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The price per share (numerator) is the market price of a single share of the stock. The Earnings per share (denominator) is the Net Income of the company for the most recent 12 month period, divided by number of shares outstanding.
The PE of a stock describes the price of a share relative to the earnings of the underlying asset. The lower the PE, the less you have to pay for the stock, relative to what you can expect to earn from it. The higher the PE the more over-valued the stock is.
For example, if a stock is trading at $24 and the Earnings per share for the most recent 12 month period is $3, then the PE ratio is 24/3=8. The stock is said to have a PE of 8 (or a multiple of 8). Put another way, you are paying $8 for every one dollar of earnings.
The main reason to calculate PEs is for investors to compare the value of stocks, one stock with another. If one stock has a PE twice that of another stock, it is probably a less attractive investment. But comparisons between industries, between countries, and between time periods are dangerous. To have faith in a comparison of PE ratios, you should be comparing comparable stocks.
An easy and perhaps intuitive way to understand the concept is with an analogy:
If a stock has a relatively high PE ratio, let's say, 100, what does this tell you? The answer that it depends. A few reasons a stock might have a high PE ratio are:
In practice, decisions must be made as to exactly how to specify the inputs used in the calculations. Does the current market price accurately value the organization? How is income to be calculated and for what periods? How do we calculate total capitalization? Can these values be trusted? What are the revenue and earnings growth prospects over the time frame one is investing in? Was there special one time charges which artificially lowered (or artificially raised) the earnings used in the calculation, and did those charges cause a drop in stock price or were they ignored? What kind of PE ratios is the market giving to similar companies, and also the PE ratio of the entire market?
A distinction has to be made between the fundamental (or intrinsic) PE and the way we actually compute PEs. The fundamental or intrinsic PE examines earnings forecasts. That is what was done in the analogy above. In reality, we actually computed PEs using the latest 12 month corporate earnings. Using past earnings introduces a temporal mismatch, but it is felt that having this mismatch is better than using future earnings, since future earnings estimates are notoriously inaccurate and susceptible to deliberate manipulation.