Residual Income Valuation

READING 23

RESIDUAL INCOME VALUATION

EXAM FOCUS

This topic review introduces the fourth type of valuation model found in the CFA curriculum: residual income models. Understand the differences between these models and the dividend discount, free cash flow, and market multiple models. Successful application of residual income models depends on making appropriate adjustments to the financial statements, so you should be able to use techniques from financial statement analysis when applying these models. The concept of continuing residual income is linked to industry analysis. Given these connections with other Level II concepts, this material is highly testable.

MODULE 23.1: RESIDUAL INCOME DEFINED

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LOS 23.a: Calculate and interpret residual income, economic value added, and market value added.

Residual income (RI), also called economic profit, is the firm's net income less a charge that represents the stockholders' opportunity cost of equity capital. Residual income recognises the cost of equity capital in the measurement of income. Traditional accounting net income may show a positive figure while the firm fails to meet equity investors' required return; accounting net income includes a cost of debt (interest expense) but does not reflect an explicit cost for equity. Therefore, accounting income can overstate returns from equity investors' perspective. Residual income explicitly deducts all capital costs.

EXAMPLE: Calculating residual income

Madeira Fruit Suppliers, Inc. (MFS) distributes fruit to grocery stores in large U.S. cities. The book value of MFS's assets is $1.4 billion, financed with $800 million in equity and $600 million in debt. Its before-tax cost of debt is 3.33%, and its marginal tax rate is 34%. MFS has a cost of equity of 12.3%. MFS's abbreviated income statement shows accounting net income of $80,520,000.

Determine whether MFS is profitable by calculating residual income and explaining its relationship to reported accounting income.

Answer:

While accounting net income of $80,520,000 indicates MFS is profitable in a traditional accounting sense, we must deduct the equity charge to see whether the company covers shareholders' opportunity cost of capital.

The dollar-based equity charge is equal to beginning book value of equity multiplied by the cost of equity:

Equity charge = Beginning book value of equity × Cost of equity

Using the data provided:

Equity charge = $800,000,000 × 12.3% = $98,400,000

Residual income (RI) = Net income - Equity charge

RI = $80,520,000 - $98,400,000 = -$17,880,000

Even though MFS reports positive accounting profit, after charging equity capital at shareholders' required return the firm is economically unprofitable: residual income is negative.

EVA and MVA

Economic value added (EVA®) measures the value added for shareholders by management during a period. EVA is calculated as:

EVA = NOPAT - (WACC × Total capital)

where NOPAT is net operating profit after tax, and WACC is the weighted average cost of capital applied to beginning-of-year total capital for EVA computation.

PROFESSOR'S NOTE

Residual income differs from EVA in the accounting items used. Residual income is based on net income (which deducts interest expense and thus reflects debt costs) and subtracts an equity charge. EVA is based on NOPAT (which excludes interest expense) and subtracts a capital charge for both debt and equity (WACC × total capital). Conceptually, both measure economic income. For EVA computation we typically use beginning-of-year total capital; for MVA computation we use end-of-year total capital (the same point at which market value is determined).

Analysts should make several adjustments (if applicable) to financial statements before calculating NOPAT and invested capital. Common adjustments include:

• Capitalize and amortize research and development (R&D) charges rather than expensing them; add back amortization to calculate NOPAT.
• Add back charges on strategic investments that will generate returns in the future.
• Eliminate deferred taxes and consider only cash taxes as an expense when appropriate.
• Treat operating leases as capital leases and adjust for nonrecurring items.
• Add the LIFO reserve to invested capital and add back the change in LIFO reserve to NOPAT (when converting from LIFO to FIFO).

Market value added (MVA) is the difference between the market value of a firm's long-term debt and equity and the book value of invested capital; it measures value created by management since the firm's inception. MVA is calculated as:

MVA = Market value - Total capital

EXAMPLE: Calculating EVA and MVA

VBM, Inc. reports NOPAT of $2,100, a WACC of 14.2%, and invested capital of $18,000 at the beginning of the year and $21,000 at the end of the year. The market price (year-end) of the firm's stock is $25 per share, and VBM has 800 shares outstanding. The market value (year-end) of the firm's long-term debt is $4,000. Calculate VBM's EVA and MVA.

Answer:

First calculate EVA:

WACC charge = 0.142 × $18,000 = $2,556

EVA = NOPAT - WACC charge = $2,100 - $2,556 = -$456

The market value of the company is equity market value plus debt market value:

Market value of equity = $25 × 800 = $20,000

MV of company = $20,000 + $4,000 = $24,000

MVA = Market value - Total capital

MVA = $24,000 - $21,000 = $3,000

LOS 23.b: Describe the uses of residual income models.

Several commercial residual income-based models exist. Like EVA and MVA, they commonly apply residual income to measure managerial effectiveness and executive compensation. For valuation we focus on equity-valuation applications of residual income models. Residual income models have also been proposed for goodwill impairment testing.

MODULE 23.2: RESIDUAL INCOME COMPUTATION

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LOS 23.c: Calculate the intrinsic value of a common stock using the residual income model and compare value recognition in residual income and other present value models.

We can forecast residual income given accounting data and assumptions about future earnings growth. Residual income for period t is:

RI_t = E_t - r × B_{t-1}

where E_t is end-of-period reported earnings (net income) for period t, r is the required return on equity, and B_{t-1} is beginning book value of equity (book value at the start of period t).

EXAMPLE: Forecasting residual income

Laura Kraft, CFA, forecasts residual income for Delilah Cosmetics, Inc. over the next two years. She uses a required rate of return of 11% and assembles basic forecasting information (earnings forecasts, beginning book value, etc.). Forecast Delilah's residual income for 2025 and 2026.

Answer:

Compute RI for each forecast year using the formula RI_t = E_t - r × B_{t-1}. (Specific numeric table omitted here in the narrative but retained in the worked example set used for instruction.)

The residual income valuation model separates intrinsic value into two elements:

V_0 = B_0 + PV of expected future RI

In words: the current intrinsic value, V0, equals current book value per share, B0, plus the present value of all expected future residual income (each period's earnings less an equity charge on beginning book value).

The main practical difficulty is that residual income is an infinite stream, so we must make assumptions about long-term behaviour of residual income. In the simplest case, assume operations cease after a finite number of years and discount only those residual incomes; otherwise use multistage methods or constant-growth assumptions to approximate the infinite tail.

EXAMPLE: Computing intrinsic value with a residual income model

Consolidated Pipe Products has a required return on equity of 14%. The current book value is C$6.50. Forecast earnings per share for 2025, 2026, and 2027 are C$1.10, C$1.00, and C$0.95 respectively. Dividends in 2025 and 2026 are C$0.50 and C$0.60 respectively. In 2027 the dividend is a liquidating dividend equal to entire book value and the firm ceases operations. Calculate the value of Consolidated's stock using the residual income model.

Answer:

Calculate residual income in each forecast year using RI_t = E_t - r × B_{t-1}, discount each RI back to present at the required return, and add current book value B0. (A residual income forecast table is used to show the arithmetic; the final intrinsic value equals B0 plus the PV of the forecasted residual incomes.)

You may use a financial calculator to treat the sequence of residual incomes as cash flows to compute NPV at required return r. Residual income models tend to recognise value earlier compared with DDM or FCFE because they include current book value explicitly; the terminal value in DDM or FCFE often dominates intrinsic value, adding uncertainty that residual income models reduce.

LOS 23.d: Explain fundamental determinants of residual income.

General residual income models do not require assumptions about long-term growth. However, if we assume constant growth in dividends and earnings, we can derive a single-stage residual income model that highlights fundamental drivers.

Under the single-stage assumption (constant growth g in earnings and dividends), and when market price equals intrinsic value (P0 = V0), value can be rearranged to give an expression equivalent to the Gordon growth model. The result shows that a firm's additional value relative to book value depends on ROE - r and the growth rate.

The single-stage residual income model is mathematically equivalent to the Gordon growth model when inputs are consistent. From this formulation we identify the fundamental drivers:

• ROE in excess of required return on equity (ROE - r).
• Retention ratio (b) and consequently growth rate g = b × ROE.

If ROE = r, then justified market value equals book value. If ROE > r, residual income is positive and market value exceeds book value. The present value of the firm's expected economic profits is the premium over book value generated by returns in excess of cost of equity.

Tobin's Q is related: it measures market value of assets relative to replacement cost (or book value) and captures similar economic profitability concepts.

PROFESSOR'S NOTE

The single-stage model assumes constant ROE and constant earnings growth, implying residual income persists indefinitely. In practice residual income tends to approach zero over time as competition erodes excess returns. Thus single-stage models are usually modified to allow declining RI via a persistence factor or multistage forecasts.

LOS 23.e: Explain the relation between residual income valuation and the justified price-to-book ratio based on forecasted fundamentals.

Residual income models can be used to derive justified price-to-book (P/B) ratios because the model links market price directly to book value plus the PV of future residual incomes. From the single-stage model, if ROE > r, the present value of future residual income is positive and P/B > 1. If ROE = r, then P/B = 1.

MODULE QUIZ 23.1, 23.2

1.

The present value of Sporting Shoes (SS) projected residual income for the next five years plus beginning book value is C$75.00 per share. Beyond that time horizon, the firm will sustain a residual income of C$11.25 per share, which is the residual income for Year 6. The cost of equity is 10%. The justified value of SS's common stock is closest to:

A.

C$69.85.

B.

C$112.50.

C.

C$144.85.

MODULE 23.3: CONSTANT GROWTH MODEL FOR RI

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LOS 23.f: Calculate and interpret the intrinsic value of a common stock using single-stage (constant-growth) and multistage residual income models.

f

f

f

EXAMPLE: Calculating value with a single-stage residual income model

Western Atlantic Railroad has a book value of $23.00 per share. The company's ROE on new investments is 14%, and its required return on equity is 12%. The dividend payout ratio is 60%. Calculate the value of the shares using a single-stage residual income model and the present value of expected economic profits.

Answer:

First, calculate the growth rate:

g = retention ratio × ROE = (1 - 0.6) × 0.14 = 0.4 × 0.14 = 0.056 = 5.6%

Then calculate intrinsic value using the single-stage model:

The present value of the firm's expected economic profits (the PV of RI) in this case is $7.19, leading to an intrinsic value equal to book value plus $7.19 (the worked arithmetic is presented in a teaching table in the original material).

EXAMPLE: Western Atlantic Railroad valuation with Gordon growth model

Use the same information to calculate value using the Gordon growth (dividend discount) model to show equivalence.

Answer:

E1 = Beginning BV × ROE = $23.00 × 0.14 = $3.22

D1 = E1 × Payout ratio = $3.22 × 0.6 = $1.932

Using the Gordon growth formula P0 = D1 / (r - g), substituting D1, r = 12% and g = 5.6% yields the same intrinsic value as the single-stage residual income model, illustrating algebraic equivalence when assumptions align.

PROFESSOR'S NOTE

Multistage residual income models will be discussed in later learning outcome statements.

LOS 23.g: Calculate the implied growth rate in residual income, given the market price-to-book ratio and an estimate of the required rate of return on equity.

Rearranging the single-stage residual income model allows solving for the implied growth rate given the market P/B ratio, ROE, and required return. This expression yields the market's implied expectations of residual income growth if current price equals intrinsic value under the single-stage assumption.

EXAMPLE: Calculating implied growth rate

Tellis Telecommunications, Inc. has a P/B ratio of 2.50. ROE is expected to be 13%, current book value per share is €8.00, and cost of equity is 11%. Calculate the growth rate implied by the current P/B ratio.

Answer:

Market price implied by P/B is P0 = €8.00 × 2.50 = €20.00. Plugging into the rearranged single-stage formula solves for the implied growth rate; the algebraic steps follow the standard derivation for g in the single-stage residual income relation.

MODULE QUIZ 23.3

1.

Jill Smart is an analyst with Allenton Partners. Jill is reviewing the valuation of three companies (P, Q, and R) using the residual income model and their corresponding current market prices.

The information below summarizes the findings:

Based on the above information, which statement best describes the market's valuation of P, Q, and R?

A.

P is overvalued, Q is undervalued, and R is fairly valued.

B.

P is undervalued, Q is fairly valued, and R is overvalued.

C.

P is undervalued, Q is overvalued, and R is fairly valued.

2.

An investor is considering the purchase of Capital City Investments, Inc., which has a price-to-book value (P/B ratio) of 5.00. Return on equity (ROE) is expected to be 18%, the market price per share is $25.00, and the growth rate is expected to be 8%. Assume the shares are currently priced at their fair value. The cost of equity implied by the current P/B ratio is closest to:

A.

12%.

B.

16%.

C.

10%.

3.

Century Scales has a required return on equity of 12% and is expected to grow indefinitely at a rate of 5%. The expected return on equity (ROE) that would justify a price-to-book multiple of 2.14 is closest to:

A.

10%.

B.

15%.

C. 20%.

4.

Marg Myers, CFA, has determined that Rocky Romano Ice Cream Company can be valued using a single-stage residual income model. Myers estimates Rocky's return on equity (ROE) is greater than the cost of equity capital, which is greater than the sustainable growth rate. Book value per share is greater than zero. What can Myers conclude about Rocky's present value (PV) of future expected residual income (RI) and Rocky's justified price-to-book ratio?

5.

Krackel, Inc., has a book value per share as of FYE 2023 of $4.50. The required return on equity is 10%. Earnings per share in 2024 are forecast to be $0.45. Assume Krackel can be valued using a single-stage residual income model. The justified price-to-book ratio and the present value of expected residual income are closest to:

MODULE 23.4: CONTINUING RESIDUAL INCOME

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LOS 23.h: Explain continuing residual income and justify an estimate of continuing residual income at the forecast horizon, given company and industry prospects.

Forecasting residual income indefinitely is difficult. As with DDM and FCF models, we typically use a multistage approach: forecast RI over a short-term horizon (e.g., five years) and then make assumptions about long-term behaviour. Continuing residual income is the residual income expected over the long term after the explicit forecast horizon.

The projected decay of residual income after the forecast horizon is captured by a persistence factor, ω, where 0 ≤ ω ≤ 1:

• ω = 1: residual income persists at the year-T level forever.
• ω = 0: residual income drops immediately to zero after year T.
• 0 < ω=""><>: residual income declines over time toward zero as ROE falls to the cost of equity.

To simplify the terminal calculation for RI, typical assumptions include:

• Residual income persists at its current level forever.
• Residual income drops immediately to zero.
• Residual income declines over time and approaches zero as competition normalises ROE.
• Residual income declines to a long-run average level consistent with a mature industry.

Industry and firm analysis is needed to justify which assumption is appropriate. Persistence factors tend to be higher when a firm has a sustainable competitive advantage and better industry prospects. Higher persistence is associated with low dividend payouts, historically high RI persistence in the industry, and similar indicators. Lower persistence is associated with high ROE that is likely unsustainable, significant nonrecurring items, or high accounting accruals.

Treat the continuing residual income model as a multistage model:

V0 = B0 + (PV of interim high-growth RI) + (PV of continuing RI)

Procedure

1. Calculate current book value per share, B0.
2. Calculate residual income in each year 1 to T and discount each RI back to present at the required return on equity.
3. Calculate continuing residual income that begins at the end of the high-growth period (year T) and compute its present value as of time T - 1 using the chosen persistence assumption.

Assumption #1: Residual Income Persists at the Current Level Forever

If ω = 1, residual income after year T remains constant at RI_T each year. The present value of continuing residual income at time T - 1 is a perpetuity:

PV_{T-1} = RI_T / r

Assumption #2: Residual Income Drops Immediately to Zero

If ω = 0, residual income after year T is zero and the present value of continuing residual income at time T - 1 is:

PV_{T-1} = 0

Assumption #3: Residual Income Declines Over Time to Zero

If residual income declines after T and ω is between 0 and 1, the present value at time T - 1 is:

PV_{T-1} = RI_T × ω / (r - ω)

This formula captures geometric decay of RI with persistence ω and discount rate r.

Assumption #4: Residual Income Declines to a Long-Run Level in a Mature Industry

A simpler approach when long-run industry fundamentals are known is to estimate the stock price at time T, P_T, using an assumed price-to-book ratio and book value at T:

P_T = B_T × Forecasted P/B

Then the present value of continuing residual income at time T equals the difference between market price and book value at T:

PV of continuing RI at T = P_T - B_T

Convert this to a PV at time T - 1 by discounting as appropriate (or use algebraic equivalence with persistence factor formula).

EXAMPLE: Calculating value with a multistage residual income model (part 1)

Java Metals expects ROE = 15% for each of the next five years. Current book value is $5.00 per share, the company pays no dividends and reinvests all earnings. Required return on equity is 10%. Earnings in Years 1-5 equal ROE × beginning book value each year. Assume after five years continuing residual income falls to zero. Calculate intrinsic value using a residual income model.

Answer:

Forecast earnings and book values for Years 1-5 as:

Year 1: Beginning BV = $5.00, E1 = 0.15 × $5.00 = $0.75, RI1 = E1 - 0.10 × $5.00 = $0.75 - $0.50 = $0.25.

Year 2: B1 = B0 + E1 - D1 (no dividends, so B1 = B0 + E1 = $5.00 + $0.75 = $5.75), E2 = 0.15 × $5.75 = $0.8625, RI2 = E2 - 0.10 × $5.75 = $0.8625 - $0.575 = $0.2875 (rounded $0.29).

Year 3: Repeat the process to compute RI3 ≈ $0.33.

Year 4: RI4 ≈ $0.38.

Year 5: RI5 ≈ $0.44.

Under the assumption that residual income after five years is zero (ω = 0), intrinsic value today is:

V0 = B0 + PV(RI1...RI5) = $5.00 + PV($0.25, $0.29, $0.33, $0.38, $0.44) at r = 10%

Computed NPV = $6.25 (illustrative calculator cash flow sequence provided in original teaching material: CF0 = 5, C01 = 0.25, C02 = 0.29, C03 = 0.33, C04 = 0.38, C05 = 0.44, I = 10, CPT → NPV = $6.25).

EXAMPLE: Calculating value with a multistage residual income model (part 2)

Now assume RI after five years persists at $0.44 forever (ω = 1). Calculate intrinsic value.

Answer:

A perpetuity of $0.44 starting in Year 5 is worth $0.44 / 0.10 = $4.40 at the end of Year 4. Discount that back along with interim RIs; intrinsic value is larger than the ω = 0 case due to the nonzero perpetuity.

EXAMPLE: Calculating value with a multistage residual income model (part 3)

Assume after Year 5 Java's RI decays with persistence factor ω = 0.4. Calculate intrinsic value.

Answer:

The terminal value in Year 4 now includes the present value at Year 4 of the declining residual income stream using ω = 0.4, reducing terminal value relative to the ω = 1 case. The intrinsic value today equals current book value plus the PV of interim RIs plus the PV of the terminal value in Year 4. A lower persistence factor reduces intrinsic value.

EXAMPLE: Calculating value with a multistage residual income model (part 4)

Suppose at the end of Year 5 Java's ROE falls to a long-run average and the forecasted P/B ratio falls to 1.2. Calculate intrinsic value.

Answer:

Book value per share at the end of Year 5 is $10.05, so market price at that time is expected to be $10.05 × 1.2 = $12.06. The present value of continuing residual income at the end of Year 4 equals P5 - B5 as of time 5 and discounted back to time 4; intrinsic value is book value plus the PV of interim RIs plus PV of continuing RI as computed from P/B assumption.

PROFESSOR'S NOTE

If the market price is higher than the model's intrinsic price, the stock is overvalued. If market price is lower than the model price, the stock is undervalued. If they are equal, the stock is fairly valued.

MODULE QUIZ 23.4

1.

Meyer Henderson, CFA, estimates the value of Trammel Medical Supplies to be $68 per share using a residual income model. In his estimate of continuing residual income, he assumes that, after Year 6, residual income will persist at the same level forever. How many of the following assumptions concerning residual income would most likely cause his value estimate to fall below $68?

A.

One.

B.

Two.

C.

Three.

2.

The residual income per share in 2026 and the present value of continuing residual income as of the end of 2025 are closest to:

3.

The value per share of BCB stock using the residual income model is closest to:

A.

£39.17.

B.

£49.80.

C.

£53.20.

4.

Based on the residual income model, the intrinsic value and the most likely recommendation Mechanic would issue for the stock of DRL are:

5.

Mechanic revises his expectation of continuing RI after year 4 to remain constant at the Year-4 forecast level. Based on the residual income model, the intrinsic value and the most likely recommendation for DRL are:

6.

George Karanopoulos, CFA, suggests Mechanic re-estimate DRL value with persistence factor ω = 0.3 after Year 4. Based on the residual income model, the intrinsic value and recommendation are:

MODULE 23.5: STRENGTHS/WEAKNESSES

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LOS 23.i: Compare residual income models to dividend discount and free cash flow models.

DDM and FCFE measure value by discounting expected cash flow streams. Residual income starts with book value and adds PV of expected future RI. Theoretically, if forecasts and assumptions are consistent, DDM, FCFE and RI approaches produce identical intrinsic values. In practice forecast errors and different ease of forecasting inputs mean model outputs often differ. Using residual income alongside DDM or FCFE helps check consistency of valuation results.

LOS 23.j: Explain strengths and weaknesses of residual income models and justify selection of a residual income model to value common stock.

Strengths of residual income models include:

• Terminal value typically does not dominate the intrinsic value estimate, unlike many DDM and FCF models.
• They use accounting data, which is widely available.
• Applicable to firms that pay no dividends or that have negative or volatile free cash flows in the short run.
• Applicable when cash flows are volatile.
• Focus on economic profitability (earnings in excess of equity charge) rather than only accounting profit.

Weaknesses include:

• Rely on accounting data that can be manipulated by management.
• Require numerous and significant adjustments to reported accounting figures to reflect economic reality.
• Assume the clean surplus relation holds (or that any violation has been properly addressed).

PROFESSOR'S NOTE

Clean surplus relation: Bt = Bt-1 + Et - Dt (ending book = beginning book + earnings - dividends), excluding ownership transactions. This relation was used to forecast end-of-period book value in previous examples. Items bypassing the income statement (e.g., currency translation adjustments) cause the clean surplus relation to fail; the analyst must adjust forecasts accordingly if such items do not offset in future periods.

Residual income models are appropriate when:

• The firm does not pay dividends or dividend stream is too volatile to forecast reliably.
• Expected free cash flows are negative for the foreseeable future.
• Terminal value forecast is highly uncertain, making DDM or FCFE less useful.

Residual income models are not appropriate when:

• The clean surplus accounting relation is violated significantly and cannot be corrected.
• There is significant uncertainty about estimates of book value or ROE.

LOS 23.k: Describe accounting issues in applying residual income models.

PROFESSOR'S NOTE

This section summarises financial statement analysis material relevant to residual income valuation. Analysts must convert GAAP or IFRS financial statements into economics-based statements to estimate value. Typical adjustments are described below.

Clean Surplus Violations

The clean surplus relation may not hold when items bypass the income statement and flow directly to shareholders' equity. Adjust net income to account for items not expected to reverse if they affect future earnings or book value forecasts. Items that can bypass the income statement include:

• Foreign currency translation gains and losses recorded directly in equity under the current rate method.
• Certain pension adjustments recorded in equity.
• Gains/losses on certain hedging instruments recorded in equity.
• Changes in revaluation surplus (IFRS) for long-lived assets.
• Changes in the value of certain liabilities due to changes in credit risk (IFRS).
• Changes in market value of available-for-sale securities (IFRS or prior GAAP presentations).

If the clean surplus relation is violated, net income may be incorrect for forecasting ROE unless such items are temporary or expected to offset over time. For example, cumulative translation adjustments (CTA) that reverse over time may not require adjustments to the ROE forecast.

Variations from Fair Value

Accrual accounting often reports many balance-sheet items at book values different from market values. Common adjustments include:

• Capitalise operating leases by increasing assets and liabilities by the PV of future lease payments; interest expense in the income statement should reflect the true cost of debt.
• Consolidate special purpose entities (SPEs) whose assets and liabilities are not on the parent balance sheet where control/benefit exists.
• Adjust reserves and allowances (e.g., allowance for bad debts) to expected loss experience.
• Adjust inventory for LIFO users to FIFO by adding the LIFO reserve to inventory and equity (assuming no deferred tax impact or adjust for deferred tax appropriately).
• Adjust pension asset/liability to reflect funded status = fair value of plan assets - projected benefit obligation (PBO).
• Eliminate deferred tax liabilities when appropriate (e.g., liabilities that are not expected to reverse) and report as equity adjustments if justified.

Intangible Asset Effects on Book Value

Two intangible-asset issues require attention:

• Intangibles recognised at acquisition: When a combined entity recognises identifiable intangibles that were not on the investee balance sheet, amortisation of these intangibles reduces consolidated ROE and can depress the combined entity's valuation relative to the pre-acquisition sum of values. To avoid this distortion, remove amortisation of intangibles capitalised due to acquisition when computing ROE for residual income valuation of the combined entity.
• R&D expenditures: Treatment of R&D is less definitive. For mature companies, ROE should reflect long-term productivity of R&D: productive R&D increases ROE and RI; unproductive R&D reduces ROE and RI. Analysts may capitalise productive R&D to better reflect value creation.

Nonrecurring Items and Other Aggressive Accounting Practices

Nonrecurring items should be excluded from residual income forecasts because they are not indicative of recurring operating performance. Items to adjust for include discontinued operations, accounting changes, unusual items, extraordinary items, and restructuring charges.

Firms may also use aggressive practices that overstate assets and earnings (e.g., accelerating revenue recognition or deferring expenses). The analyst must detect and correct these distortions.

International Accounting Differences

Residual income models depend on accrual accounting; national accounting differences may limit their usefulness in global valuation. Consider:

• Reliability of earnings forecasts under local accounting rules.
• Systematic violations of clean surplus relation under local reporting.
• Poor quality accounting rules that make financial statements depart from economic reality.

MODULE QUIZ 23.5

1.

Karuba Manufacturing has a book value of $15 per share and is expected to earn $3.00 per share indefinitely. The company does not reinvest any of its earnings. Karuba's beta is 0.75, the risk-free rate is 4%, and the expected market risk premium is 8%. The value of Karuba stock according to the dividend discount model and the residual income model are closest to:

2.

Kim Dae-Eun, CFA, values Olympic Productions at $78 per share with a residual income model using historical data to estimate ROE and book value as reported. He later determines Olympic improperly capitalised and amortised expenditures that should have been expensed. What is the effect on his forecasts of ROE, book value, and intrinsic value after correcting for this?

3.

Kim Dae-Eun, CFA, values Zues Printing Company at $46 per share using historical ROE and reported book value. He later determines Zues uses the current rate method of foreign currency translation and has consistently reported translation gains in comprehensive income for the past ten years, and he expects these gains to continue. What is the effect on his ROE forecast, book value, and intrinsic value if he revises his valuation accordingly?

KEY CONCEPTS

LOS 23.a

Residual income = net income - charge for common stockholders' opportunity cost of capital.

EVA = NOPAT - (WACC × total capital) = [EBIT × (1 - t)] - WACC × total capital

MVA = Market value - Total capital

LOS 23.b

Residual income and related models are used for equity valuation, goodwill impairment testing, measurement of managerial effectiveness and executive compensation.

LOS 23.c

Residual income is calculated from accounting data as:

RI_t = E_t - r × B_{t-1}

Intrinsic value by residual income model:

V_0 = B_0 + PV(E[RI_1, RI_2, ...])

Residual income valuation is typically less sensitive to terminal value estimates than DDM or FCFE because current book value (observable) often comprises a substantial share of intrinsic value.

LOS 23.d

Fundamental drivers of residual income are ROE in excess of cost of equity and the earnings growth rate.

LOS 23.e

If ROE = required return on equity, justified market value = book value. If ROE > required return, firm earns positive residual income and market value > book value; P/B > 1.

LOS 23.f

The single-stage residual income model is the algebraic form that links book value, ROE, retention ratio, and required return to intrinsic value under constant growth assumptions (equivalent to the Gordon model when inputs are consistent).

LOS 23.g

The market-implied growth rate under the single-stage residual income model can be obtained by rearranging the model to solve for g given P/B, ROE, and r.

LOS 23.h

For multistage residual income models: forecast RI over a short horizon, then make assumptions about continued RI. The PV of continuing RI at time T - 1 is determined by the chosen persistence assumption (ω = 0, 0<><1, or="" ω="1)" or="" via="" a="" forecasted="" p/b="" ratio="" at="" time="" t.="">

V0 = B0 + PV(interim RI) + PV(continuing RI)

LOS 23.i

DDM and FCFE estimate value as discounted expected cash flows. Residual income estimates value as book value plus PV of expected future RIs. Use RI models to cross-check other models for consistency.

LOS 23.j

Strengths:

• Terminal value does not dominate intrinsic estimate.
• Uses readily available accounting data.
• Appropriate for firms with no dividends or negative short-run FCFE.
• Applicable with volatile cash flows.
• Focuses on economic (not just accounting) profitability.

Weaknesses:

• Reliance on accounting data subject to manipulation.
• Requires many adjustments to accounting figures.
• Assumes clean surplus relation holds or is corrected for.

Residual income models are appropriate when dividends or FCFE forecasts are unreliable; they are inappropriate when clean surplus is significantly violated or when book value/ROE forecasts are highly uncertain.

LOS 23.k

In applying RI valuation, analysts commonly address: violations of clean surplus, balance sheet fair value adjustments, treatment of intangible assets, removal of nonrecurring items, detection and correction of aggressive accounting practices, and international accounting differences.

ANSWER KEY FOR MODULE QUIZZES

Module Quiz 23.1, 23.2

1.

C The stock's terminal value as of Year 5 is computed as a perpetuity of Year-6 residual income discounted to Year-5 and then to present. The present value of this Year-5 terminal value is added to the given C$75.00 to obtain the justified value: C$75.00 + C$69.85 = C$144.85. (Module 23.2, LOS 23.c)

Module Quiz 23.3

1.

C Stock P has model price higher than market (undervalued). Stock Q has model price lower than market (overvalued). Stock R has model price equal to market (fairly valued). (LOS 23.f)

2.

C Use P0 = V0 = $25.00 and the single-stage RI relation to solve for implied cost of equity. Algebraic rearrangement yields the implied r (detailed algebra present in instructional materials). (LOS 23.f)

3.

C Use the single-stage residual income model to solve for justified P/B and rearrange to obtain ROE given r and g. (LOS 23.f)

4.

A With ROE > r and r > g, the PV of future RI is positive; intrinsic value exceeds book value and justified P/B > 1. (LOS 23.f)

5.

A ROE = EPS / BV = $0.45 / $4.50 = 10%. Since ROE equals cost of equity (10%), the PV of future RI is zero and intrinsic value equals book value; P/B = 1. (LOS 23.f)

Module Quiz 23.4

1.

C All three alternate assumptions (immediate drop to zero, decline to zero with ω < 1,="" or="" decline="" to="" a="" lower="" long-run="" level)="" reduce="" continuing="" ri="" relative="" to="" the="" assumption="" of="" perpetual="" constant="" ri.="" each="" reduces="" the="" value="" below="" $68.="" (los="" 23.h)="">

2.

B Compute required return r via CAPM:

r = Risk-free rate + Beta × Equity risk premium = 4.5% + 0.7 × 5.0% = 4.5% + 3.5% = 8.0%

The RI computations for the next three years and their present values are tabulated in the instructional material and used to compute the PV of continuing RI as of the end of 2025. (LOS 23.h)

3.

B The present value of residual income computed at the valuation date yields the per-share value close to choice B. (LOS 23.h)

4.

C For DRL, ω = 0 leads to a computed intrinsic value per share of €8.34; since market price is €8.75, the shares are overpriced and a sell recommendation is appropriate. (LOS 23.c)

5.

B With ω = 1 (RI persists), intrinsic value exceeds market price of €8.75 and the analyst should consider issuing a buy recommendation. (LOS 23.c)

6.

C With ω = 0.3, RI decays, the intrinsic value computes to €8.45, below market price (€8.75); shares are overpriced and a sell recommendation is appropriate. (LOS 23.c)

Module Quiz 23.5

1.

C Dividend discount model: with no reinvestment and perpetual EPS = $3.00, D1 = $3.00, required return r using CAPM yields the DDM price; residual income model yields the same result here when applied correctly. (LOS 23.i)

2.

C Improperly capitalised expenditures that should have been expensed overstate both book value and ROE. Correcting these reduces ROE, reduces book value per share and reduces intrinsic value from the RI model. (LOS 23.k)

3.

B Translation gains were recorded in equity (comprehensive income), not in net income. If expected to continue, ROE forecast should be revised upward; book value is unchanged (gains are already in equity); intrinsic value increases. (LOS 23.k)

End of answer key.