Gordon growth model: use D1, not D0 (52.50 vs 50.00)

Equity Investments·August 25, 2026·5 min read

A company just paid a dividend of 2.00, dividends are expected to grow at 5% forever, and the required return is 9%. A candidate who divides the 2.00 straight into 0.04 gets 50.00. The correct value is 52.50, because the Gordon growth model discounts next year's dividend, and next year's dividend is 2.10.

The subscript is the whole trap

Written out, the model is short enough that the error hides in one character.

V_0 = D_1 / (r − g), where D_1 = D_0 × (1 + g) and r > g

D_0 is the dividend that has already been paid. D_1 is the one the model actually values. Skipping the growth step does not produce a slightly different answer, it produces an answer that is wrong by exactly one factor of (1 + g), every time. At g = 5%, the D_0 version undervalues the stock by 4.76%. At g = 8% it undervalues it by 7.41%. The error scales with the growth rate, which is why it survives a sanity check: 50.00 next to 52.50 looks close enough to be a rounding difference, and it is not.

The r > g condition is not decoration either. If a question sets growth above the required return, the denominator turns negative and the model returns a negative value for a positive dividend stream. That is the signal to stop, not to take the absolute value.

Where the wording hides D_0 and D_1

Exam questions rarely label the dividend. They describe it, and the description carries the subscript.

"Just paid", "recently paid", and "last year's dividend" all give D_0. That figure needs to be grown once before it enters the numerator. "Will pay", "is expected to pay next year", and "the forecast dividend for the coming year" all give D_1 directly, and multiplying that by (1 + g) is the mirror-image mistake. Growing 2.10 a second time gives 2.205, which divides into 0.04 for 55.13. Both errors come from the same habit of reading the number and ignoring the tense.

The safest reading order is tense first, number second. Decide whether the sentence is describing a payment that has happened or one that is expected, then write D_0 or D_1 next to the figure before doing any arithmetic. Answer choices are usually built so that 50.00, 52.50, and 55.13 all appear, one for each reading.

Working the 2.00 dividend example

Take the numbers from the opening: D_0 = 2.00, g = 5%, r = 9%.

D_1 = 2.00 × 1.05 = 2.10

V_0 = 2.10 / (0.09 − 0.05) = 2.10 / 0.04 = 52.50

The check runs backwards through the same relationship. Dividend yield is 2.10 / 52.50 = 0.04, and 0.04 + 0.05 = 0.09, which returns the required return. That identity is worth carrying into the exam on its own:

r = D_1 / P_0 + g

Required return splits into a dividend yield and a growth rate, so the denominator r − g is the dividend yield the price implies. When a question supplies a market price and asks for the implied growth rate, this is the same equation rearranged, and D_1 is still the numerator.

The denominator also explains why these questions feel unstable. A single percentage point on g moves value more than most candidates expect. Raise g to 6% and the numerator becomes 2.12 while the denominator falls to 0.03, giving 70.67. That is 34.6% higher for a one-point change in an input nobody can observe.

The same subscript rule governs terminal value

In a multistage model the Gordon formula does the tail, and the subscripts shift by one again.

V_n = D_(n+1) / (r − g_L)

V_n is the value at the end of year n, and it uses the dividend of year n + 1. Two things go wrong here. Candidates pair D_n with V_n, repeating the original error one stage later, or they compute V_n correctly and then discount it back over n + 1 periods. V_n already sits at time n, so it comes back n periods, and the year n+1 dividend belongs inside it rather than beside it.

Where g itself comes from is a separate question with its own formula. Sustainable growth is the retention ratio times return on equity, g = b × ROE. A company retaining 40% of earnings at a 12.5% ROE supports 5% growth, which is where the 5% in this example could have originated. If a question gives payout ratio and ROE rather than g, that is the step it wants first.

Quick reference

Nothing in this model is computationally hard. One multiplication, one subtraction, one division. What makes it a reliable source of exam questions is that the inputs all look interchangeable on the page, and only the tense of a sentence separates the dividend that has been paid from the dividend being valued.

The same pattern shows up in money-weighted and time-weighted returns, where one set of cash flows supports two defensible answers and the question wording picks the one being asked for.

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