From the Gordon growth model:

P₀ = D₁ / (r - g)

If we divide this expression by last 12 months' earnings, we get the formula for the trailing P/E multiple:

P₀ / E₀ = D₀ (1 + g) / [E₀ (r - g)] = (1 - b) (1 + g) / (r - g)

where b is the earnings retention rate, and 1- b is the dividend payout ratio.

We can also compute the leading P/E multiple by dividing both sides of the Gordon equation by the forecasted value of next 12 months' earnings:

P₀ / E₁ = D₁ / [E₁(r - g)] = (1 - b) / (r - g)

Implications:

• P/E is positively related to dividend growth rate, all else equal.
• P/E is inversely related to required return, all else equal.

Example

• Payout ratio = 40%.
• Equity required return = 12%.
• Expected dividend growth rate = 4%.

Calculate the trailing and leading P/E multiple based on these forecasted fundamentals.

Trailing P/E = P₀/E₀ = (0.40 x 1.04) / (0.12 - 0.04) = 5.2.
Leading P/E = P₀/E₁ = 0.40 / (0.12 - 0.04) = 5.0.

Predicted P/E from regression.

Regressing P/E multiples of a population of stocks on the fundamental components of the Gordon model gives us a simple formula for a justified P/E multiple given the fundamentals for a specific stock. Instead of using the required rate of return as one of the independent variables, analysts usually employ the associated risk measure, beta, which can be readily calculated from available price variation history.

Example

• Dividend payout ratio = 0.40
• Beta = 0.60
• Expected earnings growth rate of 3%.
• A regression on other public utilities produces the following equation:
  Predicted P/E = 5 + (6 x dividend payout) + (10 x growth) - (0.5 x beta)

Calculate the predicted P/E.

Predicted P/E = 5 + (6 x 0.4) + (10 x 0.03) - (0.50 x 0.6) = 7.4.

Analysts should watch out for:

• changing relationships.
• multicollinearity.
• unknown predictive power.