How this instrument works
The dividend discount model prices a share as the present value of every dividend it will ever pay, and the constant-growth version used here — Gordon Growth — assumes those dividends grow at one steady rate forever. Feed in next year's expected dividend, the return you require for holding a stock this risky, and the growth rate you expect the payout to keep compounding at, and the formula collapses an infinite sum into three numbers: P₀ = D₁ ⁄ (r − g). An investor comparing a utility or a real-estate investment trust against its quoted market price reaches for this version because those firms actually pay steady, rising dividends — the model has nothing to say about a company that plows every dollar back into growth instead.
The shape of the formula comes straight out of summing a geometric series: an infinitely growing dividend stream discounted at a constant rate collapses to D₁ divided by the gap between the discount rate and the growth rate, r − g. That gap is doing almost all the work. Because it sits in the denominator, a required return of 8% and growth of 4% produce the same fair value as a required return of 10% and growth of 6% — both leave a four-point gap — while narrowing the 8%-and-4% pair to a 7%-and-4% gap alone lifts the fair value from $50 to roughly $66.67. Small, hard-to-pin-down assumptions about long-run growth move the answer by outsized amounts, which is the model's best-known weakness.
The model only holds together for firms with an established, growing dividend — feed it a non-payer and D₁ is zero, so the fair value collapses to zero along with it, which says nothing about that company's actual worth. It also assumes one constant growth rate stretching to infinity, with no allowance for a young company's fast early growth settling into a mature company's slower pace later, and it requires the required return to exceed growth or the sum never converges — hence the built-in check on this sheet. The required rate of return itself is not derived here; it is an assumption you bring, typically a CAPM estimate or a personal hurdle rate, so the fair value this instrument returns is only as trustworthy as that input.
- Enter the payout you expect over the next twelve months into Expected next dividend, $.
- Set Required rate of return, % to the return you would demand for holding a stock this risky — your own hurdle rate or a CAPM estimate.
- Enter the long-run pace you expect that dividend to keep growing into Expected dividend growth rate, %.
- Read Fair value per share — what the model says the stock is worth if those three assumptions hold exactly.
- Narrow or widen the gap between the return and growth fields to see how sharply the fair value swings.
Worked example — the $2 dividend at 8% and 4%
Take a stock expected to pay a $2.00 dividend next year, held by an investor who requires an 8% return for a stock this risky, with the payout expected to keep growing 4% a year indefinitely. The formula divides the dividend by the four-point gap between return and growth: P₀ = 2 ⁄ (0.08 − 0.04) = 2 ⁄ 0.04 = $50.00. That $50.00 is the price at which the stock would deliver exactly the required 8% return, once the 4% dividend yield and the 4% growth are added together.
The same three inputs feed the cost-of-equity calculator on this site, which runs the identical relationship in the opposite direction — it takes the price as known and solves for the return that price implies, while this instrument takes the return as a target and solves for the price that would satisfy it. Hold the return at 8% and cut the growth rate to zero instead, and the fair value falls to $25.00 — the dividend divided by the return alone, the plain no-growth perpetuity case that ignores any future increases.
Questions
Why does a small change in the growth rate swing the fair value so much?
Because growth sits inside the denominator's gap against the required return, not multiplied against the dividend. Narrowing an 8%-and-4% pair to 8%-and-6% shrinks the gap from four points to two, which doubles the fair value from $50.00 to $100.00 even though the dividend never moved. Treat any long-run growth assumption near a mature economy's growth rate with real caution — it does more work on the answer than it looks like it should.
What happens if I enter a growth rate at or above the required return?
The sheet blocks it, because the model prices dividends growing forever and that sum only has a finite value when the required return exceeds growth. A growth rate equal to or above the return implies dividends compounding faster than they are discounted, which makes the fair value infinite or negative — a sign the growth assumption is not one a company can sustain indefinitely, not a usable output.
How is this different from just using dividend yield to judge a stock?
Dividend yield is only the D₁ ⁄ P₀ half of the story — the income return on a share bought at a known price. This model instead builds a price from scratch by adding a growth assumption to that yield relationship, which is why it needs a growth rate as an input and a dividend-yield-only view does not. Two stocks with identical yields can carry very different fair values here once their growth outlooks diverge.
Does this work for a company that does not pay a dividend?
No. With no dividend, D₁ is zero and the formula returns a fair value of zero regardless of how fast the company is growing, which says nothing about what the business is actually worth. Non-payers are typically valued with a discounted cash flow approach or a market-based comparison instead, not this constant-growth dividend model.
How is this the same calculation as the cost-of-equity calculator?
Both run P₀ = D₁ ⁄ (r − g), just solved for a different unknown. The cost-of-equity version takes a quoted price and works out the return the market is implicitly demanding; this version takes a required return you supply and works out the price that would satisfy it. Feeding this instrument's output price back into the cost-of-equity calculator as the price returns your original required return exactly.
Where should the required rate of return actually come from?
It is an assumption you bring, not something this sheet derives — commonly a CAPM estimate built from a risk-free rate, a stock's beta, and an equity risk premium, or simply the return an investor has decided they need to accept the stock's risk. The fair value answer moves directly with whatever number goes in here, so it is worth being deliberate about where it comes from rather than treating it as fixed.
References
- U.S. SEC Investor.gov — investing basics, risk, and glossary
- NYU Stern (Damodaran) — valuation and dividend discount model notes
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.