The Gordon Growth Model Implies a Constant Dividend Yield

Summary

The document corrects the claim that dividend yield must converge to zero when a stock earns its required return. Under the constant-growth dividend discount model, dividends grow perpetually at a fixed rate below the required return. The stock price at any point is the next dividend divided by the difference between the required return and the growth rate. Dividing the dividend by that price gives a constant yield equal to that difference.

The explanation also notes the model’s convergence condition: if perpetual dividend growth is at least as large as the discount rate, the infinite valuation sum does not converge and the model is not usable as stated. This is a simplified model that assumes constant growth and discounting indefinitely. The excerpt provides an algebraic derivation, not empirical evidence, and its conclusion applies within those assumptions rather than to all dividend-paying stocks.

Key ideas

• The constant-growth dividend discount model values a stock as the next dividend divided by the required return minus dividend growth.
• Within the model, dividend yield remains constant at the required return less the growth rate.
• The infinite dividend valuation requires growth to remain below the discount rate.
• The result depends on perpetual constant-growth and constant-discount-rate assumptions.

Tags

# Why do dividend yields converge to zero?


# Why do dividend yields converge to zero?












According to the dividend discount model, a stock price is the discounted value of its dividends, where one assumes the dividends grow annually by some rate $g$ and are discounted at $r$, the required return on the stock, where $g < r$.

However this implies that if the stock delivers its required return, the dividend yield (the ratio of dividend to price) converges to zero.

That makes no sense tho?

## Answer by Attack68 (score 3)

https://quant.stackexchange.com/a/79253

No, that is not true.

The dividend discount model is a model (a fairly crude model) for the price of a stock. It suggests that a dividend grows at a constant rate for perpetuity and that that cashflow is discounted by some constant rate of interest for perpetuity.

$$ P = \sum_{i=1}^\infty D_0 \frac{(1+g)^i}{(1+r)^i} $$

Using the regular trick for the geometric sum of a series, this is equivalent to,

$$ P = D_0 \frac{1+g}{r-g} = \frac{D_1}{r-g} $$

It is quite clear that if $g>r$ this sum does not converge and hence the model is useless.

At any future point one could say that the value of the price under this model was,

$$ P_t = \frac{D_t}{r-g} $$

and the dividend yield (dividend divided by price) is an assumed constant under this model,

$$ \frac{D_t}{P_t} = (r-g) $$

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.