A dividend discount model calculator answers one narrow question: if a company pays the dividend stream you have assumed, and you discount that stream at the return you require, what is it worth per share today? Everything else follows from that. The model has no view about the company, the sector or the market. It arithmetically converts your assumptions into a single number, and if the assumptions are wrong the number is wrong with total confidence.
Arb Digital publishes this in its free tools library beside the intrinsic value calculator, which discounts owner earnings rather than dividends, and the DCF calculator, which takes an explicit year-by-year cash flow forecast instead of a constant growth rate. Where the dividend yield calculator divides the current dividend by the current price to report what a holder is being paid right now, this page values the whole future stream. Those are different questions, and confusing them is the most common error people make with dividend arithmetic.
What This Dividend Discount Model Calculator Does
It implements the Gordon growth model, published by Myron J. Gordon and Eli Shapiro in 1956 and refined by Gordon in 1959, with an optional explicit high-growth stage placed in front of it. The single-stage form is the one most people mean by "the dividend discount model": a share is worth next year's dividend divided by the difference between the required return and the perpetual growth rate.
The multi-stage form exists because very few companies grow their dividend at one constant rate forever. A stage-one length above zero grows the dividend at your stage-one rate for that many years, discounts each of those dividends individually, then capitalises the year after into a Gordon perpetuity at the terminal rate and discounts that back. A length of zero collapses the page to the pure single-stage model, and the fourth grid item shows that single-stage figure at all times.
The output is what the model returns given your inputs. It is not a fair price, not a target, and not a reason to do anything. Two people running this page on the same company will produce different numbers, and neither will have made an arithmetic mistake.
How to Use It
- Enter the trailing dividend, not a forecast. The model applies growth to the figure you supply. If you enter next year's expected dividend and leave growth on, you have compounded the first year twice and overstated everything downstream.
- Set the required return yourself. This page hardcodes no rate, because there is no correct universal one. Many people build it from a cost of equity; the CAPM calculator handles that construction, and the WACC calculator blends it with debt when a whole-firm rate is what you need.
- Keep the terminal growth rate below the required return. The perpetuity divides by the difference between them. When that difference reaches zero or turns negative the formula stops describing anything, and this page refuses to print a number rather than showing you a negative or an infinity.
- Use the stage-one option when the current payout is clearly not sustainable at its present growth. A company raising its dividend 15% a year is not going to do that for a century. Model the high rate for the years you can defend and let the terminal rate carry the rest.
- Run the terminal rate across a range. The spread of outputs is the honest answer; a single figure quoted to the cent implies precision this method does not have.
The Formula and How It Is Calculated
The single-stage Gordon growth model is:
P0 = D0 × (1 + g) ÷ (r − g), which is the same as P0 = D1 ÷ (r − g)
where D0 is the dividend just paid, r is the required return and g is the perpetual growth rate. It is the closed-form sum of an infinite geometric series, and converges only when r exceeds g.
The multi-stage form discounts each explicit dividend and then adds the discounted perpetuity. For years 1 to N:
PVstage one = Σ D0(1 + g1)t ÷ (1 + r)t
TV = DN × (1 + gt) ÷ (r − gt), then PV(TV) = TV ÷ (1 + r)N
Worked example, matching the figures the page loads with. The trailing dividend is $2.40, growing 7% for five years, terminal growth 3%, required return 9%. Year-one dividend is $2.5680 and discounting at 1.09 gives $2.3560. The five discounted dividends are $2.3560, $2.3127, $2.2703, $2.2287 and $2.1877, summing to $11.3554. The year-five dividend itself is 2.40 × 1.075 = $3.3661, so year six is $3.4671 and the terminal value is 3.4671 ÷ (0.09 − 0.03) = $57.7851. Discounting that by 1.095 = 1.538624 gives $37.5564. Adding the two produces $48.91 per share, of which the terminal block is 76.8%. The pure single-stage model on the same required return and terminal rate would give 2.40 × 1.03 ÷ 0.06 = $41.20, so the five-year high-growth stage adds $7.71.
Every Assumption the Model Rests On
This section matters more than the arithmetic, because the arithmetic is trivial and the assumptions are where the answer actually comes from. The Gordon growth model requires all of the following to be true, and states none of them out loud:
- The company pays a dividend and will keep paying one. A company that pays nothing has a model value of zero, which is obviously false as a statement about the business and perfectly true as a statement about this model.
- Growth is constant within each stage. Real dividend growth is lumpy. Boards raise the payout in steps, freeze it through downturns and occasionally cut it. Constant growth is a smoothing convenience, not an observation.
- The terminal growth rate continues forever. Not for thirty years. Forever. This is why terminal rates above long-run nominal economic growth are indefensible: a company compounding faster than the whole economy eventually becomes the whole economy.
- The required return is constant across all future years. Discount rates move with interest rates and risk appetite. Holding r flat for a perpetuity is an assumption nobody would defend if it were written on its own line.
- r is strictly greater than gt. Not a preference, a mathematical requirement for the series to converge.
- The dividend is the right measure of what a shareholder receives. Companies that return cash mainly through buybacks distribute real value this model cannot see, and a shifting share count changes what "per share" even means.
When g Is Greater Than or Equal to r
This is the failure mode that produces most of the wrong dividend-discount numbers circulating online, and it is worth understanding rather than merely avoiding.
The Gordon formula is a compressed infinite sum. Each future dividend is worth D0(1+g)t ÷ (1+r)t today, so each term is the previous one multiplied by (1+g)/(1+r). When g is below r that ratio is less than one, the terms shrink, and the infinite sum converges on a finite number. When g equals r every term is identical and an infinite sum of identical positive numbers is infinite. When g exceeds r the terms grow and the sum diverges faster still.
What the algebra does at that point is quietly vicious. Divide by (r − g) with g larger and the denominator is negative, so the formula returns a confident, tidy, negative share value. It looks like a computed answer. It is a divergent series being read backwards. Any calculator that prints a negative Gordon value, or an eight-figure one as the denominator approaches zero, has failed rather than computed. This page checks the spread first and prints a plain message instead. The practical response is not to nudge the terminal rate down until the number looks reasonable: model the fast growth explicitly in stage one for as long as it is defensible and apply a sustainable terminal rate afterwards.
Why the Terminal Block Dominates
In the worked example, five years of dividends you thought carefully about contribute 23.2% of the value. One line built from two rates contributes 76.8%. That ratio is normal, not a defect, and it changes how any discounted valuation should be read.
The cause is the size of the denominator. At a 9% required return and 3% terminal growth the divisor is 0.06, applying a multiple of about 16.7 to one year's dividend. Move terminal growth to 4% and the multiple becomes 20 — a 20% jump from a one-point change in a figure nobody can observe.
Two things follow. Sensitivity analysis is not optional; it is the output. And a cross-check from a different method adds far more than another decimal place in the forecast, which is why the P/E ratio calculator and the price to book calculator belong beside this page rather than in competition with it.
Where the Dividend Discount Model Does Not Apply
The model has a defined domain and outside it returns numbers that look authoritative and mean nothing.
Non-payers. A profitable company that has never paid a dividend gets a model value of zero. That is the model working correctly and answering a question you did not want to ask.
Buyback-heavy payers and cyclicals at a peak. When most cash return happens through repurchases, the dividend understates distributions badly. And growing a peak-cycle dividend at a peak-cycle rate compounds one good year into a perpetuity, so normalise first.
Anything with an unstable payout ratio. A company paying out 95% of earnings cannot grow the dividend faster than earnings for long, because there is nothing left to retain. The dividend payout ratio calculator is the sanity check that catches this. Aswath Damodaran's dividend fundamentals data set at NYU Stern publishes sector-level payout and dividend growth figures worth checking your assumptions against.
Companies whose dividend policy is about to change. A newly initiated dividend has no history to extrapolate, and a company approaching a cut is being valued on a number that is about to stop existing. The US Securities and Exchange Commission's stocks FAQ on Investor.gov states plainly that dividends are declared at a board's discretion and are not guaranteed, which is the assumption the whole model quietly depends on.
Arb Digital works on the part a valuation model can only assume — search visibility, content and acquisition economics that turn an assumed growth rate into something a business can actually defend.
See Web Growth Services Talk to Arb DigitalCommon Mistakes to Avoid
- Entering next year's dividend as D0 — the model multiplies by (1 + g) itself, so supplying a forecast dividend applies the first year's growth twice.
- Setting terminal growth just under the required return — the denominator collapses toward zero and the value runs away to a figure with no economic meaning. A number that changes tenfold on a half-point input is not an estimate.
- Reading the gap against the market price as a verdict — it is the distance between your assumptions and the market's. Either the market is wrong or your inputs are, and the second is far more often true.
- Extrapolating a recent dividend growth spurt forever — a company recovering from a freeze can post enormous percentage increases for two or three years without any change in underlying earning power.
- Ignoring withholding and personal tax entirely — the model values gross dividends, and what a holder actually receives depends on jurisdiction and account type. The dividend tax calculator handles that separately.
Related Free Tools From Arb Digital
Build the required return with the CAPM calculator or the WACC calculator, sanity-check dividend sustainability with the dividend payout ratio calculator, and see what a holder is paid today with the dividend yield calculator. For a cash-flow rather than dividend view, the intrinsic value calculator and the DCF calculator cover the same company from a different angle, and the EPS calculator builds the earnings figure a payout ratio needs. Everything else sits in the free online tools hub.
Frequently Asked Questions
The Gordon growth model, published by Myron Gordon and Eli Shapiro in 1956 and refined by Gordon in 1959, with an optional explicit high-growth stage in front of it. Set the stage-one length to zero and the page runs the pure single-stage form: next year's dividend divided by the required return minus the perpetual growth rate.
The infinite series stops converging, so the formula has no finite answer. Algebraically the denominator turns negative and the arithmetic returns a confident negative share value, which is meaningless. This page checks the spread first and prints a message instead of a number. The correct response is to model the fast growth explicitly in stage one and apply a sustainable terminal rate afterwards.
The calculator does not supply one, because the right rate depends on the risk being taken and the return the holder requires. Many people build it as a cost of equity from a risk-free rate, a beta and an equity risk premium. On this page it is always an input, never a hardcoded value.
Not usefully. With a dividend of zero every term in the series is zero and the model returns zero, which is a correct statement about the model and a false one about the business. Companies that return cash mainly through buybacks, or return none at all, need a cash-flow or earnings-based method instead.
No. It is what the model returns given the inputs you chose, and the inputs dominate the result. It is not a recommendation, not a target, and not a prediction of any future price. The gap it shows against the market price measures the distance between your assumptions and the market's, nothing more.
Because a perpetuity divides by the difference between the required return and the terminal growth rate, and that difference is small. At 9% and 3% the divisor is 0.06, which applies a multiple of roughly 16.7 to a single year's dividend. Seventy per cent or more of the total sitting in the terminal block is typical.
One below the required return and below long-run nominal economic growth, since a company growing faster than the economy forever would eventually become the economy. Rates in the low single digits are the usual ceiling. Running a range rather than committing to one figure tells you far more than any single choice.
Dividend yield divides the current annual dividend by the current share price and reports what a holder is being paid right now as a percentage. This page discounts the entire future dividend stream to a present value per share. One measures a current cash return; the other values a projected stream on assumptions you supply.
This tool performs a published valuation calculation on assumptions you supply. It is not investment advice, not a recommendation to buy, sell or hold any security, and its output is not a price target or a prediction. Dividends are declared at a board's discretion and can be reduced or stopped. Decisions about your money should involve a licensed financial adviser who is regulated to advise on them and who can see your full circumstances.
