# Price to Earnings Ratio

P/E ratio (i.e. price to earnings ratio) is the ratio of a company’s current stock price to its earnings per share. By comparing P/E ratios, we can identify undervalued and overvalued stocks. There are two variants: (a) trailing P/E ratio, which is calculated by dividing current stock price by last year EPS and (a) forward P/E ratio, which is calculated by dividing the current stock price with expected next year EPS.

Price to earnings ratio tells us the dollars that must be invested in a company to earn one dollar each year. It measures how costly a stock is with reference to its ability to earn income. P/E ratio is compared across time and cross sectionally i.e. between different companies. When the P/E ratio is higher than competitors, there is a possibility that the stock might be overvalued and vice versa.

## Trailing P/E ratio

Trailing P/E ratio is calculated by dividing the current stock price of a company by the last year earnings per share (EPS). It is the most common definition of price-to-earnings ratio. When we say just the P/E ratio, we mean the trailing P/E ratio.

$$ Trailing\ P/E\ Ratio=\frac{P_0}{{\rm EPS}_0} $$

Where P_{0} is the current stock price and EPS_{0} is the last year annual earnings per share.

## Forward P/E ratio

Forward P/E ratio is the price-to-earnings ratio variant which is calculated by dividing the current stock price by the earnings per share expected in the next 12 months.

Many investors and analysts prefer the forward P/E ratio because they believe that historical performance is not a very good indicator of future performance and that a undervaluation or overvaluation of a stock should be determined by comparing its current price with earnings expected in future.

$$ Forward\ P/E\ Ratio=\frac{P_0}{{\rm EPS}_1} $$

Where EPS_{1} is the earning per share expected in the next 12 months.

## Justified P/E ratio

A justified P/E ratio is the price to earnings ratio which is justified by the company’s underlying fundamentals, i.e. growth rate and cost of equity, etc.

Justified P/E ratio can be determined by linking the P/E ratio with the Gordon growth model. Gordon growth model (GGM) is a single stage dividend discount model which determines a stock’s current stock as equal to the present value of a perpetuity comprising of the stock’s dividends. GGM equation is as follows:

$$ P_0=\frac{D_1}{r-g} $$

Where P0 is the current stock price, D1 is the dividend per share next year, r is the cost of equity and g is the growth rate.

Dividing both sides by E_{1}, the earning per share expected next year, the left hand of the above equation equals the forward P/E ratio and the numerator of the right-hand side equals the dividend payout ratio (DPR):

$$ \frac{P_0}{E_1}=\frac{\frac{D_1}{E_1}}{r-g}=\frac{DPR}{r-g} $$

The above equation can be used to find out the P/E ratio indirectly based on the company’s dividend payout ratio, cost of equity and dividend growth rate. This P/E ratio is called the fundamental P/E ratio or justified P/E ratio.

## Example

Let’s calculate the trailing P/E ratio and forward P/E ratio for Intel Corporation and compare it with its justified P/E ratio to see if the stock is overvalued or undervalued:

- Current stock price is $54.51
- Trailing twelve-month (TTM) earnings per share (EPS) is $1.99
- EPS expected in next 12 months is $2.15
- Dividend payout ratio is 48%, cost of equity is 9.5%% and growth rate is 7.6%

The trailing P/E ratio equals current stock price of $54.51 divided by last year EPS of $1.99. It works out to 27.31 (=$54.51/$1.99).

The forward P/E ratio (also called leading P/E ratio) equals P_{0} of $54.51 divided by next-year EPS (EPS_{1}) of $2.15; it works out to 25.35 (=$54.51/$2.15)

The justified P/E ratio can be calculated as follows:

$$ \frac{P_0}{E_1}=\frac{DPR}{r-g}=\frac{48\%}{9.5\%-7.6\%}=25 $$

Since the justified P/E ratio is close to the current forward P/E ratio, the stock seems to be fairly priced.