The H-Model for Two-Stage Growth

A basic two-stage dividend discount model assumes a company grows fast for a fixed number of years, then abruptly drops to a stable, mature growth rate the year after. Real companies rarely transition that cleanly — growth tends to fade gradually as a business matures, not overnight. The H-model captures that gradual fade with a single closed-form formula, avoiding the need to forecast every intermediate year's dividend by hand.

The formula is:

$$P_0 = \frac{D_0 \times (1 + g_L)}{r - g_L} + \frac{D_0 \times H \times (g_S - g_L)}{r - g_L}$$

In words: the first term is an ordinary Gordon growth value using the stable long-run rate $g_L$; the second term adds a premium for the extra growth $g_S - g_L$ the company enjoys today, tapered down over the half-life of the transition, $H$ (half the number of years the decline takes).

Worked example. A company just paid a $2.00 dividend ($D_0$), currently growing at 20% ($g_S$), fading in a straight line to a stable 5% ($g_L$) over 10 years, so $H = 5$. The discount rate $r$ is 12%. Stable-growth term: 2.00 \times 1.05 / (0.12 - 0.05) = \30.00$. Extra-growth term:$2.00 \times 5 \times (0.20 - 0.05) / (0.12 - 0.05) = $21.43$. Total value:$$30.00 + $21.43 = $51.43$ per share.

The H-model is a convenience, not a law of nature — it forces the growth decline to be linear, which is only ever an approximation of how a real company's growth actually fades.