Dividend Discount Models for Mature Companies
The Logic Behind DDM (Why It Matters)
When you buy a stock and hold it forever, what do you actually receive? Dividends. That is the entire premise of dividend discount models: a stock is worth the present value of all future dividends it will pay.
The general DDM formula:
V0 = Sum of [Dt / (1+r)^t] from t=1 to infinity
Where:
- V0 = Intrinsic value today
- Dt = Dividend in period t
- r = Required rate of return (cost of equity)
The point is: DDM forces you to think about what you actually receive as a shareholder. For mature, dividend-paying companies, this creates a direct link between valuation and cash returned to investors.
The Gordon Growth Model (Single-Stage DDM)
Published by Myron J. Gordon and Eli Shapiro in 1956, this remains the most widely used dividend model.
V0 = D1 / (r - g)
Where:
- D1 = Expected dividend next period = D0 x (1 + g)
- r = Required return on equity
- g = Constant dividend growth rate forever
Worked Example: Basic GGM
A utility company pays a $2.50 annual dividend (D0). You expect dividends to grow at 5% annually (g). Your required return is 11% (r).
Step 1: Calculate next year's dividend D1 = $2.50 x 1.05 = $2.625
Step 2: Apply the GGM formula V0 = $2.625 / (0.11 - 0.05) = $2.625 / 0.06 = $43.75
The stock is worth $43.75 if your assumptions hold.
The Critical Constraint: r Must Exceed g
If g >= r, the formula breaks. You get infinite or negative values—mathematical impossibility.
Why this matters: A company cannot grow its dividends faster than your required return forever. Eventually, the company would become larger than the entire economy (at g = 10% for 50 years, a $100 million company becomes $11.7 trillion).
The durable lesson: If your model produces g >= r, either your growth assumption is too aggressive or your required return is too low. Adjust until the relationship makes economic sense.
Two-Stage DDM (When Growth Eventually Slows)
Most companies do not grow at constant rates forever. The two-stage model captures high initial growth followed by stable mature growth.
V0 = Sum of [Dt / (1+r)^t] for high-growth period + Terminal Value / (1+r)^n
Where terminal value uses the Gordon formula at the stable growth rate.
Worked Example: Two-Stage DDM
A technology company with these characteristics:
- Current dividend (D0): $1.00
- High-growth rate (years 1-5): 15%
- Stable growth rate (year 6+): 4%
- Required return: 12%
Step 1: Calculate dividends during high-growth phase
| Year | Dividend Calculation | Dividend | PV Factor | Present Value |
|---|---|---|---|---|
| 1 | $1.00 x 1.15 | $1.15 | 0.893 | $1.03 |
| 2 | $1.15 x 1.15 | $1.32 | 0.797 | $1.05 |
| 3 | $1.32 x 1.15 | $1.52 | 0.712 | $1.08 |
| 4 | $1.52 x 1.15 | $1.75 | 0.636 | $1.11 |
| 5 | $1.75 x 1.15 | $2.01 | 0.567 | $1.14 |
PV of high-growth dividends: $5.41
Step 2: Calculate terminal value at end of Year 5
D6 = $2.01 x 1.04 = $2.09
Terminal Value = $2.09 / (0.12 - 0.04) = $2.09 / 0.08 = $26.13
Step 3: Discount terminal value to present
PV of Terminal Value = $26.13 x 0.567 = $14.81
Step 4: Sum for total value
V0 = $5.41 + $14.81 = $20.22
The point is: Two-stage DDM is more realistic for growth companies transitioning to maturity. Notice that terminal value still dominates (73% of total value)—the stable growth period matters more than the high-growth period.
The H-Model (Gradual Growth Decline)
What if growth does not drop abruptly from 15% to 4%? The H-model assumes dividend growth declines linearly from a supernormal rate to a stable rate over time.
V0 = D0(1 + gL) / (r - gL) + D0 x H x (gS - gL) / (r - gL)
Where:
- gL = Long-term stable growth rate
- gS = Short-term supernormal growth rate
- H = Half-life of high-growth period (in years)
Worked Example: H-Model
Company with:
- D0: $2.00
- Short-term growth (gS): 14%
- Long-term growth (gL): 4%
- Half-life (H): 5 years (meaning full transition takes 10 years)
- Required return (r): 10%
V0 = $2.00(1.04) / (0.10 - 0.04) + $2.00 x 5 x (0.14 - 0.04) / (0.10 - 0.04)
V0 = $2.08 / 0.06 + $2.00 x 5 x 0.10 / 0.06
V0 = $34.67 + $16.67 = $51.34
The durable lesson: The H-model is elegant when you believe growth will taper gradually rather than step down overnight. It produces slightly different values than the two-stage model but often matches reality better.
When to Use Each Model
Gordon Growth Model (single-stage):
- Mature companies with stable dividend histories
- Utilities, consumer staples, established REITs
- Companies with capital expenditure roughly equal to depreciation
- Beta at or below 1
Two-Stage DDM:
- Companies currently growing faster than sustainable long-term
- Tech companies transitioning from growth to value
- Companies where you can identify a clear transition point
H-Model:
- Companies where growth will decline gradually
- Situations where abrupt growth drop seems unrealistic
- Sectors with slowly changing competitive dynamics
Common Errors That Break DDM
Error 1: Applying DDM to Non-Dividend Payers
DDM requires dividends. For companies that do not pay dividends (or pay inconsistently), the model produces nothing useful. Use DCF or relative valuation instead.
Error 2: Assuming Constant Growth for Cyclical Companies
A company that grew dividends 8% last year might cut them 20% next year in a recession. DDM assumes smooth growth trajectories that cyclical businesses cannot deliver.
Why this matters: Dividend cuts destroy DDM valuations. If you modeled a $40 stock that cuts its dividend by 30%, the new value might be $28—a 30% hit to your position.
Error 3: Ignoring Dividend Policy Changes
Companies change their dividend policies. Share buybacks compete with dividends. Special dividends distort growth rates. A dividend increase today does not guarantee the same trajectory tomorrow.
Stability Criteria for DDM Candidates
A company is suitable for Gordon Growth Model when:
- Consistent dividend history: 10+ years of uninterrupted payments (and ideally, growth)
- Payout ratio stability: Neither too high (unsustainable) nor too low (unpredictable)
- Beta near or below 1: Lower systematic risk indicates stability
- CapEx approximately equals depreciation: The company is maintaining, not expanding aggressively
- Predictable business model: Regulated utilities, consumer staples with pricing power
The point is: DDM precision depends entirely on dividend predictability. Apply it to companies where that predictability exists.
Cross-Checking Your DDM Value
Your DDM output should make sense relative to:
- Current market price: If your DDM says $45 and the stock trades at $80, either the market is wrong or your assumptions are
- P/E multiples: A DDM value implying a 25x P/E for a utility suggests aggressive assumptions
- Dividend yield: Your implied yield (D1/V0) should match what similar companies pay
If your DDM value differs dramatically from market price, identify which assumption drives the gap. Usually it is the growth rate or required return.
Next Step
Find three mature dividend payers in different sectors (utility, consumer staples, REIT). Calculate their Gordon Growth Model values using current dividends, 5-year dividend growth rates, and your required return (start with 10-year Treasury + 4-5% equity risk premium). Compare your intrinsic values to current market prices. Document which assumptions would need to change to justify current prices—that exercise reveals what the market believes about each company's future.