###### Pricing and Valuing Currency Swap Cont ...

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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.

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.

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

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

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:

$$\begin{align*}\frac{\text{P}_0}{\text{E}_0} &=\frac{\text{D}_{0}(1+\text{g})/\text{E}_{0}} {(\text{r}-\text{g})} \\ \\ &= \frac{(1-\text{b})(1+\text{g})}{\text{r}-\text{g}}\\ \\ &= \frac{(0.333)(1.04)}{0.08}\\ \\ & = 4.33\end{align*}$$

$$\begin{align*}\frac{\text{P}_0}{\text{E}_1} &=\frac{\text{D}_1⁄\text{E}_1}{\text{r}-\text{g}}\\ \\&= \frac{1-\text{b}}{\text{r}-\text{g}}\\ \\&=\frac{0.333}{0.08}\\ \\&=4.16\end{align*}$$

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

closestto:

- 8.00.
- 3.50.
- 6.91.
## Solution

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

Reading 23: Discounted Dividend Valuation

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