Dividend Discount Model (DDM): The Complete, Practical Guide

Dividend Discount Model (DDM): The Complete, Practical Guide

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:

$$ P_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1 + k_e)^t} $$
  • 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

When to use multistage DDM

When not to use DDM

Core Inputs You Must Estimate

  1. 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.
  2. The growth rate of dividends (call it g)
  3. 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%.
  4. 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).
  5. 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):

$$ P_0 = \frac{D}{k_e} $$
  • P0: intrinsic value today
  • D: fixed dividend
  • ke: required return on equity

2) Gordon Constant Growth

Dividends grow at a constant rate ggg forever:

$$ P_0 = \frac{D_1}{k_e – g}, \quad k_e > g $$
  • 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:

$$ P_0 = \frac{D_1}{1 + k_e} + \frac{P_1}{1 + k_e} $$

(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

A) One-Period Example (exam style)
  • D0 = $1.00, next year’s growth = 5% ⇒ D1 = $1.05
  • Expected year-end price P1 = $13.45
  • ke = 13.2%
$$ P_0 = \frac{1.05}{1.132} + \frac{13.45}{1.132} = 0.93 + 11.88 = \boxed{12.81} $$
B) Gordon Constant Growth
  • D0 = $2.00, g = 4% ⇒ D1 = 2.08
  • ke = 9%
$$ P_0 = \frac{2.08}{0.09 – 0.04} = \boxed{41.60} $$
C) Two-Stage DDM (high growth → stable)
  • D0 = $1
  • Growth 25% for two years, then 6% forever
  • ke = 10%
  1. Forecast:
    D1 = 1.25
    D2 = 1.5625
    D3 = 1.5625 × 1.06 = 1.65625
  2. Terminal at t = 2:
    $$ P_2 = \frac{D_3}{k_e – g} = \frac{1.65625}{0.10 – 0.06} = 41.40625 $$
  3. Discount to today:
    $$ P_0 = \frac{1.25}{1.10} + \frac{1.5625}{1.10^2} + \frac{41.40625}{1.10^2} = \boxed{36.65} $$
D) Short Multiyear + Terminal (practical)
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%
  1. D1 = 2.16, D2 = 2.3328, D3 = 2.4261, D4 = 2.5232
  2. D5 = 2.5989 ⇒ P4 = D5 / (0.09 – 0.03) = 43.3142
  3. PV of D1..4 and P4 at 9% →
    $$ P_0 \approx \boxed{38.29} $$
Preferred Stock as a DDM Special Case

Non-callable, non-convertible preferred with fixed $5 dividend and required return 8%:

$$ P_0 = \frac{5}{0.08} = \boxed{62.50} $$

Trading below par is normal if the coupon (5%) < required return (8%).

Practical Tips, Checks, and Pitfalls

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.