A single year's earnings-per-share can be misleadingly high or low — a one-time tax benefit, a legal settlement, a temporarily depressed margin during a downturn. Normalizing smooths that out.
Graham formula's approach. Intrinsic averages diluted EPS across the last 5 fiscal years (falling back to trailing-twelve-month EPS, flagged as lower confidence, when 5 years of history isn't available) rather than using the most recent year alone. A single volatile year — good or bad — carries less weight this way.
Forward P/E's approach. Instead of averaging past EPS directly, this method reconstructs a normalized EPS from the ground up: it takes the company's 5-year average operating margin (also smoothed) and applies it to a forward revenue estimate, after tax. This asks a different question than the historical average — "if this company earns its typical margin on next year's expected revenue, what would EPS be?" — which can differ meaningfully from a straight average of noisy historical EPS figures, especially for a business whose margins are improving or deteriorating over time.
Why this matters. Valuing a business off one unusually good (or bad) year is one of the most common ways investors mis-price a stock. Normalization is a deliberate hedge against that mistake.