LM 22: Residual Income Valuation
READING 23
RESIDUAL INCOME VALUATION
EXAM FOCUS
The fourth type of valuation model considered in typical equity curriculum is the residual income (RI) model. Understand how residual income models differ from the dividend discount model (DDM), free cash flow (FCF) models, and market multiples. Successful application of RI models requires appropriate adjustments to financial statements using financial statement analysis techniques so that accounting figures better reflect economic reality. The concept of continuing residual income is related to industry analysis, and this material is often highly testable.
MODULE 23.1: RESIDUAL INCOME DEFINED
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 for the common stockholders' opportunity cost of equity capital. The RI approach recognises the cost of equity capital explicitly in the measurement of income. Traditional accounting net income includes interest expense and thus reflects the cost of debt but does not reflect a cost for equity (such as dividends or the return required by shareholders). As a result, accounting net income can overstate economic profitability from the perspective of equity investors. Residual income explicitly deducts a dollar charge for equity capital.
EXAMPLE: Calculating residual income
Madeira Fruit Suppliers, Inc. (MFS) distributes fruit to grocery stores in large U.S. cities. The following facts are given:
- Book value of total assets = $1.4 billion
- Financing: Equity = $800 million; Debt = $600 million
- Before-tax cost of debt = 3.33%
- Marginal tax rate = 34%
- Cost of equity = 12.3%
- An abbreviated income statement shows net income = $80,520,000
Determine whether MFS is profitable economically by calculating residual income and explaining the relationship to reported accounting net income.
Answer:
While the accounting net income of $80,520,000 indicates that MFS is profitable in the accounting sense, we must deduct a dollar-based charge for equity capital to assess economic profit.
The dollar equity charge is calculated as the beginning (or appropriate) book value of common equity multiplied by the cost of equity:
Equity charge = cost of equity × book value of equity
Equity charge = 0.123 × $800,000,000 = $98,400,000
Residual income (RI) is calculated as:
RI = Net income - Equity charge
RI = $80,520,000 - $98,400,000 = -$17,880,000
Even though MFS reports positive accounting net income, it is economically unprofitable after charging the required return to equity capital: residual income is negative.
EVA and MVA
Economic value added (EVA) measures value added for shareholders by the firm's management during a period. A common formulation is:
EVA = NOPAT - (WACC × invested capital)
where NOPAT = net operating profit after tax and WACC is the weighted average cost of capital. EVA measures economic income with operating profit adjusted for taxes and capital charged at the firm's WACC.
Market value added (MVA) is the difference between the market value of the firm's long-term financing (market value of equity plus market value of long-term debt) and the book value of total invested capital supplied by investors; it measures the cumulative value created since inception:
MVA = market value - total capital (book value of invested capital)
PROFESSOR'S NOTE
Residual income and EVA differ in their base accounting measures. Residual income uses net income (which includes interest expense) and subtracts a charge for equity capital. EVA uses NOPAT (ignoring interest expense) and subtracts a charge for all capital (debt and equity) using the WACC. Conceptually both measure economic income. For EVA computation we typically use beginning-of-year total capital. MVA uses end-of-year total capital (to match market value measured at year-end).
The analyst should consider the following adjustments (as applicable) when computing NOPAT and invested capital for EVA and for accurate residual income analysis:
- Capitalize and amortize research and development (R&D) where appropriate, instead of expensing it entirely in the period incurred; add the capitalized amount to invested capital and amortization to NOPAT adjustments.
- Add back strategic investment charges that are expected to produce returns in future periods.
- Use cash taxes rather than deferred taxes where deferred taxes are not representative of future cash taxes; eliminate deferred taxes if not expected to reverse.
- Treat operating leases as capital leases by capitalizing the present value of lease payments and treating related expense as interest and depreciation.
- Add the LIFO reserve to invested capital (if converting LIFO to FIFO) and add back the change in LIFO reserve to NOPAT.
EXAMPLE: Calculating EVA and MVA
VBM, Inc. reports the following:
- NOPAT = $2,100
- WACC = 14.2% = 0.142
- Invested capital = $18,000 (beginning of year) and $21,000 (end of year)
- Year-end market price of stock = $25 per share
- Shares outstanding = 800
- Market value of long-term debt (year-end) = $4,000
Calculate VBM's EVA and MVA.
Answer:
First calculate the capital charge based on beginning invested capital:
WACC charge = 0.142 × $18,000 = $2,556
EVA = NOPAT - (WACC × beginning invested capital)
EVA = $2,100 - $2,556 = -$456
The market value of the company is the market value of equity plus the market value of debt:
Market value of equity = $25 × 800 = $20,000
Market value of company = $20,000 + $4,000 = $24,000
Market value added (MVA) = market value - total capital (use end-of-year invested capital)
MVA = $24,000 - $21,000 = $3,000
LOS 23.b: Uses of residual income models
There are commercially available residual income-based models. In practice, residual income concepts (including EVA and MVA) are often used to measure managerial effectiveness and to design executive compensation. For valuation, residual income models are applied to equity valuation (estimating intrinsic value of common stock). Residual income models have been proposed for applications such as goodwill impairment testing.
MODULE 23.2: RESIDUAL INCOME COMPUTATION
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.
The formula to forecast residual income in a given period is:
RI_t = E_t - r × B_{t-1}
where E_t is earnings in period t, r is the required return on equity, and B_{t-1} is the beginning book value of equity for period t.
EXAMPLE: Forecasting residual income
Analysts forecast residual income using forecasts of earnings, beginning book values, and the required return on equity. Forecasting a multi-period series of RI allows calculation of the intrinsic value via the RI valuation model described below.
Residual income valuation model
The residual income valuation model separates intrinsic value into two elements:
V0 = B0 + Σ_{t=1}^{∞} (RI_t / (1 + r)^t)
This formula states that the intrinsic value of the stock at time 0, V0, equals the current book value per share, B0, plus the present value of expected future residual income streams. Implementing the model requires assumptions about the pattern of future residual income because the summation is infinite in general. In practice, a finite forecasting horizon is used followed by an assumption about continuing residual income (a terminal or continuing residual income estimate).
Residual income models often recognise value earlier than DDM or FCFE models because they include current book value (observable and known) as part of the intrinsic value. This reduces sensitivity to terminal value assumptions common in DDM and FCFE models.
EXAMPLE: Computing intrinsic value with a residual income model
Consolidated Pipe Products example (finite horizon with liquidation):
- Required return on equity = 14% = 0.14
- Current book value (B0) = C$6.50
- Forecasted earnings: E1 = C$1.10 (2025), E2 = C$1.00 (2026), E3 = C$0.95 (2027)
- Forecasted dividends: D1 = C$0.50 (2025), D2 = C$0.60 (2026), D3 = liquidating dividend (2027) - the firm pays out its entire book value in dividends and ceases operations at end of 2027
Calculate the value of the stock using the residual income model.
Answer:
We compute residual income for each year using RI_t = E_t - r × B_{t-1} and update book value using the clean surplus relation (assuming it holds): B_t = B_{t-1} + E_t - D_t. Compute year by year.
Year 1 (2025):
B0 = 6.50
E1 = 1.10
D1 = 0.50
RI1 = E1 - r × B0 = 1.10 - 0.14 × 6.50 = 1.10 - 0.91 = 0.19
B1 = B0 + E1 - D1 = 6.50 + 1.10 - 0.50 = 7.10
Year 2 (2026):
E2 = 1.00
D2 = 0.60
RI2 = E2 - r × B1 = 1.00 - 0.14 × 7.10 = 1.00 - 0.994 = 0.006 (approximately)
B2 = B1 + E2 - D2 = 7.10 + 1.00 - 0.60 = 7.50
Year 3 (2027) - liquidation:
E3 = 0.95
At liquidation the firm pays out its entire ending book value as the dividend in Year 3. First compute book value before the final dividend:
B2 = 7.50 (beginning of Year 3)
RI3 = E3 - r × B2 = 0.95 - 0.14 × 7.50 = 0.95 - 1.05 = -0.10
Ending book value before liquidation = B2 + E3 - (liquidating dividend). Because the firm liquidates by paying out entire book value, the dividend in Year 3 equals B2 + E3 (i.e., it distributes all resources). The precise PV calculation for the final cashflows can also be performed by computing the residual income series and discounting.
The intrinsic value is:
V0 = B0 + PV(RI1/(1+r)^1 + RI2/(1+r)^2 + RI3/(1+r)^3)
Compute present values using r = 0.14 to obtain the numerical V0 (calculator or cashflow function may be used for expediency).
Note: The example in the source demonstrates the calculation and also shows that present value computations can be performed with financial calculator cash flow functions to speed calculations.
Comparison with DDM and FCFE
Value is often recognised earlier under the RI approach because B0 (book value) is included directly in the valuation. Dividends or free cash flows that support valuation models often place more weight on terminal values relative to the RI model, which reduces potential forecast error arising from uncertain terminal-value estimates.
LOS 23.d: Fundamental determinants of residual income
While general RI models make no assumptions about long-term growth, a single-stage constant-growth residual income model can be derived by assuming constant growth in earnings and dividends. Under the constant-growth assumption and correct pricing (P0 = V0), value can be expressed in terms of book value and growth, leading to a version of the Gordon growth model.
Key drivers of residual income are:
- Return on equity (ROE) in excess of the required return on equity (r).
- Earnings growth rate (g), which itself depends on the retention ratio and ROE.
If ROE = r, then the justified market value equals book value (P/B = 1). If ROE > r, residual income is positive and market value exceeds book value (P/B > 1).
The additional value generated by ROE exceeding r is the present value of expected future economic profits (residual income).
Tobin's Q is related; it is the ratio of market value of assets to the replacement cost (or book value) and is another measure of the premium the market places above book value due to expected economic profits.
PROFESSOR'S NOTE: The single-stage model assumes constant ROE and earnings growth indefinitely. In practice, residual income tends to fade toward zero as competition erodes economic profits; therefore multistage models with declining RI persistence are commonly used.
LOS 23.e: Relation between residual income valuation and the justified price-to-book ratio
Residual income models relate directly to the price-to-book (P/B) multiple because the single-stage model expresses price as book value plus the present value of residual income. If ROE > r, the present value of future residual income is positive and the justified P/B ratio is greater than 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
LOS 23.f: Calculate and interpret the intrinsic value of a common stock using single-stage (constant-growth) and multistage residual income models.
Single-stage residual income model assumes constant ROE and constant earnings growth rate g. This produces a closed form that is algebraically equivalent to the Gordon growth model when the same forecasts (ROE, payout, growth) are used.
EXAMPLE: Calculating value with a single-stage residual income model
Western Atlantic Railroad example:
- Book value per share = $23.00
- ROE on new investments = 14% = 0.14
- Required return on equity = 12% = 0.12
- Dividend payout ratio = 60% = 0.60
Calculate value using single-stage residual income model.
Answer:
First compute the growth rate from retention ratio × ROE:
Retention ratio = 1 - payout ratio = 1 - 0.60 = 0.40
g = retention ratio × ROE = 0.40 × 0.14 = 0.056 = 5.6%
Using single-stage RI formula (equivalent derivation to Gordon), the present value of expected economic profits equals:
The worked calculation in the source yields a present value of expected economic profits of $7.19. Adding to book value gives the intrinsic value.
EXAMPLE: Western Atlantic Railroad valuation with Gordon growth model
Using the same inputs, compute value via Gordon growth model to demonstrate equivalence.
Answer:
Earnings in Year 1, E1 = B0 × ROE = $23.00 × 0.14 = $3.22
Dividend in Year 1, D1 = E1 × payout ratio = $3.22 × 0.6 = $1.932
Using the Gordon growth model:
P0 = D1 / (r - g) = 1.932 / (0.12 - 0.056) = 1.932 / 0.064 = $30.1875 ≈ same as RI model result when added to book value and present value of RI term.
Observed: Both approaches provide the same estimate when supplied with consistent inputs.
PROFESSOR'S NOTE
Multistage residual income models (allowing transitions of ROE and growth) are discussed later.
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.
The single-stage residual income model can be rearranged to solve for the implied growth rate g that the market is pricing into the P/B ratio, assuming the model holds and that the firm is correctly priced (P0 is market price).
EXAMPLE: Calculating implied growth rate
Tellis Telecommunications example:
- P/B ratio = 2.50
- ROE = 13% = 0.13
- Book value per share = €8.00
- Cost of equity = 11% = 0.11
Compute the growth rate implied by the current P/B ratio.
Answer:
Market price implied = P = B0 × (P/B) = €8.00 × 2.50 = €20.00
Substitute into the single-stage RI relation and solve for g (see source for algebraic rearrangement). The source shows the implied growth rate computation and result based on the formula.
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
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 impractical. Use a multistage approach: forecast RI over a short-term horizon (e.g., five years) and then estimate continuing residual income (the long-term RI stream beyond the explicit forecast horizon). The rate at which residual income fades after the explicit forecast period is captured by the persistence factor, ω, where 0 ≤ ω ≤ 1.
Common simplifying assumptions for continuing residual income after year T are:
- Persistence at current level forever: RI_T persists unchanged for all subsequent years (ω = 1).
- Drop immediately to zero: RI_{T+1} and beyond = 0 (ω = 0).
- Decline over time to zero: RI declines asymptotically as ROE falls to the cost of equity (0 < ω < 1).
- Decline to a long-run normal level: RI declines to a mature industry long-run level; terminal price may be estimated via a forecasted P/B.
Justifying the chosen assumption requires analysis of the firm's competitive advantage, industry structure, and sustainability of economic profits. The persistence factor ω depends on the sustainability of competitive advantage and industry prospects.
Characteristics associated with higher persistence factors include:
- Low dividend payout ratios (more reinvestment to sustain RI)
- Historically high RI persistence in the industry
Characteristics associated with lower persistence factors include:
- High current ROE (may attract competition and erosion)
- Significant nonrecurring items contributing to current earnings
- High accounting accruals indicating lower quality earnings
Residual income multistage valuation structure:
V0 = B0 + (PV of interim high-growth RI) + (PV of continuing residual income)
Valuation steps:
- Calculate current book value per share, B0.
- Forecast RI for each year 1 to T-1 and discount them at the required equity return r to time 0.
- Estimate continuing residual income starting in year T and compute its present value as of time T-1 (using ω or other terminal assumptions).
Assumption #1: Residual income persists at the current level forever (ω = 1)
If ω = 1, RI remains at the level RI_T in every year after T. The present value at the end of year T-1 is the present value of a perpetuity:
PV_{T-1} = RI_T / r
Assumption #2: Residual income drops immediately to zero (ω = 0)
If ω = 0, residual income after year T is zero. Thus the present value of continuing residual income as of end of year T-1 is zero.
Assumption #3: Residual income declines over time to zero (0 < ω < 1)
If RI is expected to decline over time and ROE falls to r, the persistence factor ω (0 < ω < 1) represents the fraction of RI that persists each year. The present value at T-1 of continuing residual income is:
PV_{T-1} = RI_T × ω / (r - ω)
(This is the formula you obtain by summing a geometrically declining stream RI_T, RI_T × ω, RI_T × ω^2, ..., discounted at rate r.)
Assumption #4: Residual income declines to a long-run level in a mature industry
An alternative approach uses an expected terminal price-to-book (P/B) ratio at time T. From the single-stage RI model the market price at time T equals book value at T plus present value of future RI at T. Thus:
PV of continuing RI at time T = P_T - B_T
Given a forecasted P/B_T, estimate P_T = B_T × (forecasted P/B_T), then compute PV of continuing RI at time T-1 as (P_T - B_T)/(1 + r).
EXAMPLE: Calculating value with a multistage residual income model (part 1)
Java Metals:
- ROE = 15% each of next five years
- Current book value (B0) = $5.00 per share
- Dividends = 0 (no dividends; all earnings reinvested)
- Required return on equity = 10% = 0.10
- Assumption: continuing residual income after 5 years falls to zero (ω = 0)
Forecast earnings in Years 1-5 = ROE × beginning book value each year. Calculate intrinsic value using RI model.
Answer:
Compute RI for Years 1-5, discount to present at r = 10%, and add B0.
Example table (as in source) provides RI each year and the present value. Using the numbers from the source, the intrinsic value calculates to $6.25.
Financial calculator shortcut: 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 residual income remains constant at $0.44 forever after Year 5 (ω = 1). Calculate new intrinsic value.
Answer:
Terminal perpetuity beginning Year 5: value in Year 4 = 0.44 / 0.10 = $4.40.
Intrinsic value = B0 + PV(Years 1-4 RI) + PV(terminal perpetuity in Year 4).
Intrinsic value is larger than in Part 1 because RI persists indefinitely at Year 5 level.
EXAMPLE: Calculating value with a multistage residual income model (part 3)
Assume residual income begins to decline after Year 5 with persistence factor ω = 0.4. Calculate intrinsic value.
Answer:
Terminal value at Year 4 includes the present value of a geometrically declining stream of RI starting in Year 5 with RI5 known and persistence factor ω = 0.4. Compute terminal value in Year 4 as RI5 × ω / (r - ω) (if applying formula in the context provided) or by explicit discounted sum. Add PV of interim RIs and B0 to get intrinsic value. Lower persistence reduces intrinsic value compared with ω = 1.
EXAMPLE: Calculating value with a multistage residual income model (part 4)
Assume at the end of Year 5 Java's ROE falls to a long-run average level and price-to-book ratio falls to 1.2. Calculate intrinsic value.
Answer:
Book value per share at end of Year 5 is $10.05 (per source). Market price at end of Year 5 is expected to be 10.05 × 1.2 = $12.06.
Present value of continuing residual income as of end of Year 4 is (P5 - B5)/(1 + r) = (12.06 - 10.05) / (1 + 0.10) = 2.01 / 1.10 = $1.8273 (approx.).
Intrinsic value = B0 + PV(interim RIs) + PV(continuing RI as computed above).
PROFESSOR'S NOTE
If the market price exceeds the model price the stock is overvalued; if market price is below model price the stock is undervalued; equality implies fair value.
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.
Use the following information to answer Questions 2 and 3.
Josef Robien, CFA, is valuing the common stock of British Cornucopia Bank (BCB) as of December 31, 2023, when the book value per share is £10.62. Robien's assumptions:
- EPS will be 20% of the beginning book value per share for each of the next three years.
- BCB will pay cash dividends equal to 40% of EPS.
- At the end of three years, BCB's common stock will trade at four times its book value.
- Beta for BCB = 0.7, risk-free rate = 4.5%, equity risk premium = 5.0%.
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.
Use the following information to answer Questions 4 through 6.
Aaron Mechanic, CFA, values Duotronics Research Laboratories (DRL). Given:
- Stock currently trading at €8.75
- ROE expected = 16% annually for next four years
- Current book value (BV) of equity = €435,000,000
- Shares outstanding = 60 million
- Required return on equity = 12%
- No dividends paid - all earnings reinvested
- Continuing residual income = 0 after four years
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 is considering revising his expectation of the continuing residual income after the 4-year horizon period and believes that it will remain constant at the Year 4 forecast level of residual income for the foreseeable future. Based on the residual income model, the intrinsic value and the most likely recommendation Mechanic would issue for the stock of DRL are:
6.
George Karanopoulos, CFA, suggests Mechanic re-estimate the value of DRL using a persistence factor of ω = 0.3 after Year 4. Based on the residual income model, the intrinsic value and the most likely recommendation Mechanic would issue for the stock of DRL are:
MODULE 23.5: STRENGTHS / WEAKNESSES
LOS 23.i: Compare residual income models to dividend discount and free cash flow models.
DDM and FCFE models value equity by discounting expected dividends or expected free cash flows to equity, respectively. The residual income model values equity as:
Value = book value + present value of expected future residual income
Theoretically, DDM, FCFE, and RI approaches yield the same intrinsic value if inputs (earnings, dividends, book values, free cash flow forecasts) and discount rates are consistent across models. In practice, differences in useful inputs and forecasting accuracy mean the models often produce different estimates. Using RI alongside DDM or FCFE can reveal inconsistencies in assumptions and highlight where forecasts produce divergent values.
LOS 23.j: Strengths and weaknesses of residual income models and justification for selection
Strengths of RI models:
- Terminal value typically does not dominate the intrinsic value estimate as it often does in DDM or FCFE models.
- They use accounting data, which is generally readily available.
- Applicable to firms that do not pay dividends or that have negative free cash flows in the short run.
- Applicable when cash flows are volatile because RI uses accounting earnings and book values.
- Focus on economic profitability (returns in excess of required equity return) rather than solely on accounting profitability.
Weaknesses of RI models:
- They rely on accounting measures that can be manipulated by management (earnings management).
- Accurate implementation often requires numerous and significant adjustments to accounting statements.
- They assume the clean surplus relation holds or that any violation is properly adjusted for; if the relation is violated without adjustment, RI forecasts will be biased.
RI models are appropriate when:
- A firm does not pay dividends or dividends are too unpredictable.
- Expected free cash flows are negative for the foreseeable future.
- The terminal value forecast in other models would be highly uncertain.
RI models are not appropriate when:
- The clean surplus accounting relation is significantly violated and cannot be adjusted.
- There is large uncertainty in forecasts of book value or ROE.
PROFESSOR'S NOTE
The clean surplus relation is expressed as B_t = B_{t-1} + E_t - D_t, meaning ending book value equals beginning book value plus earnings less dividends, excluding transactions with owners (such as share issuances or repurchases). If items bypass the income statement (e.g., some components of comprehensive income) the clean surplus relation does not hold and adjustments to net income or book values are required before applying RI valuation. We used the clean surplus relation in examples to forecast ending book values; if violations exist, adjust forecasts accordingly.
LOS 23.k: Accounting issues in applying residual income models
PROFESSOR'S NOTE
This is a summary of financial statement analysis adjustments necessary to produce economic measures for valuation. The analyst must convert GAAP/IFRS financial statements to measures that better reflect economic reality before forecasting residual income. The discussion that follows highlights common accounting issues and typical adjustments.
Clean surplus violations
The clean surplus relation may fail when items are charged directly to shareholders' equity and do not pass through the income statement. If these items are persistent and not expected to reverse, net income must be adjusted when forecasting RI. Items that can bypass the income statement include:
- Foreign currency translation gains and losses under the current rate method (cumulative translation adjustment).
- Certain pension adjustments (e.g., remeasurements recorded in OCI).
- Gains/losses on certain hedging instruments recorded in other comprehensive income (OCI) and later reclassified.
- Changes in revaluation surplus under IFRS (revaluation of long-lived assets).
- Changes in the value of liabilities due to changes in credit risk (IFRS accounting for own-credit changes in OCI).
- Unrealised changes in fair value of available-for-sale securities (IFRS; historically included in OCI).
If the clean surplus relation is violated, book value remains a correct accounting balance, but net income is not a complete measure of economic performance. If violations are temporary and expected to reverse, ROE forecasting may ignore them; if persistent, adjust net income forecasts.
Variations from fair value
Many balance sheet items are recorded at historical or accrual values that differ from economic (market) values. Common adjustments include:
- Operating leases: Capitalize operating leases by increasing assets and liabilities by the present value of future lease payments; treat associated expenses as depreciation and interest so NOPAT and invested capital reflect capitalized leases.
- Special purpose entities (SPEs): Consolidate SPEs when the economic substance requires consolidation and assets/liabilities are absent from financials.
- Reserves and allowances: Adjust allowances (e.g., allowance for bad debts) to reflect expected loss experience so receivables and equity are correct.
- LIFO inventory: Convert LIFO to FIFO by adding the LIFO reserve to inventory and equity (adjust for deferred taxes if applicable).
- Pension funded status: Adjust pension asset/liability to fair value of plan assets minus projected benefit obligation (PBO) to reflect funded/unfunded status.
- Deferred tax liabilities: If not expected to reverse (for example, arising from permanently different tax treatment), consider treatment in equity rather than debt.
Intangible asset effects on book value
Two intangible asset issues require attention:
- Intangibles recognized at acquisition: When identifiable intangible assets are recognized in combined financials that were not in the target's stand-alone balance sheet, their amortization reduces combined ROE and can distort residual income valuation of the acquirer versus the sum of individual valuations. Remove amortization of acquired intangibles when computing ROE for valuation if it obscures economic earnings.
- Research & development (R&D): The treatment of R&D affects ROE forecasts. If R&D is productive and increases future returns, capitalizing R&D in invested capital and amortizing over its useful life may be appropriate. If expenditures are unproductive, capitalizing them will overstate ROE.
Nonrecurring items and aggressive accounting
Nonrecurring items (discontinued operations, unusual/extraordinary items, restructuring charges) should typically be excluded from residual income forecasts because they are not expected to persist. Aggressive accounting (revenue acceleration, expense deferral) that inflates book value or earnings must be corrected.
International accounting differences
When valuing foreign firms, consider national accounting standards and quality of reporting. Issues to consider:
- Reliability of earnings forecasts (earnings quality).
- Systematic violations of clean surplus (e.g., items commonly going to OCI in certain jurisdictions).
- Poor accounting rules that cause financial statements to differ materially 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 return on equity and book value as reported on the balance sheet. Subsequently, he determines that Olympic has, for the past five years, been improperly capitalizing and amortizing expenditures that it should have expensed as they were incurred. What will be the effect on his forecasts of return on equity (ROE), book value, and intrinsic value if he revises his valuation estimate to take these "financial shenanigans" into account?
3.
Kim Dae-Eun, CFA, values Zues Printing Company at $46 per share with a residual income model using historical data to estimate return on equity and book value as reported on the balance sheet. Subsequently, he determines that Zues uses the current rate method of foreign currency translation and has, for the past ten years, consistently reported foreign currency translation gains as part of comprehensive income. He expects these foreign currency gains will continue in the future. What will be the effect on his forecasts of return on equity (ROE), book value, and intrinsic value if he revises his valuation estimate to take this new information into account?
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 × invested capital.
MVA = market value - total capital.
LOS 23.b
Residual income and related measures are used for equity valuation, goodwill impairment tests, measurement of managerial effectiveness, and executive compensation calculations.
LOS 23.c
Residual income is computed as:
RI_t = E_t - r × B_{t-1}
Intrinsic value via RI model:
V0 = B0 + Σ_{t=1}^{∞} (RI_t / (1 + r)^t)
Residual income valuation is relatively less sensitive to terminal value than DDM and FCFE because B0 (observable book value) forms a substantial part of intrinsic value.
LOS 23.d
The 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 equals book value. If ROE > r, the firm will have positive residual income and market value > book value (P/B > 1).
LOS 23.f
The single-stage residual income model can be expressed in a closed form analogous to the Gordon growth model (see earlier derivation under single-stage examples).
LOS 23.g
The growth rate implied by market price under the single-stage RI model can be solved algebraically by rearranging the model to isolate g given P/B, ROE, and r.
LOS 23.h
For multistage RI models, forecast residual income over a near-term horizon and then make a justified assumption about the pattern of continuing residual income (persistence factor ω). The present value of continuing residual income in year T-1 under the persistence model is:
PV_{T-1} = RI_T × ω / (r - ω) (for the geometrically declining case) or use PV_{T-1} = (P_T - B_T) / (1 + r) if a forecasted P/B is used to infer terminal premium.
LOS 23.i
DDM and FCFE discount expected cash flows; RI adds the present value of expected economic profits to current book value. Use RI to cross-check other valuation approaches.
LOS 23.j
Strengths and weaknesses summarised: Terminal value influence reduced; easy availability of accounting data; useful for dividend-less or negative FCFE firms; sensitive to accounting manipulations; requires adjustments; depends on clean surplus relation holding.
LOS 23.k
Analysts applying RI must consider:
- Violations of the clean surplus relation (OCI items bypassing income statement)
- Balance sheet adjustments to approximate fair value (capitalizing leases, consolidating SPEs, adjusting reserves, converting LIFO)
- Treatment of intangible assets (acquired intangibles, R&D)
- Nonrecurring items
- Aggressive accounting practices
- 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 included in the problem; discounting it to present yields the present value shown in the source. The present value of the Year 5 terminal value and the earlier RI forecasts sum to produce the justified value of C$144.85. Thus the correct option is C$144.85.
Module Quiz 23.3
1.
C Stock P has model price higher than market price → undervalued. Stock Q has model price lower than market price → overvalued. Stock R has model price equal to market price → fairly valued. ((LOS 23.f))
2.
C Use the single-stage model and algebraic rearrangement. In the source, the algebraic steps show solving for the implied cost of equity consistent with P0 = 25.00 and other given inputs - concluding option C is correct. ((LOS 23.f))
3.
C Use the single-stage RI model to solve for the justified P/B, and then solve for ROE given r and g (per the methodology in the source). ((LOS 23.f))
4.
A Using single-stage RI model the PV of future RI is positive because ROE > r, implying intrinsic value > book value and P/B > 1. ((LOS 23.f))
5.
A Compute ROE = EPS / B0 = 0.45 / 4.50 = 0.10 = 10%. With r = 10%, the RI term is zero, so intrinsic value equals book value and P/B = 1. ((LOS 23.f))
Module Quiz 23.4
1.
C All three alternative assumptions for continuing residual income (persistence at lower levels, immediate drop to zero, or decline) will lower continuing residual income compared with the assumption of constant persistence forever. Therefore the value estimate will fall below $68 in all three cases. ((LOS 23.h))
2.
B BCB's required rate of return, r, computed by CAPM:
r = risk-free rate + beta × equity risk premium = 0.045 + 0.7 × 0.05 = 0.045 + 0.035 = 0.08 = 8%
Compute forecasted RI = Earnings_t - r × Book_{t-1} for years 2024-2026, discount RI for 2024 and 2025 to present, and compute book value at end of 2026. The market price in 2026 is assumed 4 × B2026. The present value of continuing RI as of end of 2025 equals (P2026 - B2026) discounted to end of 2025. The source shows the numeric computations and the PV values. ((LOS 23.h))
3.
B The present value calculations per the source yield the value option B. ((LOS 23.h))
4.
C In the DRL example with ω = 0 (continuing RI = 0 after 4 years) the present value of continuing residual income in Year 3 = 0. Using the forecasted RIs and B0, the modeled intrinsic value per share works to €8.34 while the market price is €8.75, implying the stock is overpriced; recommendation: sell. ((LOS 23.c))
5.
B If RI persists at the Year 4 level forever (ω = 1), continuing residual income in Year 3 is RI4 / r, which increases intrinsic value above the current market price and suggests a buy recommendation. ((LOS 23.c))
6.
C With ω = 0.3, continuing RI is smaller than in the ω = 1 case; intrinsic value computed per the source is €8.45, below market price €8.75 → sell. ((LOS 23.c))
Module Quiz 23.5
1.
C Dividend discount model valuation: D = earnings = $3.00 (no reinvestment means dividends equal earnings). Require r from CAPM: r = 0.04 + 0.75 × 0.08 = 0.04 + 0.06 = 0.10 = 10%. DDM value = D / r = 3.00 / 0.10 = $30. Residual income model: B0 = 15, RI = E - r × B0 = 3.00 - 0.10 × 15 = 3.00 - 1.50 = 1.50. V0 = B0 + RI/r = 15 + 1.50/0.10 = 15 + 15 = $30. Both approaches give $30. ((LOS 23.i))
2.
C If previously capitalized expenditures should have been expensed, then book value and ROE (computed from inflated earnings history) were overstated. Correcting the accounting reduces ROE and reduces book value; intrinsic value under RI decreases. ((LOS 23.k))
3.
B If foreign currency translation gains were recorded in OCI and not in income, ROE was understated. Expecting these gains to continue increases the forecasted ROE; book value already reflects the gains (since they were recorded to equity), so book value stays the same; intrinsic value from RI increases. ((LOS 23.k))
