The Gordon growth model: D₀ versus D₁

◈ 10 cards

Next year’s dividend over (r − g) — and the paper’s favourite trap: a “just paid” dividend is D₀ and must be grown one year first. Both answers shown.

The growing perpetuity, renamed

Module 7's growing perpetuity — a payment that rises at a constant rate $g$ forever, discounted at $r$ — is worth the first payment over the spread:

$P_{0} = \frac{D _{1}}{r - g}$

Applied to a common share whose dividend grows steadily, this is the Gordon growth model (the constant-growth dividend discount model). Everything turns on which dividend goes in the numerator: $D_{1}$ , the dividend one year from now — not the one just paid.

Worked example — Tamarack Foods

Tamarack just paid a dividend of $1.80 * * ($ D_0$). Dividends grow at 4 % a year; the market requires 9 %. Next year's dividend is =1.80*(1+0.04) = 1.872**, and:

=1.80*(1+0.04)/(0.09-0.04) = 1.872 ÷ 0.05 = $37.44

The trap. Plug the dividend that was just paid: =1.80/(0.09-0.04) = $36.00. It is wrong by exactly the factor $(1+g)$ — 37.44 ÷ 36.00 = 1.04 — because a dividend already paid belongs to the seller and is not in the stream the buyer receives. The paper offers 36.00 as an option every time; so does this lesson.

When the stem gives $D_{1}$ . Ossington Brewing's dividend next year is expected to be $2.10 * *, g r o w in g 3$ 38.18. No growing-up — the stem handed you $D_{1}$ . Read the words: just paid, last year's, current, most recent → $D_{0}$ , multiply by $(1 + g)$ ; next year's, expected, will pay, forecast → $D_{1}$ , use as is.

Conditions

$g < r$ . If growth matched or exceeded the required return the denominator would be zero or negative and the price infinite — the model says nothing. Growth must be sustainable forever, which rules out a start-up's 30 %.
A dividend must exist. A firm that pays nothing has no $D_{1}$ ; its shares are valued another way (earnings multiples, Lesson 11.6, or a two-stage model that starts paying later, Lesson 11.5).
Annual only in this course: one dividend a year, one growth step, one discount.

Sensitivity

Raise Tamarack's growth to 5 %: =1.80*1.05/(0.09-0.05) = $47.25 — one point of growth adds 26 % to the price, because both the numerator rises and the spread narrows. The model is exquisitely sensitive to $r - g$; an exam that changes $g$ by a point is testing whether you recompute both.

Recompute

A share that just paid $2.40 * *, g = 3$ 49.44. Wrong answer waiting: 2.40 ÷ 0.05 = 48.00. Cold: just paid means D₀ — grow it first.

The stream the buyer receives starts at t = 1. D₀ = 1.80 has already been paid to the seller; the model’s numerator is D₁ = 1.872, and the price is 1.872 ÷ (0.09 − 0.04) = 37.44.