# About P/E ratios – Equity Valuation

Determinants of the P/E Ratio:

P0= estimated price
E1= estimated earnings per share
P0/ E1 = justified price earnings ratio

The determinants of the P/E ratio can be derived from the dividend discount model, which is the foundation for valuing equity stocks.

P0 = D1/ r-g ——————- Eq 1

In this model D1 = E1 (1 – b) , b stands for the plough back ratio, and g = ROE x b. Note that ROE is return on equity. Making these substitutions we find that:

P0 = E1(1—b) / r – ROE x b —————-Eq 2

Dividing both the sides by E1we get

P0/ E1= (1—b) / r – ROE x b ——————Eq 3

Eq 3 indicates that the factors that determines the P/E ratio are:

*The dividend payout ratio, (1 – b)
* The required rate of return, r
* The expected growth rate ROE x b

P/E ratio and Plough back Ratio: Note that b, the plough back ratio, appears in the numerator as well as the denominator of the ratio on the right hand side of Eq 3 What is the effect of a change in be in the P/E ratio? It depends on how ROE compares with r. If ROE is greater than r, an increase in b leads to an increase in P/E ; if ROE is equal to r an increase in b has no effect on P/E; of ROE is less than r an increase in b leads to decrease in P/E.

P/E ratio and interest Rate: The required rate of return on equity stocks reflects interest rate and risk. When interest rates increase, required rates of return on all securities, including equity stocks increase, pushing security process downward. When interest rates fall security prices rise. Hence there is an inverse relationship between P/E ratios and interest rates.

P/E ratio and Risk:

Other things being equal riskier stocks have lower P/E multiples. This can be seen easily by examining the formula of the P/E ratio of the constant

P/E = 1—b / r—g

Riskier stocks have higher required rate of return (r) and hence lower P/E multiples. This is true in all cases, not just the constant growth model. For any expected earnings and dividend stream, the present value will be lower when the stream is considered to be riskier. Hence the P/E multiple will, be lower.

Other things being equal being equal stocks which are highly liquid command higher P/E multiples. The reason for this is not far to seek. Investors value liquidity just the way they value safety and hence are willing to give higher P/E multiples to liquid stocks.

Other influences:

In addition to the above factors, there are some other influences too that seem to have a bearing on the price earnings multiple. These are described below:

* Size of the company: other thing being equal a larger company (measured say in terms of paid up capita) tends to command a higher price earnings multiple because of greater investor interest in it.
* Reputation of management: If the management of a company is reputed for its integrity and investor friendliness, its shares are likely to command a higher price earnings multiple.

Empirical Estimation:

Numerous studies have been conducted to empirically relate the price earnings multiple to key fundamental and economic variables. Typically, these studies have employed cross section regression analysis.

Whitbek and Kisor in one of the earlier studies conducted in the US found the following relationship:

In scores (or even hundreds, if unpublished works are considered) of such studies conducted with data relating to various capital markets, empirical researchers have tried every conceivable and every possible combination if variables. Almost each of these models has been fairly successful in explaining the price earnings multiples at a given point of time.