Are stocks overpriced? How much growth is required to justify a P/E of 100?

In this article, we shall explore how the one- and two-stage Gordon Growth Models, and Dividend Discount Model, relate growth rates, valuations, earnings, dividends, inflation, and return on investment.

Let
E = earnings
d = dividend
P = price
r = discount rate
g = (terminal) dividend growth rate

Then
y = d/P is dividend yield
Y = E/P is earnings yield
P/E = 1/Y
p = d/E is dividend payout ratio

According to the Gordon Growth Model (GGM),

y = d/P = r - g.

Hence,

Y = y/p.

So, for example, if r = 10% is the required return, and growth rate is g = 3%, then dividend yield should be y = 7%.

If also the payout ratio is 70%, then the P/E must be 10.
If the payout ratio is p = 100%, then the P/E can be ~14.

It may appear counter-intuitive that higher retention requires a lower P/E. But remember that we are talking about dividend growth rates, g, not earnings growth rates.

So if a firm is able to grow dividends without retaining earnings, this likely means that it benefits from pricing power, protecting from inflation, or that it has conservative accounting.

However, when the dividend is zero, g cannot be measured, and the model breaks down.