Cost of Equity (Dividend Discount)

Builds onGrowing Perpetuity (Gordon Growth) — if this page feels steep, start there.

r_e = \frac{D_1}{P_0} + g

$D_1$: NEXT year's expected dividend (one year of growth already applied)
$P_0$: today's share price — the market's verdict, taken as given
$D_1 / P_0$: the forward dividend yield: the cash return you collect
$g$: the perpetual dividend growth rate: the return you ride
$r_e$: the cost of equity: yield plus growth, decoded from the price

Why it must be true

Flip the Gordon growth model inside out. Gordon says a growing dividend stream is worth $P_0 = D_1/(r_e - g)$ . But the market has already set the price — so the price is a message about what return shareholders demand. Decode it and the required return splits into two visible pieces: **the dividend yield you collect ( $D_1/P_0$ ) plus the growth you ride ( $g$ )**.

It's an appealingly observable formula: yield is on every quote screen, and growth can be disciplined by fundamentals ( $g = b \times ROE$ ). This is the CAPM's main rival for estimating what equity costs — same question, different evidence.

The derivation

Start from the Gordon growth valuation:

P_0 = \frac{D_1}{r_e - g}

Multiply both sides by $(r_e - g)$ , divide by $P_0$ , and isolate the rate:

r_e - g = \frac{D_1}{P_0} \quad\Rightarrow\quad r_e = \frac{D_1}{P_0} + g

Note it needs next year's dividend $D_1$ . If given today's $D_0$ , grow it one year first: $D_1 = D_0(1+g)$ .

When to reach for it

Estimating the cost of equity from market data for a dividend-paying firm — especially when a beta is unreliable or a second estimate is wanted beside CAPM.

Listen for

“cost of equity using the dividend discount model”“expected to pay a dividend of … next year”“dividends growing at … indefinitely”“current share price of …”

Back-of-the-envelope

Estimate it in your head first — then the calculator only confirms.

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Two ingredients you can eyeball: dividend yield (≈2–5% for payers) plus growth (≈3–8% sustainable) → r_e almost always lands in 7–13%. Answers outside that band deserve suspicion.
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D₀ vs D₁ check: if the given dividend is 'just paid', bump it by g before dividing. The un-bumped answer is usually sitting among the distractors.

Traps in applying it

✗Using D₀ (just paid) instead of D₁ (next year's) in the yield — the model wants the forward dividend.
✗Adding a g that exceeds any defensible long-run economy growth — the formula explodes as g approaches r.
✗Applying it to non-payers or erratic payers — no dividend, no dividend discount.

Limits & criticisms

Everything rides on g, an assumption about forever — small changes swing the answer by whole points, which is why rate-case testimony wars over it. The model needs a stable, dividend-paying firm (useless for growth companies that retain everything), assumes the market price is "right," and hides buybacks, which have replaced much of dividends as the payout channel — modern practice often adds them back into D.

Where it came from

The valuation this inverts is Myron Gordon's (1959) — but using it backwards to extract the cost of equity is the regulator's classic move: US utility rate cases have set allowed returns with the "DCF method" (this formula) since the 1960s, with expert witnesses arguing over nothing but the g. Corporate finance teams still triangulate their cost of equity between this and the CAPM, and the Fed model debates about market-level expected returns are this formula applied to whole indexes.

One identity, 1 questions

The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.

Yield plus growth

r_e = \frac{D_1}{P_0} + g

The decoding face: the market price, read backwards through Gordon, reveals the return shareholders demand.

Drill this face →

On the BA II Plus

Worked example: With shares at $40.00, a forward dividend of $3.40, and perpetual growth of 4.5%, what cost of equity does the dividend discount model imply?

1.3.4 [÷] 40 [=]the forward dividend yield
2.[+] 0.045 [=]plus growth → r_e (decimal)

→ 13%

Where it leads

Master this and the following come almost for free:

Weighted-Average Cost of Capital

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