the invested capital. Invested capital can be estimated by adding together the stockholders equity, the total long and short term debt and accounts payable, and then subtracting accounts receivable and cash (all of these numbers can be found on the company's latest quarterly balance sheet). This ratio is much more useful when you compare it to other companies that you are valuing.
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| ==== Return on Assets (ROA) ====
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| Similar to ROIC, ROA, expressed as a percent, measures the company's ability to make money from its assets. To measure the ROA, take the pro forma net income divided by the total assets. However, because of very common irregularities in balance sheets (due to things like Goodwill, write-offs, discontinuations, etc.) this ratio is not always a good indicator of the company's potential. If the ratio is higher or lower than you expected, be sure to look closely at the assets to see what could be over or understating the figure.
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| ==== Price to Sales (P/S) ====
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| This figure is useful because it compares the current stock price to the annual sales. In other words, it tells you how much the stock costs per dollar of sales earned. To compute it, take the current stock price divided by the annual sales per share. The annual sales per share should be calculated by taking the net sales for the last four quarters divided by the fully diluted shares outstanding (both of these figures can be found by looking at the press releases or quarterly reports). The price to sales ratio is useful, but it does not take into account any debt the company has. For example, if a company is heavily financed by debt instead of equity, then the sales per share will seem high (the P/S will be lower). All things equal, a lower P/S ratio is better. However, this ratio is best looked at when comparing more than one company.
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| ==== Market Cap ====
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| Market Cap, which is short for Market Capitalization, is the value of all of the company's stock. To measure it, multiply the current stock price by the fully diluted shares outstanding. Remember, the market cap is only the value of the stock. To get a more complete picture, you'll want to look at the [[Enterprise Value]].
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| ==== Enterprise Value (EV) ====
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| [[Enterprise Value]] is equal to the total value of the company, as it is trading for on the stock market. To compute it, add the market cap (see above) and the total net debt of the company. The total net debt is equal to total long and short term debt plus accounts payable, minus accounts receivable, minus cash. The Enterprise Value is the best approximation of what a company is worth at any point in time because it takes into account the actual stock price instead of balance sheet prices{{Citation needed|date=September 2010}}. When analysts say that a company is a "billion dollar" company, they are often referring to its total enterprise value. Enterprise Value fluctuates rapidly based on stock price changes.
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| ==== EV to Sales ====
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| This ratio measures the total company value as compared to its annual sales. A high ratio means that the company's value is much more than its sales. To compute it, divide the EV by the net sales for the last four quarters. This ratio is especially useful when valuing companies that do not have earnings, or that are going through unusually rough times. For example, if a company is facing restructuring and it is currently losing money, then the P/E ratio would be irrelevant. However, by applying an EV to Sales ratio, you could compute what that company could trade for when its restructuring is over and its earnings are back to normal.
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| ==== EBITDA ====
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| EBITDA stands for earnings before interest, taxes, depreciation and amortization. It is one of the best measures of a company's cash flow and is used for valuing both public and private companies. To compute EBITDA, use a company's income statement, take the net income and then add back interest, taxes, depreciation, amortization and any other non-cash or one-time charges. This leaves you with a number that approximates how much cash the company is producing. EBITDA is a very popular figure because it can easily be compared across companies, even if all of the companies are not profitable.
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| ==== EV to EBITDA ====
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| This is perhaps one of the best measurements of whether or not a company is cheap or expensive.{{Citation needed|date=September 2010}} To compute, divide the EV by EBITDA (see above for calculations). The higher the number, the more expensive the company is. However, remember that more expensive companies are often valued higher because they are growing faster or because they are a higher quality company. With that said, the best way to use EV/EBITDA is to compare it to that of other similar companies.
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| === Approximate valuation approaches ===
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| ==== Average growth approximation ====
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| Assuming that two stocks have the same [[earnings growth]], the one with a lower [[P/E]] is a better value. The [[P/E]] method is perhaps the most commonly used valuation method in the stock brokerage industry.<ref>Imam, Shahed, Richard Barker and Colin Clubb. 2008. The Use of Valuation Models by UK Investment Analysts. European Accounting Review. 17(3):503-535</ref><ref>Demirakos, E. G., Strong, N. and Walker, M. (2004) What valuation models do analysts use?. Accounting Horizons 18 , pp. 221-240</ref> By using comparison firms, a target price/earnings (or P/E) ratio is selected for the company, and then the future earnings of the company are estimated. The valuation's fair price is simply estimated earnings times target P/E. This model is essentially the same model as Gordon's model, if k-g is estimated as the dividend payout ratio (D/E) divided by the target P/E ratio.
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| ==== Constant growth approximation ====
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| The [[Gordon model]] or ''Gordon's growth model''<ref name="Ross">Corporate Finance, Stephen Ross, Randolph Westerfield, and Jeffery Jaffe, Irwin, 1990, pp. 115-130.</ref>
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| is the best known of a class of [[discounted dividend model]]s. It assumes that dividends will increase at a constant growth rate (less than the discount rate) forever. The valuation is given by the formula:
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| :<math>P = D\cdot\sum_{i=1}^{\infty}\left(\frac{1+g}{1+k}\right)^{i} = D\cdot\frac{1+g}{k-g} </math> .
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| and the following table defines each symbol:
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| {| border="1" cellspacing="0" cellpadding="5"
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| |- style="background-color: #aaddcc; "
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| ! Symbol
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| ! Meaning
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| ! Units
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| |-
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| |<math>\ P \ </math>
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| |''estimated stock price''
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| |$ or € or £
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| |-
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| |<math>\ D \ </math>
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| |''last [[dividend]] paid''
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| |$ or € or £
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| |-
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| |<math>\ k \ </math>
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| |''discount rate''
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| | %
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| |-
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| |<math>\ g </math>
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| | ''the [[earnings growth|growth rate of the dividends]]''
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| | %
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| |}
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| [http://www.fool.co.uk/qualiport/2000/qualiport000628.htm]
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| ==== Limited high-growth period approximation ====
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| When a stock has a significantly higher growth rate than its peers, it is sometimes assumed that the [[earnings growth]] rate will be sustained for a short time (say, 5 years), and then the growth rate will [[Regression toward the mean|revert to the mean]]. This is probably the most rigorous approximation that is practical.<ref>[http://www.moneychimp.com/articles/valuation/dcf.htm Discounted Cash Flow Calculator for Stock Valuation<!-- Bot generated title -->]</ref>
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| While these DCF models are commonly used, the uncertainty in these values is hardly ever discussed. Note that the models diverge for <math>\ k=g \ </math>
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| and hence are extremely sensitive to the difference of dividend growth to discount factor. One might argue that an analyst can justify any value (and that
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| would usually be one close to the current price supporting his call) by fine-tuning the growth/discount assumptions.
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| ==== Implied Growth Models ====
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| One can use the Gordon model or the limited high-growth period approximation model
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| to impute an implied growth estimate. To do this, one takes the average P/E
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| and average growth for a comparison index, uses the current (or forward) P/E of
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| the stock in question, and calculates what growth rate would be needed for
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| the two valuation equations to be equal. This gives you an estimate of the
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| "break-even" growth rate for the stock's current P/E ratio. (Note : we are using
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| earnings not dividends here because dividend policies vary and may be influenced
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| by many factors including tax treatment).
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| ===== Imputed growth acceleration ratio =====
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| Subsequently, one can divide this imputed growth estimate by recent historical
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| growth rates. If the resulting ratio is greater than one, it implies that the stock would
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| need to experience accelerated growth relative to its prior recent historical
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| growth to justify its current P/E (higher values suggest potential overvaluation).
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| If the resulting ratio is less than one, it implies that either the market expects
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| growth to slow for this stock or that the stock could sustain its current P/E
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| with lower than historical growth (lower values suggest potential undervaluation).
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| Comparison of the IGAR across stocks in the same industry may give estimates
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| of relative value. IGAR averages across an industry may give estimates of relative expected changes in industry growth (e.g. the market's imputed expectation that an industry
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| is about to "take-off" or stagnate). Naturally, any differences in IGAR between stocks
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| in the same industry may be due to differences in fundamentals,
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| and would require further specific analysis.
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| == Market criteria (potential price) ==
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| Some feel that if the stock is listed in a well organized stock market, with a large volume of transactions, the listed price will be close to the estimated fair value.{{Citation needed|date=July 2008}} This is called the [[efficient market hypothesis]].
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| On the other hand, studies made in the field of [[behavioral finance]] tend to show that deviations from the fair price are rather common, and sometimes quite large.{{Citation needed|Usable citation=http://badger.som.yale.edu/faculty/ncb25/ch18_6.pdf date=July 2008|date=January 2011}}
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| Thus, in addition to fundamental economic criteria, market criteria also have to be taken into account [[market-based valuation]]. Valuing a stock is not only to estimate its fair value, but also to determine its '''potential price range''', taking into account market behavior aspects. One of the behavioral valuation tools is the [[stock image]], a coefficient that bridges the theoretical fair value and the market price.
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| == Keynes's view ==
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| In the view of noted economist [[John Maynard Keynes]], stock valuation is not an ''estimate'' of the fair value of stocks, but rather a ''convention,'' which serves to provide the necessary stability and [[liquidity]] for investment, so long as the convention does not break down:<ref>[http://www.pimco.com/LeftNav/Featured+Market+Commentary/FF/2009/McCulley+10-09+The+Uncomfortable+Dance+Between+V%E2%80%99ers+and+U%E2%80%99ers.htm The Uncomfortable Dance Between V'ers and U'ers], [[Paul McCulley]], [[PIMCO]]</ref><!-- Reference included to underline notability of this view. -->
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| {{quotation|
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| :Certain classes of investment are governed by the average expectation of those who deal on the Stock Exchange as revealed in the price of shares, rather than by the genuine expectations of the professional entrepreneur. How then are these highly significant daily, even hourly, revaluations of existing investments carried out in practice?
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| :In practice, we have tacitly agreed, as a rule, to fall back on what is, in truth, a convention. The essence of this convention – though it does not, of course, work out so simply – lies in assuming that the existing state of affairs will continue indefinitely, except in so far as we have specific reasons to expect a change.
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| :...
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| :Nevertheless the above conventional method of calculation will be compatible with a considerable measure of continuity and stability in our affairs, so long as we can rely on the maintenance of the convention. …
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| :Thus investment becomes reasonably 'safe' for the individual investor over short periods, and hence over a succession of short periods however many, if he can fairly rely on there being no breakdown in the convention and on his therefore having an opportunity to revise his judgment and change his investment, before there has been time for much to happen. Investments which are 'fixed' for the community are thus made 'liquid' for the individual.
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| |''[[The General Theory]],'' Chapter 12}}
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| == See also ==
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| * [[Stock selection criterion]]
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| * [[Bond valuation]]
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| * [[Real estate appraisal]]
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| * [[Active management|Active portfolio management]]
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| * [[List of finance topics#Valuation|List of valuation topics]]
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| * [[Capital asset pricing model]]
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| * [[Value at risk]]
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| * [[Mosaic theory (investments)|Mosaic theory]]
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| * [[Fundamental analysis]]
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| * [[Technical analysis]]
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| * [[Fed model]] theory of equity valuation
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| * [[Undervalued stock]]
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| * [[John_Burr_Williams#Theory|John Burr Williams: Theory]]
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| * [[Chepakovich valuation model]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| {{stock market}}
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| {{DEFAULTSORT:Stock Valuation}}
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| [[Category:Fundamental analysis]]
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| [[Category:Valuation (finance)]]
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