NISM-Series-XV: Research Analyst · Valuation Principles

Dividend Discount Models: Gordon Growth and Multi-Stage Valuation

Updated 11 October 2026 · Fact-checked

The dividend discount model (DDM) values a share as the present value of all expected future dividends. The Gordon growth model assumes dividends grow at a constant rate forever: P₀ = D₁ ÷ (r − g). Multi-stage models use different growth rates for different periods, then add a terminal value.

Understand Dividend Discount Models

A share gives its owner a stream of dividends. The dividend discount model says the value of the share today is what that stream is worth today. You discount each expected dividend at the investor's required return on equity, called the cost of equity (r), and add them up.

Forecasting dividends forever is impractical. So the Gordon growth model (constant growth model) assumes dividends grow at one steady rate g for ever. The infinite sum then collapses into a simple formula: P₀ = D₁ ÷ (r − g). Note that D₁ is the dividend expected at the end of next year, not the dividend just paid.

The model only works if r is greater than g. If g is equal to or above r, the formula gives a meaningless (infinite or negative) value. It also works best for mature, stable companies that pay regular dividends and grow steadily, such as a utility-like business.

For companies growing fast now but expected to slow down, you use a multi-stage model. In a two-stage model, dividends grow at a high rate g₁ for n years, then at a stable rate g₂ for ever. You discount the dividends of the high-growth years one by one. At the end of year n, you compute a terminal value using the Gordon formula, and discount that too.

Limitations: the value is very sensitive to r and g, especially when r − g is small. The model is hard to use for companies that pay no dividends or pay irregular ones. Dividends may also not reflect a firm's earning power, since payout is a management choice.

Key formulas to remember

Gordon growth model: P₀ = D₁ ÷ (r − g); Valid only when r > g and growth is constant forever. D₁ is next year's dividend.
Next dividend from last dividend: D₁ = D₀ × (1 + g); If the question gives the dividend just paid (D₀), grow it by one year first.
General DDM: P₀ = Σ Dₜ ÷ (1 + r)ᵗ, for t = 1 to ∞; Value is the present value of all expected dividends.
Terminal value at end of year n: Pₙ = Dₙ₊₁ ÷ (r − g₂); Used in multi-stage models. Dₙ₊₁ = Dₙ × (1 + g₂). Discount Pₙ back by (1 + r)ⁿ.
Two-stage model value: P₀ = Σ Dₜ ÷ (1 + r)ᵗ (t = 1 to n) + Pₙ ÷ (1 + r)ⁿ; High-growth dividends plus discounted terminal value.
Implied growth or return: r = D₁ ÷ P₀ + g; Rearranged Gordon model: expected dividend yield plus growth.
Sustainable growth rate: g = ROE × retention ratio; Retention ratio = 1 − dividend payout ratio. Used to estimate g.

How to solve Dividend Discount Models questions

Use this order for any dividend discount model question.

1Identify what is given: D₀ or D₁, required return r, growth rate g, and what is asked (price, r or g).
2Check whether the dividend given is the one just paid (D₀) or the next one (D₁). If D₀, compute D₁ = D₀ × (1 + g).
3Check that growth is constant forever. If growth changes after some years, it is a multi-stage question.
4Convert all rates to decimals and confirm r > g.
5For Gordon: apply P₀ = D₁ ÷ (r − g). For rearranged questions, solve for r or g.
6For two-stage: compute each high-growth dividend, discount it, then compute the terminal value at the end of the high-growth period and discount it.
7Add the present values and match the result to the nearest option, checking units in rupees.

Quickest way: Gordon model in three moves

When to use it: Use for single-stage questions with a constant growth rate and four close-looking options.

Circle the dividend and ask: paid already or expected? Multiply by (1 + g) if already paid.
Subtract g from r in your head or on the screen.
Divide D₁ by (r − g). Check the answer is sensible: a small r − g gives a large price.

Common mistakes in Dividend Discount Models

Using D₀ directly in the Gordon formula.
The question gives 'dividend just paid' and the student plugs it in without thinking.
Fix: Read the wording. Just paid or last year's dividend means D₀, so multiply by (1 + g). Expected next year means D₁.
Applying the Gordon formula when g is greater than or equal to r.
Students apply the formula mechanically and ignore its condition.
Fix: Always check r > g first. If not, the constant growth model cannot be used.
Forgetting to discount the terminal value in a two-stage model.
The terminal value looks like the final answer after the Gordon step.
Fix: Pₙ is a value at year n. Divide it by (1 + r)ⁿ before adding to the other present values.
Using the wrong dividend for the terminal value.
Students use Dₙ instead of Dₙ₊₁ in the Gordon formula.
Fix: Terminal value at year n uses Dₙ × (1 + g₂), the first dividend of the stable stage.
Mixing percentages and decimals.
Typing 12 instead of 0.12 in the formula.
Fix: Convert every rate to a decimal before calculating.

Worked examples

Example 1

A company has just paid a dividend of ₹10 per share. Dividends are expected to grow at 5% a year for ever. The required return on equity is 15%. What is the value of the share using the Gordon growth model?

Show the solution

D₀ = ₹10, g = 5% = 0.05, r = 15% = 0.15.
Since D₀ is the dividend just paid, D₁ = 10 × 1.05 = ₹10.50.
r − g = 0.15 − 0.05 = 0.10.
P₀ = 10.50 ÷ 0.10 = ₹105.

Answer: ₹105

Example 2

A share will pay a dividend of ₹5 next year (D₁). Dividends will grow at 10% for the following year only, then grow at 4% for ever. The required return is 14%. Find the value of the share today, to the nearest rupee.

Show the solution

D₁ = ₹5. D₂ = 5 × 1.10 = ₹5.50. Stable growth g₂ = 4% starts after year 2.
D₃ = 5.50 × 1.04 = ₹5.72.
Terminal value at end of year 2: P₂ = 5.72 ÷ (0.14 − 0.04) = 5.72 ÷ 0.10 = ₹57.20.
PV of D₁ = 5 ÷ 1.14 = ₹4.386.
PV of D₂ = 5.50 ÷ 1.2996 = ₹4.232.
PV of P₂ = 57.20 ÷ 1.2996 = ₹44.014.
P₀ = 4.386 + 4.232 + 44.014 = ₹52.63, about ₹53.

Answer: About ₹53

Exam tips

Always check whether the question gives D₀ or D₁. This is the most common trap option source.
Expect conceptual questions too: assumptions (constant growth, r > g), suitability (mature, dividend-paying firms) and limitations (sensitivity to r and g).
In multi-stage questions, remember the terminal value is a year-n value that must be discounted back.
Use the relation r = D₁ ÷ P₀ + g for questions that ask for expected return or growth.
With negative marking, skip a long multi-stage calculation only if you cannot finish it reliably; a wrong guess costs marks.

Practice questions from Valuation Principles

Dividend Discount Models in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Dividend Discount Models: frequently asked questions

What is the dividend discount model formula?

The general form is P₀ = Σ Dₜ ÷ (1 + r)ᵗ. The constant growth (Gordon) version is P₀ = D₁ ÷ (r − g). It needs r to be greater than g.

When should I use a two-stage dividend discount model?

Use it when a company is expected to grow dividends at a high rate for a limited period and then settle at a stable rate. The Gordon model alone cannot handle two different growth rates.

Can the DDM be used for companies that do not pay dividends?

It is hard to use, because there are no dividends to discount. Analysts then prefer other approaches such as free cash flow or relative valuation.

Why is the Gordon model so sensitive to its inputs?

The price depends on r − g in the denominator. When r and g are close, a small change in either causes a large change in value.