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

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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.

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1) What is stock valuation?

  • Idea: a stock is worth the present value of the cash a shareholder expects to receive in the future.
  • In this chapter, that cash flow is dividends. If you buy a share and hold it forever, the direct cash you receive from owning it is the stream of dividends.
  • So intrinsic value today = NPV of all future dividends. We discount each expected dividend by the required return r because cash received later is worth less than cash received today.
  • Why the future selling price does not change this logic: if you sell the stock later, the buyer will only pay a price based on the dividends they expect to receive after buying it. So the resale price itself ultimately comes from later dividends.
  • Therefore: stock value goes up when expected dividends go up or risk goes down; stock value goes down when expected dividends fall or the required return rises.
Key intuition: For a shareholder who lives forever, dividends are the payoff from ownership. That is why the Dividend Discount Model says the value of a stock is the present value of all expected future dividends.

2) Why dividends matter

Dividends are the actual cash paid to shareholders. In a Dividend Discount Model, they matter because they are the cash benefit of owning the stock. If you plan to hold the share forever, the only cash you ever collect from ownership is the stream of dividends.

Even if you do not hold forever, the price you can sell for later depends on what the next investor thinks the future dividends are worth. That is why the stock’s value still traces back to dividends.

Bottom line: In DDM, a stock is valuable because it gives its owner a claim on future dividends. So the fair price today is the net present value of all expected future dividends.

Quick links — Dividend history (Nasdaq)

JUFinance dividend tool

Use the live JUFinance dividend calculator here:

Open JUFinance Dividend Calculator

Dividend profiles & DDM suitability (teaching heuristics)

Ticker Company Dividend status Payout profile Style DDM suitability Notes

Heuristics for classroom use (not investment advice). “DDM suitability” is about whether a dividend-discount model is a reasonable anchor (stable, meaningful dividend stream).

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 a public source (Company IR → Dividend History, or Nasdaq Dividend History). Use split-adjusted values.
  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.

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

4.5) Equations — Dividend Growth (Gordon)

D0 = most recent dividend; D1 = next year’s dividend; require r > g.

Boxed Gordon Model equations

P0 = D1 / (r − g)

Stock price today from next dividend, required return, and growth.

D1 = D0(1 + g)

Convert the last dividend into next year’s expected dividend.

r = D1/P0 + g

Required return = dividend yield + growth.

g = r − D1/P0

Implied growth when price and return are given.

Important: the Gordon model needs r > g. If not, the formula breaks down.

Open JUFinance Dividend Calculator

  1. Price (Gordon/constant g):
    P0 = D1 / (r − g) = D0(1 + g) / (r − g)
  2. Required return r (yield + growth):
    r = D1 / P0 + g = D0(1 + g) / P0 + g
    Components: dividend yield D1/P0 and capital-gain yield g.
  3. Growth rate g:
    g = r − D1 / P0
  4. Dividends D1 and D0 from price:
    D1 = P0(r − g),    D0 = P0(r − g) / (1 + g)
  5. Future dividends (constant g):
    Dt = D0(1 + g)t

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

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

Open the JUFinance Dividend Calculator

Single-stage (Gordon)

Gordon model
Behavioral tweak

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.

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.

9) Common pitfalls

  • Using g ≥ r (model breaks). Keep r > g.
  • Using a single-stage model when payout policy is unstable or the dividend pattern is changing a lot.
  • Ignoring repurchases (dividends aren’t the only cash returned).
  • Mixing nominal/real rates (match units).

10) Quiz 1 — Dividend Growth Model (10 T/F)

Click True or False to get instant feedback and explanation before starting the homework.

Focus: why dividends matter, Gordon model logic, required return, growth, and common DDM mistakes.

HOMEWORK (Due with Final) — Dividend Growth Model

  1. Northern Gas: D0=2.80, g=3.8%, P0=26.91. Find r. (Northern Gas recently paid a $2.80 annual dividend on its common stock. This dividend increases at an average rate of 3.8 percent per year. The stock is currently selling for $26.91 a share. What is the market rate of return? (14.60 percent))
    D1=2.80×(1+0.038)
    r = D1/P0 + g
    Excel hint: = (2.80*(1+0.038))/26.91 + 0.038
  2. Douglass Gardens: g=4.1%, r=12.6%, P0=24.90. Find D1 (Douglass Gardens pays an annual dividend that is expected to increase by 4.1 percent per year. The stock commands a market rate of return of 12.6 percent and sells for $24.90 a share. What is the expected amount of the next dividend? ($2.12)).
    D1 = P0(r − g)
    Excel hint: = 24.90*(0.126 - 0.041)
  3. IBM: D0=3.00, g=10%. Find D1(IBM just paid $3.00 dividend per share to investors. The dividend growth rate is 10%. What is the expected dividend of the next year? ($3.3)).
    D1 = D0(1+g)
    Excel hint: = 3.00*(1+0.10)
  4. Given: P0=50, D1=2, g=6%. Find r. (The current market price of stock is $50 and the stock is expected to pay dividend of $2 with a growth rate of 6%. How much is the expected return to stockholders? (10%))
    r = D1/P0 + g
    Excel hint: = 2/50 + 0.06
  5. Creamy Custard: r=15%, D0=6.00, g=6% forever. Find P0 ( Investors of Creamy Custard common stock earns 15% of return. It just paid a dividend of $6.00 and dividends are expected to grow at a rate of 6% indefinitely. What is expected price of Creamy Custard's stock? ($70.67)).
    P0 = D1/(r−g) = D0(1+g)/(r−g)
    Excel hint: = 6*(1+0.06)/(0.15-0.06)
Tools:
Open Dividend Calculator Open DCF Calculator