The Dividend Discount Model values a stock as the present value of all future dividends to common shareholders. It’s most reliable for stable, dividend-paying firms and has several flavors like perpetuity (zero-growth), Gordon constant growth, One-period holding, or Multistage (two/three-stage, H-model).
Formula for Dividend Discount Model (DDM)
In simple words, DDM is a present-value (PV) approach that says the intrinsic value of equity equals the discounted value of all expected future dividends:
- P0: intrinsic value today
- Dt: dividend at time t
- ke: required return on equity (investors’ opportunity cost)
Why it works: Dividends are the cash that flows to owners. If you can forecast them and discount at a fair required return, you have a fundamental value.
When Dividend Discount Model (DDM) Is (and Isn’t) Appropriate
When to use DDM
- Best fit: companies that already pay reliable dividends and operate in stable, non-cyclical industries (e.g., utilities, consumer staples).
- Why: DDM needs forecastable dividends. For these firms you can reasonably assume a constant growth rate (Gordon model) or a short path to stable growth.
When to use multistage DDM
- Use a two- or three-stage DDM if dividend growth will be different in the near term (very high/low/erratic) but is expected to settle to a constant rate later.
- Examples: a bank rebuilding capital (low/zero dividends now → normal later), or a firm finishing a major expansion (high growth now → normal later).
When not to use DDM
- If the company doesn’t pay dividends or the policy is unpredictable (startups, early-stage tech/biotech, deep cyclicals).
- Here, dividend forecasts are speculative, so value with FCFE/FCFF DCF (cash-flow capacity) or market multiples instead.
Core Inputs You Must Estimate
- Next dividend D1
- This is simply what you expect the company to pay over the next year. If you only know last year’s dividend (D0) and you think dividends will grow by g next year, just grow it once:
- Formula: D1= × (1+g). Example: Last year, D0 = $2.00. If you expect 4% growth, D1 = $2.00 × 1.04 = $2.0.
- The growth rate of dividends (call it g)
- This is how fast you think dividends will increase each year. Three easy, defensible ways to get it:
- Sustainable growth (business common sense)
- Think: “how much profit is reinvested” × “how well they reinvest.”
- Formula idea: g = Retention ratio × ROE
- Retention ratio = % of earnings kept (not paid out).
- ROE = return the company earns on shareholders’ money.
- Example: Payout 40% ⇒ retention 60%. ROE 12%.
g = 0.60 × 12% = 7.2%.
- Sustainable growth (business common sense)
- Long-run anchor (for the terminal stage)
- Mature firms won’t outgrow the economy forever. Use a conservative long-run number (often 2–3% in developed markets).
- Must be lower than your required return (see next item).
- Implied growth (when price looks Gordon-ready)
- If the company is very stable and today’s price already reflects steady dividends, you can solve for g:
- Formula: g = ke(required rate of return) − D1/P0
- P0 = today’s price; ke = your required return.
- Example: P0 = $50, D1= $2, ke = 9%. So, g = 9% – 2/50 = 5%
The Main DDM Variants (with formulas)
1) Zero-Growth (Perpetuity)
For fixed dividends forever (also used for non-callable, non-convertible preferred):
- P0: intrinsic value today
- D: fixed dividend
- ke: required return on equity
2) Gordon Constant Growth
Dividends grow at a constant rate ggg forever:
- P0: intrinsic value today
- D1: expected dividend next period
- ke: required return on equity
- g: constant dividend growth rate
- Condition: ke > g
3) One-Period Holding DDM
Useful for short horizons:
(Where P1 is the expected price in one year.)
4) Multistage Models (growth changes, then stabilizes)
- Two-Stage: high growth for NNN years → terminal stage at constant ggg.
- Three-Stage / H-Model: growth fades linearly from gHg_HgH to gLg_LgL before settling.
General process:
Forecast D1..DN explicitly → compute terminal value at N with Gordon PN = DN+1 / (ke−gL) → discount everything to t = 0.
Step-by-Step Worked Examples
- D0 = $1.00, next year’s growth = 5% ⇒ D1 = $1.05
- Expected year-end price P1 = $13.45
- ke = 13.2%
- D0 = $2.00, g = 4% ⇒ D1 = 2.08
- ke = 9%
- D0 = $1
- Growth 25% for two years, then 6% forever
- ke = 10%
- Forecast:
D1 = 1.25
D2 = 1.5625
D3 = 1.5625 × 1.06 = 1.65625 - Terminal at t = 2:$$ P_2 = \frac{D_3}{k_e – g} = \frac{1.65625}{0.10 – 0.06} = 41.40625 $$
- Discount to today:$$ P_0 = \frac{1.25}{1.10} + \frac{1.5625}{1.10^2} + \frac{41.40625}{1.10^2} = \boxed{36.65} $$
A mature dividend payer just paid D0 = $2.00.
- Growth 8% for Years 1–2, 4% for Years 3–4, then 3% perpetual.
- ke = 9%
- D1 = 2.16, D2 = 2.3328, D3 = 2.4261, D4 = 2.5232
- D5 = 2.5989 ⇒ P4 = D5 / (0.09 – 0.03) = 43.3142
- PV of D1..4 and P4 at 9% →$$ P_0 \approx \boxed{38.29} $$
Non-callable, non-convertible preferred with fixed $5 dividend and required return 8%:
Trading below par is normal if the coupon (5%) < required return (8%).
Practical Tips, Checks, and Pitfalls
- Use D1, not D0, in Gordon. (Grow once if only D0 is given.)
- Ensure ke > g in the terminal stage; if ke ≈ g, the value becomes overly sensitive.
- Line up payout & growth: over time, dividend growth ≈ earnings growth if payout is stable.
- Sensitivity test ke and g. A ±1% move can swing value materially.
- Dividends vs price on ex-date: Price typically drops by ≈ the dividend amount because the cash leaves the firm and new buyers don’t receive it.
- Use multistage whenever near-term growth obviously differs from long-run steady growth.
- If no/irregular dividends, switch to FCFE/FCFF or market multiples.
Bottom Line!
The Dividend Discount Model values a stock by the cash it returns to owners—its future dividends—discounted at a sensible required return. Use Gordon for steady, mature payers; use multistage when growth changes but will stabilize. Get three inputs right—next dividend, growth, and required return—and sanity-check ke>gk. Always run sensitivities and cross-check with FCFE/FCFF or multiples before acting.
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