Establishing a PE Ratio

The PE ratio maybe derived from the

1. constant growth dividend model, or
2. cross-section analysis, or
3. historical analysis.

Constant Growth Dividend Model.

We derive the PE ratio for a constant growth firm from the constant growth dividend discount model.

PE Ratio
= Dividend payout ratio/ (Required return on equity - Expected growth rate in dividends)

Dividend Payout Ratio: Most companies treat their dividend commitment seriously. Consequently, once dividends are set at a certain level, they are not reduced unless there is no alternative. Further, dividends are not increased unless it is clear that a higher level of dividends can be sustained. Thanks to these policies, dividends adjust with a lag to earnings.
If the dividend payout ratio increases the above ratio increases, which has a favourable effect ont he price-earnings multiple. However, an increasein the dividend payout ratio has the effect of lowering the expected growth rate of dividends int he denomination of the above ratio which leads to a decrease in the price-earnings multiple. On the whole, in most cases, these two effects are likely to balance out.

Required Return on Equity: The required return on equity is a function of the risk-free rate of return and a risk premium. According to the capital asset pricing model, a popularly used risk-return model, the rquired return on equity is:
= Risk-free return + (Beta of equity) ( Expected market risk premium)

Expected Growth Rate in Dividends: The third variable influencing the PE ratio is the expected growth rate in dividends. The expected growth rate in dividends is equal to:
= Retention ratio x Return on Equity.

Cross-Section Analysis

You can look at the PE ratios of similar firms in the industry and take a view on what is a reasonable PE ratio for the subject company.

Alternatively, you can conduct cross-section regression analysis wherein the PE ratio is regressed on several fundamental variables. Here is an illustrative specification:

PE ratio
= a1 + a2 Growth rate in earnings + a2 Dividend payout ratio + a3 Variability of earnings + a4 Company size.

Based on the estimated coefficients of such cross-section regression analysis, the PE ratio for the subject firm may be derived.

Historical Analysis.

You can look at the historical PE ratio of the subject company and take a view on what is a reasonable PE ratio, taking into account the changes in the capital market and the evolving competition.

As an illustration, the prospective PE ratio for Horizon Limited for the past three years was

PE Ratio 20x5 9.25, 20x6 6.63, 20x7 6.23
The average PE ratio for Horizon Limited was: (9.25+6.63+6.23)/3 = 7.37
Considering the changing conditions in the capital market and the emerging competition for Horizon Limite you may say that the average PE for the past three years is applicable in the immediate future as well.


The Weighted PE Ratio

We arrived at two PE ratio estimates:
PE ratio based on the constant growth dividend discount model: 6.36
PE ratio based on historical analysis: 7.37
We can combine these two estimates by taking a simple arithmetic average of them - this means that both the estimates are accorded equal weight. Doing so, we get the weighted PE ratio of:
(6.36+7.37)/2 = 6.87