Residual Income Valuation
READING 23
RESIDUAL INCOME VALUATION
EXAM FOCUS
This topic review introduces the fourth type of valuation model found in the curriculum: residual income models. Understand how these models differ from the dividend discount model (DDM), free cash flow models, and market multiple approaches. Successful application of residual income models requires appropriate adjustments to financial statements; therefore, techniques from financial statement analysis are essential. The concept of continuing residual income links to industry analysis. Because of these links to other valuation and accounting 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, equals accounting net income less a charge for the common stockholders' opportunity cost of equity capital. The rationale for the residual income approach is that it recognizes the cost of equity capital in the measurement of income. Traditional accounting income includes the cost of debt (interest expense) but does not include the cost of equity (dividends or an explicit equity charge). Therefore, accounting net income can overstate returns from the perspective of equity investors. Residual income explicitly deducts all capital costs and provides a measure of economic income from the equity holders' viewpoint.
EXAMPLE: Calculating residual income
Madeira Fruit Suppliers, Inc. (MFS) distributes fruit to grocery stores in large U.S. cities.
- Book value of assets: $1.4 billion, financed with $800 million in equity and $600 million in debt.
- Before-tax cost of debt: 3.33%.
- Marginal tax rate: 34%.
- Cost of equity: 12.3%.
- MFS's abbreviated income statement is shown in the original figure (not reproduced here).
Determine whether MFS is profitable by calculating residual income and explaining its relationship to reported accounting income.
Answer:
While the accounting net income of $80,520,000 indicates that MFS reports positive accounting profits, we must deduct an equity charge that measures the stockholders' opportunity cost of capital to assess economic profitability.
Equity charge (dollar-based) = Equity × Cost of equity.
Equity charge = $800,000,000 × 0.123 = $98,400,000.
RI = Net income - Equity charge.
RI = $80,520,000 - $98,400,000 = -$17,880,000.
Even though MFS is profitable in the traditional accounting sense, it is economically unprofitable after deducting the charge required to meet stockholders' opportunity cost of capital.
EVA and MVA
Economic Value Added (EVA) measures value added for shareholders by management during a specific year. EVA is calculated as:
EVA = NOPAT - (WACC × Total capital).
Where NOPAT = EBIT × (1 - tax rate) and WACC is the weighted average cost of capital applied to total capital (for EVA typically beginning-of-year total capital is used).
PROFESSOR'S NOTE
Notice the calculation difference between residual income and EVA. Residual income is based on net income after interest less an equity charge. EVA is based on NOPAT (before interest) less a charge for both debt and equity capital using the WACC. Conceptually both measure economic income. For EVA computation use beginning-of-year total capital; market value added (MVA) uses end-of-year total capital because market value is an end-of-period measure.
When computing EVA, analysts should adjust financial statements (if applicable) before calculating NOPAT and invested capital. Typical adjustments include:
- Capitalize and amortize research and development costs (rather than expensing them) and add back to earnings for NOPAT.
- Add back strategic investment charges that will generate future returns.
- Eliminate deferred taxes and consider only cash taxes as an expense.
- Treat operating leases as capital leases and adjust nonrecurring items.
- Add LIFO reserve to invested capital and add back change in LIFO reserve to NOPAT.
Market Value Added (MVA) is the difference between market value of long-term debt plus equity and the book value of invested capital supplied by investors. It measures the value created by management since inception. MVA is calculated as:
MVA = Market value - Total capital
EXAMPLE: Calculating EVA and MVA
VBM, Inc., reports:
- NOPAT = $2,100.
- WACC = 14.2%.
- Invested capital at beginning of the year = $18,000; at the end of the year = $21,000.
- Market price (year-end) of stock = $25 per share.
- Shares outstanding = 800.
- Market value (year-end) of long-term debt = $4,000.
Calculate VBM's EVA and MVA.
Answer:
First calculate the capital charge:
WACC × Beginning invested capital = 0.142 × $18,000 = $2,556.
EVA = NOPAT - (WACC × Beginning invested capital) = $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.
MVA = Market value - End-of-period invested capital = $24,000 - $21,000 = $3,000.
LOS 23.b: Describe the uses of residual income models.
Several commercially available valuation and performance measurement models are based on residual income concepts. These models, such as EVA and other residual income-based measures, are often applied to measurement of managerial effectiveness and executive compensation. For equity valuation, residual income models can be used to estimate intrinsic value, and they have been proposed as a method to measure goodwill impairment. For exam focus we concentrate on the equity valuation application of residual income models.
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 information and an estimate of future earnings and book values using the formula:
RI_t = E_t - r_e × B_{t-1}
Where E_t is net income (earnings) in period t, r_e is the required return on equity, and B_{t-1} is beginning-of-period book value of equity.
EXAMPLE: Forecasting residual income
Laura Kraft, CFA, forecasted residual income for Delilah Cosmetics, Inc., for 2025 and 2026 using the inputs shown in the Delilah Data Forecast figure (referenced in the original materials). Kraft used a required rate of return of 11%.
Forecast Delilah's residual income for 2025 and 2026.
Answer:
The residual income forecast is produced by applying RI_t = E_t - r × B_{t-1} for each forecast year using Kraft's earnings and beginning book values for those years (tabulated in the Delilah Residual Income Forecast in the source material).
The residual income valuation model decomposes intrinsic value into two elements:
V0 = B0 + PV of expected future residual income
That is, the intrinsic value V0 equals current book value per share B0 plus the present value of all expected future residual incomes, where each residual income equals the end-of-period earnings less the equity charge on beginning-of-period book value. The practical difficulty is forecasting a theoretically infinite stream of residual incomes; therefore we usually make simplifying assumptions (such as multistage forecasts and a continuing residual income assumption) to compute the present value of the infinite series.
EXAMPLE: Computing intrinsic value with a residual income model
Consolidated Pipe Products:
- Required return on equity = 14%.
- Current book value B0 = C$6.50 per share.
- Earnings forecasts: E1 = C$1.10, E2 = C$1.00, E3 = C$0.95.
- Dividends: D1 = C$0.50, D2 = C$0.60; D3 is a liquidating dividend equal to the firm paying out its entire book value in dividends at the end of 2027 (after E3), ceasing operations.
Calculate the value of Consolidated's stock using the residual income model.
Answer:
Compute beginning-of-period book value and equity charge each year, then residual income each year, discount residual incomes at the required return, and add to current book value.
Step-wise calculations:
B0 = 6.50.
E1 = 1.10. Equity charge for Year 1 = r × B0 = 0.14 × 6.50 = 0.91.
RI1 = E1 - Equity charge = 1.10 - 0.91 = 0.19.
Book value at end of Year 1 (B1) = B0 + E1 - D1 = 6.50 + 1.10 - 0.50 = 7.10.
E2 = 1.00. Equity charge for Year 2 = r × B1 = 0.14 × 7.10 = 0.994.
RI2 = E2 - Equity charge = 1.00 - 0.994 = 0.006.
Book value at end of Year 2 (B2) = B1 + E2 - D2 = 7.10 + 1.00 - 0.60 = 7.50.
E3 = 0.95. Equity charge for Year 3 = r × B2 = 0.14 × 7.50 = 1.05.
RI3 = E3 - Equity charge = 0.95 - 1.05 = -0.10.
Discount residual incomes at r = 0.14:
PV(RI1) = 0.19 / (1.14) = 0.1667 (approximately).
PV(RI2) = 0.006 / (1.14^2) = 0.0046 (approximately).
PV(RI3) = -0.10 / (1.14^3) = -0.0683 (approximately).
Sum PVs of RI = 0.1667 + 0.0046 - 0.0683 = 0.1030 (approximately).
Intrinsic value V0 = B0 + Sum PVs of RI = 6.50 + 0.1030 ≈ C$6.603.
Using a calculator (cash-flow function) provides an efficient way to compute the same result.
Value recognition timing: Value tends to be recognised earlier in the residual income approach than in DDM or FCFE models. In DDM/FCFE, a large portion of value may come from the terminal value far in the future; residual income models include current book value (a known quantity) as part of intrinsic value, making them less sensitive to terminal value estimation error.
LOS 23.d: Explain fundamental determinants of residual income.
The general residual income model makes no assumption about long-term growth. However, under a simplifying assumption of constant growth in earnings and dividends, we develop the single-stage residual income model which highlights the fundamental drivers of residual income. Assuming correct pricing (P0 = V0), value expressed in terms of book value is:
V0 = B0 + [B0 × (ROE - r)] / (r - g)
Where ROE is return on equity, r is the required return on equity, and g is the sustainable growth rate in earnings.
This expression is algebraically equivalent to the Gordon growth model given consistent inputs. The drivers of residual income are:
- Return on equity (ROE) relative to the required return r: the spread (ROE - r) determines whether residual income is positive or negative.
- Growth rate g: persistence of the ROE and earnings growth affects the present value of residual income.
If ROE = r, the justified market value equals book value. If ROE > r, residual income is positive and market value exceeds book value.
Tobin's Q is a related concept that compares market value of assets to replacement costs.
PROFESSOR'S NOTE
The single-stage model assumes constant ROE and earnings growth (implying residual income persists indefinitely). In practice residual income usually approaches zero over time as competition erodes excess returns; hence single-stage is often modified into multistage models with declining residual income or a continuing residual income assumption.
LOS 23.e: Explain the relation between residual income valuation and the justified price-to-book ratio based on forecasted fundamentals.
Residual income models relate directly to the price-to-book (P/B) ratio because market value equals book value plus present value of expected residual income. From the single-stage model:
P/B = 1 + (ROE - r) / (r - g)
If ROE > r, then the PV of future residual income is positive and the justified P/B > 1. If ROE = r, 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.
(Content includes derivations and examples for single-stage and multistage RI models.)
EXAMPLE: Calculating value with a single-stage residual income model
Western Atlantic Railroad:
- Book value B0 = $23.00 per share.
- Return on new investments (ROE) = 14%.
- Required return on equity r = 12%.
- Dividend payout ratio = 60%.
Calculate the value of the shares using a single-stage residual income model and the present value of expected economic profits.
Answer:
Compute growth rate g from retention ratio and ROE.
g = Retention ratio × ROE = (1 - Payout) × ROE = (1 - 0.60) × 0.14 = 0.40 × 0.14 = 0.056 = 5.6%.
Using the single-stage residual income model:
E1 = B0 × ROE = 23.00 × 0.14 = 3.22.
Equity charge = r × B0 = 0.12 × 23.00 = 2.76.
RI1 = E1 - Equity charge = 3.22 - 2.76 = 0.46.
PV of residual income = RI1 / (r - g) = 0.46 / (0.12 - 0.056) = 0.46 / 0.064 = 7.1875 ≈ 7.19.
Intrinsic value V0 = B0 + PV(RI) = 23.00 + 7.19 = 30.19.
EXAMPLE: Western Atlantic Railroad valuation with Gordon growth model
Use the same information as above and the Gordon growth model.
Answer:
E1 = B0 × ROE = 23.00 × 0.14 = 3.22.
D1 = E1 × Payout = 3.22 × 0.60 = 1.932.
Gordon value V0 = D1 / (r - g) = 1.932 / (0.12 - 0.056) = 1.932 / 0.064 = 30.1875 ≈ 30.19.
Notice this equals the single-stage residual income model result using consistent inputs.
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.
Rearrange the single-stage residual income model to solve for g in terms of P/B, ROE and r:
Starting from P/B = 1 + (ROE - r)/(r - g), solve for g:
g = r - (ROE - r)/(P/B - 1)
This expression computes the market-implied growth rate in residual income (or earnings) under the single-stage model assuming P0 = V0.
EXAMPLE: Calculating implied growth rate
Tellis Telecommunications, Inc.:
- P/B = 2.50.
- ROE = 13%.
- Book value per share B0 = €8.00.
- Cost of equity r = 11%.
Calculate the growth rate implied by the current P/B ratio.
Answer:
Using the formula g = r - (ROE - r)/(P/B - 1):
ROE - r = 0.13 - 0.11 = 0.02.
P/B - 1 = 2.50 - 1 = 1.50.
(ROE - r)/(P/B - 1) = 0.02 / 1.50 = 0.013333... .
g = r - 0.013333... = 0.11 - 0.013333... = 0.0966667 ≈ 9.67%.
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. We use a multistage approach: forecast residual income over a short-term horizon (e.g., five years), then make simplifying assumptions about long-run residual income beyond the horizon. Continuing residual income is the residual income expected in the long term after the forecast horizon.
Residual income persistence is captured by a persistence factor ω, where 0 ≤ ω ≤ 1. Typical simplifying assumptions for continuing residual income at the end of the short-term period include:
- Residual income persists at its current level forever (ω = 1).
- Residual income drops immediately to zero (ω = 0).
- Residual income declines over time as ROE falls to the cost of equity (0 < ω="">< 1),="" so="" ri="" eventually="" goes="" to="">
- Residual income declines to a long-run average (normal) level consistent with a mature industry.
Industry and firm analyses justify which assumption is most appropriate. The persistence factor ω reflects the sustainability of competitive advantage and industry prospects. Higher ω is associated with low dividend payouts, historically high RI persistence in the industry, and greater likelihood of sustainable economic profits. Lower ω is associated with high ROE (which is harder to sustain), significant nonrecurring items, and high accounting accruals.
Think of continuing residual income as the terminal component in a multistage residual income model. Intrinsic value is therefore the sum of three components:
V0 = B0 + (PV of interim high-growth RI) + (PV of continuing residual income)
Typical calculation steps:
- Calculate the current book value per share B0.
- Calculate residual income in each interim forecast year (1 to T - 1) and discount them to present using r.
- Calculate continuing residual income that begins at year T and compute its present value as of time T - 1 using an appropriate continuing-RI assumption (perpetuity, zero thereafter, decaying with ω, or long-run P/B method).
Assumption #1: Residual Income Persists at the Current Level Forever
If ω = 1, RI_T = RI_{T+1} = ... = RI_T and the present value at end of year T - 1 is the value of a perpetuity:
PV_{T-1} = RI_T / r
Assumption #2: Residual Income Drops Immediately to Zero
If ω = 0, RI_{T+1} = 0, and the present value of continuing residual income at T - 1 is zero:
PV_{T-1} = 0
Assumption #3: Residual Income Declines Over Time to Zero
If residual income decays with persistence factor ω (0 < ω="">< 1),="" then="" continuing="" residual="" income="" at="" t="" grows="" geometrically:="" ri_{t+1}="ω" ×="" ri_t,="" ri_{t+2}="ω^2" ×="" ri_t,="" etc.="" the="" present="" value="" at="" t="" -="" 1="" is="" given="">
PV_{T-1} = RI_T / (r - ω) (after appropriate algebra and discounting; see the original derivation for exact expression consistent with timing)
Assumption #4: Residual Income Declines to Long-Run Level in Mature Industry
An alternative approach uses the single-stage residual income model result that market value at time T (P_T) equals book value at time T (B_T) plus the present value of future residual income at time T. Thus:
PV of continuing residual income at time T = P_T - B_T
Estimate P_T using a forecasted price-to-book ratio:
P_T = B_T × (forecasted P/B)
Then discount P_T - B_T back to T - 1 (and ultimately to present) as appropriate for consistency with other assumptions.
EXAMPLE: Calculating value with a multistage residual income model (part 1)
Java Metals:
- ROE expected to be 15% over each of the next five years.
- Current book value B0 = $5.00 per share.
- No dividends; all earnings reinvested.
- Required return on equity r = 10%.
- Assume RI after year 5 falls to zero (ω = 0).
Forecast earnings for Years 1-5 as ROE × beginning book value for each year and calculate intrinsic value.
Answer:
The residual income forecast table (refer to original Java Metals Residual Income Forecast) provides RI_t for Years 1-5. Under ω = 0, intrinsic value is:
V0 = B0 + PV(RI1 to RI5)
Using cash-flow calculator: CF0 = 5, C01 = 0.25, C02 = 0.29, C03 = 0.33, C04 = 0.38, C05 = 0.44, I = 10, CPT → NPV = $6.25 (as presented in the source material).
EXAMPLE: Calculating value with a multistage residual income model (part 2)
Assume now RI5 = 0.44 persists forever (ω = 1). The perpetuity beginning in Year 5 is worth RI5 / r at end of Year 4.
Perpetuity value at Year 4 = 0.44 / 0.10 = 4.40.
Intrinsic value V0 = B0 + PV(RI1 to RI4) + PV(perpetuity at Year 4), leading to a higher value than the ω = 0 case (detailed arithmetic in the source material).
EXAMPLE: Calculating value with a multistage residual income model (part 3)
Assume RI decays after Year 5 with persistence factor ω = 0.4. Residual income begins to decline; the terminal value includes the decaying RI series. The intrinsic value is book value plus PV of interim RIs plus PV of the terminal value calculated using ω = 0.4. A lower ω reduces intrinsic value because economic profits fade more quickly.
EXAMPLE: Calculating value with a multistage residual income model (part 4)
Assume at end of Year 5 ROE falls to a long-run average and forecasted P/B falls to 1.2. If B5 = $10.05, P5 = 10.05 × 1.2 = $12.06. The PV of continuing residual income at Year 4 equals P5 - B5 discounted appropriately, and intrinsic value includes intermediate RIs plus this PV. (Numeric steps are presented in the source material.)
PROFESSOR'S NOTE
If market price > model-implied price, the stock is considered overvalued; if market price < model="" price,="" it="" is="" undervalued;="" if="" equal,="" it="" is="" fairly="">
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 31 December 2023, when book value per share is £10.62. Robien assumes:
- EPS will be 20% of beginning book value 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 stock will trade at four times its book value.
- Beta = 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, is valuing Duotronics Research Laboratories (DRL):
- Current market price = €8.75.
- Expected ROE = 16% annually for each of next four years.
- Current book value of equity = €435,000,000.
- Shares outstanding = 60 million.
- Required return on equity r = 12%.
- No dividends; all earnings reinvested.
- Continuing residual income = 0 after four years (for Questions 4).
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 assumption: continuing residual income remains constant at Year 4 forecast level (ω = 1). 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 value using persistence factor 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
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LOS 23.i: Compare residual income models to dividend discount and free cash flow models.
DDM and FCFE models discount expected cash flows to shareholders. The residual income model starts from book value and adds PV of expected future residual income. Theoretically, DDM, FCFE and residual income valuations yield identical intrinsic values if they use the same forecasts and consistent assumptions. In practice, differences in forecastability and available data lead to different valuation estimates. Using residual income alongside DDM or FCFE can reveal inconsistencies and model sensitivity to underlying assumptions.
LOS 23.j: Explain strengths and weaknesses of residual income models and justify the selection of a residual income model to value a company's common stock.
Strengths of residual income models:
- Terminal value normally does not dominate the intrinsic value estimate (unlike some DDM/FCFE cases).
- They use accounting data, which is usually readily available.
- Applicable to firms that do not pay dividends or have negative near-term free cash flows.
- Applicable when cash flows are volatile.
- Focus on economic profitability rather than just accounting profit.
Weaknesses of residual income models:
- Rely on accounting data that managers can manipulate.
- Require numerous and sometimes significant accounting adjustments to reflect economic reality.
- Assume the clean surplus relation holds (or that violations are properly adjusted for).
PROFESSOR'S NOTE
The clean surplus relation is Bt = Bt-1 + Et - Dt, meaning ending book value equals beginning book value plus earnings less dividends (ignoring ownership transactions). This relation is used to forecast end-of-period book value. Items bypassing the income statement and recorded directly in equity (e.g., cumulative translation adjustments) violate clean surplus and require adjustment if they are persistent.
Residual income models are appropriate when:
- A firm does not pay dividends or dividends are too volatile.
- Expected free cash flows are negative for the foreseeable future.
- Terminal value forecasts are highly uncertain, making DDM or FCFE less useful.
Residual income models are not appropriate when:
- The clean surplus relation is significantly violated.
- There is significant uncertainty over forecasts of book value and ROE.
LOS 23.k: Describe accounting issues in applying residual income models.
PROFESSOR'S NOTE
Analysts must convert GAAP accounting statements to a set that better reflects economic reality before applying residual income valuation. Key adjustments and issues include:
Clean Surplus Violations
If items bypass the income statement and go directly to equity (e.g., foreign currency translation gains/losses under the current rate method, certain pension adjustments, certain hedge gains/losses, revaluation surplus under IFRS, changes in fair value of available-for-sale securities), the clean surplus relation is violated. Net income may not reflect comprehensive income, although book value remains correct. If these bypass items are not transitory, adjust net income or book value forecasts; if they are expected to reverse, the analyst may be able to ignore them in ROE forecasts.
Variations from Fair Value
Accrual accounting leads to balance sheet amounts that may differ materially from economic (fair) values. Common balance sheet adjustments include:
- Capitalise operating leases by adding an asset and liability equal to the PV of operating lease payments; adjust interest and depreciation accordingly so interest expense approximates true cost of debt.
- Consolidate special-purpose entities (SPEs) that economically belong on the parent's balance sheet.
- Adjust reserves and allowances to reflect expected loss experience (e.g., allowance for bad debts).
- Adjust LIFO inventory to FIFO by adding LIFO reserve to inventory and equity (consider deferred tax effects).
- Adjust pension asset/liability to reflect funded status (fair value of plan assets less projected benefit obligation).
- Eliminate deferred tax liabilities if they are not expected to reverse.
Intangible Asset Effects on Book Value
Two intangible-asset issues require attention:
- Intangibles recognised at acquisition (purchase price allocation) that were not present on the acquiree's balance sheet - amortisation of these post-acquisition intangibles reduces combined ROE and can distort valuation. Remove acquisition-related amortisation to avoid undervaluing ongoing returns when appropriate.
- R&D expenditures - analytical treatment varies. For a mature company, ROE should reflect long-term productivity of R&D. Productive R&D increases ROE (and RI); unproductive R&D reduces ROE.
Nonrecurring Items and Other Aggressive Accounting Practices
Nonrecurring items (discontinued operations, unusual or extraordinary items, restructuring charges, certain accounting changes) should be excluded from residual income forecasts if they are not expected to recur. Aggressive accounting practices that overstate assets or earnings should be corrected for accurate ROE and book value forecasts.
International Accounting Differences
Applying residual income to foreign firms requires careful consideration of accounting standards and data quality:
- Reliability of earnings forecasts under local reporting standards.
- Systematic violations of the clean surplus relation under specific accounting regimes.
- Poor-quality accounting rules that may render financial statements unrepresentative of 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 on the balance sheet. Subsequently, he determines Olympic has, for the past five years, been improperly capitalising and amortising expenditures that should have been expensed as incurred. What will be the effect on his forecasts of ROE, book value, and intrinsic value if he revises his valuation to take these errors 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 ROE and book value. He later determines Zues uses the current rate method and has consistently reported foreign currency translation gains as part of comprehensive income. He expects these gains to continue. What will be the effect on his forecasts of ROE, book value, and intrinsic value if he revises his valuation to take this information into account?
KEY CONCEPTS
LOS 23.a
Residual income = Net income - (r_e × Beginning book value of equity).
EVA and MVA are alternatives measuring economic profit and managerial performance:
EVA = NOPAT - (WACC × Total capital) = [EBIT × (1 - t)] - (WACC × Total capital)
MVA = Market value - Total capital
LOS 23.b
Residual income models are used for equity valuation, goodwill impairment testing, measuring managerial effectiveness, and executive compensation metrics.
LOS 23.c
Residual income formula:
RI_t = E_t - r_e × B_{t-1}
Value decomposition:
V0 = B0 + PV{RI_1 + RI_2 + ...}
Residual income models are relatively less sensitive to terminal value estimates because current book value (a known quantity) is included in intrinsic value.
LOS 23.d
Fundamental drivers of residual income are ROE in excess of the required return on equity and the earnings growth rate.
LOS 23.e
If ROE = r, justified market value equals book value (P/B = 1). If ROE > r, the firm generates positive residual income and will have P/B > 1.
LOS 23.f
Single-stage residual income model:
V0 = B0 + [B0 × (ROE - r)] / (r - g)
LOS 23.g
Implied growth rate formula:
g = r - (ROE - r)/(P/B - 1)
LOS 23.h
For multistage RI models, forecast RI over a short-term horizon and apply a continuing-RI assumption thereafter. The PV of continuing RI at T - 1 depends on the chosen assumption: persist forever (ω = 1), drop to zero (ω = 0), decay with ω between 0 and 1, or decline to a long-run normal level (use P_T - B_T approach).
Intrinsic value:
V0 = B0 + (PV of interim high-growth RI) + (PV of continuing residual income)
LOS 23.i
DDM and FCFE models discount expected cash flows to equity; residual income model uses book value plus PV of expected residual income. Residual income models can be used to cross-check DDM/FCFE results.
LOS 23.j
Strengths and weaknesses of residual income models (summarised):
- Strengths: terminal value less dominant, use of widely-available accounting data, applicability to non-dividend-paying or negative-FCFE firms, applicability when cash flows are volatile, focus on economic profitability.
- Weaknesses: reliance on accounting data subject to manipulation, need for numerous adjustments, assumption of clean surplus relation.
Appropriate when dividends are absent or volatile, FCFE negative, or terminal value is highly uncertain. Not appropriate when clean surplus is significantly violated or where there is large uncertainty about book value and ROE forecasts.
LOS 23.k
Accounting issues important to residual income application include:
- Violations of the clean surplus relation.
- Balance sheet adjustments to reflect fair value.
- Treatment of intangible assets (acquisition-related intangibles and R&D).
- Removal of nonrecurring items.
- Detection and correction of aggressive accounting practices.
- Consideration of 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 the perpetuity of C$11.25 discounted to Year 5 and then discounted to present; the present value of that terminal value equals C$69.85 (as shown in the original solution). Thus the justified value is 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 price and thus is undervalued. Stock Q has model price lower than market price and thus is overvalued. Stock R has model price equal to market price and is fairly valued. (LOS 23.f)
2.
C
Given P = V0 = $25.00, P/B = 5.00 implies B0 = $5.00. Using the single-stage residual income relationships and solving for r (cost of equity) implied by the observed price yields r ≈ 10% (numeric derivation in source). (LOS 23.f)
3.
C
Use single-stage residual income model and solve for ROE given P/B = 2.14, r = 12%, g = 5% (algebra shown in the source material). (LOS 23.f)
4.
A
Single-stage residual income model: Rocky's ROE > r implies PV of future RI > 0, therefore intrinsic value > book value and the justified P/B ratio > 1. (LOS 23.f)
5.
A
ROE = EPS / B0 = 0.45 / 4.50 = 10%. In the single-stage model when ROE = r, the PV of future RI = 0 and intrinsic value = book value; thus P/B = 1. (LOS 23.f)
Module Quiz 23.4
1.
C
All three alternative assumptions (immediate drop to zero, decline to zero with ω < 1,="" or="" decline="" to="" a="" long-run="" normal="" level)="" reduce="" continuing="" ri="" below="" the="" assumption="" of="" persistence="" at="" the="" same="" level="" forever.="" a="" falling="" roe="" reduces="" ri="" over="" time,="" so="" the="" value="" estimate="" will="" fall="" below="" $68="" in="" all="" three="" cases.="" (los="">
2.
B
Compute required return r via CAPM: r = r_f + β × (Market risk premium) = 0.045 + 0.7 × 0.05 = 0.045 + 0.035 = 0.08 = 8% (as demonstrated in the source). Then compute RI and PVs according to the residual income framework (detailed RI computations shown in the source table). (LOS 23.h)
3.
B
The present value of the residual income and subsequent PV of terminal value produce a V0 equal to the selected solution in the source material (LOS 23.h).
4.
C
For DRL in the ω = 0 case, present value of continuing RI in Year 3 = 0 and the model yields intrinsic value ≈ €8.34 per share; since market price is €8.75, shares are overpriced and a sell recommendation is appropriate. (LOS 23.c)
5.
B
With ω = 1 and continuing RI perpetual at €0.45, the model value exceeds market price of €8.75 so the analyst would consider a buy recommendation. (LOS 23.c)
6.
C
With ω = 0.3, persistence is limited and intrinsic value falls to €8.45 (as shown in the source calculations); since market price is €8.75, shares are overpriced and a sell recommendation is appropriate. (LOS 23.c)
Module Quiz 23.5
1.
C
Dividend discount model valuation: D1 = Earnings per share (EPS) since no reinvestment means EPS = dividend = $3.00. Required return r = r_f + β × MRP = 0.04 + 0.75 × 0.08 = 0.04 + 0.06 = 0.10 = 10%. DDM value = D / r = 3.00 / 0.10 = $30.00.
Residual income model: RI = EPS - r × B0 = 3.00 - 0.10 × 15 = 3.00 - 1.50 = 1.50. PV of RI = 1.50 / r = 1.50 / 0.10 = 15.00. V0 = B0 + PV(RI) = 15 + 15 = 30.00. Thus both models give $30.00. (LOS 23.i)
2.
C
Improperly capitalising expenditures that should be expensed overstate both book value and ROE historically. Correcting these increases expense in historical periods, lowering historic earnings and ROE and reducing book value. Revising the valuation to reflect expensing the items lowers the ROE forecast, reduces book value, and reduces the intrinsic value from the residual income model. (LOS 23.k)
3.
B
Foreign currency translation gains were recorded directly to equity (comprehensive income) and were not included in net income; this made the ROE forecast understated. Expecting these gains to continue should increase the ROE forecast while leaving book value unchanged (since the gains are already in equity). The revised valuation increases the ROE estimate, keeps book value the same, and increases intrinsic value from the residual income model. (LOS 23.k)
