31 cards · Stock Market & Investing · answer each one, then read the explanation. Your score tallies below. Looking for DCF terminal value: perpetuity growth vs. exit multiple, worked example? Read the explainer.
Company A trades at a price-to-earnings (P/E) ratio of 35, while Company B in the same industry trades at a P/E of 12. An analyst concludes that Company A is overvalued and Company B is undervalued. Which of the following best identifies a flaw in this reasoning?
AThe P/E ratio is meaningless for comparing companies in the same industry; the price-to-book ratio should always be used instead
BCompany B's lower P/E proves it is riskier, because the market always discounts riskier stocks to lower multiples, making the analyst's conclusion exactly backwards
CA higher P/E can reflect the market pricing in faster expected future earnings growth, so a high P/E alone does not prove overvaluation — the analyst must compare each company's P/E to its own projected growth rate and the industry median before drawing a conclusion
DP/E ratios cannot be compared between two companies unless they have the identical number of shares outstanding
Correct answer: .
A high P/E ratio often reflects the market's expectation of strong future earnings growth, not necessarily overvaluation. A company growing earnings at 30% per year may justify a P/E of 35, while a company with flat or declining earnings may deserve a P/E of 12 or even less. Proper analysis requires comparing P/E to growth (the PEG ratio), industry averages, and earnings quality. The option dismissing P/E for same-industry comparison is wrong — P/E is one of the most common same-industry metrics. The option claiming lower P/E always means higher risk reverses the relationship: higher-risk companies can trade at lower multiples, but low P/E can also simply mean low expected growth. The option about share count is incorrect because P/E already normalises price against per-share earnings.
Source: CFA Institute, Equity Valuation: Concepts and Basic Tools
A company reports earnings per share (EPS) of $4.00 and pays an annual dividend of $1.20 per share. What is its dividend payout ratio, and what does this ratio indicate about the company's use of earnings?
A70%, because the payout ratio measures the percentage of earnings the company keeps rather than the percentage it distributes
B30%, meaning the company distributes 30% of its net earnings to shareholders as dividends and retains the remaining 70% for reinvestment, debt repayment, or reserves
C3.33, meaning the company earns 3.33 times as much as it pays in dividends, which is called the dividend coverage ratio, not the payout ratio
DThe payout ratio cannot be calculated without knowing the company's total revenue
Correct answer: .
The dividend payout ratio equals dividends per share divided by earnings per share: $1.20 divided by $4.00 is 0.30, or 30%. This means the company pays out 30% of its net earnings as dividends. The remainder, 70%, is the retention ratio — earnings kept for growth, buybacks, or debt reduction. The option citing 3.33 describes the reciprocal concept (the dividend coverage ratio, which is EPS divided by DPS), not the payout ratio itself. The option stating 70% confuses the payout ratio with the retention ratio, which measures the opposite. The option claiming total revenue is needed is incorrect because EPS already captures per-share profitability.
Source: SEC, Investor.gov, 'Dividends'; CFA Institute, Equity Valuation curriculum
An analyst uses a discounted cash flow (DCF) model to value a company. She estimates free cash flows of $10 million per year for the next five years and applies a discount rate of 10%. All else equal, if she raises the discount rate to 15%, what happens to her estimate of the company's intrinsic value and why?
AThe intrinsic value increases, because a higher discount rate reflects higher expected returns and therefore makes the investment more attractive
BThe effect is ambiguous without knowing the terminal value assumption; the discount rate has no impact on the five-year projection itself
CThe intrinsic value stays the same, because the discount rate only affects the timing of cash flows, not their total value over the projection period
DThe intrinsic value decreases, because a higher discount rate reduces the present value of each future cash flow — the same dollar earned in the future is worth less today when discounted at a steeper rate
Correct answer: .
In a DCF model, each future cash flow is divided by (1 + discount rate) raised to the power of the number of years until that cash flow is received. A higher discount rate produces a larger denominator, reducing the present value of every projected cash flow and therefore lowering the total intrinsic value estimate. The option claiming higher value confuses the discount rate (a cost-of-capital concept) with expected return to the investor — a higher required return actually makes a stream of cash flows less valuable today, not more. The option claiming no effect ignores the mathematical mechanics of present-value discounting. The option about terminal value is partially right that terminal value matters, but wrong that the discount rate has no impact on the explicit projection period — it discounts every year's cash flow.
Source: CFA Institute, Discounted Cash Flow Applications, Equity Valuation
An analyst wants to compare the valuations of two companies in the same industry, but one is financed heavily with debt and the other almost entirely with equity. Which valuation multiple is most appropriate for this comparison, and why?
AThe price-to-earnings (P/E) ratio, because P/E already accounts for a company's capital structure by using net income, which strips out the effect of financing choices
BEV/EBITDA (enterprise value divided by earnings before interest, taxes, depreciation and amortisation), because enterprise value includes both debt and equity while EBITDA excludes the interest expense that differs between the two companies' capital structures
CThe dividend yield, because dividend yield is unaffected by whether a company uses debt or equity financing
DThe price-to-book (P/B) ratio, because book value already nets out all debt obligations from the company's balance sheet
Correct answer: .
EV/EBITDA is capital-structure neutral because enterprise value equals market capitalisation plus debt minus cash, capturing the total claims of both debt and equity holders, and EBITDA is measured before interest expense, so it isn't distorted by how much debt financing a company uses. This makes it well suited to comparing companies with different leverage. The option favouring P/E is wrong because P/E divides share price (an equity-only value) by net income, which is calculated after interest expense — two operationally identical companies with different debt loads would show different net income and different P/E, even though EV/EBITDA would match. Dividend yield depends heavily on payout policy rather than capital structure, and many companies pay no dividend at all, making it a poor substitute here. P/B nets debt out of the balance-sheet book value, but it doesn't neutralise the effect financing has on the income statement, and book value can diverge sharply from economic value, especially for asset-light businesses.
Source: CFA Institute, Equity Valuation: Market-Based Valuation (Price and Enterprise Value Multiples)
A company has total assets of $500 million, total liabilities of $300 million, and 20 million shares outstanding. Its stock trades at $10 per share. What is its price-to-book (P/B) ratio?
A1.0 — book value per share is $10 (total assets of $500 million minus total liabilities of $300 million, divided by 20 million shares), which equals the market price of $10 per share
B0.4 — because book value per share is mistakenly calculated using total assets alone ($500 million ÷ 20 million shares = $25), without subtracting liabilities first
C0.67 — because book value per share is mistakenly calculated using total liabilities alone ($300 million ÷ 20 million shares = $15)
D0.25 — because book value per share is mistakenly calculated by adding liabilities to assets instead of subtracting them ($800 million ÷ 20 million shares = $40)
Correct answer: .
The price-to-book ratio compares market price to accounting book value per share, where book value equals total assets minus total liabilities (shareholders' equity). Here that is $500 million minus $300 million, or $200 million, which works out to $10 per share across 20 million shares outstanding — exactly matching the $10 market price, for a P/B of 1.0. The option using total assets alone ignores that a large portion of those assets is funded by creditors, not shareholders, which overstates book value per share and understates the resulting ratio. The option using total liabilities alone confuses the liabilities side of the balance sheet with shareholders' equity, which is the residual claim left over after all liabilities are settled, not the liabilities themselves. The option that adds liabilities to assets compounds the same equity-versus-liabilities confusion, roughly doubling the overstatement of the denominator and producing an even more distorted ratio.
Source: SEC Investor.gov, "Price-to-Book Ratio"; CFA Institute, Equity Valuation curriculum
Using the Gordon Growth (constant-growth dividend discount) model, a stock's intrinsic value is calculated as V = D1 / (r − g), where D1 is next year's expected dividend, r is the required rate of return, and g is the constant dividend growth rate. Why does this model produce an unreliable or even meaningless value when the assumed growth rate g is very close to the required return r?
ABecause the model requires g to be recalculated every year using the company's actual reported growth, so a close g and r simply mean the inputs need updating more frequently
BBecause the model assumes dividends only grow for a fixed number of years, so a growth rate close to the required return causes the model to stop calculating after too few years
CBecause dividends can never grow at a rate close to the required return in practice, so this scenario cannot occur for any real company
DBecause as g approaches r, the denominator (r − g) approaches zero, causing the calculated value to become extremely large or mathematically undefined — a small change in either assumption then produces a wildly different valuation
Correct answer: .
The Gordon Growth Model's value is inversely proportional to (r − g). As the assumed perpetual growth rate g rises toward the required return r, this denominator shrinks toward zero, which mathematically drives the computed value toward infinity; if g were ever to equal or exceed r, the formula becomes undefined or nonsensical. Because the output is so sensitive near this boundary, tiny, hard-to-justify differences in the growth assumption can swing the valuation enormously, which is why the model is considered unreliable whenever g sits close to r — analysts generally require g to stay meaningfully below r, often capping it near a long-run economic growth rate. The option about recalculating g every year misunderstands that the model assumes one constant perpetual growth rate rather than an annually re-estimated one. The option about a fixed number of years describes a multi-stage dividend discount model, not the constant-growth version, which assumes growth continues indefinitely. The option claiming this scenario can never happen in practice is an overgeneralization; analysts can and sometimes do input growth assumptions too close to the discount rate, which is exactly why understanding this limitation matters.
Source: CFA Institute, Equity Valuation: Dividend Discount Models; Gordon, M.J. (1962), The Investment, Financing, and Valuation of the Corporation
Under the DuPont decomposition, return on equity (ROE) is broken into three components: net profit margin × total asset turnover × financial leverage (the equity multiplier). A company's ROE rises sharply year-over-year, but its net profit margin and asset turnover are both essentially unchanged. Which of the following most directly explains the rise in ROE?
AThe company's tax rate fell substantially, which increases net profit margin without appearing separately in the DuPont formula
BThe company's total asset turnover actually increased, but this happened in a division the DuPont formula does not capture
CThe company increased its financial leverage — for example, by taking on more debt or repurchasing shares with borrowed funds — which raises the equity multiplier (total assets divided by total equity) and mechanically increases ROE even with no change in operating profitability or efficiency
DThe ROE calculation must have used average equity in one year and ending equity in the other, which alone can account for a large change
Correct answer: .
ROE equals net profit margin multiplied by total asset turnover multiplied by the equity multiplier (total assets divided by total equity). Since the margin and turnover are both given as unchanged, the entire rise in ROE has to come from the third factor. A company that takes on more debt, or repurchases stock using borrowed funds, shrinks its equity base relative to its assets, which raises the equity multiplier and mechanically lifts ROE with no improvement in profitability or operating efficiency — exactly why analysts decompose ROE this way rather than treating a rising ROE as automatically good news. The option about a falling tax rate is wrong because a lower tax rate raises net income and therefore net profit margin directly, but the question states margin is unchanged, which rules this cause out. The option about turnover improving in an unmeasured division is incorrect because total asset turnover is calculated at the whole-company level using total revenue and total assets, so any real change would show up in that ratio. The option about mixing average and ending equity describes a genuine measurement pitfall analysts must guard against, but it is a calculation artifact, not a real business explanation for an actual change in ROE.
Source: CFA Institute, Financial Statement Analysis: Financial Analysis Techniques (DuPont decomposition of ROE)
A company trades at a P/E ratio of 20 and analysts expect its earnings to grow at 10% per year. A second company in the same industry trades at a P/E of 30 with expected earnings growth of 25% per year. Using the PEG ratio (P/E divided by the expected annual earnings growth rate, expressed as a whole number), which company appears cheaper relative to its growth prospects?
AThe second company, because its PEG ratio is 30 ÷ 25 = 1.2, which is lower than the first company's PEG ratio of 20 ÷ 10 = 2.0 — a lower PEG suggests the stock is cheaper relative to its expected growth rate
BThe first company, because its P/E ratio of 20 is lower in absolute terms than the second company's P/E of 30, and a lower P/E always means a cheaper stock
CThe two companies are equally cheap, because both have the same expected-growth-to-P/E ratio when rounded to the nearest whole number
DThe first company, because its PEG ratio is 10 ÷ 20 = 0.5, which is lower than the second company's PEG ratio of 25 ÷ 30 = 0.83
Correct answer: .
The PEG ratio adjusts the P/E ratio for expected earnings growth, calculated as P/E divided by the annual growth rate. The first company's PEG is 20 ÷ 10 = 2.0, while the second company's is 30 ÷ 25 = 1.2. A lower PEG generally indicates a stock is more reasonably priced relative to how fast its earnings are expected to grow, so despite its higher absolute P/E, the second company appears cheaper on a growth-adjusted basis. The option comparing raw P/E ratios ignores growth entirely, which is exactly the flaw the PEG ratio is designed to correct — a stock with a higher P/E can still be the better relative value if its growth is high enough to justify it. The option claiming the two companies are equally cheap misreads the ratios, which are meaningfully different (2.0 versus 1.2), not equal even after rounding. The option computing 0.5 and 0.83 inverts the PEG formula, dividing the growth rate by P/E rather than dividing P/E by the growth rate, which reverses the correct interpretation.
Source: CFA Institute, Equity Valuation: Concepts and Basic Tools (PEG ratio)
A young technology company has strong and growing revenue but reports a net loss due to heavy investment in growth. Which valuation multiple can still be meaningfully calculated for this company, and why might analysts prefer it over the price-to-earnings (P/E) ratio in this situation?
AThe P/E ratio, because P/E can still be calculated using a negative denominator, and a negative P/E is interpreted the same way as a low positive P/E
BThe price-to-sales (P/S) ratio, because it divides share price by revenue per share rather than earnings per share, so it remains meaningful even when a company has negative or zero net income
CThe dividend yield, because a growing company's dividend still rises even when net income is negative
DThe price-to-book (P/B) ratio, because book value cannot be affected by a company reporting a net loss
Correct answer: .
The price-to-sales ratio divides share price, or market capitalization, by revenue, or revenue per share, and revenue is rarely negative even for a young, unprofitable company, so P/S remains a usable comparison metric when earnings are negative or too volatile for P/E to be meaningful. P/E cannot be sensibly calculated with negative earnings — a negative P/E is not interpreted the way an unusually low positive P/E would be, so the ratio is typically treated as not meaningful in that case rather than compared directly across companies. Dividend yield is not a fallback here because early-stage, loss-making growth companies typically pay no dividend at all, since available cash is being reinvested rather than distributed to shareholders. Book value is not immune to a net loss either: a net loss reduces retained earnings, which is a component of shareholders' equity, so P/B is also affected by unprofitability, just less directly and immediately than P/E is.
Source: CFA Institute, Market-Based Valuation: Price and Enterprise Value Multiples
In a typical discounted cash flow (DCF) valuation that explicitly forecasts five years of free cash flow and then estimates a terminal value for all cash flows beyond year five, which statement about the terminal value component is most accurate?
ATerminal value is a minor, largely symbolic figure in most DCF models, typically contributing less than 5% of the total estimated intrinsic value
BTerminal value should always be calculated using the same discount rate as the explicit forecast period, but never needs to be discounted back to the present separately from the explicit cash flows
CTerminal value often represents a majority — frequently well over half — of a DCF model's total estimated value, which is why the assumptions behind it, such as the perpetual growth rate or the exit multiple used, deserve as much scrutiny as the explicit forecast period
DTerminal value can be estimated using either a perpetuity growth approach or an exit multiple approach, but regulators require public companies to disclose which method they used in any published valuation
Correct answer: .
Because terminal value represents the present value of all cash flows extending indefinitely, or over a very long horizon, beyond the explicit forecast period, it frequently accounts for the majority of a DCF model's total value — commonly over half, and sometimes 70 to 80 percent or more, depending on the growth and discount rate assumptions used. This is exactly why small changes to the terminal growth rate or the exit multiple can swing the entire valuation dramatically, and why analysts should stress-test these assumptions at least as carefully as the explicit-period forecasts. The option calling terminal value minor gets the typical magnitude backwards for most real-world DCF models. The option claiming it never needs separate discounting is wrong: terminal value is calculated as of the end of the explicit forecast period, such as the end of year five, and must then be discounted back to the present using the same discount rate and the same number of periods as the final explicit-year cash flow. The option about a regulatory disclosure requirement is fabricated; the perpetuity growth method and the exit multiple method are simply two accepted modeling choices analysts select between based on judgment, with no such disclosure mandate.
Source: CFA Institute, Discounted Cash Flow Applications, Equity Valuation
An analyst is building a dividend discount model and needs a discount rate for the required return on equity, r. The risk-free rate is 4%, the expected return on the overall market is 10%, and the stock's beta is 1.2. Using the Capital Asset Pricing Model (CAPM), what required return on equity should the analyst use?
A10%, because a beta above 1.0 simply means the stock's required return equals the market return regardless of the specific beta value
B7.2%, because the analyst should use only the risk premium (beta times the market risk premium) without adding back the risk-free rate
C16%, because the beta should be multiplied by the market's full expected return of 10%, and then added to the risk-free rate of 4%
D11.2%, calculated as the risk-free rate (4%) plus beta (1.2) multiplied by the market risk premium (10% market return minus 4% risk-free rate, or 6%), giving 4% + (1.2 × 6%) = 11.2%
Correct answer: .
CAPM states that the required return on equity equals the risk-free rate plus beta multiplied by the market risk premium, where the market risk premium is the expected market return minus the risk-free rate. Here, the market risk premium is 10% minus 4%, or 6%, so the required return is 4% plus (1.2 times 6%), which is 4% plus 7.2%, or 11.2%. This is the discount rate an analyst would then use in a dividend discount model, or in an FCFE-based DCF, to value the equity. The option giving 10% ignores beta's role entirely and simply restates the market return. The option giving 7.2% correctly computes the risk-premium component, beta times the market risk premium, but forgets to add back the risk-free rate, which represents the minimum return available on a riskless investment before any equity risk is taken on. The option giving 16% incorrectly multiplies beta by the market's total expected return rather than by the market risk premium, which double-counts the risk-free rate's contribution and overstates the required return.
Source: CFA Institute, Return Concepts (Capital Asset Pricing Model); Sharpe, W.F. (1964)
In DCF valuation, analysts distinguish between free cash flow to the firm (FCFF) and free cash flow to equity (FCFE). Which statement correctly describes the difference and how each should be discounted?
AFCFF represents cash flow available to all capital providers, both debt and equity holders, and is discounted at the weighted average cost of capital (WACC) to find the value of the whole firm; FCFE represents cash flow available only to equity holders, after debt payments, and is discounted at the cost of equity to find equity value directly
BFCFF and FCFE are two names for the same calculation, and the choice between them is purely a matter of the analyst's stylistic preference, since either can be discounted at either rate with identical results
CFCFE is always larger than FCFF, because equity holders have a senior legal claim on a company's cash flows compared to debt holders
DFCFF is calculated after subtracting interest expense and net debt repayments, which is what makes it available only to the firm's equity holders
Correct answer: .
FCFF is the cash flow generated by a business's operations that is available to be distributed to every capital provider, both lenders and shareholders, before any financing payments are made, so it is discounted at the WACC, which blends the cost of debt and the cost of equity, to arrive at the value of the entire firm; subtracting net debt from that result then yields equity value. FCFE, by contrast, is what remains specifically for shareholders after interest and net debt repayments, or plus net new borrowing, have already been accounted for, so it is discounted directly at the cost of equity to estimate equity value without a further adjustment step. The two are not interchangeable stylistic choices; they represent cash available to different groups of investors and must be paired with the matching discount rate, or the resulting valuation will be systematically wrong. FCFE is not always larger than FCFF — it is typically smaller, since it comes after debt-related cash outflows are subtracted. The description of subtracting interest and debt repayments to isolate cash for equity holders is accurate, but that describes FCFE, not FCFF, which is measured before any financing cash flows.
In value investing, the concept of a 'margin of safety,' popularized by Benjamin Graham, refers to which practice?
ADiversifying across at least 20 to 30 different stocks so that no single company's decline can meaningfully hurt the overall portfolio
BOnly buying stocks that pay a consistent, growing dividend, since dividend payments provide a guaranteed cushion against price declines
CBuying a security only when its market price is meaningfully below your own estimate of its intrinsic value, so that errors in your valuation assumptions or unforeseen bad news still leave room before the investment becomes a loss
DHolding enough cash in a portfolio to cover at least six months of an investor's living expenses before making any equity investments
Correct answer: .
Margin of safety means deliberately purchasing a security at a discount to your best estimate of its intrinsic, or fair, value, rather than paying exactly what you believe it is worth. Because every valuation involves uncertain assumptions, such as growth rates, discount rates, and future cash flows, buying with a built-in cushion protects an investor against the possibility that those assumptions turn out to be too optimistic, or that unforeseen negative developments reduce the company's true value after purchase. The option describing broad diversification is a related but distinct risk-management concept, spreading exposure across many positions, rather than a discount to intrinsic value on any individual purchase. The option about dividend-paying stocks confuses income generation with valuation discipline; a dividend does not by itself create a cushion against having overpaid relative to intrinsic value. The option about holding an emergency cash cushion describes a personal-finance liquidity practice, unrelated to how a specific security is priced relative to its estimated worth.
Source: Graham, B. & Dodd, D., Security Analysis; Graham, B., The Intelligent Investor
A company has a market capitalisation of $800 million and generated $100 million of operating cash flow over the trailing twelve months. What is its price-to-cash-flow (P/CF) ratio, and why might an analyst prefer this multiple over the price-to-earnings (P/E) ratio when evaluating a company with large non-cash depreciation charges?
A8.0 ($800 million divided by $100 million), because cash flow adds back non-cash charges like depreciation and is generally harder to distort through accounting choices than reported net income
B8.0 ($800 million divided by $100 million), because operating cash flow and net income are calculated identically under US GAAP, so this ratio will always equal the company's P/E ratio
C0.125, because the ratio should be computed as operating cash flow divided by market capitalisation rather than the other way around
D8.0 ($800 million divided by $100 million), but this multiple should never be used for any company that reports depreciation, since depreciation makes cash flow entirely unrepresentative of value
Correct answer: .
The price-to-cash-flow ratio is market capitalisation divided by operating cash flow, which is $800 million / $100 million = 8.0. Operating cash flow adds back non-cash charges such as depreciation and amortisation and is less sensitive to accounting estimates (e.g., depreciation method, revenue recognition timing) than net income, so analysts often treat P/CF as a cleaner cross-company comparison when depreciation policies differ. The option claiming cash flow and net income are calculated identically under US GAAP is false: net income is reduced by non-cash charges and other accounting adjustments that operating cash flow strips out, which is precisely why the two multiples can diverge. The option inverting the ratio (0.125) has the formula backwards; a price multiple is always price (or market value) divided by the fundamental, not the reverse. The option rejecting the multiple outright for any company with depreciation gets the logic backwards: depreciation is exactly the kind of non-cash distortion that makes P/CF more, not less, useful, since it neutralises differences in depreciation policy between companies being compared.
Source: CFA Institute, Equity Valuation: Market-Based Valuation (Price Multiples) — Price to Cash Flow
A company has a return on equity (ROE) of 15% and pays out 40% of its net income as dividends, retaining the rest to reinvest in the business. Assuming its capital structure, ROE, and payout ratio all stay constant and no new shares are issued, what is its sustainable growth rate — the rate at which earnings and dividends can keep growing indefinitely using only internally generated equity?
A6% (15% multiplied by 40%), because the sustainable growth rate is found by multiplying ROE by the dividend payout ratio
B9% (15% multiplied by 60%), because the sustainable growth rate equals ROE multiplied by the retention ratio — the share of earnings reinvested rather than paid out as dividends
C15%, because the sustainable growth rate equals ROE for any company that pays a dividend at all, regardless of the payout ratio
D40%, because the sustainable growth rate is simply the dividend payout ratio itself whenever ROE exceeds the company's cost of equity
Correct answer: .
The sustainable growth rate (SGR) equals ROE multiplied by the retention ratio, where the retention ratio is 1 minus the payout ratio. Here the retention ratio is 1 − 40% = 60%, so SGR = 15% × 60% = 9%. This is the rate at which equity, earnings, and dividends can all grow together using only reinvested profits, without issuing new shares or changing leverage. The option multiplying ROE by the payout ratio (giving 6%) has swapped the two ratios: it is the retained share of earnings, not the distributed share, that funds future growth. The option setting growth equal to ROE regardless of payout ignores retention entirely — a company retaining nothing (100% payout) could not sustain any internally funded growth at all, so ROE alone cannot be the answer whenever a dividend is paid. The option equating growth with the payout ratio itself confuses the fraction of earnings distributed to shareholders with the rate at which the underlying business expands, and the comparison to cost of equity it invokes has no bearing on the sustainable growth formula.
Source: CFA Institute, Equity Valuation: Discounted Dividend Valuation — Sustainable Growth Rate
A stock just paid an annual dividend of $2.00 per share. An analyst projects the dividend will grow at 20% per year for the next three years, reflecting a temporary competitive advantage, after which growth permanently settles at 4% per year. The analyst's required rate of return is 10%. Under a two-stage dividend discount model, which of the following correctly describes how to find the stock's intrinsic value today?
ADiscount each of the three high-growth dividends at 10%, then separately discount a perpetuity of the original $2.00 dividend growing at 4% starting immediately, and add the two present values together
BApply the Gordon Growth formula directly to the current $2.00 dividend using the 10% required return and the 4% long-term growth rate for the entire valuation, since a three-year high-growth phase is too short to matter
CGrow the dividend at 20% for three years to find each interim dividend, apply the Gordon Growth model to the year-4 dividend (grown at the new 4% rate) to find a terminal value as of the end of year 3, then discount the three interim dividends and that terminal value back to the present at the 10% required return
DDiscount only the year-3 dividend using the Gordon Growth model with 4% growth, since dividends paid before the stable-growth phase begins make no contribution to intrinsic value
Correct answer: .
A two-stage dividend discount model values the stock in two pieces: first, compound the current dividend at the supernormal rate (20%) for each of the three high-growth years to get three separate interim dividends, and discount each back to today at the required return. Second, once growth drops to its permanent 4% rate at the start of year 4, that stream becomes a growing perpetuity — its value as of the end of year 3 (the terminal value) is found with the Gordon Growth formula using the year-4 dividend, and that terminal value must itself be discounted back three years to the present, since it represents a value at a future date, not today. Summing the discounted interim dividends and the discounted terminal value gives the correct intrinsic value. The option restarting a 4%-growth perpetuity from the original $2.00 dividend ignores that three years of 20% compounding happened first, and treats a future cash flow stream as if it both starts today and uses the wrong dividend base — understating the real value by skipping the high-growth phase's compounding. The option applying Gordon Growth to the whole valuation from today ignores the supernormal growth phase entirely, which is the entire reason a multi-stage model is needed instead of a single constant-growth model. The option discounting only the year-3 dividend throws away the present value of the first two high-growth dividends and the entire terminal value of all future dividends beyond year 3, capturing only a tiny fraction of the stock's worth.
Source: CFA Institute, Equity Valuation: Discounted Dividend Valuation — Multistage (Two-Stage) Growth Models
A company has net operating profit after tax (NOPAT) of $50 million, invested capital of $400 million, and a weighted average cost of capital (WACC) of 9%. What is its Economic Value Added (EVA), and what does the result indicate about the company?
A$14 million, but a positive EVA only matters if the company also reports positive net income, since EVA and net income measure the same underlying quantity using different inputs
B−$36 million ($50 million minus $400 million), because Economic Value Added subtracts invested capital directly from NOPAT without applying the cost-of-capital rate
C$450 million ($50 million plus $400 million), because Economic Value Added adds the capital charge to NOPAT to show the total capital employed in the business
D$14 million ($50 million minus $400 million multiplied by 9%), indicating the company generated $14 million more in after-tax operating profit than the minimum return required by its capital providers — true economic profit above its cost of capital
Correct answer: .
Economic Value Added equals NOPAT minus a capital charge, where the capital charge is invested capital multiplied by WACC: $400 million × 9% = $36 million, so EVA = $50 million − $36 million = $14 million. Because EVA is positive, the company earned more in after-tax operating profit than the minimum return its debt and equity providers require, meaning it created genuine economic value beyond simply covering its cost of capital — a company can be profitable on a net-income basis yet still have negative EVA if that profit doesn't clear the capital charge. The option treating EVA as meaningful only alongside positive net income is wrong because EVA already incorporates profitability (through NOPAT) and capital cost together; it is not contingent on a separate net income figure. The option subtracting invested capital directly from NOPAT skips the cost-of-capital rate entirely, confusing a capital balance with a capital charge — a $400 million deduction has no financial meaning here. The option adding NOPAT and invested capital conflates a measure of economic profit with a measure of capital employed; these are different concepts that are never combined by addition in the EVA formula.
Source: Stern Stewart & Co. Economic Value Added framework; CFA Institute curriculum coverage of residual income and economic profit measures
Two companies currently trade at the same share price and have identical trailing-twelve-month P/E ratios. Company X's forward P/E (based on next-twelve-months projected earnings) is noticeably lower than its trailing P/E, while Company Y's forward P/E is noticeably higher than its trailing P/E. What does this most likely indicate about each company's earnings expectations?
ACompany X's historical earnings were overstated by one-time items while Company Y's were understated, since that is the only situation that can cause forward and trailing P/E to diverge
BAnalysts expect Company X's earnings to grow over the next twelve months, which lowers the forward P/E's denominator relative to trailing earnings, while they expect Company Y's earnings to decline or grow more slowly, which raises its forward P/E relative to its trailing figure
CForward and trailing P/E should always be identical for any company, so this difference signals a data error rather than any real difference in earnings expectations
DCompany X is inherently riskier than Company Y, since forward P/E is primarily a measure of a stock's volatility rather than a reflection of projected earnings
Correct answer: .
Trailing P/E uses the last twelve months of actual reported earnings, while forward P/E uses analysts' projected earnings for the next twelve months; with the same current share price for both companies, a change in which P/E is higher comes entirely from a change in the earnings estimate used in the denominator. A lower forward P/E than trailing P/E means expected future earnings are higher than past earnings (a bigger denominator shrinks the ratio), consistent with anticipated earnings growth for Company X. A higher forward P/E than trailing P/E means expected future earnings are lower than past earnings (a smaller denominator enlarges the ratio), consistent with an anticipated earnings decline or slowdown for Company Y. The option citing overstated or understated historical earnings as the 'only' explanation is too narrow: a straightforward change in growth expectations, with no accounting distortion at all, is sufficient to produce this pattern. The option claiming forward and trailing P/E should always match ignores that they are built from different earnings periods by definition, so they will only coincide when expected growth is exactly zero. The option framing forward P/E as a volatility measure confuses it with risk metrics like beta or standard deviation; forward P/E is a valuation multiple based on projected earnings, not a measure of price variability.
Source: CFA Institute, Equity Valuation: Market-Based Valuation (Price Multiples) — Trailing and Leading (Forward) P/E
An analyst is valuing a company as a potential takeover target. She compares two relative-valuation approaches: using the current trading multiples of similar publicly listed companies (comparable company analysis), versus using the prices actually paid in recent acquisitions of similar companies (precedent transaction analysis). Which statement correctly describes a key difference between the two?
APrecedent transaction multiples are typically higher than comparable company trading multiples, because acquisition prices embed a control premium (and often expected synergies) that public trading prices, which reflect minority, non-control stakes, do not capture
BThe two approaches converge to the same multiple once a large enough sample is used, since both measure the same underlying business economics regardless of whether a stake is a minority position or full control
CPrecedent transaction multiples are typically lower than comparable company trading multiples, because acquirers negotiate below the public market price to offset the integration risk of combining two businesses
DComparable company analysis is the better method for pricing a takeover, because public trading multiples already include whatever premium a buyer must eventually pay for control
Correct answer: .
Prices paid in completed acquisitions reflect what a buyer pays to gain full control of a target, including a control premium over the pre-deal share price and often additional value for expected synergies from combining the two businesses; public trading prices, by contrast, reflect investors buying and selling small, minority stakes with no ability to redirect the company's strategy or cash flows. Because of this, precedent transaction multiples are systematically higher than comparable company trading multiples for otherwise similar businesses, which is exactly why precedent transactions are the more appropriate benchmark when the valuation task is pricing a takeover rather than a minority investment. The option claiming the two approaches converge with a large enough sample is wrong because the gap is structural, driven by control rights and deal-specific synergies, not sampling noise — more data points from either method do not close a gap caused by what is actually being priced. The option claiming precedent multiples are lower reverses the real-world relationship entirely; acquirers pay more than the standalone market price to induce target shareholders to sell and to compensate for execution risk being assumed by the buyer, not less. The option favoring comparable company analysis for pricing a takeover has the logic backwards: trading multiples are the ones missing the control premium, so relying on them to price a full acquisition would tend to systematically undervalue the target relative to what a real buyer would actually need to pay.
Source: Wall Street Prep, Precedent Transaction Analysis; CFA Institute, Private Company Valuation (market approach: guideline public company method vs. guideline transactions method)
A company's capital structure is financed 70% by equity (market value) with a cost of equity of 11%, and 30% by debt (market value) with a pre-tax cost of debt of 6%. The company's marginal tax rate is 25%. Using the weighted average cost of capital (WACC) formula, what discount rate should be used to value the whole firm's cash flows?
A9.5%, calculated as (0.7 × 11%) + (0.3 × 6%), applying the pre-tax cost of debt directly without any tax adjustment
B7.75%, calculated as (0.5 × 11%) + (0.5 × 4.5%), splitting the two capital sources evenly rather than using their actual market-value weights
C6.45%, calculated as (0.3 × 11%) + (0.7 × 4.5%), applying the equity weight to the cost of debt and the debt weight to the cost of equity
D9.05%, calculated as (0.7 × 11%) + (0.3 × 6% × (1 − 0.25)), applying each source's actual market-value weight and taxing only the cost of debt
Correct answer: .
WACC blends the cost of each capital source by its actual share of the company's total market value, and it applies a tax adjustment only to the cost of debt, because interest payments are tax-deductible while the return required by equity holders is not: WACC = (E/V × cost of equity) + (D/V × pre-tax cost of debt × (1 − tax rate)). Here the after-tax cost of debt is 6% × (1 − 0.25) = 4.5%, so WACC = (0.7 × 11%) + (0.3 × 4.5%) = 7.7% + 1.35% = 9.05%. The option using the pre-tax cost of debt without any tax adjustment overstates the true cost of that capital source, since it ignores the tax shield interest payments generate — a company's after-tax cost of borrowing is always lower than its stated interest rate once that deduction is accounted for. The option splitting the weights 50/50 ignores the company's actual capital structure entirely; WACC is explicitly a weighted average using each source's real proportion of total capital, not an unweighted average of the two costs. The option swapping the weights between equity and debt commits the same error from the opposite direction, overweighting the cheaper after-tax debt cost and underweighting the more expensive equity cost, which understates the true blended rate rather than reflecting how the firm is actually financed.
Source: Brealey, Myers & Allen, Principles of Corporate Finance — Weighted Average Cost of Capital
A stock has an expected dividend payout ratio of 40% (so 60% of earnings is retained), a required rate of return of 9%, and an expected constant long-run earnings and dividend growth rate of 5%. Using the Gordon Growth model, what is the stock's justified leading (forward) price-to-earnings ratio — that is, today's price divided by next year's expected earnings per share?
A10.5x, calculated as (0.40 × 1.05) ÷ (0.09 − 0.05), applying a (1 + g) growth adjustment on top of the payout ratio
B10.0x, calculated as 0.40 ÷ (0.09 − 0.05), dividing the expected payout ratio directly by the gap between the required return and the growth rate
C15.0x, calculated as 0.60 ÷ (0.09 − 0.05), dividing the retention ratio rather than the payout ratio by the gap between the required return and the growth rate
D2.86x, calculated as 0.40 ÷ (0.09 + 0.05), adding the growth rate to the required return instead of subtracting it
Correct answer: .
The Gordon Growth model's justified leading P/E (price divided by next year's expected earnings, P0/E1) is derived as (1 − b) ÷ (r − g), where (1 − b) is the expected payout ratio, r is the required return, and g is the constant growth rate. Here that is 0.40 ÷ (0.09 − 0.05) = 0.40 ÷ 0.04 = 10.0x. The option applying an extra (1 + g) factor on top of the payout ratio is calculating the justified trailing P/E (price divided by this year's already-paid earnings, P0/E0) instead of the leading P/E the question asks for — the trailing version needs that extra growth factor because last year's earnings are one year further removed from today's price, but applying it here answers a different ratio than the one specified. The option dividing the retention ratio (0.60) instead of the payout ratio swaps the two complementary figures: it is the earnings actually paid out as dividends, not the earnings retained for reinvestment, that flows directly into next year's expected dividend and therefore into the price investors will pay. The option adding the growth rate to the required return rather than subtracting it inverts the entire denominator; since growth works in the investor's favor by raising future dividends, it must reduce the required-return gap used to discount those dividends, not widen it, so adding g here produces an artificially depressed and meaningless multiple.
Source: CFA Institute, Equity Valuation — Discounted Dividend Valuation (justified leading and trailing P/E multiples derived from the Gordon Growth model)
A company reports earnings per share (EPS) of $3.00 and book value per share of $30.00. Using the Graham Number — a defensive-investor screening formula popularized by Benjamin Graham that combines his suggested ceilings of a 15 price-to-earnings ratio and a 1.5 price-to-book ratio into a single constant of 22.5 — what fair-value ceiling does the formula produce for this stock?
A$36.70, calculated as the square root of (15 × $3.00 × $30.00), using only Graham's P/E ceiling and leaving out the P/B ceiling that the 22.5 constant is built from
B$2,025.00, calculated as 22.5 × $3.00 × $30.00, without taking the square root of that product
C$45.00, calculated as the square root of (22.5 × $3.00 × $30.00)
DWhatever price the stock currently trades at in the market, because the Graham Number simply restates the prevailing market price rather than setting an independent ceiling
Correct answer: .
The Graham Number is the square root of 22.5 times EPS times book value per share, where 22.5 comes from multiplying Graham's suggested defensive-investor ceiling of a 15 P/E ratio by his suggested ceiling of a 1.5 P/B ratio (15 × 1.5 = 22.5). Here that is the square root of (22.5 × $3.00 × $30.00) = the square root of $2,025, which is $45.00. The option using only a multiplier of 15 leaves out the P/B ceiling entirely, producing the square root of $1,350 ≈ $36.70 — a number that reflects only half of Graham's two combined screening criteria and understates the formula's actual ceiling. The option stopping at $2,025 without taking the square root confuses the intermediate product inside the formula with the final per-share figure; the square root step is what converts that product, which mixes an earnings figure and a book-value figure, back into a dollar-per-share price that's comparable to the stock's actual trading price. The option treating the Graham Number as just the current market price misunderstands its purpose entirely: the formula is calculated purely from a company's own reported EPS and book value, independent of whatever price the market happens to be assigning the stock, and the entire point of a defensive investor comparing the two is to check whether the market price sits above or below that independently calculated ceiling.
Source: Benjamin Graham, The Intelligent Investor (defensive-investor stock selection criteria: P/E ≤ 15, P/B ≤ 1.5); formula and constant corroborated via WallStreetMojo, Kotak Securities, and The Motley Fool, since no direct quote of the exact 22.5 constant from the original text was independently located — medium confidence on sourcing, though the arithmetic and widely-cited formula itself are consistent across all secondary sources checked
A company's beginning-of-year book value of equity is $40.00 per share, its earnings per share (net income) for the year is $5.00, and its required return on equity (cost of equity) is 10%. Using the residual income model, what is this year's residual income per share, and what does the result indicate?
A$1.00 per share ($5.00 EPS minus a $4.00 equity charge, 10% × $40.00 beginning book value), indicating the company earned $1.00 per share more than shareholders' required return — genuine economic value created beyond the cost of equity capital
B$4.50 per share ($5.00 EPS minus a $0.50 equity charge, 10% applied to the $5.00 EPS itself rather than to the book value of equity that generated it)
C$9.00 per share ($5.00 EPS plus the $4.00 equity charge), because the residual income model adds the capital charge back to net income to show the total value created for shareholders
D$0.00 per share, because net income already reflects shareholders' required return through the income statement, so no further charge needs to be subtracted
Correct answer: .
The residual income model defines an equity charge as the required return on equity multiplied by the beginning book value of equity (the capital base that generated the period's earnings), and residual income as net income minus that charge: here the equity charge is 10% × $40.00 = $4.00, so residual income is $5.00 − $4.00 = $1.00 per share. A positive result means the company earned more than the minimum return shareholders require for the capital they have invested, which is genuine value creation above and beyond simply being profitable on a net-income basis — a company can report positive EPS and still destroy shareholder value if that EPS falls short of the equity charge. The option applying the 10% rate to the $5.00 EPS figure instead of to the $40.00 book value commits a base error: the required return is owed on the capital shareholders have tied up in the business, not on whatever profit happens to be reported that year, so charging against earnings rather than against the equity base understates the true cost of that capital. The option adding the equity charge to net income reverses the entire logic of the model, which exists specifically to subtract, not add, a capital charge in order to see what profit remains once shareholders' required return has been covered. The option concluding no charge is needed at all confuses what net income already captures: accounting net income deducts interest expense for debt financing, but it never deducts anything for the opportunity cost of the equity capital shareholders have supplied, which is precisely the gap the residual income model's equity charge is designed to fill.
Source: CFA Institute, Equity Valuation — Residual Income Valuation (V0 = B0 + present value of future residual income; equity charge = cost of equity × beginning book value of equity)
A real estate investment trust (REIT) reports net income that looks weak due to large annual depreciation charges on its properties, even though its underlying real estate portfolio has held or grown in value. Which measure do REIT analysts typically use instead of the price-to-earnings (P/E) ratio to assess valuation, and why?
AThe price-to-book (P/B) ratio, because book value already reflects the current market value of a REIT's real estate holdings
BThe price-to-funds-from-operations (P/FFO) ratio, because FFO adds real estate depreciation back to net income, removing a non-cash charge that doesn't reflect how real estate value actually behaves
CThe price-to-sales (P/S) ratio, because a REIT's rental revenue is a more stable figure than its net income
DThe dividend yield alone, because REITs are legally required to distribute all of their net income as dividends, making net income irrelevant to valuation
Correct answer: .
Funds From Operations, a measure introduced by the National Association of Real Estate Investment Trusts, starts from net income and adds back real estate depreciation and amortization, since GAAP requires depreciating buildings on a schedule even though well-maintained real estate often holds its value or appreciates over time; this produces a cash-earnings proxy that behaves much like net income does for an ordinary company, making the resulting price-to-FFO ratio a more meaningful valuation yardstick than price-to-earnings. The option relying on book value is weak because accounting book value reflects depreciated historical cost, not current market value, so it suffers from a related distortion rather than solving the original problem. The option favoring price-to-sales ignores that revenue says nothing about profitability or capital intensity, discarding information FFO preserves. The option treating dividend yield as sufficient on its own misreads the required-distribution rule, which concerns REITs' taxable income under the tax code, not GAAP net income, and in any case dividend yield alone says nothing about whether a REIT's price is cheap or expensive relative to its underlying cash earnings.
Source: National Association of Real Estate Investment Trusts (NAREIT), 2002 FFO White Paper; Wall Street Prep, 'Price to FFO (P/FFO)'
Company A, with a standalone EPS of $2.00, acquires Company B entirely in an all-stock deal, issuing enough new shares to Company B's shareholders to complete the purchase. After combining both companies' net income and dividing it by Company A's new, larger total share count, the resulting pro forma EPS comes out to $2.15. What does this result indicate about the deal, and what is this type of analysis called?
AThe deal is dilutive, because issuing new shares in a stock-for-stock acquisition always reduces EPS regardless of the target's earnings; this is called a dilution-only analysis
BThe deal is accretive, but only because the acquirer's share price rose after the announcement; this is called a market-reaction analysis
CThe result is meaningless unless Company A also compares the deal's internal rate of return to its cost of capital; this is called an IRR analysis
DThe deal is accretive, because pro forma EPS exceeds the acquirer's standalone EPS; this comparison is called accretion/dilution analysis, standard practice for evaluating the earnings impact of a proposed acquisition
Correct answer: .
Accretion/dilution analysis compares an acquirer's pro forma EPS, calculated as the combined companies' net income divided by the acquirer's new total share count after issuing shares to fund the deal, against the acquirer's own standalone EPS before the deal; when pro forma EPS is higher, as in this $2.00-to-$2.15 example, the deal is called accretive, meaning the target's earnings contribution outweighs the dilutive effect of issuing new shares, and when pro forma EPS is lower, the deal is dilutive. The option asserting that issuing shares always reduces EPS ignores that the target's own earnings are added to the numerator at the same time new shares are added to the denominator, so the net effect depends on the relative sizes and valuations involved, not share issuance alone. The option crediting a share-price move after announcement confuses stock-price reaction with the mechanical EPS comparison, which uses accounting net income and share counts, not market price. The option calling for an internal-rate-of-return comparison describes a separate capital-budgeting technique used to judge whether a project or acquisition clears a required return, not the specific EPS-based accretion/dilution comparison being described here.
Source: Wall Street Prep, 'Merger Model & Accretion/Dilution Analysis'; Corporate Finance Institute, 'Accretion/Dilution Analysis'
An analyst wants to screen stocks for cheapness using a measure based on free cash flow rather than accounting earnings. She divides each company's trailing twelve-month free cash flow by its market capitalization. What is this ratio called, and how should it generally be interpreted?
AFree cash flow yield; a higher free cash flow yield generally signals a cheaper stock relative to the actual cash it generates for equity holders, similar in spirit to a high earnings yield
BThe cash conversion cycle; a higher value indicates the company converts its cash flow into profit more slowly than its peers
CThe free cash flow margin; a higher value means free cash flow should be ignored in favor of EBITDA margin when comparing companies
DThe dividend coverage ratio; a higher value means the company pays out more of its free cash flow as dividends than it generates
Correct answer: .
Free cash flow yield, calculated by dividing free cash flow by market capitalization (or, in an alternative enterprise-value-based version, by dividing free cash flow by enterprise value to also account for a company's debt load), is read the same way an earnings yield is: a higher yield means the company is generating more free cash flow for every dollar of its valuation, which usually signals a cheaper stock relative to the actual cash available to equity holders, all else equal. The option describing a cash conversion cycle mislabels an entirely different working-capital timing metric, one that measures days between paying suppliers and collecting from customers, not a valuation ratio at all. The option describing a free cash flow margin mischaracterizes a profitability ratio, free cash flow divided by revenue, as something to be set aside in favor of EBITDA margin, when in fact the two measure different things and neither replaces the other. The option describing a dividend coverage ratio confuses this valuation screen with a completely different calculation that compares free cash flow specifically to dividends paid, not to market capitalization.
Source: Wall Street Prep, 'Free Cash Flow Yield'; CFA Institute, Equity Valuation (cash-flow-based valuation screens)
A deep-value investor applies Benjamin Graham's net current asset value (net-net) approach to screen for undervalued stocks. Under this approach, what does the investor compare a company's stock price to, and what is the underlying logic?
AThe company's total shareholders' equity per share, including both current and fixed assets, on the logic that a stock trading below any component of book value is automatically cheap
BThe company's five-year average earnings per share capitalized at a fixed multiple, on the logic that normalized earnings better reflect intrinsic value than a single year's current assets
CThe company's current assets minus total liabilities, per share, on the logic that if the market price sits below this conservative liquidation-style floor, an investor is effectively paying nothing for the company's fixed assets, intangibles, or earnings power
DThe company's replacement cost of its fixed assets alone, on the logic that current assets are too volatile a basis for any long-term buy decision
Correct answer: .
Graham's net current asset value approach, often called the 'net-net' method, takes current assets minus total liabilities, per share, deliberately excluding fixed assets and intangibles from the calculation, since those are harder to value reliably and may be worth little in an actual liquidation; a more conservative version further discounts receivables and inventory before subtracting liabilities. When a stock trades below this figure, an investor buying at that price is effectively getting the company's fixed assets, intangible value, and future earnings power for free, which Graham treated as a substantial margin of safety even without any view on future growth. The option built on total shareholders' equity is wrong because it includes fixed assets and intangibles at book value, figures the net-net method deliberately strips out as unreliable. The option built on capitalized average earnings describes an entirely different, earnings-based valuation approach, not Graham's specific asset-based liquidation screen. The option built on fixed-asset replacement cost inverts the method entirely, since net-net investing is defined by excluding fixed assets, not centering the calculation on them.
Source: Graham, B., The Intelligent Investor; GuruFocus, 'Benjamin Graham Net-Net Working Capital Screener'
An economist calculates a ratio for a company by dividing the total market value of its equity and debt by the estimated replacement cost of its physical and other assets. The ratio comes out well above 1.0. What is this ratio called, and what does a reading above 1.0 suggest?
AThe current ratio; a reading above 1.0 suggests the company can cover its short-term liabilities with its short-term assets
BThe price-to-book ratio; a reading above 1.0 suggests the company's accounting book value understates its true asset base
CThe interest coverage ratio; a reading above 1.0 suggests the company easily covers its interest expense from operating earnings
DTobin's Q; a reading above 1.0 suggests the market values the company above what it would cost to replace its assets from scratch, often reflecting unrecorded intangible value such as brand strength, patents, or growth opportunities
Correct answer: .
Tobin's Q, developed by economist James Tobin, is defined as the total market value of a firm's equity and debt divided by the estimated replacement cost of its assets; a ratio above 1.0 means the market is pricing the company above what it would literally cost to rebuild or replace its asset base today, which is typically attributed to unrecorded value such as brand reputation, patents, proprietary technology, or growth opportunities that accounting replacement cost cannot capture, while a ratio below 1.0 can flag a company whose breakup or replacement value exceeds what the market is paying for it as a going concern. The option describing a current ratio is wrong because that measures short-term liquidity using current assets and liabilities, not total firm value against asset replacement cost. The option describing a price-to-book ratio confuses this measure with one based on historical-cost accounting book value, not an estimate of current replacement cost, even though both can signal unrecorded value in some cases. The option describing an interest coverage ratio is wrong because that measures a company's ability to pay interest from operating earnings, an entirely unrelated solvency concept.
Source: Tobin, J. (1969), 'A General Equilibrium Approach to Monetary Theory,' Journal of Money, Credit and Banking; CFA Institute curriculum coverage of market-based valuation indicators
A diversified conglomerate operates three unrelated business segments: industrial equipment, consumer finance, and media. An analyst wants to value the whole company by valuing each segment separately, using the trading multiples of the most relevant pure-play peers for each one, then combining the results. What is this valuation approach called, and what must the analyst still do after adding the segment values together?
AThis is called comparable company analysis; the analyst should stop once the three segment values are added together, since the sum directly equals the company's total equity value
BThis is called sum-of-the-parts (SOTP) valuation; after adding the segment values together to get total enterprise value, the analyst must still subtract the parent company's net debt and other non-operating items, and may apply a conglomerate discount to reflect inefficiencies of running unrelated businesses under one roof
CThis is called precedent transaction analysis; the analyst should ignore the parent company's balance sheet entirely, since segment-level multiples already reflect all debt effects
DThis is called the dividend discount model applied on a segment basis; the analyst should discount each segment's expected dividends separately using the same single discount rate for all three
Correct answer: .
Sum-of-the-parts valuation values each of a conglomerate's distinct business segments separately, typically using the trading or transaction multiples of pure-play peers most comparable to that specific segment, then adds the segment values together to reach a total enterprise value for the whole company; from there, the analyst must still subtract the parent company's net debt and other non-operating liabilities (and add back non-operating assets) to reach an equity value, and often applies a conglomerate discount, a percentage haircut reflecting the inefficiencies and lost focus that can come from running unrelated businesses under one corporate umbrella. The option calling this plain comparable company analysis misses that comparable company analysis values one business as a whole using one set of peers, not several distinct segments using different peer sets that are then combined. The option invoking precedent transaction analysis is wrong on the same basis, and also wrongly claims debt can be ignored, when in fact the parent's net debt must still be removed to get from enterprise value to equity value. The option describing a single-discount-rate segment-level dividend discount model is wrong because different segments typically carry different risk profiles and growth rates, which a single shared discount rate would fail to reflect, and SOTP is fundamentally a multiples-based relative-valuation technique, not a dividend discount model.
Source: AnalystPrep, CFA Level II 'Sum of Parts Valuation'; Wall Street Prep and Umbrex, Sum-of-the-Parts Valuation frameworks
A mining company is deciding whether to invest in a new extraction project. A standard discounted cash flow analysis, using a single expected price path for the mined commodity, produces a negative net present value. However, the project also gives the company the right, but not the obligation, to pause or expand extraction later depending on how commodity prices actually move, an option a standard static DCF does not capture. What does real options valuation add to the analysis, and under what condition does this added value tend to be largest?
AIt adds a fixed percentage markup to the static NPV regardless of circumstances, typically 10%, to compensate for DCF's general tendency to undervalue all projects
BIt replaces the DCF estimate entirely with a discounted terminal value calculation, making the original cash flow forecast unnecessary
CIt adds the value of the managerial flexibility to adapt the project, such as expanding if prices rise or pausing or abandoning if prices fall, to the static NPV to get an expanded NPV; this added option value tends to be largest when the underlying commodity price is highly volatile and the company retains meaningful decision-making flexibility
DIt adds value only by assuming the company borrows against the project's future cash flows, since real options are fundamentally about using leverage rather than about operating flexibility
Correct answer: .
Real options valuation recognizes that a project's total value is its static net present value, calculated from a single expected scenario, plus the value of the managerial flexibility surrounding it, such as the ability to expand production if prices rise, scale back or pause if prices fall, or abandon the project entirely and recover some salvage value; adding this flexibility value to the static NPV produces what is often called an expanded NPV, and a project that looks unattractive under a single-scenario DCF can become genuinely attractive once this flexibility is properly valued. This added option value tends to be largest precisely when the underlying variable, here the commodity price, is highly volatile, since greater uncertainty increases the value of being able to wait, expand, or exit depending on how conditions unfold, provided the company genuinely retains that decision-making flexibility rather than being contractually locked into a fixed course of action. The option proposing a fixed universal markup invents a shortcut that has no basis in how real options are actually valued, since the correct adjustment depends on the specific flexibility and volatility involved, not a flat percentage. The option claiming DCF becomes unnecessary is wrong because real options valuation explicitly builds on top of a baseline DCF rather than discarding it. The option tying real options to borrowing confuses project-level operating flexibility, the actual subject of real options analysis, with an unrelated financing decision.
Source: Umbrex, 'Real Options Valuation'; Trigeorgis, L., Real Options: Managerial Flexibility and Strategy in Resource Allocation
An appraiser is valuing a minority, non-controlling stake in a closely held private company for estate tax purposes. After first applying a discount for the stake's lack of control, the appraiser applies a second, separate discount to reflect the fact that there is no ready public market in which to sell the shares quickly. What is this second discount called, and what is its underlying justification?
AThe discount for lack of marketability (DLOM); it is justified by the reduced value of an ownership interest that cannot be readily converted to cash on a public exchange, unlike a freely traded stock, with its size often benchmarked against restricted-stock and pre-IPO studies
BThe discount for lack of control (DLOC); it is justified by the stake's inability to direct the company's strategy, dividend policy, or management decisions
CThe blockage discount; it is justified specifically by the fact that selling a very large block of a publicly traded stock all at once would depress its market price
DThe key person discount; it is justified by the company's dependence on a single founder or executive whose departure would impair the business
Correct answer: .
The discount for lack of marketability compensates for the fact that an interest in a private company cannot be quickly converted to cash through a public exchange the way a freely traded stock can, and also often reflects contractual transfer restrictions in a shareholder or operating agreement; appraisers commonly size this discount using empirical evidence from restricted-stock studies, which compare prices of otherwise-identical restricted and freely tradable shares of the same public company, and pre-IPO studies, which compare private transaction prices to a company's eventual IPO price. It is applied separately from, and in addition to, a discount for lack of control, which instead reflects a minority stake's inability to direct the company's strategy, dividends, or management, since marketability and control are distinct attributes of an ownership interest that must each be addressed on their own. The option describing a discount for lack of control actually describes the first discount already applied in the scenario, not the second, marketability-based one being asked about. The option describing a blockage discount is a narrower, specific concept that applies to large blocks of publicly traded stock whose sale would itself move the market price, not to an illiquid private-company interest with no public market at all. The option describing a key-person discount addresses a completely different risk, business dependence on a specific individual, unrelated to the liquidity of the ownership interest itself.
Source: IRS Revenue Ruling 59-60; Corporate Finance Institute, 'Discount for Lack of Marketability (DLOM)'
About Valuation & Financial Ratios
Valuation ratios compress a company's price and its fundamentals into a single comparable number. The most common, the price-to-earnings (P/E) ratio, divides the current share price by earnings per share over the trailing twelve months (or, for a forward P/E, by analysts' projected next-twelve-month earnings) — a higher multiple generally signals that investors expect faster future growth, not that the stock is automatically "expensive." Related ratios swap the denominator: price-to-book (P/B) compares price to net asset value, useful for asset-heavy or financial businesses, while EV/EBITDA (enterprise value over earnings before interest, tax, depreciation and amortization) is capital-structure-neutral, so it compares companies carrying different amounts of debt more fairly than P/E can.
None of these ratios substitute for projecting a company's actual cash flows. A discounted cash flow (DCF) model estimates intrinsic value by forecasting several years of free cash flow and discounting it back at a required rate of return, then adding a terminal value for everything beyond the forecast window — which is usually the majority of the total value and the step most sensitive to the method and assumptions used, as the terminal value guide works through in detail. Ratios and DCF are complements, not rivals: a quick ratio screen flags which companies are worth modeling in depth, while a DCF forces explicit assumptions about growth and margins that a ratio alone never makes visible.