# Price Earnings Ratio (PER) and Discounted Cash Flow

The value of a share that promises constant cash flow is equal to the constant annual cash flow discounted at a K rate which is what the investor hopes to obtain from the investment, according to the risk that the investment has.

An example of this can clarify this theme: lets suppose that the share of XYZ is going to give some annual profit of 10 dollars and everyone agrees on this (which is a difficult thing though because according to some analysts XYZ will give 10 dollars of profit, according to others it will give 8 dollars, and there will be others that will estimate the profit will be that of 12 dollars; but in order to simplify it we will assume that all the analysts and investors agree with the 10 dollars). All right, let’s say Mr. Smith who is very conservative is going to ask for a profit of 10 by 100 dollars of his investment of a the share of XYZ, whereas Mr. Chadwick who is more risky will only ask for 5 of 100. By applying the formula Mr. Smith will be wiling to pay 100 dollars for the share of XYZ (10/0,10), whereas Mr. Chadwick will be willing to pay 200 dollars (10/0,05). In other words, each investor perceives a different risk in the share (because the aversion of risk is a very subjective topic), and therefore, they will use a higher K – the most adverse to the risk – or a lower K – those that are more risky -. The result will be that the share will have a different value for each investor. This is what justifies that the shares increase and decrease since the rate that the investors are asking for varies continuously, according to the perception of risk and this is affected by a multitude of factors (good or bad political happenings, economic etc.).

Let’s see now how the Price Earnings Ratio (PER) comes into the game. If in the equation we substitute cash flow by earnings per share (EPS) and we clear we will obtain the PER and this PER is the inverse of the profit that the investor hopes to obtain.

If the investor Mr. Smith wants to obtain a profit of 10 for 100, he will be willing to buy the XYZ share at a PER of 10 (1/0,10). To buy at a PER of 10, he will pay 100 dollars (PER x EPS = Price 10 x 10 dollars = 100 dollars. If in the market the XYZ share quotes at 120 dollars, in other words, at PER 12 (PER = Price/EPS = 120/10 = 12), the investor Mr. Smith will not buy because he will think that this share is expensive. To the contrary, the investor Mr. Chadwick will be willing to buy a PER 20 (1/0,05), equal to a price of 200 dollars and will think that the XYZ share is cheap at 120 dollars.

Now we need to see what factors make the investors willing to pay a PER of 10, of 20 or of 30, and what factors influence in the PER.