The Gordon growth model
A share is worth the present value of its growing dividends: P₀ = D₁ / (r − g), with D₁ = D₀(1 + g). Value rises with growth g and falls with the required return r. The denominator is the gap r − g, so as g approaches r the price explodes, and for g ≥ r the model breaks down.
Intrinsic value P₀$41.60
Next dividend D₁ = D₀(1 + g) $2.08Denominator r − g +5.0%
Current dividend D₀$2.00
Growth rate g4.0%
Required return r9.0%
The share is worth $41.60: next year's dividend $2.08 divided by the gap 5.0%. As g rises toward r the gap shrinks and the value climbs steeply.
Try this
Push g toward r and watch P₀ run off the chart. A declining firm (g < 0) still has a finite value: the gap r − g simply widens.
Reflect: a one-point change in g or r can swing P₀ by tens of percent when the two are close. Is that sensitivity a flaw in the model, or an honest signal that the value of a perpetual-growth stock genuinely is fragile to its assumptions?