# Gordon Growth Model and the Price-to-Earnings Ratio

The price-to-earnings ratio (P/E) is the most widely recognized valuation indicator. Using the Gordon growth model, a P/E multiple can be developed. When forecasted inputs are used in the multiple, a justified fundamental P/E multiple is obtained. The expression of P/E can be stated in terms of current or leading P/E.

#### i. Current (or Trailing) P/E

This is calculated using today’s market price per share divided by the trailing 12 months’ earnings per share.

\begin{align*} \frac{P_0}{E_0} & = \frac{(\text{D}_0(1+\text{g}))⁄\text{E}_0}{\text{r}-\text{g}}\\ \\ &=\frac{(1-\text{b})(1+\text{g})}{\text{r}-\text{g}} \end{align*}

Where:

$$\text{b}=$$ Retention ratio.

$$(1-\text{b})=$$ Dividend payout ratio.

#### ii. Leading (or Forward) P/E

This is calculated using today’s market price per share divided by a forecast of the 12 months’ earnings per share.

\begin{align*} \frac{\text{P}_0}{\text{E}_1} & = \frac{\text{D}_1⁄\text{E}_1}{\text{r}-\text{g}}\\ \\ &= \frac{1-\text{b}}{\text{r}-\text{g}} \end{align*}

#### Example: Gordon Growth Model and the Price-to-Earnings Ratio

Given the following information:

• Current stock price = $24.00 • Trailing earnings per share =$1.80
• Current annual dividends = 0.60 • Required rate of return = 12% • Dividend growth rate = 4% The justified trailing and leading P/Es based on the Gordon growth model would be: #### i. Justified Trailing P/E \begin{align*}\frac{\text{P}_0}{\text{E}_0} &=\frac{\text{D}_{0}(1+\text{g})/\text{E}_{0}} {(\text{r}-\text{g})} \\ \\ &= \frac{(1-\text{b})(1+\text{g})}{\text{r}-\text{g}}\\ \\ &= \frac{(0.333)(1.04)}{0.08}\\ \\ & = 4.33\end{align*} #### ii. Justified Leading P/E \begin{align*}\frac{\text{P}_0}{\text{E}_1} &=\frac{\text{D}_1⁄\text{E}_1}{\text{r}-\text{g}}\\ \\&= \frac{1-\text{b}}{\text{r}-\text{g}}\\ \\&=\frac{0.333}{0.08}\\ \\&=4.16\end{align*} Notice that the market is valuing the firm’s earnings more than that is justified by the firm’s fundamentals; thus, the stock is overvalued. $$\text{Actual P/E}=\frac{24}{1.80}=13.33$$ ## Question Given the following information, • Current stock price =22.00
• Trailing earnings per share = $3.80 • Current annual dividends =$1.20
• Required rate of return = 13%
• Dividend growth rate = 8%

The trailing P/E ratio is closest to:

1. 8.00.
2. 3.50.
3. 6.91.

#### Solution

\begin{align*}\frac{\text{P}_0}{\text{E}_0}& =\frac{\text{D}_0 (1+\text{g})⁄\text{E}_0}{\text{r}-\text{g}} \\ \\&= \frac{(1-\text{b})(1+\text{g})}{\text{r}-\text{g})}\\ \\&= \frac{(0.32)(1.08)}{0.05}\\ \\&=6.91\end{align*}

LOS 23 (g) Calculate and interpret the justified leading and trailing P/Es using the Gordon growth model.

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