Derive justified leading and trailing P/Es from the Gordon growth model and explain what they mean
The idea
Dividing the constant-growth model by earnings gives the justified P/E. On forward earnings, the leading multiple is P/E = P0 ÷ E1 = (D1 ÷ E1) ÷ (r − g), the payout ratio divided by r minus g. On current earnings the trailing multiple is higher by exactly 1 + g, because E0 is smaller than E1: P/E = P0 ÷ E0 = payout × (1 + g) ÷ (r − g). A higher payout, a lower required return or higher growth each raises the justified multiple, but payout and growth are linked because growth is funded by retained earnings, so raising the payout lowers growth unless return on equity changes. The usual error is leaving out the 1 + g factor when computing the trailing P/E.
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