Stock X has r=12%, g=8%, D₁=$2, giving a Gordon Growth Model price of $50. Analysts revise g upward from 8% to 10%. The new model price is:
A$100 — the denominator halved from 4% to 2%, doubling the price
B$60 — the price increases by the same percentage as the growth rate increase
C$50 — growth revisions affect future dividends but not the current model price
D$25 — higher growth increases risk, which raises r and lowers the price
P = D₁ / (r - g) = $2 / (0.12 - 0.10) = $2 / 0.02 = $100. The denominator fell from 0.04 to 0.02 — halved — so the price doubled. This illustrates the extreme sensitivity of the Gordon model to growth assumptions. A 2 percentage point change in g produced a 100% change in price. This is why growth stocks are so volatile: investors react sharply to any revision in long-run growth expectations.
Question 2 Multiple Choice
A company has r=8% and g=9%. Applying the Gordon Growth Model gives P = D₁/(0.08-0.09) = -D₁/0.01, a negative price. The correct interpretation is:
AThe stock has negative value — investors should demand payment to hold it
BThe model is inapplicable because g must be strictly less than r for the perpetuity formula to converge
CThe formula requires absolute values; the correct price is D₁/0.01
DThe negative sign indicates the stock is overvalued relative to intrinsic value
The Gordon Growth Model is derived from a geometric series that only converges when g < r. When g ≥ r, the sum of discounted future dividends is infinite (or undefined), reflecting the economically impossible claim that the firm grows faster than the required return forever. No firm can sustain g ≥ r indefinitely — it would eventually exceed the size of the entire economy. The model's constraint g < r is not a mathematical quirk but an economic requirement.
Question 3 True / False
In the Gordon Growth Model, a firm with a higher sustainable growth rate will typically command a higher stock price, most else equal.
TTrue
FFalse
Answer: False
This is true only when g < r and D₁ is held constant — but D₁ is not independent of g. Higher growth requires more reinvestment, which means a lower payout ratio and thus a lower current dividend D₁. The two effects partially offset: higher g raises the price through the denominator but lowers it through D₁. Additionally, if g rises toward r, the denominator approaches zero and the price formula breaks down. The full relationship requires the sustainable growth rate identity (g = ROE × retention) to assess the net effect.
Question 4 True / False
The Gordon Growth Model can value any publicly traded stock, provided you use accurate near-term dividend forecasts for the next few years.
TTrue
FFalse
Answer: False
The Gordon Growth Model requires a single constant perpetual growth rate — it assumes dividends grow at rate g forever from the very next period. It cannot accommodate a high near-term growth phase followed by slower long-run growth. For companies with variable growth (most real companies), two-stage or multi-stage models are required: explicitly forecast dividends for the high-growth period, then apply the Gordon model as a terminal value at the point where growth stabilizes. Using Gordon for fast-growing companies produces wildly optimistic valuations.
Question 5 Short Answer
Why must the growth rate g be strictly less than the required return r in the Gordon Growth Model? What does violating this constraint mean economically?
Think about your answer, then reveal below.
Model answer: The model is derived from an infinite geometric series with ratio (1+g)/(1+r). This series only converges when the ratio is less than 1, i.e., when g < r. Economically, g > r would mean the firm's dividends grow faster than investors' required return forever — implying the firm eventually becomes infinitely large relative to the economy, which is impossible. No firm can sustainably grow faster than the overall economy indefinitely, so any assumed g must eventually be bounded below nominal GDP growth.
The constraint is both mathematical (series convergence) and economic (no firm can grow faster than the economy forever). In practice, analysts use nominal GDP growth as a ceiling for terminal growth rates in two-stage models. Violations of the constraint often reveal that a near-term high-growth rate has been mistakenly applied as a perpetual rate — the most common misuse of the Gordon model.