Equity valuation item sets

Practice equity valuation through linked case questions

Level II equity valuation asks you to connect a company’s fundamentals, forecasts, and model assumptions to an investment value. In a vignette set, a case can provide operating data, earnings, payout policy, required returns, or peer multiples. The question then determines which valuation method and input basis matter. The original practice cases below teach that selection process with full calculations; they are not copied exam questions.

Set 1: Dividend discount model and growth

Vignette: Ardent Utilities

Ardent Utilities just paid an annual dividend of $2.00 per share. Dividends are expected to grow 4% annually indefinitely. The required return on equity is 9%. The current share price is $39.50. Assume the constant-growth dividend discount model is appropriate.

Question 1: Estimate intrinsic value

A) $38.00 B) $41.60 C) $50.00

Answer: B. The next dividend is D1 = D0(1 + g) = $2.00 × 1.04 = $2.08. Under the Gordon growth model, V0 = D1 / (r − g) = 2.08 / (0.09 − 0.04) = $41.60. Choice A uses the just-paid dividend in the numerator, which understates value. Choice C may divide by the growth rate or confuse a 4% payout growth assumption with the required return.

Question 2: Estimate expected return at the current price

Under the same constant-growth assumptions, the expected return at $39.50 is closest to A) 8.6%, B) 9.3%, or C) 10.0%.

Answer: B. For a constant-growth dividend model, expected return is dividend yield plus growth: D1/P0 + g = 2.08/39.50 + 4% = 5.27% + 4% = 9.27%. The nearest choice is B, 9.3%. This explicit check is part of good valuation work: derive the value first, then see whether the market price implies a return consistent with the stated inputs. The 8.6% and 10.0% choices reflect arithmetic or input confusion.

Question 3: Sensitivity to required return

If the required return rises to 10%, with dividend growth unchanged, the estimated value is closest to A) $34.67, B) $41.60, or C) $52.00.

Answer: A. V0 = $2.08/(0.10 − 0.04) = $34.67. Value falls because the spread between required return and growth widens. Choice B reuses the original 9% required return. Choice C reverses the direction or uses an inconsistent denominator. The model is very sensitive when r − g is small.

Question 4: Test model suitability

Which change would most directly weaken the constant-growth model’s suitability? A) Ardent’s near-term dividend growth is unusually high and then expected to settle at 4%. B) The current price is below estimated value. C) The required return is greater than the growth rate.

Answer: A. A stable perpetual growth assumption is inappropriate when growth follows distinct stages. A multistage dividend model may be needed. A price below estimated value is a conclusion, not a model assumption. A required return above growth is necessary for the denominator to remain positive and the constant-growth value to be finite.

Set 1 lesson: protect assumptions

The calculation depends on a sustainable perpetual growth rate below the required return and on the next dividend, not the last dividend, in the numerator. Before calculating, check whether the company pays dividends and whether a stable-growth model fits its life cycle. A correct formula can produce a misleading number if its assumptions do not match the case.

Set 2: FCFE valuation and per-share value

Vignette: Beacon Medical Systems

Beacon has 40 million common shares and no preferred stock. Forecast free cash flow to equity for next year is $96 million. The required return on equity is 10%, and long-run FCFE growth is 4%. Net debt is $160 million. The forecast FCFE is already after interest payments and net borrowing. Assume constant growth is appropriate.

Question 1: Estimate equity value per share

A) $40.00 B) $60.00 C) $80.00

Answer: A. The constant-growth FCFE value of equity is FCFE1/(r − g) = $96m/(0.10 − 0.04) = $1,600m. Divide by 40m shares to obtain $40.00. Choice B may subtract net debt even though the cash flow is already FCFE; choice C may use an incorrect denominator. This arithmetic check exposes a common divide error: 96/.06=1,600, and 1,600/40=40.

Question 2: Compare with market price

If Beacon trades at $44 per share, the stock is closest to A) 10% undervalued, B) 10% overvalued, or C) fairly valued under the estimate.

Answer: B. Estimated value is $40, below the $44 market price. The market premium to estimated value is ($44 − $40)/$40 = 10%. If a question instead asks for downside relative to market price, the denominator would be $44 and the result would be 9.1%. Read the comparison basis.

Question 3: Identify the correct cash flow

If the analyst instead has free cash flow to the firm (FCFF), which additional adjustment is generally required to move from enterprise value to common equity value? A) Subtract net debt. B) Add net debt. C) Divide FCFF by shares before discounting.

Answer: A. FCFF is available to all capital providers and is discounted at the weighted average cost of capital to estimate enterprise value. Subtract net debt and other senior claims to arrive at equity value, then divide by common shares. Choice B reverses the claim adjustment; choice C treats a firm-level cash flow as a per-share cash flow.

Question 4: Check growth sensitivity

If long-run growth increases from 4% to 5% while required return remains 10%, value per share becomes closest to A) $32.00, B) $48.00, or C) $64.00.

Answer: B. Value = $96m/(0.10 − 0.05) = $1,920m; per share = $1,920m/40m = $48.00. The close distractors test whether the candidate recomputes the spread and avoids carrying the previous denominator forward.

Set 2 lesson: match cash flow to claim

FCFE is cash flow available to common equity after financing effects, so discount it at the required return on equity and divide equity value by shares. FCFF is before debt financing cash flows, so discount it at WACC to estimate enterprise value and then bridge to equity. Do not subtract net debt twice if the cash flow measure has already incorporated the relevant financing effects.

Set 3: Residual income and justified multiples

Vignette: Cedar Analytics

Cedar’s beginning common equity book value is $25 per share. Forecast earnings per share are $3.00. The required return on equity is 10%, and the expected long-run growth in residual income is 3%. The analyst assumes clean surplus accounting for the illustration. The stock trades at $31.

Question 1: Compute next-period residual income per share

A) $0.50 B) $1.00 C) $3.00

Answer: A. Residual income is earnings minus the equity charge: RI1 = EPS1 − r × beginning book value = $3.00 − 0.10 × $25 = $0.50. Choice B fails the arithmetic; choice C reports earnings without subtracting the required return on beginning equity. This method asks whether earnings exceed the required charge, not simply whether earnings are positive.

Question 2: Calculate the justified forward P/B

Using the stable-growth residual-income relation, the justified forward P/B is closest to A) 1.05, B) 1.20, or C) 1.29.

Answer: C. Forward P/B = (ROE − g)/(r − g), where ROE = EPS1/B0 = 3/25 = 12%. Thus (0.12 − 0.03)/(0.10 − 0.03) = 0.09/0.07 = 1.286, or about 1.29. Choice A uses an incorrect input; B understates the spread ratio. Calculate independently and select the closest choice.

Question 3: Apply the justified P/B

Using the calculated justified forward P/B of 1.286 and the $25 beginning book value, implied value per share is closest to $32.15. At a market price of $31, the model suggests about $1.15 per share of upside, or 3.7% relative to market price. This is conditional on the stable-growth and clean-surplus assumptions.

Question 4: Interpret the result

A rise in expected ROE relative to the required return, all else equal, generally increases justified P/B because the firm is expected to earn more than its equity charge. If ROE equals the required return, the justified premium to book value disappears under the stable assumptions. Growth alone does not guarantee a higher P/B: the result depends on whether growth creates value by earning above the required return.

A reliable valuation workflow

• Name the claim being valued: common equity, enterprise, or a share.
• Choose the model that matches the vignette’s cash flow or profitability information.
• Match the cash-flow period and discount rate: FCFE with required return on equity; FCFF with WACC.
• Write the requested output and units before calculating.
• Check whether growth and discount assumptions make the model mathematically valid.
• Compare value and market price using the denominator named in the question.
• State key model limitations and do not treat intrinsic value as certainty.

Valuation errors worth checking

A frequent error is mixing FCFF with the cost of equity, or FCFE with WACC. Another is using a dividend just paid rather than the next expected dividend in the constant-growth model. A third is dividing enterprise value by shares without first adjusting for debt and other claims. In a justified multiple, confirm whether the numerator uses forward earnings and whether payout, growth, and required return are expressed consistently.

Also inspect the difference between price upside and discount to value. If estimated value is $52.50 and market price is $48, upside over market is 4.50/48 = 9.375%. The market discount to estimated value is 4.50/52.50 = 8.57%. Both are valid ratios, but they answer different questions.

Practice the explanation, not only the formula

After completing a valuation set, write a short interpretation: what assumptions drive the result, which variable creates the greatest sensitivity, and what information would change the conclusion? A valuation output is not a fact about the market; it is the implication of a model and inputs. Level II questions may ask you to assess that implication or choose the model limitation that matters.

Use fresh numbers and vary one assumption at a time. If increasing the required return does not lower your estimated value, check the formula and direction. If increasing sustainable growth changes the value in an unexpected way, verify that growth remains below the discount rate and that the model’s assumptions still hold. Such checks make calculations faster and more reliable under timed conditions.

How residual income links earnings to value

Residual income begins with current book value and adds the present value of future residual income. Residual income for a period is earnings minus the equity charge on beginning book value. The method can help when dividend or cash-flow forecasts are difficult, provided accounting and clean-surplus assumptions are appropriate. In a stable setting, justified forward P/B can be expressed as (ROE − g)/(r − g), where ROE is forward earnings divided by beginning book value. If ROE equals the required return, justified P/B is one. If ROE exceeds the cost of equity, a premium to book may be justified, subject to assumptions.

Run model and unit checks

Before accepting a valuation, ask whether it is per share, total equity, or enterprise value. FCFE is discounted at the cost of equity; FCFF is discounted at WACC, then net debt and senior claims are subtracted to reach equity value. Do not subtract net debt twice. In a constant-growth dividend model, use the next expected dividend, and confirm that growth is below the required return.

Check direction: a higher required return should lower value, all else equal. A higher perpetual growth rate can increase value while remaining below the discount rate. Residual-income value depends on returns relative to the equity charge, so growth does not automatically create value. Estimates remain conditional on forecasts; sensitivity analysis communicates uncertainty better than false precision.

The current Level II curriculum defines required equity valuation knowledge and learning outcomes. CFA Institute’s Level II exam guide describes the vignette format; its practice resources provide official candidate questions and mock exams.