 # Price Multiples Based on Forecasted Fundamentals

## Justified Leading P/E Multiple based on Fundamentals

$$\text{Justified leading}\ \frac{\text{P}_{0}}{\text{E}_1} =\frac{\text{D}_{1}⁄\text{E}_1}{\text{r}-\text{g}}=\frac{1-\text{b}}{\text{r}-\text{g}}$$

Where:

$$1-\text{b}=$$ Payout Ratio

\begin{align*}\text{Justified leading}\ \frac{\text{P}_{0}}{\text{E}_0} &=\frac{\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}}=\bigg(\frac{1-\text{b}}{\text{r}-\text{g}}\bigg)(1+\text{g})\\ \text{Justified trailing}&=\text{Justified leading}\ \frac{\text{P}}{\text{E}}\times(1+\text{g})\end{align*}

• If earnings are expected to grow by $$g$$, next year’s earnings will be greater than last year’s earnings by the growth rate, and the justified trailing P/E ratio will be greater than the justified, leading P/E ratio by ($$1 + g$$).
• A higher justified P/E ratio indicates relative overvaluation.

#### Example: Calculating Justified P/E Based on Fundamentals

Given the following forecasted fundamentals:

• Retention ratio = 40%
• Required rate of return = 10%
• Dividend growth rate = 3%

Calculate the justified trailing and justified leading multiples based on the above-forecasted fundamentals.

#### Solution

\begin{align*}\text{Justified trailing P/E} &= \frac{(1-\text{b})(1+\text{g})}{\text{r}-\text{g}}\\ &=\frac{(1-40\%)(1.03)}{0.10-0.03}\\&=8.83\\ \\ \text{Justified leading P/E}&=\frac{1-0.40}{0.10-0.03}\\&=8.57\end{align*}

## Justified P/B Multiple based on Fundamentals

$$\text{Justified}\ \frac{\text{P}_{0}}{\text{B}_{0}}=\frac{\text{ROE}-\text{g}}{\text{r}-\text{g}}$$

Where:

$$\text{ROE}=$$ Return on equity.

$$\text{r}=$$ Required return on equity.

$$\text{g}=$$ Sustainable growth rate.

#### Example: Calculating P/B Multiple Based on Fundamentals

The following information relates to ABC Ltd:

• ROE = 16%
• Required rate of return = 12%
• Expected growth rate = 10%

The firm’s justified P/B based on the above fundamentals is closest to:

#### Solution

\begin{align*}\text{Justified}\ \frac{\text{P}_{0}}{\text{B}_{0}}&=\frac{\text{ROE}-\text{g}}{\text{r}-\text{g}}\\&=\frac{0.16-0.10}{0.12-0.10}\\&=3\end{align*}

All else equal, P/B is positively related to ROE.

• The bigger the spread between ROE and $$r$$, the higher the P/B ratio, all else equal.
• A higher justified P/B ratio indicates relative overvaluation.

## Justified P/S Multiple Based on Fundamentals

$$\text{Justified P/S}=\frac{(\text{E}_{0}/\text{S}_{0})(1-\text{b})(1+\text{g})}{\text{r}-\text{g}}$$

Where:

$$\text{E}/\text{S}_{0}=$$ Net profit margin.

$$1-\text{b}=$$ Payout ratio.

P/S ratio increases with an:

• Increase in profit margin
• Increase in earnings growth rate

#### Example: Calculating P/S Multiple Based on Fundamentals

Consider the following information:

$$\small{\begin{array}{l|r}\text{Dividend payout ratio} & 30\% \\ \hline\text{ROE} & 12\% \\ \hline\text{EPS} & \6 \\ \hline\text{Sales per share} & \328 \\ \hline{\text{Expected growth rate in}\\ \text{dividend and earnings}} & 7.50\% \\ \hline\text{Required rate of return} & 15\%\\ \end{array}}$$

Calculate justified P/S based on these fundamentals.

#### Solution

\begin{align*}\text{Justified P/S}&=\frac{(\text{E}_{0}/\text{S}_{0})(1-\text{b})(1+\text{g})}{\text{r}-\text{g}}\\&=\frac{(\frac{6}{328})(0.30)(1.075)}{0.15-0.075}=0.0786\end{align*}

A low justified P/S ratio may indicate the stock is undervalued, while a significantly above-average ratio may suggest overvaluation.

## Question

Consider the following information:

• Earnings growth ratio = 12%
• Required rate of return = 13%
• Long term profit margin = 6.5%
• Dividend payout ratio = 30%

The justified P/S ratio is closest to:

1. 2.184.
2. 2.451.
3. 2.662.

### Solution

\begin{align*}\text{Justified P/S}&=\frac{(\text{E}_{0}/\text{S}_{0})(1-\text{b})(1+\text{g})}{\text{r}-\text{g}}\\&=\frac{(0.065)(0.30)(1.12)}{0.13-0.12}= 2.184\end{align*}

Reading 25: Market-Based Valuation: Price and Enterprise Value Multiples

LOS 25 (h) Calculate and interpret the justified price-to-earnings ratio (P/E), price-to-book ratio (P/B), and price-to-sales ratio (P/S) for a stock, based on forecasted fundamentals.

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