CFA Program — Equity Valuation

Question 1

An analyst uses the residual income model to value a stock. The model is generally most appropriate when:

• A) The company pays no dividends and has volatile or negative near-term free cash flow, but reliable accounting book value and earnings estimates
• B) The company has no book value of equity
• C) Only dividend-paying, stable, mature companies can be analyzed with this model
• D) The company's earnings are entirely non-recurring

Question 2

A company has a required rate of return on equity of 11%, an expected constant dividend growth rate of 3%, and just paid a dividend of $2.50. Using the Gordon Growth Model, what is the estimated intrinsic value of the stock?

• A) $27.75
• B) $31.25
• C) $32.19
• D) $35.00

Question 3

In a two-stage dividend discount model, the terminal value at the end of the high-growth stage is typically calculated using:

• A) The Gordon Growth Model applied to the dividend expected in the first year after the high-growth period, using a stable long-term growth rate
• B) The company's book value at that point in time only
• C) A simple average of all dividends paid during the high-growth period
• D) The risk-free rate as the discount rate

Question 4

Free cash flow to equity (FCFE) differs from free cash flow to the firm (FCFF) primarily in that FCFE:

• A) Is calculated before deducting interest expense and net borrowing effects
• B) Reflects cash flow available to equity holders after accounting for net borrowing and interest payments to debt holders
• C) Ignores capital expenditures entirely
• D) Is always identical to net income

Question 5

A stock is trading at a P/E ratio well below comparable companies, despite similar growth prospects and risk profiles. Assuming the market is not mispricing the stock for reasons the analyst has failed to identify, this most likely suggests the stock is:

• A) Overvalued relative to peers
• B) Undervalued relative to peers, all else being genuinely comparable
• C) Fairly valued by definition
• D) Impossible to compare using relative valuation

Question 6

Which of the following is a key limitation of using price-to-book (P/B) ratios to value companies with significant intangible assets, such as technology or pharmaceutical firms?

• A) P/B ratios cannot be calculated for such companies
• B) Book value may significantly understate the economic value of internally generated intangible assets like R&D or brand value, which are often expensed rather than capitalized
• C) P/B ratios are only usable for financial sector companies
• D) Book value always exceeds market value for such companies

Question 7

A company's FCFE next year is projected at $8,000,000, growing at a constant 4.5% rate thereafter. Using a required return on equity of 11% and 4,000,000 shares outstanding, the value per share is closest to:

• A) $20.00
• B) $16.67
• C) $30.77
• D) $18.18

Question 8

An analyst valuing a company using a two-stage FCFF model estimates explicit free cash flows for the next 5 years, then applies a terminal value at the end of year 5. Which of the following is most likely to introduce the greatest source of valuation uncertainty in this model?

• A) The specific font used in the valuation report.
• B) The terminal value calculation, since it typically represents the largest proportion of total estimated value and relies on long-term assumptions (terminal growth rate and discount rate) that are inherently uncertain.
• C) The explicit forecast period cash flows, which always represent the majority of total value.
• D) The choice of currency used to present the valuation.

Question 9

A private company is being valued using a market multiple derived from comparable publicly traded companies. Which adjustment is most likely necessary to reflect the private company's lack of an active public market for its shares?

• A) A discount for lack of marketability (DLOM), reducing the indicated value to reflect the private company's reduced liquidity relative to its public comparables.
• B) A premium for lack of marketability, increasing the indicated value.
• C) No adjustment is necessary, since private and public companies are always valued identically.
• D) A discount that eliminates the entire value of the company.

Question 10

A company reports net income of $5,000,000, 2,500,000 shares outstanding, and total book value of equity of $40,000,000. Return on equity (ROE) is closest to:

• A) 10.0%
• B) 15.0%
• C) 8.0%
• D) 12.5%

Question 11

An analyst uses the residual income model to value a company and finds that the model's implied value is significantly higher than the current market price, while a DCF model using similar underlying assumptions produces a value close to the current market price. What is a plausible explanation for this discrepancy?

• A) Theoretically consistent models must always produce identical valuations regardless of any input assumptions.
• B) This discrepancy is impossible and indicates a fundamental error in either model.
• C) Differences in the models' sensitivity to specific inputs (such as the persistence and fade rate of residual income versus terminal growth assumptions in the DCF) can cause the two theoretically equivalent approaches to produce different results if not calibrated consistently.
• D) The residual income model is always correct and the DCF model is always wrong.

Question 12

Which of the following is a key advantage of the residual income valuation model relative to a dividend discount model, particularly for companies with low or no current dividends?

• A) The residual income model produces identical results to the dividend discount model in all cases regardless of dividend policy.
• B) The residual income model does not require the company to actually pay dividends, since it is based on book value and accounting earnings rather than requiring an assumption about distributed cash flow.
• C) The residual income model requires more subjective assumptions than the dividend discount model in every case.
• D) The residual income model can only be applied to companies with negative book value.

Question 13

An analyst valuing a bank using a residual income approach notes that traditional FCFF/FCFE models are difficult to apply reliably to financial institutions. Which of the following best explains this difficulty?

• A) FCFF and FCFE models work identically well for banks as for any other industry with no adjustment needed.
• B) Residual income models can never be applied to any company in any industry.
• C) For financial institutions, capital expenditures and working capital are not well-defined in the same way as for non-financial companies, and debt is a raw material for the business rather than a source of financing, making free cash flow harder to define meaningfully.
• D) Financial institutions never have any earnings, making all valuation models inapplicable.

Question 14

A company's current dividend is $2.50. Dividends are expected to grow at 18% for 3 years, then settle into a stable 4% long-run growth rate. Using a required return of 10.5%, the two-stage DDM value is closest to:

• A) $38.46
• B) $45.00
• C) $60.00
• D) $57.28

Question 15

An analyst is valuing a technology company with significant losses in its early years but strong projected future profitability. Which valuation approach is generally most appropriate for capturing this company's value?

• A) A model that assumes the company's losses will continue indefinitely with no path to profitability.
• B) Ignoring the valuation entirely since the company currently has negative earnings.
• C) A multi-stage DCF or FCFE model with an explicit forecast period capturing the transition from current losses to future profitability, followed by a terminal value reflecting mature, stable growth.
• D) A single-stage dividend discount model, since the company currently pays no dividends.

Question 16

Which of the following best describes a key assumption underlying the use of a single-stage (constant growth) FCFE model to value a company?

• A) The company must have zero debt outstanding for the model to be applicable.
• B) The model assumes the company will never generate any free cash flow.
• C) The model requires no assumption about growth whatsoever.
• D) The company is expected to grow its free cash flow to equity at a stable, sustainable rate indefinitely, making the model most appropriate for mature, stable companies rather than early-stage or highly cyclical ones.

Question 17

An analyst comparing a company's current EV/EBITDA multiple to its 5-year historical average notices the current multiple is well below the historical average, even though the company's growth outlook and risk profile appear unchanged. Which of the following is a plausible explanation, aside from the stock being genuinely undervalued?

• A) A broader re-rating of the industry or market (such as declining overall risk appetite for the sector) could compress multiples across many similar companies, independent of company-specific fundamentals.
• B) This situation is impossible unless the company's fundamentals have changed.
• C) Historical average multiples are always a perfectly reliable guide to appropriate current value.
• D) EV/EBITDA multiples never change over time for any reason.

Question 18

A company has book value per share of $25, an ROE of 14%, a required return of 10%, and an expected long-term growth rate of 4%. Using the justified P/B framework [P/B = (ROE-g)/(r-g)], the justified value per share is closest to:

• A) $50.00
• B) $41.67
• C) $35.00
• D) $25.00

Question 19

An analyst estimates that Company A will pay dividends of $1.00, $1.20, and $1.44 in years 1, 2, and 3 respectively. Starting in year 4, dividends are expected to grow at 4% indefinitely. If the required return is 10%, the intrinsic value today is closest to:

• A) $20.18
• B) $21.54
• C) $18.77
• D) $22.43

Question 20

A company has a ROE of 15%, a required return of 10%, and retains 40% of earnings. Using the residual income model, the P/B ratio is closest to:

• A) 1.00
• B) 1.50
• C) 2.25
• D) 1.90

Question 21

Company X trades at a forward P/E of 12x. Its sector peers trade at an average forward P/E of 18x. An analyst concludes Company X is undervalued. Which of the following factors would most weaken this conclusion?

• A) Company X has superior revenue growth prospects
• B) Company X has significantly lower leverage than peers
• C) Company X's earnings are expected to decline next year
• D) Company X has a higher dividend payout than peers

Question 22

In a free cash flow to equity (FCFE) model, FCFE is calculated as:

• A) Net income + depreciation − capital expenditures − change in working capital
• B) Net income + depreciation − capital expenditures − change in working capital + net borrowing
• C) EBIT(1−t) + depreciation − capital expenditures − change in working capital
• D) Operating cash flow + interest paid × (1 − tax rate)

Question 23

An analyst values a mining company using asset-based valuation. The most appropriate reason to use this method over DDM or FCFF is:

• A) The company pays no dividends and has irregular free cash flows
• B) The company's value is primarily in its natural resource reserves, which are better captured by asset values
• C) Asset-based valuation always produces the highest estimate of intrinsic value
• D) The company has high earnings growth that makes DCF unreliable

Question 24

An analyst is valuing a technology company using the H-model. The current dividend is $1.00, the short-term high growth rate is 20%, the long-term sustainable growth rate is 4%, the transition period is 10 years, and the required return is 10%. The intrinsic value is closest to:

• A) $30.67
• B) $16.67
• C) $41.67
• D) $36.67

Question 25

A company just paid an annual dividend of $3.00 per share. Dividends are expected to grow at a constant 5% rate indefinitely. Using a required return of 11%, the value of the stock today is closest to:

• A) $52.50
• B) $50.00
• C) $27.27
• D) $60.00

Question 26

A company's current dividend is $2.00 per share. Dividends are expected to grow at 20% annually for the next 3 years, then settle into a stable 5% long-run growth rate thereafter. Using a required return of 12%, the two-stage DDM value of the stock is closest to:

• A) $28.57
• B) $40.00
• C) $35.00
• D) $43.80

Question 27

The Gordon Growth (constant growth) dividend discount model is generally considered most appropriate for valuing which type of company?

• A) A company currently in bankruptcy proceedings.
• B) A company that has never paid or is not expected to ever pay a dividend.
• C) A mature, stable company with a consistent, sustainable long-term dividend growth rate.
• D) A young, high-growth company with no current dividend and highly uncertain future growth.

Question 28

A company's FCFE next year is expected to be $5,000,000, growing at a constant 4% rate thereafter. Using a required return on equity of 10% and 2,000,000 shares outstanding, the value per share is closest to:

• A) $33.33
• B) $41.67
• C) $45.00
• D) $50.00

Question 29

When using free cash flow to the firm (FCFF) to value a company, the appropriate discount rate is:

• A) The weighted average cost of capital (WACC), since FCFF represents cash flow available to all capital providers (debt and equity).
• B) The cost of equity alone.
• C) The risk-free rate alone.
• D) The pre-tax cost of debt alone.

Question 30

An analyst using the FCFF approach calculates the value of total firm (enterprise) value. To estimate the value of equity from this figure, the analyst should:

• A) Add the market value of debt to the total firm value.
• B) Divide the total firm value by the number of employees.
• C) The FCFF approach cannot be used to estimate equity value under any circumstances.
• D) Subtract the market value of debt (and other non-equity claims) from the total firm value.

Question 31

A company's current free cash flow to the firm (FCFF) is $100 million, expected to grow at 8% per year for the next three years, then settle into a stable long-run growth rate of 3% thereafter. The company's WACC is 9%. Using a two-stage FCFF valuation model, the estimated total firm value (enterprise value) is closest to:

• A) $2,162.5 million, which incorrectly reports the undiscounted terminal value at the end of Year 3 as if it already represented the present value of the entire firm.
• B) $1,964 million: FCFF1=$108.00M, FCFF2=$116.64M, FCFF3=$125.97M, FCFF4=$129.75M. Terminal value at end of Year 3 = FCFF4/(WACC-g) = $129.75M/0.06 = $2,162.51M. PV(FCFF1)=$99.08M, PV(FCFF2)=$98.17M, PV(FCFF3 + TV3)=$1,767.12M. Total firm value = $99.08M+$98.17M+$1,767.12M = approximately $1,964 million.
• C) $1,111.1 million, which incorrectly applies the single-stage Gordon growth formula directly to FCFF0 using only the long-run growth rate (100/(0.09-0.03)), ignoring the higher explicit near-term growth phase entirely.
• D) $1,296 million, which incorrectly discounts the terminal value using four years of discounting (dividing by 1.09^4) rather than the correct three years applicable to a terminal value calculated as of the end of Year 3.

Question 32

A company has a return on equity of 12%, an expected long-run growth rate (g) equal to ROE multiplied by a retention ratio of 60% (so g = 0.12 x 0.60 = 7.2%), and a required return on equity of 9.7%. Using the Gordon growth model relationship for justified forward P/E, the company's justified leading (forward) P/E ratio is closest to:

• A) 8.33x, which incorrectly uses the retention ratio (0.60) rather than the dividend payout ratio (1 - 0.60 = 0.40) in the numerator of the justified P/E formula.
• B) 41.2x, which incorrectly divides the payout ratio by the required return alone (0.097), ignoring the growth rate entirely.
• C) 16.0x, calculated as justified forward P/E = (dividend payout ratio) / (r - g) = (1 - 0.60) / (0.097 - 0.072) = 0.40 / 0.025 = 16.0x.
• D) 4.95x, which incorrectly divides the payout ratio by ROE (0.12) instead of by the correct (r - g) spread of 0.025.

Question 33

A company's current book value per share is $20.00, its return on equity (ROE) is expected to remain constant at 15%, and the required return on equity is 10%. Assuming no growth in book value or residual income beyond the current level (a single-period residual income perpetuity), the residual income model value per share is closest to:

• A) $20.00, which incorrectly ignores the residual income component entirely and reports only the current book value per share.
• B) $30.00, calculated as V0 = B0 + [(ROE - r) x B0] / r = $20.00 + [(0.15 - 0.10) x $20.00] / 0.10 = $20.00 + $1.00/0.10 = $20.00 + $10.00 = $30.00.
• C) $50.00, which incorrectly divides the full ROE of 15% (rather than the excess spread of ROE minus the required return, 5%) by the required return, before adding book value.
• D) $10.00, which incorrectly reports only the capitalized residual income component (the $10.00 add-on) while omitting the starting book value per share of $20.00.

Question 34

A company reports free cash flow to the firm (FCFF) of $500 million for the year. The company's interest expense is $80 million, its marginal tax rate is 25%, and it had net new borrowing (new debt issued minus debt repaid) of $30 million during the year. The company's free cash flow to equity (FCFE) for the year is closest to:

• A) $470 million, calculated as FCFE = FCFF - [Interest expense x (1 - tax rate)] + Net borrowing = $500M - [$80M x 0.75] + $30M = $500M - $60M + $30M = $470 million.
• B) $450 million, which incorrectly subtracts the full pre-tax interest expense of $80M rather than the after-tax interest expense of $60M.
• C) $410 million, which incorrectly subtracts net borrowing rather than adding it back, reversing the correct sign of the financing flow adjustment.
• D) $610 million, which incorrectly adds back the after-tax interest expense instead of subtracting it when converting from FCFF to FCFE.

Question 35

A company's current free cash flow to equity (FCFE) per share is $2.00, expected to grow at a constant 6% per year in perpetuity. Using a required return on equity of 11%, the estimated value per share using the single-stage FCFE model is closest to:

• A) $40.00, which incorrectly divides the current-year FCFE0 of $2.00 (rather than the next-year FCFE1 of $2.12) by the required return minus growth spread.
• B) $18.18, which incorrectly divides FCFE1 by the required return alone (0.11), ignoring the growth rate entirely rather than using the (r - g) spread in the denominator.
• C) $21.20, which incorrectly divides FCFE1 by 0.10 rather than by the correct (r - g) spread of 0.05.
• D) $42.40, calculated as FCFE1/(r - g) = ($2.00 x 1.06) / (0.11 - 0.06) = $2.12 / 0.05 = $42.40.

Question 36

A rapidly growing specialty retailer just paid an annual dividend of $4.00 per share and is expected to sustain 22% annual dividend growth for three years while it completes a national store rollout, before growth normalizes to a stable 4.5% rate as the store base matures. Using a required return on equity of 10%, the three-stage-to-terminal dividend discount model value of the stock is closest to:

• A) $138.00, which incorrectly reports the undiscounted terminal value at the end of Year 3 as if it were already the present value of the entire stock today.
• B) $80.00, which incorrectly applies the single-stage Gordon growth formula directly to D0 using only the long-run growth rate, entirely ignoring the three years of much higher explicit near-term growth.
• C) $118.50: D1 = $4.88, D2 = $5.9536, D3 = $7.2634. Terminal value at end of Year 3 = D4/(r-g) = [$7.2634 x 1.045]/(0.10-0.045) = $7.5902/0.055 = $138.00. PV = ($4.88/1.10) + ($5.9536/1.10^2) + [($7.2634+$138.00)/1.10^3] = $4.436 + $4.920 + $109.142 = $118.50.
• D) $103.85, which incorrectly discounts the terminal value using four years of discounting (dividing by 1.10^4) rather than the correct three years applicable to a terminal value calculated as of the end of Year 3.