## Sunday, 30 April 2017

### Multiples based on Fundamentals - the Justified P/E ratio

A price multiple may be related to fundamentals through a dividend discount model such as the Gordon growth model.

The expressions developed in such an exercise are interpreted as the justified (or based on fundamental) values for a multiple.

The justified P/E Ratio:

P/E = D/E/(r-g)

r = required rate of return
g = growth

Gordon Growth Model

r = D/P + g
D/P = r-g
P= D/(r-g)
P/E = D/E(r-g)
P/E = Dividend Payout Ratio / (r-g)

Inference

The P/E ratio is inversely related to the required rate of return.
The P/E ratio is positively related to the growth rate.
The P/E ratio appears to be positively related to the dividend payout ratio.

• However, this relationship may not always hold because a higher dividend payout ratio implies that the company's earnings retention ratio is lower.
• A lower earnings retention ratio translates into a lower growth rate.
• This is known as the "dividend displacement" of earnings.

Notes:

Higher the growth rate (g), higher the P/E.
Higher the required rate of return (r), lower the P/E.
Higher the DPO ratio, higher the P/E.
Also, higher the DPO ratio, lower the retained earnings,  leading to lower growth rate (g), thus lower P/E. ("dividend displacement" of earnings)