Practice: Equity Valuation: Concepts and Basic Tools
Equity Investments. 46 question(s) in this unit's pool
(2 above the exam). Free up to ten a day; the coach picks which ones based on what you have
already answered and when each is next due.
Equity InvestmentsEquity Valuation: Concepts and Basic Tools
Pick an answer, say how sure you are, then reveal. Every wrong choice gets its own
explanation. Questions you have already answered correctly and confidently stay out of the way until they
are due for review again.
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 9Harder
A company currently pays an annual dividend of $2.00 (D0). The company's ROE is 12% and its earnings retention ratio is 50%. Using the sustainable growth rate and Gordon Growth Model, the intrinsic value of the stock, given a required rate of return of 10%, is closest to:
How sure are you?
Correct: C. g = ROE x retention ratio = 12% x 50% = 6%. D1 = D0 x (1+g) = $2.00 x 1.06 = $2.12. V0 = D1/(r-g) = $2.12/(0.10-0.06) = $2.12/0.04 = $53.00 exactly. The keyed choice, $52.00, is the closest of the three offered values to that exact result. A roughly 2% rounding gap, wider than typical for a CFA 'closest to' item, recorded here rather than smoothed over.
A. Uses D0 without growing it to D1: $2.00/0.04 = $50.00. The dividend must be grown one year to D1 = D0 x (1+g) before applying the Gordon Growth Model.
B. Does not match the Gordon Growth Model computation: g = 6%, D1 = $2.12, V0 = D1/(r-g) = $53.00, closest to the keyed $52.00.
Unit: equity-valuation-concepts-and-basic-tools
Question 10Exam level
A two-stage DDM analysis values a company with supernormal growth of 15% for the first 3 years, then constant growth of 4% thereafter. D0 = $1.00, required return = 12%. Which step is most likely performed FIRST when solving for V0?
How sure are you?
Correct: A. The two-stage DDM process: (1) Explicitly forecast dividends during the supernormal growth phase (D1, D2, D3 at 15%). (2) Calculate the terminal value at the end of the supernormal period using the Gordon Growth Model with the stable growth rate (D4/(r-g_stable)). (3) Discount all cash flows back to today using the required return. Step B is always first. Choice A is Step 2, not Step 1. Choice C is wrong. All discounting uses the required return r, not the growth rate.
B. Choice C is wrong. All discounting uses the required return r, not the growth rate.
C. Choice C is wrong. All discounting uses the required return r, not the growth rate.
Unit: equity-valuation-concepts-and-basic-tools
Question 11Exam level
A stock pays a quarterly dividend of $0.50. If the annual required rate of return is 8%, the value of this preferred stock using the DDM is closest to:
How sure are you?
Correct: A. Annual dividend = $0.50 x 4 quarters = $2.00. Since this is preferred stock with no growth, V0 = D/r = $2.00 / 0.08 = $25.00. Always annualize the dividend before dividing by the annual required return.
B. You might be tempted to choose $6.25 if you mistakenly used the quarterly dividend of $0.50 without annualizing it, leading to an incorrect calculation of $0.50 / 0.08. However, the dividend discount model requires annualizing the dividend, which is why you should multiply the quarterly dividend by 4 to get the annual dividend before dividing by the annual required return.
C. You might be tempted to double the annual dividend to $4.00, thinking it compounds, but preferred stock dividends do not compound; they are fixed, so you should not multiply the annual dividend by two, leading to an incorrect value of $50.00.
Unit: equity-valuation-concepts-and-basic-tools
Question 12Exam level
An investor purchases a stock for $45.00. During the year, the stock pays a dividend of $1.80 and the price rises to $50.40. The holding period return is closest to:
A. Dividend yield only. You might ignore capital appreciation
C. You might add dividend yield to capital gain incorrectly using wrong base
Unit: equity-valuation-concepts-and-basic-tools
Question 13Exam level
A stock currently trades at $60.00 and is expected to pay a dividend of $2.40 at year-end. The sustainable growth rate is estimated at 5.0%. Using the Gordon Growth Model, the required return on equity is closest to:
How sure are you?
Correct: B. r = D1/P0 + g = $2.40/$60.00 + 0.05 = 0.04 + 0.05 = 9.0%. D1 is already given as the next dividend ($2.40), so no adjustment needed. Dividend yield = 4.0%, growth component = 5.0%, required return = 9.0%.
A. You might report only the growth rate
C. You might use a different price or adjusts D1 incorrectly
Unit: equity-valuation-concepts-and-basic-tools
Question 14Exam level
Company XYZ has a return on equity (ROE) of 15% and a dividend payout ratio of 40%. The sustainable growth rate for XYZ is closest to:
How sure are you?
Correct: B. g = ROE x b, where b = retention ratio = 1 - payout ratio = 1 - 0.40 = 0.60. g = 0.15 x 0.60 = 0.09 = 9.0%. The sustainable growth rate is not the ROE itself (15%). ROE is only the return on reinvested earnings.
A. You might multiply ROE by payout ratio (0.15 x 0.40 = 6%) instead of retention ratio
C. Arithmetic error or incorrect formula application
Unit: equity-valuation-concepts-and-basic-tools
Question 15Exam level
An analyst decomposes a stock's expected return into its components. The stock has a current price of $80, expected dividend of $2.00 next year, and an expected price of $86 in one year. The dividend yield component of the HPR is closest to:
How sure are you?
Correct: A. Dividend yield = D1 / P0 = $2.00 / $80.00 = 2.50%. Capital gain yield = (P1 - P0) / P0 = ($86 - $80) / $80 = 7.50%. Total HPR = 2.50% + 7.50% = 10.00%.
B. You might report capital gain yield instead of dividend yield
C. You might report total HPR instead of only the dividend yield
Unit: equity-valuation-concepts-and-basic-tools
Question 16Harder
In the context of the Gordon Growth Model, if a company's stock is fairly valued, the relationship between the expected return from CAPM and the required return implied by the dividend discount model is most likely described as:
How sure are you?
Correct: B. In an efficient market where stock prices reflect all available information, the required return estimated from CAPM (systematic risk pricing) and the expected return implied by the DDM (dividend yield + growth) should converge. If they diverge, it implies the stock is mispriced. This convergence is a core insight the CFA curriculum tests.
A. No directional dominance exists. This confuses risk premium with total return
C. Both estimates represent required return on equity. They are directly comparable
Unit: equity-valuation-concepts-and-basic-tools
Question 17Exam level
A portfolio manager buys a stock at $100, receives dividends of $3.00 and $3.50 at the end of years 1 and 2 respectively, and sells the stock at $112 at the end of year 2. The two-year holding period return is closest to:
How sure are you?
Correct: A. Two-year HPR = (P2 - P0 + D1 + D2) / P0 = ($112 - $100 + $3.00 + $3.50) / $100 = $18.50 / $100 = 18.5%. The exam typically uses the simple (non-compounded) version unless it explicitly states dividends are reinvested.
B. You might count only one dividend: ($112 - $100 + $3.00) / $100 = 15%. Or similar arithmetic error
C. You might reinvest the first dividend at some assumed rate and gets a higher total
Unit: equity-valuation-concepts-and-basic-tools
Question 18Exam level
A stock with a current price of $50 has a required return of 10% and an expected sustainable growth rate of 6%. Using the Gordon Growth Model, the expected next dividend (D1) is closest to:
How sure are you?
Correct: A. Rearranging r = D1/P0 + g: D1 = P0 x (r - g) = $50 x (0.10 - 0.06) = $50 x 0.04 = $2.00. The GGM can be rearranged in multiple directions. Here we solve for D1 given price and return inputs.
B. You might use r instead of (r - g): $50 x 0.10 / something
C. You might use r - g incorrectly: $50 x 0.05 = $2.50 (uses wrong spread)
Unit: equity-valuation-concepts-and-basic-tools
Question 19Exam level
Which of the following statements about the components of equity return is MOST accurate?
How sure are you?
Correct: B. HPR = dividend yield + capital gains yield. This decomposition is definitionally true regardless of holding period length. Option A is a generalization that is not always true. Option C is false. Zero-dividend stocks generate returns entirely from price appreciation.
A. A plausible generalization but not definitionally true. Value stocks sometimes have low dividend yields too
C. Classic misconception: total return requires dividends. Price-only appreciation is a valid and complete return
Unit: equity-valuation-concepts-and-basic-tools
Question 20Exam level
An investor purchases a stock at $40, sells it one year later at $38, and receives a $3.00 dividend during the year. The holding period return is closest to:
How sure are you?
Correct: B. HPR = (P1 - P0 + D) / P0 = ($38 - $40 + $3.00) / $40 = $1.00 / $40 = 2.5%. The price fell by $2.00 (capital loss of -5.0%) but the dividend of $3.00 (yield of 7.5%) more than offset the loss, producing a positive total return of 2.5%.
A. You might calculate only the capital loss: ($38 - $40)/$40 = -5.0%
C. You might calculate only the dividend yield: $3.00/$40 = 7.5%
Unit: equity-valuation-concepts-and-basic-tools
Question 21Exam level
A firm's ROE is 12% and its earnings retention ratio is 50%. If the required return on the stock is 9% and next year's expected dividend is $1.50, the estimated stock value using the Gordon Growth Model is closest to:
How sure are you?
Correct: C. Step 1: g = ROE x b = 12% x 50% = 6%. Step 2: P0 = D1 / (r - g) = $1.50 / (9% - 6%) = $1.50 / 3% = $50.00. This is the standard GGM valuation, which is the inverse of solving for required return.
A. You might use r alone as denominator: $1.50 / 0.09 = $16.67 (ignores growth)
B. You might use (r - ROE) instead of (r - g): $1.50 / (0.09 - 0.12) gives a negative denominator, which cannot be a stock price. The growth rate g (6%), not ROE (12%), belongs in the denominator.
Unit: equity-valuation-concepts-and-basic-tools
Question 22Exam level
Which of the following BEST describes why the Gordon Growth Model is most appropriate for valuing dividend-paying companies in mature industries?
How sure are you?
Correct: B. The GGM assumes a constant, perpetual dividend growth rate. This assumption is most realistic for mature, stable companies whose dividends grow at a rate close to the long-run GDP growth rate. High-growth companies violate the constant-growth assumption because their growth rates are high but unsustainable in perpetuity.
A. Mature companies do not have zero growth. They have stable, modest growth. Zero-growth would be the zero-growth DDM (P0 = D/r)
C. The model explicitly assumes constant growth. This assumption fails for high-growth firms
Unit: equity-valuation-concepts-and-basic-tools
Question 23Exam level
An analyst is valuing Greenfield Corp., a mature utility company that has paid stable dividends for 15 consecutive years. The company's dividend payout ratio is approximately equal to its free cash flow to equity. The analyst is taking a minority shareholder perspective. Which valuation approach is MOST appropriate?
How sure are you?
Correct: A. DDM is most appropriate when: (1) the company pays dividends, (2) dividends approximate free cash flow to equity, and (3) the valuation is from a minority shareholder perspective. All three conditions are met here. FCFE (A) would give the same answer as DDM when dividends equal FCFE, so it is not wrong. But the exam tests that DDM is the 'most appropriate' choice in this scenario because it directly uses the cash flow the minority investor actually receives. Asset-based valuation (D) is used for holding companies and liquidation scenarios, not operating utilities valued as going concerns.
B. You might find the P/E multiple tempting because it seems straightforward for industry comparisons, but it overlooks the specific relevance of dividends as the actual cash flow to minority shareholders, which the DDM directly accounts for.
C. You might be tempted by the idea that asset values are crucial for regulated assets, but asset-based valuation focuses on replacement costs rather than the cash flows received by shareholders, which is why the dividend discount model is more suitable for valuing the future dividends Greenfield Corp. pays out.
Unit: equity-valuation-concepts-and-basic-tools
Question 24Exam level
TechVenture Inc. is a fast-growing software company that has never paid a dividend and retains all earnings to fund expansion. Its earnings per share this year were $2.50. Which of the following valuation models is LEAST appropriate for valuing TechVenture?
How sure are you?
Correct: B. The DDM requires that the company pays dividends to shareholders. TechVenture has never paid dividends and retains all earnings. DDM cannot be applied because there are no dividends to discount. FCFE (B) is applicable because it values the cash flow the company could distribute to equity holders regardless of whether it actually does so. P/S (A) and EV/EBITDA (D) are applicable for non-dividend-paying growth companies where earnings-based multiples may also be problematic if earnings are volatile.
A. You might be tempted to think FCFE is inappropriate because TechVenture does not pay dividends, but FCFE actually evaluates the cash flow available to equity holders, making it suitable even for companies that retain all earnings, unlike DDM which specifically requires dividend payments.
C. You might find the EV/EBITDA multiple tempting because it is a common valuation method for growth companies, but it is not the least appropriate choice here; the DDM is least suitable since TechVenture does not pay dividends, making the DDM irrelevant for valuation.
Unit: equity-valuation-concepts-and-basic-tools
Question 25Exam level
A CFA analyst is comparing two companies in the same industry: Company A has a debt-to-equity ratio of 0.2, and Company B has a debt-to-equity ratio of 2.8. The analyst wants to compare the fundamental operating performance of both companies, eliminating the effect of their different capital structures. Which valuation multiple is MOST appropriate?
How sure are you?
Correct: B. EV/EBITDA is the correct multiple when comparing companies with different capital structures. Enterprise Value (EV = market cap + total debt - cash) captures the value available to all capital providers (debt and equity), and EBITDA is a pre-interest, pre-tax measure of operating profitability. Together, EV/EBITDA removes the distorting effect of leverage. P/E (A) is an equity multiple that is directly affected by leverage. Higher debt increases interest expense, reducing EPS, which artificially lowers P/E for the more-leveraged firm. P/B (B) and dividend yield (D) do not solve the capital structure comparison problem.
A. You might be tempted by the P/B ratio because it seems to offer a direct comparison of asset values, but this choice overlooks the fact that P/B is equity-focused and thus affected by different capital structures, unlike EV/EBITDA which adjusts for debt and provides a clearer picture of operating performance.
C. You might be tempted by the idea that dividends indicate a company's financial health and management's confidence, but dividend yield does not account for capital structure differences, unlike EV/EBITDA which adjusts for leverage, making it unsuitable for comparing companies with varying debt levels.
Unit: equity-valuation-concepts-and-basic-tools
Question 26Exam level
Wolverine Holdings is a conglomerate that owns stakes in 12 different private companies across diverse industries. None of the subsidiaries pay dividends to the holding company. An analyst is asked to estimate the intrinsic value of Wolverine Holdings. Which valuation approach is MOST appropriate?
How sure are you?
Correct: B. Asset-based valuation is the most appropriate method for holding companies that derive their value from ownership stakes in other entities. The value of Wolverine Holdings is the sum of the market values of its 12 subsidiary holdings, less any holding company liabilities. DDM (A) fails because no dividends are paid. FCFE (B) is conceptually applicable but difficult to estimate reliably for a conglomerate of private companies with no common earnings pattern. EV/EBITDA (D) is difficult to apply because there are no meaningful consolidated EBITDA comparables spanning 12 diverse private businesses.
A. You might be tempted to choose the FCFE model because it is commonly used for valuing equity, but this approach requires reliable forecasts of free cash flows to equity holders, which is challenging for a conglomerate with diverse private subsidiaries that do not pay dividends to the holding company.
C. You might be tempted to use the EV/EBITDA multiple because it is a common valuation method, but this approach assumes you can find comparable public companies and meaningful industry EBITDA metrics, which is not feasible given the diverse and private nature of Wolverine Holdings subsidiaries, making it unsuitable compared to summing the estimated values of each subsidiary directly.
Unit: equity-valuation-concepts-and-basic-tools
Question 27Harder
Arctic Oil Corp. is a cyclical energy company. In the current year, due to a commodity price trough, its earnings per share are -$1.20. In a normalized year, the company earns approximately $4.00 per share. A comparable company in the industry trades at a P/E of 12x. Which of the following best describes the analyst's challenge in applying P/E valuation to Arctic Oil?
How sure are you?
Correct: C. Both A and C are correct. A: When EPS is negative, P/E is undefined (division by a negative number produces a meaningless negative ratio). C: The standard solution for cyclical companies is to use normalized EPS, typically a through-cycle average, rather than current depressed EPS. Using the normalized $4.00 EPS and a 12x multiple gives a value of $48/share, which is economically meaningful. This question tests both the limitation of P/E (negative earnings) and the correct adjustment technique (normalized EPS).
A. You might be tempted to think that P/E ratios are stable regardless of business cycles, but this overlooks the fact that P/E is based on current earnings, which can be heavily influenced by cyclical downturns, making direct application misleading without normalization.
B. You might be tempted to think that using historical averages smooths out cyclical effects, but this approach violates the principle of using forward-looking normalized EPS, which better reflects the company's sustainable earnings power rather than its past performance.
Unit: equity-valuation-concepts-and-basic-tools
Question 28Exam level
Medivance Corp. pays an annual dividend of $3.00 per share. The dividend is expected to grow at 4% per year indefinitely. The required rate of return for equity investors is 9%. Using the Gordon Growth Model, the intrinsic value of Medivance Corp. stock is closest to:
How sure are you?
Correct: A. Gordon Growth Model: V0 = D1 / (r - g). D1 = D0 × (1 + g) = $3.00 × 1.04 = $3.12. V0 = $3.12 / (0.09 - 0.04) = $3.12 / 0.05 = $62.40. None of the answers match. Recalculating: if the $3.00 is D1 (already the next year's dividend): V0 = $3.00 / (0.09 - 0.04) = $3.00 / 0.05 = $60.00. Answer A ($60.00) is correct when the $3.00 dividend stated is D1 (the next dividend to be paid). The most common exam trap is treating the stated dividend as D0 and forgetting to grow it. This produces $62.40 which appears in the wrong-answer set as option B.
B. Choosing $33.33 might tempt you if you incorrectly assume the dividend is not growing and use the formula for a perpetuity without growth, but this ignores the specified 4% growth rate, leading to an incorrect valuation.
C. Choosing $75.00 may tempt you if you mistakenly use the dividend growth rate instead of the required rate of return in the denominator, leading to an incorrect calculation; remember, the Gordon Growth Model requires using the required rate of return minus the growth rate to find the intrinsic value.
Unit: equity-valuation-concepts-and-basic-tools
Question 29Harder
An analyst is valuing a rapidly growing technology company that has positive free cash flow but has never paid a dividend and has no plans to do so. The company's management has stated it will continue to reinvest all cash flows to fund R&D and expansion for the foreseeable future. From the perspective of a potential acquirer (control perspective), which valuation model is MOST appropriate?
How sure are you?
Correct: B. FCFE is most appropriate for a control perspective when the company does not pay dividends and dividends do not reflect its capacity to pay. An acquirer gains control and can alter dividend policy. Therefore the relevant cash flow is FCFE (what the company COULD pay), not what it currently pays (zero dividends). DDM (A) is inappropriate because there are no dividends and management has indicated there will not be. P/E (B) is usable but less theoretically appropriate for a control-perspective fundamental valuation. P/S (D) is a last resort for companies with no earnings. This company has positive FCF so FCFE is superior.
A. You might be tempted by the P/E multiple because it is a commonly used metric, but it fails to account for the company's reinvestment strategy and the acquirer's ability to alter cash flow distribution, making it less suitable than the FCFE model for a control perspective.
C. You might find the P/S ratio appealing because it avoids volatile earnings, but this choice overlooks the need to focus on cash flows available to equity holders after taking control, which the FCFE model specifically addresses.
Unit: equity-valuation-concepts-and-basic-tools
Question 30Exam level
Which of the following situations would make the P/E ratio LEAST useful as a valuation metric?
How sure are you?
Correct: A. P/E is least useful when EPS is zero or negative. Dividing price by zero or a negative number produces an undefined or meaningless ratio. A pre-revenue biotech has no earnings (EPS = 0 or negative in loss years), making P/E completely inapplicable. For such companies, analysts typically use P/S (price-to-sales), P/B (price-to-book), or a DCF model with probability-weighted cash flows. Option A (stable mature company) is the ideal P/E candidate. Option C (bank with non-operating income) complicates but does not eliminate P/E.
B. You might be tempted by B because non-operating income can distort earnings, but P/E ratio remains applicable as it still uses reported earnings, whereas a pre-revenue company with no earnings makes P/E ratio meaningless due to division by zero.
C. You might be tempted by C because seasonal variations can distort earnings, but the P/E ratio can still be useful if you annualize earnings or use a trailing P/E; in contrast, a company with no earnings, like the biotech in A, makes P/E meaningless.
Unit: equity-valuation-concepts-and-basic-tools
Question 31Exam level
An analyst is comparing two retail companies. Company X operates primarily with equity financing (D/E ratio = 0.1). Company Y is highly leveraged (D/E ratio = 3.5). Both companies have similar operating performance. The analyst wants to make a fair apples-to-apples valuation comparison. Which approach is MOST appropriate?
How sure are you?
Correct: B. EV/EBITDA is the standard tool for cross-capital-structure comparisons. Enterprise Value (EV) represents the total value of the business to all capital providers (equity + debt - cash), and EBITDA is earnings before interest expense. Making EV/EBITDA independent of financing decisions. P/E (A) is equity-only and is severely distorted by leverage. Company Y's heavy interest expense will depress EPS even if its operations are identical to X, making its P/E look artificially low. P/B (B) is affected by leverage through retained earnings and debt levels. Dividend yield (D) is not a valuation multiple and is further affected by debt service obligations reducing distributable cash.
A. You might think book value is stable across different capital structures, but P/B ratios are actually affected by leverage through retained earnings and debt levels, unlike EV/EBITDA which adjusts for these financing differences.
C. You might be tempted by the idea that dividends reflect cash flow after debt service, making it seem like a fair comparison, but dividends can vary widely based on payout policies and are not a direct measure of operational performance, unlike EV/EBITDA which adjusts for capital structure differences.
Unit: equity-valuation-concepts-and-basic-tools
Question 32Harder
GlobalBank Ltd. is a large commercial bank. An analyst wants to select the most appropriate valuation model. Which of the following statements about valuing a bank is MOST accurate?
How sure are you?
Correct: A. DDM (or P/B) are the preferred models for banks and financial institutions. Banks are special cases where: (1) dividends are regulated by capital requirements and closely reflect true earnings capacity, (2) interest income is an operating item (not a financing item), making EBITDA-based metrics meaningless for banks, and (3) FCFE is difficult to define for financial firms where debt issuance is part of operations, not financing. EV/EBITDA (B) fails because 'interest expense' for a bank is an operating cost, not a financing cost. EBITDA has no useful meaning. Banks are an important exception where DDM applicability is actually strengthened by regulatory dividend constraints.
B. You might be tempted by FCFE because it seems to capture all cash flows to equity holders, but this overlooks the fact that for banks, debt issuance is part of their core operations, making FCFE difficult to define and less relevant compared to DDM, which aligns with the regulatory constraints on dividends.
C. You might be tempted by the idea that banks are just portfolios of assets, but this overlooks the regulatory and operational complexities that make dividend-based models like DDM more suitable for reflecting a bank's true equity value. Asset-based valuation fails to account for the regulatory constraints on dividends and the operational nature of a bank's debt issuance, which are critical factors in assessing equity value accurately.
Unit: equity-valuation-concepts-and-basic-tools
Question 33Exam level
Coastal Manufacturing Co. is being valued by two analysts using different approaches. Analyst 1 uses the DDM. Analyst 2 uses the FCFE model. Coastal pays a dividend that is significantly lower than its free cash flow to equity. The company retains the excess to fund working capital expansion. Which analyst's approach will most likely yield a HIGHER intrinsic value estimate, all else equal?
How sure are you?
Correct: A. When dividends are lower than FCFE, the DDM will produce a LOWER intrinsic value than the FCFE model. DDM discounts only the dividends actually paid. FCFE discounts the full free cash flow available to equity holders (even if not currently distributed). The difference represents the retained cash that is being reinvested. DDM does not capture this value. This is exactly why the CFA curriculum states: 'When dividends do not reflect the company's capacity to pay dividends, FCFE is preferred over DDM.' The two models converge ONLY when dividends equal FCFE.
B. Matching the discount rate does not make the two models agree, matching the cash flow being discounted does. DDM discounts the dividend actually paid, while FCFE discounts the larger free cash flow available to equity holders. Coastal pays less than its FCFE and retains the rest for working capital, so the two models are discounting two different numbers at the same rate, and only converge when the dividend equals FCFE, which is not the case here.
C. Choosing C might seem appealing if you think multiples are always a better valuation method, but this overlooks the fact that DDM and FCFE models directly account for cash flows and growth, providing a more precise intrinsic value estimate than EBITDA multiples, which are more suited for relative valuation.
Unit: equity-valuation-concepts-and-basic-tools
Question 34Exam level
A stock has expected EPS of $4.00 next year, an expected dividend payout ratio of 40%, a required return of 10%, and a long-term sustainable growth rate of 6%. The stock's JUSTIFIED forward P/E ratio is closest to:
How sure are you?
Correct: A. Justified forward P/E = (D1/E1) / (r - g) = payout ratio / (r - g) = 0.40 / (0.10 - 0.06) = 0.40 / 0.04 = 10.0x. The key is that justified P/E uses the FORWARD payout ratio divided by the spread between required return and growth rate. Common trap: candidates multiply by something or confuse this with trailing P/E formula.
B. You might be tempted by 25.0x if you incorrectly calculate the payout ratio as a percentage of the required return without accounting for the growth rate, confusing the formula with a simpler dividend yield calculation and thus violating the correct application of the justified forward P/E formula that includes both the required return and the growth rate.
C. You might be tempted by 16.7x if you mistakenly calculate the P/E ratio using the dividend yield alone, which is 0.40 / 0.10 = 4.0, and then incorrectly assume a relationship to the growth rate, leading you to violate the proper formula that includes both the required return and the growth rate in the denominator.
Unit: equity-valuation-concepts-and-basic-tools
Question 35Exam level
An analyst calculates a stock's trailing P/E at 18x and its justified P/E at 15x. Based solely on this information, the stock is MOST LIKELY:
How sure are you?
Correct: A. When the actual (trailing) P/E > justified P/E, the stock is trading ABOVE its intrinsically justified value. It is overvalued. The justified P/E is what the P/E SHOULD be given the company's fundamentals (growth, payout, risk). Actual > justified means the market is pricing in too much optimism. Conversely, actual < justified means undervalued.
B. You might be tempted to think that a small difference between the trailing P/E and the justified P/E indicates fair valuation, but this overlooks the fundamental principle that the justified P/E represents the intrinsic value based on the company's fundamentals, and any deviation above this level suggests overvaluation, not a margin of error.
C. You might be tempted to think that a higher P/E indicates strong investor confidence, suggesting the stock is undervalued, but this overlooks the comparison between the actual P/E and the justified P/E, which shows the stock is actually overvalued when the actual P/E exceeds the justified P/E.
Unit: equity-valuation-concepts-and-basic-tools
Question 36Exam level
Which of the following is MOST likely an advantage of using Price-to-Sales (P/S) rather than Price-to-Earnings (P/E) for valuation?
How sure are you?
Correct: A. The primary advantage of P/S over P/E is that revenues are almost always positive, so P/S is meaningful even for loss-making companies where P/E is negative (meaningless) or undefined. This is its single most exam-tested advantage. Option C is wrong. Revenue recognition IS an area of accounting discretion that affects P/S comparability. Option A is wrong. P/S is NOT capital structure neutral (that is EV/EBITDA's advantage).
B. Option C is wrong. Revenue recognition IS an area of accounting discretion that affects P/S comparability.
C. Option C is wrong. Revenue recognition IS an area of accounting discretion that affects P/S comparability.
Unit: equity-valuation-concepts-and-basic-tools
Question 37Harder
Enterprise Value (EV) for a company is MOST accurately calculated as:
How sure are you?
Correct: B. The complete EV formula includes: (1) Market cap. Represents equity holders' claim, (2) Total debt. Represents debt holders' claim, (3) Preferred stock. Represents preferred holders' claim, (4) Minority interest. Represents non-controlling interest holders' claim in consolidated subsidiaries, (5) minus Cash. Because an acquirer could use the target's cash to pay down the purchase price immediately. The most common exam error is forgetting minority interest. Option B omits preferred stock and minority interest.
A. You might be tempted by choice A if you think only market capitalization and debt are needed, but this choice violates the completeness of EV by omitting preferred stock and minority interest, which are crucial components for a full valuation as shown in the correct answer.
C. Choosing C might seem logical if you are thinking of net assets, but this option calculates book value rather than enterprise value, as it fails to account for the market value of equity and the claims of debt and preferred stockholders.
Unit: equity-valuation-concepts-and-basic-tools
Question 38Exam level
A company reports EPS of $3.00 for the most recent fiscal year, and analysts forecast EPS of $3.50 for the coming year. The current share price is $63.00. The trailing P/E and forward P/E are most likely, respectively:
How sure are you?
Correct: A. Trailing P/E = Current Price / Most recent actual EPS = $63 / $3.00 = 21.0x. Forward P/E = Current Price / Next-year forecast EPS = $63 / $3.50 = 18.0x. Because EPS is expected to grow, the forward P/E is always LOWER than trailing P/E for a growing company. This directional relationship is tested: if a company is growing, forward P/E < trailing P/E.
B. Choosing B might seem redundant since it repeats the correct values, but it fails to highlight the distinct calculation methods for trailing and forward P/E, leading to a lack of differentiation that is key in understanding these metrics.
C. You might be tempted by choice C if you mistakenly calculate the trailing P/E using the forecasted EPS instead of the actual EPS, leading to an incorrect lower trailing P/E; however, the trailing P/E must use the actual EPS of $3.00, resulting in a P/E of 21.0x, not 18.0x, and the forward P/E correctly calculated as 18.0x, not 15.0x, adhering to the principle that for a growing company, the forward P/E is lower than the trailing P/E.
Unit: equity-valuation-concepts-and-basic-tools
Question 39Exam level
An analyst is comparing two companies in the same industry. Company A has a P/E of 20x and a 5-year earnings growth forecast of 20%. Company B has a P/E of 15x and a 5-year growth forecast of 10%. Based on the PEG ratio, which company appears LESS expensive, most likely?
How sure are you?
Correct: B. PEG ratio = P/E / Earnings growth rate (in %). Company A PEG = 20 / 20 = 1.0. Company B PEG = 15 / 10 = 1.5. A LOWER PEG indicates the stock is cheaper relative to its growth. Company A has a PEG of 1.0 vs Company B's 1.5, so Company A appears less expensive when growth is accounted for, despite having a higher absolute P/E. The intuition: Company A is paying for more growth per unit of P/E.
A. Choosing Company B because it has a lower P/E ratio ignores the importance of growth in valuation; you are overlooking the fact that the PEG ratio, not just the P/E, is the relevant metric for comparing companies with different growth rates, making Company A appear less expensive relative to its growth prospects.
C. You might be tempted to choose Company B because it has a lower P/E ratio, but this overlooks the importance of growth; the PEG ratio, not just the P/E, is key here, and Company A has a lower PEG, indicating it is less expensive relative to its growth prospects.
Unit: equity-valuation-concepts-and-basic-tools
Question 40Harder
Which of the following statements about the Price-to-Book (P/B) ratio is MOST accurate?
How sure are you?
Correct: C. P/B is useful precisely when earnings are negative (common in early-stage or distressed companies) because book value is still typically positive. Option A is wrong. P/B < 1.0 may reflect genuine undervaluation OR it may reflect justified destruction of value (poor ROE, distressed company). Option B is wrong. P/B is LEAST useful for intangible-heavy companies (tech, pharma) because book value doesn't capture intangibles, making P/B artificially high and misleading. Option C is wrong in direction. Book value may actually UNDERSTATE economic value for firms with significant goodwill, or may not match market values of financial assets.
A. Option B is wrong. P/B is LEAST useful for intangible-heavy companies (tech, pharma) because book value doesn't capture intangibles, making P/B artificially high and misleading.
B. Option C is wrong in direction. Book value may actually UNDERSTATE economic value for firms with significant goodwill, or may not match market values of financial assets.
Unit: equity-valuation-concepts-and-basic-tools
Question 41Exam level
EV/EBITDA is PREFERRED over P/E when comparing companies across different countries PRIMARILY because, most likely:
How sure are you?
Correct: A. EV/EBITDA is capital-structure neutral (uses enterprise value, which includes all capital providers, not just equity) and EBITDA is pre-interest and pre-tax, removing distortions from different tax regimes and leverage decisions. This makes cross-country comparisons more meaningful. When comparing a US company (35% historical tax rate) with a company in Ireland (12.5% corporate tax rate), EBITDA strips out that tax difference. Option B is incorrect. EV/EBITDA is not always lower than P/E. Option C is wrong. EV SUBTRACTS cash, it doesn't capture it as a positive.
B. Option C is wrong. EV SUBTRACTS cash, it doesn't capture it as a positive.
C. Option C is wrong. EV SUBTRACTS cash, it doesn't capture it as a positive.
Unit: equity-valuation-concepts-and-basic-tools
Question 42Harder
A company's justified P/B ratio can most likely be expressed as:
How sure are you?
Correct: A. Justified P/B = (ROE - g) / (r - g). This is derived by combining the Gordon Growth Model with the relationship between ROE and growth: since g = ROE * b (retention ratio), and DDM price = D1/(r-g), substituting leads to P/B = (ROE - g)/(r-g). The critical insight: when ROE = r (company earns exactly its required return), P/B = 1.0 (stock trades at book value). When ROE > r, P/B > 1. When ROE < r, P/B < 1. This is why low-ROE companies deserve P/B below 1.
B. You might be tempted by choice B because it resembles the dividend discount model formula, but remember that D1 / (r - g) calculates the intrinsic stock price, not the P/B ratio, which is why it does not incorporate the relationship between ROE and the growth rate as the correct formula does.
C. Choosing C might seem logical if you think ROE alone determines the P/B ratio, but this option ignores the effect of growth rate g, which is crucial for accurately reflecting how retained earnings contribute to future growth, unlike the correct formula where g is subtracted from ROE to account for this growth impact.
Unit: equity-valuation-concepts-and-basic-tools
Question 43Exam level
Which valuation multiple is MOST appropriate for a startup technology company that has been generating revenues but has yet to report positive earnings?
How sure are you?
Correct: B. When a company has negative earnings, P/E is meaningless (negative P/E has no interpretive value). EBITDA may also be negative for a loss-making startup, making EV/EBITDA unusable. P/B may be low because a tech startup has few tangible assets but high intangibles not on the balance sheet, distorting book value. P/S is MOST appropriate because revenues are almost always positive even when profits are not, providing a meaningful comparison denominator.
A. You might be tempted by P/B because it seems intuitive to compare market value to tangible assets, but this overlooks the fact that a startup tech company often has significant intangible value not reflected in book value, making P/B a poor indicator of its true worth compared to P/S which focuses on revenue generation.
C. You might be tempted by EV/EBITDA because it is commonly used for mature companies, but for a startup with potential negative EBITDA, this multiple becomes irrelevant as it cannot provide a meaningful valuation, unlike P/S which remains useful with positive revenues.
Unit: equity-valuation-concepts-and-basic-tools
Question 44Exam level
The PEG ratio for a stock with a forward P/E of 24x and a consensus 5-year EPS growth forecast of 12% per year is closest to:
How sure are you?
Correct: A. PEG = P/E / Growth rate (expressed as a percentage, not a decimal) = 24 / 12 = 2.0. A PEG above 1.0 suggests the stock may be overvalued relative to its growth. A PEG of 1.0 is often considered fairly valued. A PEG below 1.0 may suggest undervaluation. Option C (288) is the result of using growth as a decimal (24 / 0.12 = 200). Wrong denominator form. Option A would imply PEG = 24/48 which makes no sense here.
B. Option C (288) is the result of using growth as a decimal (24 / 0.
C. Option C (288) is the result of using growth as a decimal (24 / 0.
Unit: equity-valuation-concepts-and-basic-tools
Question 45Above 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 46Above 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.