CFA Level II Exam · Discounted Dividend Valuation

Multistage Dividend Discount Models Explained

Updated 7 October 2026 · Fact-checked

A multistage dividend discount model values a share as the present value of dividends over a high-growth period plus a terminal value, where growth settles to a stable rate. Forecast the dividends, find the terminal value with the Gordon growth model at the end of the supercharged phase, then discount everything at the required return.

Understand Multistage Dividend Discount Models

The Gordon growth model assumes dividends grow at one constant rate forever. Many firms do not behave that way. A young firm may grow fast for years, then slow down as it matures. A multistage model fits this by splitting the future into phases.

In a two-stage model, dividends grow at a high rate gS for n years, then at a stable rate gL forever. You value the dividends in stage one one by one, then add a terminal value at time n. The terminal value is the Gordon growth value of all dividends from year n+1 onward, so it sits at time n and must be discounted back n years.

A three-stage model adds a transition phase. Growth starts high, falls (often in a straight line) to the stable rate, then stays at the stable rate. It is more realistic but needs more steps. In an exam you usually build a short table of dividends year by year, then apply the terminal value at the end of the transition.

The H-model is a shortcut for growth that declines linearly from a high rate to a stable rate over a period. It gives an approximate value without a year-by-year table. The first part is the value with no extra growth; the second part adds the value of the above-normal growth, which is averaged over the decline.

The key discipline is timing. The terminal value uses the first dividend of the final stage, D(n+1), and it is valued at time n. Also, the required return r must be greater than the stable growth rate gL, or the Gordon step breaks down.

Key formulas to remember

Two-stage DDM: V0 = Σ [D0 × (1 + gS)^t ÷ (1 + r)^t] for t = 1 to n + [Vn ÷ (1 + r)^n]; gS is the short-term (high) growth rate. The sum covers the n years of stage one.
Terminal value (Gordon growth): Vn = D(n+1) ÷ (r − gL); D(n+1) = Dn × (1 + gL). Requires r > gL. Value is at time n, so discount it n years.
H-model: V0 ≈ [D0 × (1 + gL) ÷ (r − gL)] + [D0 × H × (gS − gL) ÷ (r − gL)]; H = half the length of the decline period in years. gS is the starting high growth rate, gL the long-run rate. This is an approximation.
Three-stage DDM: V0 = PV(stage 1 dividends) + PV(stage 2 dividends) + PV(terminal value); Terminal value at the end of stage 2 = D(next year) ÷ (r − gL), discounted by the total years of stages 1 and 2.
Dividend payout and growth link: g = b × ROE, where b = 1 − payout ratio; Useful when the vignette gives retention and ROE instead of growth rates.

How to solve Multistage Dividend Discount Models questions

Use the same routine for any multistage dividend question. Write out the timeline before you touch the calculator.

1Read the vignette and list D0 (or the next dividend), the required return r, each growth rate, and the length of each stage.
2Check whether the given dividend is D0 (already paid) or D1 (next year's). This changes how you grow it.
3Choose the approach: year-by-year for two-stage or three-stage with stated growth, or the H-model if growth declines linearly and the question asks for an approximate value.
4Forecast dividends for each year of the high-growth and transition stages, growing each from the previous one.
5Compute D(n+1) using the stable growth rate, then the terminal value Vn = D(n+1) ÷ (r − gL).
6Discount each dividend and the terminal value to time zero. The terminal value is discounted n years, not n+1.
7Add the present values. Then check: is the answer sensible against the Gordon value with no high growth?
8If asked for implied return, enter the market price as a negative cash flow at time 0, then the dividends and terminal value as positive flows, and solve for IRR. Note the terminal value itself depends on r, so it is a trial-and-error solution.

Quickest way: Table-and-terminal shortcut

When to use it: Use for two-stage questions with a short high-growth period of 2 to 5 years, where you need the answer quickly.

Write D1, D2 … Dn in one line using the high growth rate.
Compute Dn × (1 + gL) ÷ (r − gL) as the terminal value in one calculator chain.
Discount each earlier dividend (D1 to D(n−1)) with its own factor 1 ÷ (1 + r)^t, using the calculator memory.
Combine only the year-n dividend and the terminal value (Dn + Vn), then discount that sum by (1 + r)^n. Earlier dividends are discounted by (1 + r)^t at their own t.
For linear fade questions, jump to the H-model and skip the table.

Common mistakes in Multistage Dividend Discount Models

Discounting the terminal value n+1 years instead of n years.
The terminal value uses D(n+1), so students think it belongs to year n+1.
Fix: The Gordon formula values dividends one period ahead, so the result sits at time n. Discount it n years.
Using the high growth rate to compute D(n+1).
Students keep growing the dividend at the earlier rate out of habit.
Fix: D(n+1) = Dn × (1 + gL). The new stage starts with the stable rate.
Treating H as the full length of the decline period.
The letter H is not defined clearly in memory.
Fix: H = half the length of the transition period. A 6-year decline gives H = 3.
Forgetting to grow D0 once for the first dividend.
Vignettes may give D0 or the expected next dividend, and students mix them.
Fix: Mark whether the number is paid already. If D0, multiply by (1 + g) to get D1.
Applying the Gordon model when r is not above gL.
Students focus on mechanics and skip the sanity check.
Fix: Always confirm r > gL. If not, the model gives meaningless or negative values and a different approach is needed.
Treating the H-model as exact.
It looks like a formula with a precise answer.
Fix: Remember it is an approximation. A year-by-year model may give a slightly different value.

Worked examples

Example 1

Vignette: A firm just paid a dividend of ₹10 per share (D0). Dividends will grow 20% a year for 2 years, then 5% forever. The required return is 10%. Q1: What is the dividend in year 3? Q2: What is the terminal value at the end of year 2? Q3: What is the value per share today?

Show the solution

D1 = 10 × 1.20 = ₹12.00. D2 = 12 × 1.20 = ₹14.40.
D3 = D2 × 1.05 = 14.40 × 1.05 = ₹15.12.
Terminal value V2 = D3 ÷ (r − gL) = 15.12 ÷ (0.10 − 0.05) = 15.12 ÷ 0.05 = ₹302.40.
PV of D1 = 12 ÷ 1.10 = 10.9091.
PV of D2 = 14.40 ÷ 1.21 = 11.9008.
PV of V2 = 302.40 ÷ 1.21 = 249.9174.
Value = 10.9091 + 11.9008 + 249.9174 = 272.7273.

Answer: Q1: ₹15.12. Q2: ₹302.40. Q3: about ₹272.73 per share.

Example 2

Vignette: A firm paid a dividend of ₹8 per share (D0). Its growth rate is now 12% but will decline linearly over 6 years to a long-run rate of 6%. The required return is 11%. Q1: What is H? Q2: Using the H-model, what is the value per share?

Show the solution

H = 6 ÷ 2 = 3.
Stable-growth component: D0 × (1 + gL) ÷ (r − gL) = 8 × 1.06 ÷ 0.05 = 8.48 ÷ 0.05 = 169.60.
Growth premium component: D0 × H × (gS − gL) ÷ (r − gL) = 8 × 3 × 0.06 ÷ 0.05 = 1.44 ÷ 0.05 = 28.80.
Value = 169.60 + 28.80 = 198.40.

Answer: Q1: H = 3. Q2: about ₹198.40 per share.

Exam tips

Circle whether the vignette gives D0 or D1 before you start. This single check saves marks in most DDM items.
Draw a quick timeline with stage lengths and growth rates. Terminal-value timing errors become obvious.
Expect the H-model to be asked as an approximation; the options may differ only slightly, so keep full precision in your calculator.
Some questions ask for the implied required return or the terminal value's share of total value. Be ready to reuse your table for these.
There is no penalty for wrong answers, so never leave a question blank, but still check r > gL to eliminate options.

Multistage 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.

Multistage Dividend Discount Models: frequently asked questions

What is the difference between a two-stage and a three-stage DDM?

A two-stage model has one high-growth phase followed by stable growth. A three-stage model adds a transition phase in which growth falls toward the stable rate. The three-stage model is more flexible but needs more calculations.

How do you calculate terminal value in a DDM?

Grow the last forecast dividend by the stable growth rate to get D(n+1). Then divide by (r − gL). The result is the value at time n, so discount it back n years.

What does H mean in the H-model?

H is half the length of the period over which growth declines from the high rate to the long-run rate. If growth fades over 8 years, H = 4.

When should I use the H-model instead of a full table?

Use it when growth declines in a straight line and you only need an approximate value. If the vignette gives separate growth rates for each year, build the table.