Set out what the Gordon growth model takes for granted and how sensitive its output is to inputs

CFA® Level I · Equities · Discounted Cash Flow (DCF) and Growth Models · EQ.1.b

The idea

The constant growth model assumes dividends grow forever at a single rate strictly below the required return, and that the required return itself is stable. Both assumptions are strong: no company grows faster than the economy in perpetuity, and a growth rate set even slightly too close to the required return sends the denominator toward zero and the value toward infinity. The growth input has a natural starting point in the sustainable growth rate, g = b × ROE, where b is the retention ratio (the share of earnings kept) and ROE is the return on equity: a firm earning 15% on equity that keeps 60% of its profit can fund growth of 9% from its own earnings, a pace it can finance but not necessarily hold for ever. Sensitivity is therefore extreme precisely where the inputs are least certain, which is why the model is used for stable mature payers and why a sensitivity table matters more than a point estimate.

Formulas

Gordon growth model

V₀ = D₁ ÷ (r − g)

D₁: next year's dividend, not the one just paid
r: the required return on the equity
g: the constant growth rate of the dividend, for ever

Dividends growing at one rate for ever, with g below r. As g approaches r the denominator approaches zero and the value explodes, which is why a mature, stable payer is the only company this suits.

Sustainable growth rate

g = b × ROE

b: the retention rate, the share of earnings not paid out
ROE: return on equity

The growth a company can fund from its own earnings without raising new equity or changing its leverage. It is where the g in a growth model comes from when nobody hands you one.

A practice question

From the question bank, with the reason each wrong option is wrong.

What does the constant growth model assume about the required return?

That it is stable over time - correct
That it rises with the dividendWhy not: Nothing in the model links them. The required return reflects risk, not the size of the payout.
That it equals the growth rateWhy not: That would make the denominator zero. It must exceed the growth rate.

The constant growth model (Gordon growth model) values a share using dividends that grow at a steady rate forever. Formula: Value = Next year's dividend / (r - g), where r is the required return and g is the growth rate. It uses one value of r for ever, so it assumes the required return is stable. It also needs r to be greater than g, otherwise the bottom of the fraction is zero or negative and the formula fails. The required return reflects risk, not the size of the dividend.

A harder one

Arjun Rao, an analyst at a pension fund, wants to value one company from a shortlist using the Gordon growth model. Wexford Water is a regulated utility that has raised its dividend by about 3% a year for four decades. Orbit Software began paying dividends two years ago and expects them to grow 35% a year for a decade. Pinnacle Biotech pays no dividend and expects its first profit in eight years. For which company is the model most appropriate?

Wexford Water, the long-standing regulated utility - correct
Orbit Software, the fast-growing recent payerWhy not: A growth rate of 35% cannot continue forever and would exceed any plausible required return. The model needs one stable growth rate below the required return, so Orbit needs a multi-stage model.
Pinnacle Biotech, the company paying no dividendWhy not: With no dividend there is no stream of cash flows for the model to discount, so it cannot produce a meaningful value for Pinnacle.

The Gordon growth model values a share as: Value = Next dividend / (r - g). It assumes dividends grow at one steady rate for ever, and that this rate is below the required return r. Wexford, a utility with 40 years of steady 3% growth, fits best. Orbit's 35% growth cannot last for ever, so it needs a model with several stages. Pinnacle pays no dividend, so there is nothing to discount. Because the answer is very sensitive to the gap r - g, the model should be kept for stable, mature dividend payers.

The hardest tier

Rosa Delgado, an analyst, values Stanton Consumer Products, which has just paid an annual dividend of $2.00 per share. She assumes the required return is 10% and dividend growth is 5% a year forever. After a review, she raises the growth assumption to 7% a year, leaving the required return unchanged. By what percentage does the Gordon growth value of the share rise as a result of this single revision?

Up 40.0%Why not: The percentage fall in the gap between the required return and growth (from 5% to 3%) has been reported as the rise in value. Value is proportional to 1 divided by that gap, so it rises by much more than the gap falls.
Up 66.7%Why not: The next dividend was left at the old figure of $2.10. The higher growth rate also lifts D1 to 2.00 x 1.07 = $2.14, so the true increase is slightly larger.
Up 69.8% - correct

The $2.00 has just been paid, so each time grow it one year first. Formulas: D1 = D0 x (1 + g), Value = D1 / (r - g). Old value: D1 = 2.00 x 1.05 = $2.10, so value = 2.10 / (0.10 - 0.05) = $42.00. New value: D1 = 2.00 x 1.07 = $2.14, so value = 2.14 / (0.10 - 0.07) = $71.33. Change = 71.33 / 42.00 - 1 = +69.8%. The gap on the bottom shrank from 5% to 3%, so a small change in one input moved value a lot. Keeping D1 at $2.10 gives $70.00, a 66.7% rise.

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