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

CFA® Level I · Equity Investments · 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. 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 must be true of the growth rate in the constant growth dividend discount model?

It must equal the required returnWhy not: That makes the denominator zero and the value infinite.
It must be strictly less than the required return — correct
It must exceed the risk-free rateWhy not: No such requirement, and many stable firms grow more slowly than the risk-free rate. The constraint is against the *required return*.

If growth equalled or exceeded the required return the denominator would be zero or negative, and the geometric series would not converge to a finite value.

A harder one

A stock pays a dividend next year of 2.00, the required return is 9% and growth is 4%. What is the value, and what happens if growth is revised to 5%?

40.00, rising to 50.00 — correct
50.00, rising to 66.67Why not: Both figures are one step further than they should be: 2.00 ÷ 0.04 and 2.00 ÷ 0.03. The spreads here are 0.05 and 0.04.
22.22, rising to 25.00Why not: 2.00 ÷ 0.09 and 2.00 ÷ 0.08 — growth omitted from the denominator in both cases.

2.00 / 0.05 = 40.00; a one-point change in growth narrows the spread to 0.04 and gives 50.00. A single percentage point moved the value by a quarter.

The hardest tier

Why does a sensitivity table matter more here than a point estimate?

Because the model is not widely acceptedWhy not: It is widely used and taught. Its limitation is input sensitivity, not acceptance.
Because the output is extremely sensitive — correct
Because the dividend is unknownWhy not: The dividend is usually the *best* known of the three inputs, often announced in advance. It is r and g that are uncertain.

The inputs it is most sensitive to are themselves highly uncertain. Reporting one number conceals that a small revision to growth can change the answer by more than the analysis is worth.

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