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In financial markets, there are several methods used to calculate theoretical values of companies and their stocks. 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 (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.

In the view of fundamental analysis, stock valuation based on fundamentals aims to give an estimate of their 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?

In the view of others, such as John Maynard Keynes, stock valuation is not a prediction but a convention, which serves to facilitate investment and ensure that stock are liquid, despite being underpinned by an illiquid business and its illiquid investments, such as factories.

[edit] Fundamental criteria (fair value)

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 disposition.^[1] The discounted rate normally includes a risk premium which is commonly based on the capital asset pricing model.

[edit] Approximate valuation approaches

Average growth approximation: 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.^[2]^[3]^{[citation needed]} 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.

Constant growth approximation: The Gordon model or Gordon's growth model^[4] is the best known of a class of discounted dividend models. It assumes that dividends will increase at a constant growth rate (less than the discount rate) forever. The valuation is given by the formula:

$P = D\cdot\sum_{i=1}^{\infty}\left(\frac{1+g}{1+k}\right)^{i} = D\cdot\frac{1+g}{k-g}$ .

and the following table defines each symbol:

Symbol	Meaning	Units
$\ P \$	estimated stock price	$ or € or £
$\ D \$	last dividend paid	$ or € or £
$\ k \$	discount rate	%
$\ g$	the growth rate of the dividends	%

[1]

Limited high-growth period approximation: 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 revert to the mean. This is probably the most rigorous approximation that is practical.^[5]

While these DCF models are commonly used, the uncertainty in these values is hardly ever discussed. Note that the models diverge for $\ k=g \$ 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 would usually be one close to the current price supporting his call) by fine-tuning the growth/discount assumptions.

[edit] Market criteria (potential price)

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]} This is called the efficient market hypothesis.

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]}

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.

[edit] Keynes's view

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:^[6]

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?

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.

...

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. …

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.

– The General Theory, Chapter 12

[edit] On-line valuation calculators

InValueAble.net: Free stock valuation site using full financial statement approach to calculate intrinsic value. Sign-in required.
http://www.moneychimp.com/articles/valuation/dcf.htm: Discounted Cash Flows Calculator that assumes that a higher growth can be sustained for a limited number of years.
http://intelligentinvesting.googlepages.com/DCF.xls: A DCF spreadsheet that allows different growth rates to be specified for years 1, 2 to 4, 5 to 7 and 8 to 10.
Baseline evaluation: Automatically fetches baseline data for popular stocks. Allows valuation with different assumptions like variable excess return period.
Public Company Valuations: Free discounted cash flow (DCF) valuation tool for major listed companies.
[2]: Behavioral stock pricer.

[edit] See also

[edit] References

^ William F. Sharpe, "Investments", Prentice-Hall, 1978, pp. 300 et.seq.
^ Imam, Shahed, Richard Barker and Colin Clubb. 2008. The Use of Valuation Models by UK Investment Analysts. European Accounting Review. 17(3):503-535
^ Demirakos, E. G., Strong, N. and Walker, M. (2004) What valuation models do analysts use?. Accounting Horizons 18 , pp. 221-240
^ Corporate Finance, Stephen Ross, Randolph Westerfield, and Jeffery Jaffe, Irwin, 1990, pp. 115-130.
^ Discounted Cash Flow Calculator for Stock Valuation
^ The Uncomfortable Dance Between V'ers and U'ers, Paul McCulley, PIMCO

[edit] External links

[0] William F. Sharpe, "Investments", Prentice-Hall, 1978, pp. 300 et.seq.

[1] Imam, Shahed, Richard Barker and Colin Clubb. 2008. The Use of Valuation Models by UK Investment Analysts. European Accounting Review. 17(3):503-535

[2] Demirakos, E. G., Strong, N. and Walker, M. (2004) What valuation models do analysts use?. Accounting Horizons 18 , pp. 221-240

[Ross-3] Corporate Finance, Stephen Ross, Randolph Westerfield, and Jeffery Jaffe, Irwin, 1990, pp. 115-130.

[4] Discounted Cash Flow Calculator for Stock Valuation

[5] The Uncomfortable Dance Between V'ers and U'ers, Paul McCulley, PIMCO

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