Stock Non-Constant Growth Calculator

What this non-constant growth calculator does

A young company might grow its dividend at 20 percent a year for a while. It cannot do that forever, because nothing grows faster than the economy indefinitely. So at some point the growth rate has to settle down to something modest and stay there.

Valuing a stock like that needs two pieces: the high growth years handled individually, and everything after them handled as a perpetuity. That is what this calculator does, and it is usually called a multi-stage or non-constant growth dividend discount model.

Give it the current dividend, a growth rate for each of up to eight years, and the return you require. It works out what each of those dividends is worth today, adds a value for everything beyond them, and returns a price per share.

Before you use it, read the next section. There is one rule about how the growth rates are interpreted that is not obvious from the form and that changes the answer completely if you get it wrong.

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How to use it, and the one rule that matters

1. Dividend (D0). The dividend just paid, per share. Not next year's, the most recent one.
2. Growth Rates. Fill in year 1, then year 2, and so on. Fill them from the top with no gaps, because the tool stops reading at the first blank box.
3. Required Return. The annual return you want from this investment, as a percentage. Often a cost of equity from CAPM, or from our WACC calculator if you are valuing the firm rather than the equity.

Press Calculate. Press Reset to clear it.

Now the rule. The last growth rate you enter becomes the permanent growth rate for everything after your final year. It is not just that year's rate, it is the rate the model assumes will continue forever.

So if you want three years at 20 percent and then 5 percent thereafter, you enter four figures: 20, 20, 20, then 5. The fourth box does double duty, giving you year four's dividend and setting the perpetual rate from year five onward.

Enter only 20, 20, 20 and the model will assume 20 percent growth forever, which is not what you meant. In that case it will refuse to calculate at all, because a perpetual growth rate above your required return produces a nonsensical value, and that refusal is the tool protecting you rather than failing.

Your final growth rate should be modest. Long run economic growth is the practical ceiling, so something between 2 and 4 percent is usual, and anything above your required return is impossible by construction.

The model in two parts

Part one, the explicit years. Each year's dividend grows from the one before it, then gets discounted back to today:

D_n = D_n-1 × (1 + g_n)

PV of D_n = D_n ÷ (1 + r)ⁿ

Part two, everything afterwards. Once growth is constant, an infinite stream of dividends has a finite value, which is the Gordon growth model:

Terminal value = D_n+1 ÷ (r − g)

That terminal value sits at the end of your final explicit year, so it needs discounting back too:

PV of terminal value = terminal value ÷ (1 + r)ⁿ

Add the two parts and you have the stock's value.

The reason an infinite stream is finite is that the (r − g) denominator shrinks the further apart those two numbers are. It also explains why g must be below r. If growth equalled the required return the denominator would be zero and the value infinite, and if growth exceeded it the value would come out negative, which is the model telling you the assumption is impossible rather than telling you the stock is worthless.

A worked example, line by line

A company that just paid a dividend of 2.00, expected to grow it at 20 percent for three years and then 5 percent indefinitely. Required return 12 percent.

So you would enter growth rates of 20, 20, 20, 5.

Present value of those four dividends: 9.2049

Now the perpetuity. Year five's dividend is 3.6288 × 1.05 = 3.8102.

Terminal value at the end of year four: 3.8102 ÷ (0.12 − 0.05) = 54.4320

Discounted to today: 54.4320 ÷ 1.12⁴ = 34.5925

Value of the stock: 9.2049 + 34.5925 = 43.80

If the shares trade below that, the model says they are cheap on these assumptions. The phrase "on these assumptions" is carrying an enormous amount of weight, and the next section explains why.

Most of your answer is the terminal value

Look again at the two components of that 43.80. The four years of dividends you thought carefully about contributed 9.20. The perpetuity contributed 34.59.

The terminal value is 79 percent of the answer.

That is not a quirk of this example. It is the normal result, and it gets more extreme the longer your required return sits above your terminal growth rate and the shorter your explicit forecast period.

Which means something uncomfortable. The part of the model you can actually reason about, the next few years of a business you might know something about, is a fifth of the answer. Four fifths comes from a single assumption about what happens forever, starting in a year you cannot see.

This is worth knowing because of how these models get used. Someone builds a careful forecast, debates each year's growth rate, then types a terminal growth rate almost as an afterthought. The afterthought is the valuation.

The practical response is not to abandon the method, which is sound, but to treat the terminal growth rate as the most important input on the page and to test it rather than pick it. Which brings us to the next section.

How much the assumptions move the answer

Same company, same three years at 20 percent, same 12 percent required return. Only the terminal growth rate changes:

From 3 percent to 10 percent the value goes from 35 to 142. A four fold change, driven by an assumption about the indefinite future that nobody can verify.

Notice the acceleration. Each extra point of terminal growth costs more than the last, because you are shrinking the (r − g) denominator toward zero. At 10 percent against a 12 percent required return the denominator is down to 0.02 and the model is becoming unstable. That is the region where these valuations produce absurd numbers and where you should stop trusting them.

The required return moves things too, in the opposite direction:

Two percentage points on the required return takes roughly a fifth off the value. So the honest way to use this tool is not to produce one number. Run it across a range of terminal growth rates and required returns, see what band of values comes out, and compare the market price against the band rather than against a point.

If the shares look cheap across the whole range, that is interesting. If they only look cheap at your most optimistic assumptions, that is the model agreeing with you rather than telling you something.

What kind of company this suits

The model values a stream of dividends, which means it needs there to be one.

It works well for mature dividend payers with a stable and predictable payout: utilities, consumer staples, established banks, big pharmaceutical companies. Anything where the dividend genuinely tracks the health of the business and management has a track record of raising it steadily.

It works badly, or not at all, for companies that pay no dividend, which includes most growth and technology companies. Zero dividends make the model return zero, which is obviously not the value of the business. For those, a free cash flow model is the right tool, and buybacks in particular are a form of shareholder return this model cannot see at all.

It is unreliable for companies whose payout is erratic, cyclical businesses where the dividend gets cut in downturns, and any business undergoing a structural change that makes the past a poor guide.

One further caution about the shape of the inputs. A high growth rate followed by an abrupt drop to a terminal rate is a simplification. Real businesses decelerate gradually, and a more realistic model fades the growth rate down over several years rather than dropping it in one step. You can do that here by entering a declining series, something like 20, 17, 14, 11, 8, 5, which uses more of the eight boxes and produces a smoother and usually more defensible result.

Finally, the output is a value, not a price. If your figure is well away from where the shares trade, the honest first question is not whether the market is wrong but whether your assumptions are.

Questions people ask

Why does my last growth rate keep going forever?

Because the model needs a permanent rate for the perpetuity and takes the final figure you entered. To model three years of high growth then a settled rate, enter four figures with the settled rate last.

It says the growth rate must be less than the required return. Why?

The perpetuity formula divides by (required return minus growth). If growth equals the return, that is division by zero, and if it exceeds it the answer goes negative. Perpetual growth above your required return is not a possible assumption.

What terminal growth rate should I use?

Something no higher than long run economic growth, since nothing outgrows the economy forever. Two to four percent is the usual range, and check what a point either way does to your answer.

Do I enter the dividend just paid or the next one?

The one just paid. The model applies year one's growth to it to get the first future dividend.

The company pays no dividend. Can I use this?

No. The model would value it at zero. Use a free cash flow model instead, which also captures buybacks.

Why is the terminal value such a large share of the answer?

Because it represents every year from your forecast horizon to infinity, while the explicit years cover only a handful. On our example it is 79 percent. That is normal and it is the main reason to test the terminal assumption hard.

I left a growth rate box blank in the middle. What happened?

The tool stops reading at the first blank, so anything after it is ignored. Fill the boxes from the top with no gaps.

What if I need more than eight years?

Eight is the limit here. In practice a long explicit forecast rarely helps, because the terminal value dominates regardless. A fading series across the eight available years is usually more useful than more years would be.

References

A note on sourcing. The idea that an asset is worth the present value of the cash it will pay out goes back to Williams in 1938, and the constant growth perpetuity used for the terminal value here is generally attributed to Gordon's 1959 paper. The required return input is normally derived from a cost of equity or cost of capital estimate, and Damodaran publishes free industry data for both.

1. Gordon, M. J., Dividends, Earnings, and Stock Prices, The Review of Economics and Statistics, Vol. 41, No. 2, May 1959, pp. 99 to 105.
2. Williams, J. B., The Theory of Investment Value, Harvard University Press, 1938.
3. Damodaran, A., Cost of Capital Central, NYU Stern School of Business. https://pages.stern.nyu.edu/~adamodar/New_Home_Page/wacccentral.html
4. Damodaran, A., Useful Data Sets, NYU Stern School of Business. https://pages.stern.nyu.edu/~adamodar/New_Home_Page/data.html
5. OpenStax, Principles of Finance, Section 7.2, Time Value of Money Basics. https://openstax.org/books/principles-finance/pages/7-2-time-value-of-money-tvm-basics