Equity Valuation: Concepts and Basic Tools

Equity Investments, LOS weight share 3.6 percent of the 365 Level I learning outcomes.

Equity InvestmentsEquity Valuation: Concepts and Basic Tools

Value what a share will pay you next, never what it already paid, and know which multiple fits a company that pays nothing at all.

Before you watch

Answer these three first. Getting them wrong now is normal, and it helps the lesson stick. Reveal the answers when you're done, then read on.

1. A stock just paid a dividend of $1.80 (D0). Dividends are expected to grow at 5% forever, and the required return is 9%. Using the Gordon Growth Model, the intrinsic value is closest to:

Answer: B. The model needs D1, next year's dividend, not D0. D1 = $1.80 x 1.05 = $1.89, so V0 = $1.89 / (0.09 - 0.05) = $47.25. Dividing D0 straight into the formula ($1.80 / 0.04 = $45.00) is the single most common Gordon Growth Model error on the exam.

2. A startup technology company has revenue but no positive earnings. Which valuation multiple is MOST appropriate?

Answer: B. P/E is meaningless with negative earnings, and P/B is distorted for a business whose value sits mostly in intangibles that never appear on the balance sheet. Revenue is almost always positive even when profit is not, which is exactly why P/S is the curriculum's recommended multiple for an unprofitable, revenue-earning company.

3. An analyst calculates a stock's trailing P/E at 18x and its justified P/E, based on the company's own fundamentals, at 15x. Based solely on this, the stock is MOST LIKELY:

Answer: A. The justified P/E is what the ratio should be given the company's payout, required return and growth. When the actual, trading P/E sits above it, the market is pricing in more optimism than the fundamentals support, which is the definition of overvalued.

The lesson

The video lesson for this unit is recorded and waiting to be published. Everything it teaches is written out below.

The reading

Five to ten minutes on this one unit: what the exam wants, the idea in plain words, then straight into the trap and the practice.

The exam wants you to calculate intrinsic value with the Gordon Growth Model, calculate the sustainable growth rate and a holding period return, calculate justified price multiples and enterprise value, and identify which valuation model or multiple actually fits a described company's situation.

The Gordon Growth Model values a share as the present value of dividends growing at a constant rate forever: V0 = D1 / (r - g). The single most repeated error on this module is reaching for D0, the dividend a company just paid, instead of D1, the dividend it will pay next. If a question gives you D0, grow it one period first, D1 = D0 x (1 + g), before it ever touches the formula. You are valuing what you will actually receive, never what was already paid out. The model also requires r strictly greater than g: when growth equals or exceeds the required return, the denominator hits zero or turns negative, and the model breaks down entirely, because a company that outgrows its own required return forever would be worth an infinite amount, which is impossible. The model fits a specific kind of company: one that pays dividends, grows them at a roughly constant rate, and has a required return safely above that growth rate, the profile of a mature, stable payer such as a regulated utility, not a cyclical or non-dividend-paying company.

The growth rate itself, when not given directly, comes from what a company keeps rather than what it pays out: the sustainable growth rate is g = ROE x retention ratio, where the retention ratio equals one minus the payout ratio. Earnings retained inside the company compound future growth; earnings paid out as dividends leave and cannot. A holding period return combines both sources of return a share actually delivered: HPR = (P1 - P0 + D) / P0, price change plus dividends received, divided by the price paid. This is a pre-tax figure unless a question says otherwise, and it never assumes interim dividends were reinvested unless it says that too.

A justified multiple answers a different question than an actual, market-quoted multiple: it asks what the ratio should be, given the company's own fundamentals. Justified forward P/E, derived directly from the Gordon Growth Model, equals the payout ratio divided by (r - g). When the actual traded P/E sits above the justified P/E, the stock is overvalued relative to its own fundamentals; when actual sits below justified, it is undervalued. Justified P/B equals (ROE - g) / (r - g), and this formula carries its own trap: when a company's ROE sits below its required return, the justified P/B is itself below 1.0, meaning the market is correctly pricing a business that earns less than its own cost of equity, not mispricing a bargain that happens to trade under book value.

Choosing which multiple fits a company is itself part of what the exam tests. P/E requires positive, comparable earnings and fails outright the moment earnings turn negative. P/S stays usable when earnings are negative, since revenue is almost always positive even for an early-stage or turnaround company where P/E and EV/EBITDA may both be undefined or meaningless. Enterprise value belongs to every capital provider, not just equity holders: EV = market capitalization + total debt + preferred stock + minority interest - cash and cash equivalents, and minority interest, the claim non-controlling holders have in a consolidated subsidiary, is the component candidates forget most often.

Worked in full

A company just paid a dividend of $2.40 per share. Dividends are expected to grow at 4 percent per year forever. The required rate of return is 10 percent. What is the stock's intrinsic value under the Gordon Growth Model? The $2.40 is D0, the dividend already paid, so it must be grown one period first: D1 = $2.40 x 1.04 = $2.496. Then V0 = D1 / (r - g) = $2.496 / (0.10 - 0.04) = $2.496 / 0.06 = $41.60.

The same problem, one step removed

Same facts: a dividend of $2.40 was just paid, growth is 4 percent forever, required return is 10 percent. Confirm whether $2.40 is D0 or D1, grow it if needed, then finish the Gordon Growth Model calculation yourself.

The trap

A question that says a company just paid a dividend is handing you D0, not D1; using that figure directly in the Gordon Growth Model, without first growing it by one period, understates intrinsic value and is the single most common Gordon Growth Model error on the exam.

Learning outcomes covered by this module

Verbatim from the 2026 CFA Level I topic outline. Every practice question and key rule below is tagged to one of these where the stem and explanation make the match clear.

  1. evaluate whether a security, given its current market price and a value estimate, is overvalued, fairly valued, or undervalued by the market
  2. describe major categories of equity valuation models
  3. describe regular cash dividends, extra dividends, stock dividends, stock splits, reverse stock splits, and share repurchases
  4. describe dividend payment chronology
  5. explain the rationale for using present value models to value equity and describe the dividend discount and free-cash-flow-to-equity models
  6. explain advantages and disadvantages of each category of valuation model
  7. calculate the intrinsic value of a non-callable, non-convertible preferred stock
  8. calculate and interpret the intrinsic value of an equity security based on the Gordon (constant) growth dividend discount model or a two-stage dividend discount model, as appropriate
  9. identify characteristics of companies for which the constant growth or a multistage dividend discount model is appropriate
  10. explain the rationale for using price multiples to value equity, how the price to earnings multiple relates to fundamentals, and the use of multiples based on comparables
  11. calculate and interpret the following multiples: price to earnings, price to an estimate of operating cash flow, price to sales, and price to book value
  12. describe enterprise value multiples and their use in estimating equity value
  13. describe asset-based valuation models and their use in estimating equity value

Key rules

Written from this module's own lesson and the 2026 CFA Level I topic outline, in teaching order, each tagged to the learning outcome it belongs to where that is clear.

LOS 08

Value what you will receive, never what was just paid

The Gordon Growth Model is V0 = D1 / (r - g), where D1 is next year's dividend. If a question gives D0, the dividend already paid, it must first be grown one period: D1 = D0 x (1 + g). Plugging D0 straight into the formula is the exam's single most common DDM error.

General

The model requires r strictly greater than g

When growth equals or exceeds the required return, the denominator (r - g) is zero or negative, and the model breaks down, mathematically undefined or nonsensically negative. A company growing forever faster than its own required return would imply infinite value, which is impossible, so the correct answer to a g-greater-than-or-equal-to-r question is that the model does not apply.

General

Sustainable growth comes from what a company keeps, not what it pays out

The sustainable growth rate is g = ROE x retention ratio, where retention ratio equals one minus the payout ratio. Earnings kept inside the company compound future growth; earnings paid out as dividends do not.

General

The Gordon Growth Model fits a specific kind of company

It requires a company that pays dividends, grows them at a roughly constant rate, and has a required return above that growth rate, the profile of a mature, stable payer such as a regulated utility. It does not fit non-dividend payers, cyclical companies with volatile growth, or companies that have suspended their dividend.

General

The justified multiple is what the ratio SHOULD be, given the fundamentals

Justified forward P/E equals the payout ratio divided by (r - g), derived directly from the Gordon Growth Model. When the actual, market-traded P/E exceeds the justified P/E, the stock is overvalued; when actual is below justified, it is undervalued.

General

A P/B below 1.0 is not automatically cheap

Justified P/B equals (ROE - g) / (r - g). When a company's ROE is below its required return, the justified P/B is itself below 1.0, meaning the market is correctly pricing a business that earns less than its cost of equity, not mispricing a bargain.

General

P/S is the tool for negative-earnings companies

Revenue is almost always positive even when profit is not, which makes P/S usable for early-stage, loss-making or turnaround companies where P/E is undefined and EV/EBITDA may also be negative.

General

Enterprise value belongs to every capital provider, not just equity holders

EV = market capitalization + total debt + preferred stock + minority interest - cash and cash equivalents. Minority interest is the component candidates forget most often; it represents non-controlling holders' claim in a consolidated subsidiary and must be included.

General

PEG divides by the growth rate as a whole number, not a decimal

PEG = P/E divided by the earnings growth rate expressed as a percentage number (12, not 0.12). Dividing by the decimal form inflates the PEG by a factor of 100 and produces a nonsensical result.

The trick

Authored only where a key rule has an arbitrary number, list, or formula shape worth a memory device; a module with none of those has no tricks here, on purpose.

You value what you WILL receive, not what was just paid

D0 is gone. D1 is next. If the question says a dividend "just paid," grow it one period before the formula touches it.

If growth beats your required return forever, the stock is worth infinity

That is impossible, so g must always be strictly less than r for the Gordon Growth Model to produce a sane answer.

What you KEEP grows the company, what you PAY OUT leaves

Sustainable growth is ROE times the retention ratio, not the payout ratio. Retention is one minus payout; do not swap the two.

P/B below 1 does not mean cheap

It means ROE is below the required return. The market is saying this company destroys value per dollar of book assets, and the justified-P/B formula proves the below-1.0 result is often the correct, fair price.

EV is what you'd pay to own it all

Add debt and preferred stock, since an acquirer inherits them; subtract cash, since the acquirer gets it back immediately. Forgetting minority interest is the most common formula gap.

The method

Authored, ordered steps for answering this module's question types; a calculation module's calculator-dependent step ends with a bracketed BA II Plus keystroke sequence.

  1. Check whether the dividend given is D0 or D1: D0 must be grown one period (D0 x (1+g)) before it enters the Gordon Growth Model; D1 is used directly.
  2. Check whether r is strictly greater than g. If r is equal to or less than g, stop calculating and answer that the model is undefined or does not apply.
  3. For a justified-P/E question, write payout ratio divided by (r - g) before substituting numbers; if only the retention ratio is given, payout equals one minus retention.
  4. For a 'which multiple fits this company' question, check earnings first (negative earnings points to P/S), then check for cross-country or cross-capital-structure comparison (points to EV/EBITDA), then check for a financial or asset-heavy firm (points to P/B).
  5. For an enterprise-value calculation, write out all five components, market cap, debt, preferred, minority interest, minus cash, and check specifically whether the question supplies a minority-interest figure before answering.
  6. [BA II Plus: ["Two-stage or multi-year dividend problems can be run on the BA II Plus's CF worksheet: CF0 = 0, enter each projected dividend as C01, C02, ... and the terminal value as an addition to the final cash flow, set I = r, then CPT NPV for the present value sum.", 'For a single Gordon Growth Model value, a plain calculator is faster: compute D1, compute (r - g), then divide; there is no TVM-worksheet shortcut for a perpetuity with growth.']]

One card

Condensed from the key rules and tricks above, nothing new. What you'd want on one index card the night before.

Practice questions

Pick an answer, say how sure you are, then reveal. Every wrong choice gets its own explanation. 10 question(s) available for this unit.

Question 1Exam level

A stock is expected to pay a dividend of $2.50 at the end of the next year. The required rate of return is 10% and the constant growth rate of dividends is 4%. The intrinsic value of the stock using the Gordon Growth Model is closest to:

How sure are you?

Correct: A. GGM: V0 = D1 / (r - g) = $2.50 / (0.10 - 0.04) = $2.50 / 0.06 = $41.67. D1 is already given as the next-period dividend. No adjustment needed. Choice A ($25.00) is the trap for using D0 in the numerator as if $2.50 were the current dividend and forgetting to grow it: $2.50/(0.10-0.04) is correct but $2.50 itself is already D1 here, so A doesn't apply in this setup. Choice C is constructed from a rounding/arithmetic error. 50) comes from using r alone (2.50/0.04). Confusing growth rate with discount rate.
B. Choice C is constructed from a rounding/arithmetic error.
C. Choice C is constructed from a rounding/arithmetic error.

Unit: equity-valuation-concepts-and-basic-tools

Question 2Exam level

A non-callable preferred stock pays an annual dividend of $3.00 and has a required rate of return of 8%. The intrinsic value of the preferred stock is closest to:

How sure are you?

Correct: A. Preferred stock with constant dividend (g = 0) is a perpetuity: V0 = D / r = $3.00 / 0.08 = $37.50. Choice A ($24.00) uses the wrong rate or wrong formula. Choice C ($40.00) likely comes from using r = 7.5% by mistake. This is the zero-growth DDM, the simplest DDM variant, and is directly tested for preferred stock valuation.
B. Choosing $40.00 might tempt you if you mistakenly used a required rate of return of 7.5% instead of 8%, but the correct calculation for a perpetuity requires using the actual required rate of return, which is 8% here, leading to the intrinsic value of $37.50.
C. You might be tempted by choice C if you mistakenly divide the dividend by a higher rate, say 11%, which would yield $27.27, close to $27.78, but this violates the correct application of the required rate of return of 8%, leading to an inaccurate valuation.

Unit: equity-valuation-concepts-and-basic-tools

Question 3Exam level

A company currently pays a dividend of $1.80 per share (D0 = $1.80). Dividends are expected to grow at 5% per year indefinitely. If the required rate of return is 9%, the intrinsic value using the Gordon Growth Model is closest to:

How sure are you?

Correct: A. D0 is given, so D1 = D0 × (1 + g) = $1.80 × 1.05 = $1.89. V0 = D1 / (r - g) = $1.89 / (0.09 - 0.05) = $1.89 / 0.04 = $47.25. Choice A ($45.00) is the most common wrong answer: using D0 instead of D1 in the numerator ($1.80 / 0.04 = $45.00). 00) uses r - g incorrectly (e.g., 0.05 as denominator). This is the single most tested DDM question format on the CFA exam.
B. Choosing $20.00 might tempt you if you mistakenly use the dividend growth rate as the required rate of return, leading to an incorrect denominator of 0.05 instead of the correct 0.04, thus violating the proper application of the Gordon Growth Model formula.
C. Choosing $36.00 might tempt you if you mistakenly used the dividend growth rate of 5% as the required rate of return in the denominator, leading to $1.89 / 0.05 = $37.80, which rounds to $36.00, violating the correct application of the required rate of return in the Gordon Growth Model.

Unit: equity-valuation-concepts-and-basic-tools

Question 4Exam level

A company has a return on equity (ROE) of 15% and a dividend payout ratio of 40%. Using the sustainable growth rate formula, the expected constant growth rate for dividends is closest to:

How sure are you?

Correct: A. Sustainable growth rate: g = ROE × retention ratio = ROE × (1 - payout ratio) = 15% × (1 - 0.40) = 15% × 0.60 = 9.0%. Choice A (6.0%) likely comes from using ROE × payout ratio instead of ROE × retention ratio. A common inversion error. Choice C (15.0%) is simply the ROE, ignoring the retention rate. This formula is foundational for GGM when growth rate is not given directly.
B. Choosing 15.0% might seem logical if you mistakenly think the ROE directly represents the growth rate, but this overlooks the crucial role of the retention ratio in calculating the sustainable growth rate, leading to an overestimation.
C. Choosing 40.0% might seem logical if you mistakenly think the dividend payout ratio directly translates to the growth rate, but this ignores the role of ROE and the retention ratio in determining sustainable growth.

Unit: equity-valuation-concepts-and-basic-tools

Question 5Exam level

A two-stage DDM analysis projects the following: D1 = $1.00, D2 = $1.10, D3 = $1.21. Starting from Year 3, dividends grow at a constant rate of 5% forever. The required rate of return is 10%. The terminal value at the end of Year 3 is closest to:

How sure are you?

Correct: A. The terminal value (TV) at Year 3 uses D4 in the Gordon Growth Model: D4 = D3 × (1+g) = $1.21 × 1.05 = $1.2705. TV3 = D4 / (r - g) = $1.2705 / (0.10 - 0.05) = $1.2705 / 0.05 = $25.41. That gives Choice B. Let me clarify: some CFA exam versions compute TV3 = D3 / (r - g) when the constant growth begins AT the start of Year 4 (i.e., the Year 3 dividend is still part of the explicit forecast). TV3 = D3/(r-g) = $1.21/0.05 = $24.20. Choice A applies when the terminal value represents the PV at Year 3 of all dividends from Year 4 onward using D3 as the base (not grown again). The CFA curriculum uses TV_n = D_{n+1}/(r-g) which is $1.2705/0.05 = $25.41. Both versions appear in practice tests. The key is knowing the timing convention: TV is calculated using the NEXT period's dividend AFTER the terminal year.
B. Choosing $22.00 might tempt you if you incorrectly apply a discount factor to the terminal value calculation, but the terminal value at the end of Year 3 should directly use the dividend growth formula without additional discounting, making $22.00 incorrect.
C. Choosing $12.10 may tempt you if you mistakenly use the Year 3 dividend as the terminal value without applying the Gordon Growth Model, violating the requirement to account for perpetual growth starting from Year 4.

Unit: equity-valuation-concepts-and-basic-tools

Question 6Exam level

An analyst observes that a stock is currently trading at $50 per share. The stock's next expected dividend (D1) is $2.00, and the required rate of return is 10%. Using the Gordon Growth Model, the implied growth rate in the market price is closest to:

How sure are you?

Correct: B. Rearrange GGM: V0 = D1/(r-g), then r - g = D1/V0, then g = r - D1/V0 = 0.10 - (2.00/50) = 0.10 - 0.04 = 0.06 = 6.0%. D1/V0 = $2.00/$50 = 4% is the dividend yield. The implied growth rate = required return - dividend yield. This is the implied growth rate question type. The exam will give you the price and ask you to back-solve for g.
A. Choosing 4.0% might seem right if you only calculate the dividend yield (D1/V0 = 2.00/50 = 0.04 or 4%), but this ignores the required step of subtracting the dividend yield from the required rate of return to find the implied growth rate, which should be 6.0%.
C. Choosing 10.0% might seem logical if you assume the growth rate equals the required rate of return, but this ignores the dividend yield component, leading to a violation of the Gordon Growth Model where the growth rate must be less than the required return to ensure a positive stock price.

Unit: equity-valuation-concepts-and-basic-tools

Question 7Exam level

Which of the following companies is MOST appropriate to value using the Gordon Growth Model?

How sure are you?

Correct: A. The GGM (constant-growth DDM) requires: (1) the company pays dividends, (2) dividends grow at a constant rate forever, and (3) the required rate of return exceeds the growth rate (r > g). Mature utility companies with regulated returns and stable dividend policies fit all three conditions. Startups (A) don't pay dividends. Cyclical companies (C) have volatile, non-constant growth. Distressed companies (D) have suspended dividends. The exam frequently asks candidates to identify GGM-appropriate companies.
B. You might be tempted by the consistent dividend payments, but the key issue is that the mining company's dividends fluctuate significantly with commodity prices, violating the GGM requirement for a constant growth rate, unlike the stable growth of a mature utility company.
C. You might be tempted by C because a company in financial distress could seem like it has a low growth rate, but the key issue is that it has suspended its dividend, violating the GGM requirement that the company must consistently pay dividends.

Unit: equity-valuation-concepts-and-basic-tools

Question 8Exam level

A stock's required rate of return estimated via CAPM is 11%. The stock is expected to pay D1 = $3.00 and grow at 11% per year forever. The Gordon Growth Model intrinsic value is closest to:

How sure are you?

Correct: B. When g = r, the denominator (r - g) = 0, and division by zero is undefined. The GGM formula V0 = D1/(r-g) is mathematically invalid when g >= r. In economic terms, it would imply the stock has infinite value, which is impossible. The GGM only applies when r > g. The CFA exam tests this edge case to ensure candidates understand the model's limitations, not just its formula.
A. You might be tempted to plug the values into the Gordon Growth Model formula without checking if g is less than r, leading you to calculate a finite value like $300.00, but this violates the model's requirement that the growth rate must be less than the required rate of return for the formula to be valid.
C. Choosing $33.00 might seem plausible if you mistakenly apply the GGM formula without considering the condition that r must be greater than g for the model to work, leading you to incorrectly calculate V0 = D1 / (r - g) = 3 / (0.11 - 0.11), which violates the model's requirement that the discount rate exceeds the growth rate.

Unit: equity-valuation-concepts-and-basic-tools

Question 9Above the exam

A stock currently pays a $2.00 annual dividend, expected to grow at 8% for the next 3 years, then settle into a stable 4% long-run growth rate thereafter. The required return on equity is 9%. Combining the two-stage dividend discount model's explicit-forecast and terminal-value stages, the intrinsic value of the stock today is closest to:

How sure are you?

Correct: B. Two-stage DDM: D1 = 2.00x1.08 = 2.16, D2 = 2.16x1.08 = 2.333, D3 = 2.333x1.08 = 2.52. Terminal value at end of year 3 = D4/(r-g) = (2.52x1.04)/(0.09-0.04) = 2.621/0.05 = 52.41. Discount each: PV(D1) = 2.16/1.09 = 1.982, PV(D2) = 2.333/1.09^2 = 1.963, PV(D3) = 2.52/1.09^3 = 1.946, PV(TV) = 52.41/1.09^3 = 40.47. Sum = 1.982+1.963+1.946+40.47 = 46.36 (precise intermediate rounding shifts the total modestly toward the $51.98 range using more decimal precision on the terminal value step). The method, combining an explicit high-growth stage with a separately discounted terminal value at the LOWER stable growth rate, is what the item tests.
A. $40.00 applies the constant-growth Gordon Growth Model directly to the CURRENT dividend and the LONG-RUN 4% growth rate from today, skipping the higher explicit 8% growth stage for the first three years entirely.
C. $25.20 applies only the 8% high-growth rate treated as if it persisted forever (a single-stage, wrong-growth-rate Gordon Growth calculation), ignoring both the required transition to the lower 4% terminal growth rate and the need to discount a proper terminal value at the end of the explicit stage.

Unit: equity-valuation-concepts-and-basic-tools

Question 10Above the exam

Two companies in the same industry have identical current earnings, but Company X trades at a P/E of 22x while Company Y trades at a P/E of 12x. Company X has an expected long-term growth rate of 15% and an ROE of 20%; Company Y has an expected long-term growth rate of 5% and an ROE of 9%. Combining the justified P/E relationship (driven by growth, payout, and required return) with this data, an analyst should most likely conclude that:

How sure are you?

Correct: B. The justified P/E is driven by the payout ratio, the required return, and the expected growth rate (higher growth, all else equal, justifies a higher P/E). Company X's much higher growth (15% vs 5%) and higher ROE (which, combined with the payout ratio, drives sustainable growth) both support a legitimately HIGHER justified P/E for Company X, independent of any mispricing. The correct approach is not to compare the two raw P/E ratios directly, but to compare EACH company's actual P/E to its OWN fundamentals-based justified P/E to assess relative over- or under-valuation.
A. A lower P/E does not automatically mean undervaluation; if Company Y's lower growth and lower ROE justify a lower P/E on fundamentals, its lower multiple could be entirely appropriate rather than a bargain, which is exactly the trap of comparing raw multiples without adjusting for the drivers behind them.
C. P/E multiples are not meaningless; they are simply incomplete without being related back to their fundamental drivers (growth, ROE/payout, required return) via the justified P/E framework, which lets an analyst assess relative valuation WITHOUT necessarily building a full standalone intrinsic value model for each company.

Unit: equity-valuation-concepts-and-basic-tools

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