Dividend Discount Model — clear, practical explainer
What it is (short definition)
– The dividend discount model (DDM) is a valuation method that estimates a stock’s intrinsic price by discounting the company’s expected future dividend payments back to today. It rests on the time value of money: a dollar received in the future is worth less than a dollar today.
Key variables and definitions
– Dividend (D): the cash payment per share expected to be distributed to shareholders in a future period. D0 denotes the most recent dividend; D1 denotes the dividend expected next period.
– Required rate of return (r): the return investors demand for owning the stock (also called cost of equity). It reflects risk and opportunity cost.
– Dividend growth rate (g): the expected percentage increase in dividends per period going forward.
– Discounting: converting future cash flows into present value using r.
– Present value (PV): the sum today of all discounted future dividends; the DDM’s estimate of fair stock value.
Core formulas
– General (infinite-sum) DDM: P0 = Σ (Dt / (1 + r)^t) for t = 1 to ∞, where Dt is the dividend in period t.
– Constant-growth (Gordon Growth) DDM (when dividends grow at a fixed rate g forever): P0 = D1 / (r − g), where D1 = D0 × (1 + g).
– Assumption requirement: r > g (otherwise the formula is invalid).
– Zero-growth (perpetuity): if dividends are expected to remain constant (g = 0), P0 = D / r.
When to use which version
– Zero-growth: for stable companies that pay a fixed dividend each year.
– Constant-growth (Gordon): for mature firms with steady dividend growth.
– Multi-stage (two-stage, three-stage): when dividends are expected to grow at different rates over time (e.g., high-growth phase then stable mature growth).
Step-by-step checklist for applying the DDM
1. Confirm the company pays dividends and has a plausible dividend policy.
2. Gather recent dividend data (D0) and historical growth trends.
3. Choose the DDM variant (zero, constant, two-stage, etc.) that matches expected dividend behavior.
4. Forecast future dividends (compute D1 and, if needed, subsequent Dt).
5. Estimate the required return r (e.g., using CAPM: r = risk-free rate + beta × market risk premium).
6. Compute present value(s) of projected dividends and sum them to get P0.
7. Run a sensitivity check: vary r and g to see how valuation changes.
8. Compare P0 with current market price; interpret differences cautiously.
Worked numeric example (constant-growth/Gordon)
– Inputs:
– Last paid dividend D0 = $1.00
– Expected dividend growth g = 5% = 0.05
– Required return r = 10% = 0.10
– Step 1: Compute next year’s dividend D1 = D0 × (1 + g) = $1.00 × 1.05 = $1.05.
– Step 2: Apply Gordon formula: P0 = D1 / (r − g) = $1.05 / (0.10 − 0.05) = $1.05 / 0.05 = $21.00.
– Interpretation: Under these assumptions, the DDM implies a fair value of $21 per share. If the market price is lower than $21, the model indicates the stock may be undervalued given the inputs; if higher, it may be overvalued. (Do a sensitivity check: if r were 9% while g stays 5%, P0 = $1.05 / 0.04 = $26.25.)
Practical notes and common variations
– Estimating r: The Capital Asset Pricing Model (CAPM) is widely used: r = risk-free rate + beta ×
market risk premium. In formula form: r = risk-free rate + beta × (market risk premium), where
– risk-free rate is typically the yield on long-term government bonds,
– beta measures the stock’s systematic volatility relative to the market,
– market risk premium = expected market return − risk-free rate.
Estimating g (the dividend growth rate)
– Historical growth: compound annual growth rate (CAGR) of past dividends. Use 5–10 years if available.
– Sustainable growth: g ≈ ROE × retention ratio, where
– ROE = return on equity,
– retention ratio = 1 − payout ratio (portion of earnings retained).
– Analyst forecasts: consensus long-term growth rates (use cautiously).
Note the critical requirement: the Gordon model needs g g2. If the discount rate r is not greater than the long‑term growth rate g2, the Gordon (perpetuity) formula produces an undefined or negative terminal value and the model breaks down.
4. Discount each forecasted dividend and the terminal value to present value
– Formula for present value of all cash flows:
P0 = sum_{t=1 to n} [Dt / (1 + r)^t] + [Pn / (1 + r)^n],
where Pn = D_{n+1} / (r − g2) and D_{n+1} = Dn*(1 + g2).
– In words: discount each projected dividend in the high‑growth period back to today, discount the terminal (continuing) value back to today, and add them.
Worked numeric example (step‑by‑step)
Assumptions:
– D0 (most recent annual dividend) = $2.00.
– High‑growth rate g1 = 15% for n = 3 years.
– Long‑term stable growth rate g2 = 4%.
– Discount rate r = 10% (required return on equity).
Step A — project dividends for years 1..3:
– D1 = D0*(1 + g1) = 2.00 * 1.15 = 2.30
– D2 = D1*(1 + g1) = 2.30 * 1.15 = 2.645
– D3 = D2*(1 + g1) = 2.645 * 1.15 = 3.04175
Step B — compute D4 (first payment in perpetuity) and the terminal value P3:
– D4 = D3*(1 + g2) = 3.04175 * 1.04 = 3.16342
– P3 = D4 / (r − g2) = 3.16342 / (0.10 − 0.04) = 3.16342 / 0.06 = 52.7237
Step C — discount dividends and terminal value back to present:
– PV(D1) = 2.30 / (1.10)^1 = 2.0909
– PV(D2) = 2.645 / (1.10)^2 = 2