Chapter 8 — Stock Valuation: Dividend Growth Model (Gordon)

FIN509Interactive

0) Overview

Forward-looking valuation asks: what is a fair price today given the cash we expect tomorrow and the return we require? In the Dividend Discount Model (DDM), the relevant cash to shareholders is the dividend stream. Under constant growth forever, we get the Gordon Growth Model.

1) What is stock valuation?

  • Goal: convert future cash flows into a present price using a required return (r).
  • Price ↑ when expected cash flows ↑ or risk ↓; return ↑ when price ↓ relative to future cash flows.
  • Different models focus on different cash definitions (FCFE, FCFF, dividends). Here we focus on dividends.

2) Dividends as cash flow

Dividends are the actual cash paid to equity holders. For firms with stable payout policies, valuing the dividend stream is intuitive and tractable.

Reminder: Buybacks also return cash. For heavy repurchasers, consider total shareholder yield or an FCFE model.

2.5) Why dividends can forecast price

Bottom line: A stock’s fair price equals the present value of future cash distributions. Dividends are the most direct, observable cash flow to shareholders, so a view on the path of dividends and the required return lets us forecast price.

Valuation identity

P0 = Σt=1∞ Dt / (1+r)t

If dividends grow at constant g (r > g): P0 = D1 / (r − g)

Expected return ≈ dividend yield + growth: r ≈ D1/P0 + g

Why dividends work as a forecasting anchor

  • Cash, not accounting: dividends are real cash; earnings/book can be noisy.
  • Policy is sticky: boards smooth dividends, so paths are more predictable.
  • Signal of capacity: raises reveal confidence in future cash generation.
  • Ties straight to r: the DDM pins down price once you choose r and g.
  • Anchors terminal value: Gordon logic underlies long-run DCF terminal value.
  • Clean long-run series: split-adjusted dividend history helps estimate g.

Quick recipe to forecast price

  1. Get D0: use the Dividend History tool (WMT/KO), split-adjusted.
  2. Estimate g: 5-yr dividend CAGR, or sustainable g ≈ ROE × (1 − payout).
  3. Set r: from CAPM or your course’s required return.
  4. Compute D1: D1 = D0(1+g).
  5. Price: P0 = D1 / (r − g). Check r > g.
  6. Cross-check: r ≈ D1/P0 + g (does it match your r?).
Tip: If payout policy is changing (buybacks vs. dividends), use a multi-stage path for D and transition to a stable g.

3) Gordon model — infinite horizon derivation

Assume dividends grow at a constant rate g forever and the investor lives forever.

Dt = D1(1+g)t−1,   t = 1,2,3,…

P0 = ∑t=1∞ Dt/(1+r)t = D1/(r − g),   r > g

This is the PV of a growing perpetuity. Not constant? Use a multi-stage model (below).

4) Key equations

Price (given r, g, D1)

P0 = D1 / (r − g)

Often we’re given D0 (the most recent dividend). Then D1 = D0(1+g).

Required return (given P0, g, D1)

r = D1 / P0 + g = dividend yield + growth

5) The growth rate g — what it is & how to estimate

g is the long-run growth rate of dividends per share (not revenue). It should be plausible and sustainable (for mature firms, usually ≤ nominal GDP).

Common approaches

  • Historical dividend CAGR (5–10y), adjusted for cyclicality/payout changes.
  • Sustainable growth: g ≈ ROE × (1 − payout)
  • Analyst long-term EPS growth as a proxy.
  • Macro anchor for mature names: inflation + real growth.

Why it’s hard

  • Payout policy shifts (buybacks vs. dividends).
  • Leverage/ROE changes alter sustainable g.
  • Industry/regulatory/structural changes.

6) Interactive DDM calculator

Set any two and solve the third. All numbers are annualized. Constraint: r must be greater than g.

Single-stage (Gordon)

Gordon model
Behavioral tweak

Two-stage (optional)

Years 1…N at g₁; N+1→∞ at g₂

Stage 1: years 1…N at g₁. Terminal is at year N using DN+1 = DN(1+g₂).

7) Worked examples

Example A — Price from r and g

Suppose D₀ = $1.80, g = 5%, r = 8%. Then D₁ = 1.80×1.05 = 1.89 and

P₀ = D₁/(r−g) = 1.89 / 0.03 = $63.00 (illustrative).

Example B — r from P₀ and g

P₀ = $50, D₀ = $2.00, g = 4% ⇒ D₁ = 2.08.

r = D₁/P₀ + g = 2.08/50 + 0.04 = 8.16%.

7.2) Dividend history — Walmart & Coca-Cola

Classroom data for practice (summarized). Verify with sources: Macrotrends: WMT, Nasdaq: WMT, Macrotrends: KO, Nasdaq: KO.

Use in DDM next

Note (WMT): 2024 shows smaller per-share dividends due to a 3-for-1 stock split.

7.5) Non-Constant Dividend Growth (multi-stage)

What you do in this model

  1. Project the early dividends (or FCF) year by year.
  2. When growth turns constant at year n, compute a terminal price at n: Pn = Dn+1 / (r − g).
  3. Discount everything back to today and add: P0 = D1/(1+r) + … + (Dn+Pn)/(1+r)n.

Calculator: Non-Constant Dividend Growth Calculator

Exercise 1 — Enterprise/FCF (AAA)

Given

  • FCF (millions): 75, 84, 96, 111, 120 for years 1–5.
  • From year 6 on: constant growth g = 6%; WACC r = 15%.

Asked

  • Enterprise value today (EV).
  • With debt = $500m and shares = 14m, what is the stock price?
Show solution
  1. Terminal at t=5: FCF6/(r−g) = 120·1.06/(0.15−0.06) = 1,413.33
  2. PV today: NPV(15%; 75, 84, 96, 111, 120 + 1,413.33) = 1,017.66
  3. Equity value ≈ 1,017.66 − 500 = 517.66 (millions)
  4. Price ≈ 517.66 / 14 = $36.98 per share
Note: In steady state, Firm value ≈ FCF1/(WACC−g) = FCF0·(1+g)/(WACC−g).

Exercise 2 — Zero dividends until year 2

Given

  • D₀=0; D₂=0.56; afterwards dividends grow at g = 4%
  • Required return r = 12%

Asked: Stock price today, P₀.

Show solution
  1. At t=2 (start of perpetual growth): P₂ = D₃/(r−g) = 0.56·1.04/0.08 = 7.28
  2. Today: P₀ = [D₂ + P₂]/(1+r)² = (0.56 + 7.28) / 1.12² = 6.25

Exercise 3 — High growth then stable

Given

  • Required return r = 12%, D₀ = 1.00
  • Dividends grow at 30% for the next 4 years (D₁..D₄)
  • Then grow at g = 6.34% forever

Asked: Stock price today (≈ $40).

Show solution
  1. D₁..D₄ = 1.30, 1.69, 2.197, 2.8561
  2. D₅ = 2.8561·1.0634 = 3.0372
  3. Terminal at t=4: P₄ = D₅/(r−g) = 3.0372 / (0.12 − 0.0634) = 53.6604
  4. Today: P₀ = Σ(Dₜ/(1+r)ᵗ, t=1..4) + P₄/(1+r)⁴ ≈ $40.00
Workflow: (1) project early dividends/FCF; (2) compute terminal when growth stabilizes; (3) discount back and add.

8) Behavioral finance — why prices wander from value

Everyday biases (student-life examples)

  • Yield chasing: 9% yield “looks safe,” no check of payout ratio → yield trap.
  • Extrapolation: last 5 hikes ≠ forever; setting g too high.
  • Loss aversion/attention: scary headline → sell a solid utility at lows.
  • Sentiment/limits to arbitrage: flows push price ±15% from intrinsic.
Use the calculator’s Sentiment premium/discount to see mood move observed price.

Mini-cases

“Gold is ripping — dump my dividend stock?”

Hot narratives raise your opportunity cost (higher r) or lower your g assumption → P* falls. Ask: did the firm’s dividend outlook or risk change?

High-yield telecom at 8% — free money?

Check FCF vs dividends, leverage, capex. High yield can signal an impending cut.

Utilities as “bond proxies”

When rates jump, r rises even if D₁ and g are unchanged → price down. Reverse when rates fall.

Quick simulator: mood → price & implied return

Uses your DDM inputs from Section 6 (D₀, g, r). Run once above, then try mood here.

−20 to +20 typical

9) Common pitfalls

  • Using g ≥ r (model breaks). Keep r > g.
  • Single-stage on firms with non-constant growth or changing payout policy.
  • Ignoring repurchases (dividends aren’t the only cash returned).
  • Mixing nominal/real rates (match units).

10) Instructor notes

  • Homework: estimate g three ways for a mature payer.
  • Extend to a two-stage model for a transitioning firm.
  • Connect DDM ↔ WACC/FCFF when consistent assumptions align.
© FIN509 • Teaching use. Examples are illustrative.