# Stock valuation

There are several methods used to value companies and their stocks. They attempt to give an estimate of their fair value, by using fundamental economic criteria. This theoretical valuation has to be perfected with market criteria, as the final purpose is to determine potential market prices.

## Fundamental criteria (fair value)

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.

### 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. 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[2] 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 [3].

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.

## 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. 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.

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.