Fundamentally, the investor must decide how many years to look forward. A company is often valued at some-number-of-years times the current earnings.
But, for example, the company has $1 in earnings per-share and a 10% earnings growth and so include the 10% earnings growth by some means:
Valued at the current year's earnings along with four-year's forward earnings, the
valuation is $1.22 average-annual-earnings times 5 years or $6.1 . Then the P/E ratio
based on current earnings is 6.1 . Or the P/E ratio is 5 based on the expected average
annual earnings for the five-year period.
Valued at the current year's earnings along with nine-year's forward earnings, the
valuation is $1.59 average-annual-earnings times 10 years or $15.90. Then the P/E ratio
based on current earnings is 15.9 . Or the P/E ratio is 10 based on the expected average
annual earnings for the ten-year period.
Then calculate the 10 year period valuation with $1 in earnings per-share and 20% earnings growth and the valuation is $25.96. Then the P/E ratio is 25.96 as based on current earnings. Compare the P/E ratio increasing from 15.9 to 25.96 as the earnings growth increased from 10% to 20%. The P/E ratio did not double as the earnings growth doubled. (Eleven year's valuation of 20% earnings growth produces a P/E ratio of 32.12 but there is really no particular target that must be hit.)
Now if the earnings growth is known what is missing in this subject is the profit-margin which is not known. Then realize that an increase in profit-margin represents a higher price-to-sales ratio. One point here is that a high price-to-sales ratio does not necessarily represent an expensive stock. A higher profit-margin can produce the same amount of earnings with less revenue. But in this subject the profit-margin is fixed and the earnings growth is known which means that the revenue growth and the earnings growth are the same percentage.