In plain English
Owning a share means owning a slice of future profits. Valuation asks what that slice is worth once you have accounted for growth and risk.
The advanced view
Dividend discount, free-cash-flow-to-equity and residual income models are algebraically equivalent under clean-surplus accounting; they differ in which forecast is easiest to make reliably. Multiples embed the same drivers, so a defensible comparison controls for growth, risk and returns on incremental capital.
A share is a claim on residual cash flows with no maturity date, so its value is the present value of everything shareholders will ever receive. The dividend discount model states this directly, and the Gordon growth form collapses it into one line: value equals next year's dividend divided by the required return minus the growth rate. Its power is not precision but sensitivity analysis — it shows exactly how much of a share price is a bet on growth.
Equity value
P₀ = D₁ / (r − g) g = ROE × retention ratio (sustainable growth) P/E = payout ratio / (r − g) Justified P/B = (ROE − g) / (r − g) Earnings yield = 1 / P/E; Total return ≈ dividend yield + growth
Multiples are shorthand for the same discounted logic. A P/E of 20 embeds assumptions about growth, risk and payout; if you can rewrite a multiple as its implied growth rate you can argue about the assumption instead of the number. Use EV-based multiples (EV/EBITDA, EV/EBIT, EV/Sales) when capital structures differ, and equity multiples (P/E, P/B) when comparing within a sector with similar leverage. Always match the numerator to the claim: enterprise value pairs with pre-interest earnings, price pairs with post-interest earnings.
Two-stage models handle real companies: an explicit high-growth phase, then a terminal Gordon phase once growth converges toward the economy's rate. Terminal growth above long-run GDP growth implies a company eventually becomes the entire economy, which is where most amateur models break. Discipline the terminal value — if it exceeds roughly 75% of your total value, your answer is a growth assumption wearing a spreadsheet.
Essential vocabulary
- Retention ratio
- The share of earnings kept in the business (1 − payout ratio). Multiplied by ROE it gives sustainable growth.
- Required return (r)
- What investors demand for the risk taken, usually estimated with CAPM. The discount rate for equity cash flows.
- Equity risk premium
- Expected return of equities over the risk-free rate. Typically estimated at 4–6% in developed markets.
- Free cash flow to equity
- Cash available to shareholders after reinvestment and debt service. The cash-based alternative to dividends.
- Multiple expansion
- A rise in value from the market paying a higher multiple, not from earnings growth. In deals it is luck, not skill.
Strategy connection
The share price already contains a strategy. Back out the growth and margin path implied by today's multiple, and the strategic question becomes concrete: does our plan beat what the market has already priced in? Beating expectations, not beating last year, is what creates shareholder value.
Intuition
Equity value is the residual claim, so small changes in operating assumptions swing it hard once leverage is involved. The dividend-discount and Gordon models are the same perpetuity you already know; the discipline is in sustainable payout and sustainable growth (g = ROE × retention).
Common pitfalls
- ×Assuming a growth rate the balance sheet cannot fund — check g against ROE × retention.
- ×Using a trailing P/E to value a company mid-turnaround.
- ×Ignoring dilution from options and convertibles in per-share value.
Worked example — Gordon growth
Step 1 of 4
- 1DPS next year 3.0, cost of equity 9%, ROE 12%, payout 50%
Why it works
Gordon growth, P = D₁/(r − g), works because a growing perpetuity is a geometric series that converges when g < r. It also explains the multiple: divide by earnings and P/E = payout/(r − g), showing that a high multiple is a claim about growth, risk or payout — never about the multiple itself.
How it is used — justify a peer's premium
Step 1 of 4
- 1Company A trades at 15× earnings, peer B at 20×.
Deeper
Deeper: what a multiple is really saying
Rearranging the Gordon model gives P/E = payout ÷ (ke − g), so a multiple is a statement about growth, risk and how much of earnings must be reinvested. Two companies with the same growth deserve different multiples if one needs twice the capital to get it — that is the reinvestment rate, g ÷ ROIC.
PEG, EV/sales and price/book are crude versions of the same logic. Price/book only means something when book approximates replacement cost (banks, insurers). EV/sales only means something when you have a view on the terminal margin.
Must know cold
- ✓P/E = payout ratio ÷ (ke − g); reinvestment rate = g ÷ ROIC.
- ✓Forward multiples beat trailing multiples for decisions.
- ✓Use EV multiples when leverage differs across the peer set.
- ✓A multiple is a comparison, never a valuation on its own.
Exercises
Try each one on paper before revealing the worked solution.
Exercise 1
ke 9%, g 4%, ROIC 16%. What payout and P/E does the model imply?
Exercise 2
A peer trades at 20× earnings with 5% growth; your company grows 10% and trades at 25×. Is it cheap?