A distinction has to be made between the fundamental (or intrinsic) P/E and the way we actually compute P/Es. The fundamental or intrinsic P/E examines earnings forecasts. That is what was done in the analogy above. In reality, we actually compute P/Es 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.
On the other hand, merely because a stock is trading at a low fundamental P/E is not an indicator that the stock is undervalued. A stock may be trading at a low P/E because the investors are less optimistic about the future earnings from the stock. Thus, one way to get a fair comparison between stocks is to use their primary P/E. This primary P/E is based on the earnings projections made for the next years to which a discount calculation is applied.