CFA Program Level I

Gordon growth model and two-stage DDM: CFA Level I

The Gordon growth model values a share as next year's dividend divided by the required return minus the constant growth rate, V0 = D1 / (r - g), with r above g. Rearranged, the dividend yield equals r - g. A two-stage model discounts the high-growth dividends and a Gordon terminal value back to today.

The constant-growth model

If dividends grow at a constant rate g forever, V0 = D0 x (1 + g) / (r - g) = D1 / (r - g), where r must exceed g.

Example: the dividend just paid is USD2.00, g is 4% and r is 9%. D1 = 2.00 x 1.04 = USD2.08. V0 = 2.08 / (0.09 - 0.04) = USD41.60.

The model suits companies whose dividends grow at a stable rate comparable to or below the economy's nominal growth rate, and broad equity indexes. Its values are very sensitive to r and g.

Yield plus growth

Rearranged, D1 / V0 = r - g, and if price equals value, r = D1 / P0 + g. In the example, 2.08 / 41.60 = 5.0% = 9% - 4%.

With the same required return, a lower dividend yield means faster expected growth. Two shares priced at r = 8%, one yielding 2.5% and one 5.0%, imply growth of 5.5% and 3.0%.

The model can be turned round to find the growth rate implied by a price. If only the dividend just paid is known, D1 = D0 x (1 + g), so g appears on both sides and must be solved for.

Two-stage DDM, worked

Value = present value of the high-growth dividends + present value of a terminal value at the end of the high-growth period. The terminal value uses the Gordon model with the first dividend of the stable period.

Example: D0 = USD1.00, growth 10% for two years then 3% forever, r = 8%. D1 = 1.10, D2 = 1.21, D3 = 1.21 x 1.03 = 1.2463.

Terminal value at the end of year 2 = 1.2463 / (0.08 - 0.03) = USD24.926. V0 = 1.10 / 1.08 + (1.21 + 24.926) / 1.08^2 = 1.019 + 22.407 = USD23.43.

Where the exam catches people

Believing the Gordon model uses the dividend just paid in the numerator: it uses D1, next period's dividend.
Believing a high dividend yield means a higher expected return when r is the same: it means slower expected growth.
Believing the terminal value is already a present value: the Gordon formula gives a value one period before the dividend used, which must still be discounted to today.
Believing the model works when g is at or above r: it requires r greater than g.

Written from CFA Institute's documentation

Try 3 questions on this

Pick an answer to see why each option is right or wrong.

An analyst values Halvern Utilities with the constant-growth (Gordon) dividend discount model, using a required return on equity of 8.5% and dividend growth of 3.5% a year in perpetuity. If Halvern's shares trade at the model's value, the dividend-price ratio is closest to:
Right. In the game that’s Renown for your Equities building.
Not that one: A is right. In the game your Equities building would lose a little Renown, and this question would come back later.
The answerA.5.0%In the constant-growth model V = D/(r - g), so the dividend-price ratio is D/V = r - g. Here D/V = 8.5% - 3.5% = 5.0%. The rest of the 8.5% required return is expected to come from 3.5% a year of dividend growth.Your answerB.8.5%8.5% is the required return itself. In the Gordon model only part of that return comes from the dividend: D/V = r - g = 8.5% - 3.5% = 5.0%, and growth supplies the other 3.5%.Your answerC.12.0%12.0% comes from 8.5% + 3.5%, adding growth to the required return. The model rearranges to D/V = r - g, so growth is subtracted: 8.5% - 3.5% = 5.0%.
Written from www.federalreserve.gov/pubs/feds/2000/200005/200005pap.pdf
Larkspur Robotics has just paid an annual dividend of USD1.50 per share. An analyst expects the dividend to grow 12% next year and 4% a year thereafter in perpetuity, and uses a required return on equity of 10%. Using a two-stage dividend discount model with the terminal value set at the end of Year 1, Larkspur's intrinsic value per share is closest to:
Right. In the game that’s Renown for your Equities building.
Not that one: A is right. In the game your Equities building would lose a little Renown, and this question would come back later.
The answerA.USD28.00Two-stage DDM: value = PV of the high-growth dividends + PV of the terminal value as of the end of the high-growth phase, the terminal value found with the Gordon growth model.Your answerB.USD30.0430.04 grows the Year 2 dividend at the 12% high-growth rate (1.68 x 1.12 = 1.8816). High growth lasts only for next year; from Year 2 on, dividends grow 4%, so D2 = 1.68 x 1.04 = 1.7472, the terminal value is 29.12 and the value is (1.68 + 29.12) / 1.10 = 28.00.Your answerC.USD30.6530.65 adds the terminal value of 29.12 at face value. The terminal value is a value at the end of Year 1, so it must be discounted to today along with the Year 1 dividend: (1.68 + 29.12) / 1.10 = 28.00.
Show the full explanation and doc quotes
D1 = 1.50 x 1.12 = 1.68. D2 = 1.68 x 1.04 = 1.7472. Terminal value at end of Year 1 = D2 / (r - g) = 1.7472 / (0.10 - 0.04) = 29.12. Value = (1.68 + 29.12) / 1.10 = 30.80 / 1.10 = USD28.00.
Written from www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/equity-valuation-concepts-basic-tools
Two utilities, Ashcombe and Brennock, are judged equally risky, so an analyst applies the same required return on equity to both. Each share trades at its constant-growth dividend discount model value. Ashcombe's dividend yield is 2.5% and Brennock's is 5.0%. Which statement is most accurate?
Right. In the game that’s Renown for your Equities building.
Not that one: B is right. In the game your Equities building would lose a little Renown, and this question would come back later.
Your answerA.The higher-yielding share offers the higher expected returnThe dividend yield is only part of the return. Priced at model value, each share is expected to earn its required return, which is the same for both: Ashcombe's lower yield is made up by faster growth.The answerB.The lower-yielding share has faster expected dividend growthIn the constant-growth model the dividend-price ratio equals the required return minus dividend growth, D/V = r - g, so g = r - D/V.Your answerC.The higher-yielding share has faster expected dividend growthThe dividend-price ratio falls as dividend growth rises. With the same required return, Brennock's higher yield means slower expected growth, by 2.5 percentage points.
Show the full explanation and doc quotes
With the same r for both, Ashcombe's lower yield means its expected dividend growth is 2.5 percentage points higher than Brennock's.
Written from www.federalreserve.gov/pubs/feds/2000/200005/200005pap.pdf