OK so struggling to get my head around why a high price earnings ratio is preferable to a low P.E. . If there is a big gap between a company's share price and its earnings per share surely that would drive potential investors away?
The P/E ratio is a measure of historic (the previous financial year) earnings against the current share price.
If the P/E is high, this means that the market perceives a big increase in future earnings per share. In other words, the perception is that this is a fast growing company. Higher earnings may also equate to big increases in dividends and rapid expansion.
On the other hand, if the P/E is low, then there is a perception that either earnings per share are decreasing or that future growth in earnings is negligible. In other words, low P/E equates to a perception of low future growth and therefore low prospects for future payout increases - possibly even decreases.
The market is (rightly) usually willing to pay a premium for fast growing companies.
Your question asks us to explain why a false statement is true. From the point of view of an investor, a high price to earnings ratio is not necessarily desirable.
From the point of view of an investor, a desirable stock is one that is likely to provide future dividends or price increases that more than compensates for the risk of the stock. This information cannot be inferred from the P/E ratio.
So what does the P/E ratio tell us? The P/E ratio measures a stock's current price (i.e., the market's belief about its future earnings) divided by its recent past earnings. A high ratio means the market thinks earnings in the future will be higher than they are now and have therefore bid the price up. These can thought of as expensive stocks, and are often called "growth" stocks because their price is driven by the market's belief in future growth.
Some individual high P/E stocks do live up to or exceed the market's expectation, but there's no evidence that this happens enough that they are more desirable as a group than low P/E stocks. If anything, the empirical evidence goes the other way.