# Calculating and Interpreting a Predicted P/E

A predicted P/E is estimated from the cross-sectional regressions of P/E on the fundamentals that are considered to determine investment value, e.g., the growth rate of earnings and payout ratio.

### Example: Calculating a Predicted P/E

Consider a firm with a beta of 0.8, a dividend payout ratio of 0.40, and an earnings growth rate of 0.09. The estimated regression for a group of stocks in the same industry is:

$$\text{Predicted P/E} = 11.12 + (2.15\times\text{DPR}) – (0.15\times\text{Beta}) + (12.43\times\text{EGR})$$

Where DPR is the dividend payout ratio, and EGR is the five-year earnings growth rate.

Based on this cross-sectional regression, the company’s predicted P/E is 12.979.

\begin{align*} \text{Predicted P⁄E} & =11.12+(2.15 \times 0.40)-(0.15 \times 0.8)+(12.43 \times 0.09) \\ & = 12.979 \end{align*}

If the stock’s actual trailing P/E is 17, the stock is overvalued as it is selling at a higher multiple than is justified P/E by its fundamentals.

The predicted P/E has three limitations:

1. It summarizes valuation relationships only for the specific stock over a particular period. The relationship may have poor predictive quality when applied to other stocks or outside the sample period.
2. The relationship between company fundamentals and P/E changes over time, diminishing the model’s predictive power.
3. Such regressions tend to suffer from multicollinearity making it difficult to interpret individual regression coefficients.

## Question

A company has a beta of 0.6, a dividend payout ratio of 0.30, and an earnings growth rate of 0.07. The predicted P/E is closest to:

1. 12.62.
2. 14.50.
3. 16.32.

#### Solution

\begin{align*}\text{Predicted P/E}& = 11.12 + (2.15\times\text{DPR}) – (0.15\times\text{Beta}) \\ & + (12.43\times\text{EGR})\\&= 11.12 + (2.15 \times 0.30)– (0.15 \times 0.6)+ (12.43 \times 0.07)\\&=12.62\end{align*}

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

LOS 25 (i) Calculate and interpret a predicted P/E, given a cross-sectional regression on fundamentals, and explain limitations to the cross-sectional regression methodology.

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