Two-stage (multistage) dividend discount model

How do you value a company whose growth will slow down?

The Gordon model needs one growth rate forever. A company with a hot product has a high growth rate now that cannot last, because competitors arrive and the market fills. The two-stage DDM handles that, and it is the simplest multistage dividend discount model . It gives the company two growth rates: a high rate $g_S$ for a finite number of years $n$, the high-growth phase , and then a lower sustainable rate $g_L$ forever, the mature phase .

Choose the model by the growth pathmatch the stages to how growth will actually fade

• Constant growth (Gordon) Use it already at a sustainable rate; mature
• Two-stage DDM Use it a finite spell of unusually high (or low) growth, then a sustainable rate
  • Typical case new product or advantage that fades as competitors arrive
  • Also fits an older firm with a temporary burst or dip in growth
• Three-stage DDM Know the idea growth, then a transition of declining growth, then maturity
  • Typical case a young company just entering its growth phase
• Not a dividend model Use it no dividend or dividends unrelated to capacity: FCFE or multiples

The method has two parts. Forecast the dividends of the high-growth phase one at a time, because they follow no single formula over the whole life. Then collapse everything after that into one number at year $n$, the terminal value , using the Gordon model.

$$V_0 = \sum_{t=1}^{n} \frac{D_0(1 + g_S)^t}{(1 + r)^t} + \frac{V_n}{(1 + r)^n}$$

$$V_n = \frac{D_{n+1}}{r - g_L}$$

$$D_{n+1} = D_0(1 + g_S)^n(1 + g_L)$$

The Gordon formula values dividends starting one year after the date it is applied. So $V_n$, applied at year $n$, values dividends from year $n+1$ on, and it needs $D_{n+1}$. The terminal value is a value at year $n$, so it is discounted $n$ years, the same as the year-$n$ dividend.

The three classic slips

Each of these changes the answer to the example above, and each appears as an option in exam questions.

Slip	What it does	Result
Terminal value from $D_n$ instead of $D_{n+1}$	V₃ = 1.8251 ÷ 0.05 = 36.50	V₀ = 31.36
Discount $V_n$ for $n + 1$ years	38.33 ÷ 1.10⁴	V₀ = 30.11
Use $g_S$ in the terminal formula	the formula breaks, because 15% is above r = 10%	no valid value

The correct answer is 32.73.

How sensitive is it?

Because the terminal value dominates, small changes to $g_L$ or $r$ move the result a lot. In the example, with everything else unchanged:

Long-term growth g_L	V₀
4%	27.70
5%	32.73
6%	40.27

Required return r	V₀
9%	41.00
10%	32.73
11%	27.22

Analysts therefore test the terminal value, for example by comparing the multiple it implies with the multiples of mature peers.

Which companies need a multistage model?

Use the stages that match how growth will really behave. A mature company already growing at a sustainable rate suits the Gordon model. A company with an unusually high rate now, perhaps from a new product or a competitive advantage that will fade as rivals arrive, suits two stages. A three-stage DDM suits a young company at the start of its growth phase: growth, then a transition of declining growth, then maturity. Two stages is the better fit for an older company already in transition.

Age is not the only test. An old company can find fresh growth, for example by launching a new product line or buying a rival, and that burst is expected to fade back toward a normal rate. Two stages fit. So does a company going through a weak spell that is expected to climb back to its normal growth rate. The test is the shape of the growth path, not the company’s age.

Exam tip Count the growth regimes you can defend with evidence. One regime: Gordon. Two: two-stage. Three: three-stage. If you cannot defend any, use free cash flow to equity (FCFE) or multiples.

Go deeper A three-stage model without the numbers

Suppose growth is $g_1$ for $n_1$ years, falls to $g_2$ for the next $n_2$ years and then settles at $g_L$ forever. Forecast the dividends year by year through the first two stages. At year $n_1 + n_2$ compute the terminal value $V = D_{n_1+n_2+1} \div (r - g_L)$. Discount every dividend and that terminal value to today. The same rule applies: the terminal value is dated at the end of the last explicit stage, and it uses the next dividend.

Go deeper Checking the terminal value

A terminal value is a forecast of what the company will be worth at year $n$. To check it, convert it to a multiple. In the example, $V_3$ of 38.33 against an expected earnings per share can be turned into a P/E and compared with the P/E of mature companies. If the implied multiple is far above what mature peers trade at, the long-term growth rate or the required return is probably too generous. The next lesson shows how a multiple relates to $r$ and $g$.