Estimated study time: 60 minutes
Content:
Residual income (RI) is the earnings of a business after deducting a charge for the opportunity cost of equity capital employed. The residual income in a period is: RI_t = Net Income_t - (r_e * Book Value_{t-1}), where r_e is the required return on equity and Book Value_{t-1} is the equity book value at the beginning of the period. This is equivalent to: RI_t = (ROE_t - r_e) * Book Value_{t-1}. Residual income is positive when the firm earns more than its cost of equity (ROE > r_e) and negative when it earns less. The concept is closely related to economic value added (EVA), which applies the same framework to total capital (using NOPAT and WACC instead of net income and cost of equity).
The residual income valuation model expresses intrinsic stock value as book value per share plus the present value of all future per-share residual incomes: V0 = B0 + Sum[RI_t / (1 + r_e)^t]. Under the simplest single-stage assumptions with constant ROE and growth g, this simplifies to: V0 = B0 + [RI1 / (r_e - g)] = B0 + [(ROE - r_e)*B0 / (r_e - g)]. Dividing by B0 gives the justified P/B: V0/B0 = 1 + (ROE - r_e)/(r_e - g). This confirms the earlier result: when ROE = r_e, the stock is worth exactly book value (no value added or destroyed); when ROE > r_e, the stock is worth more than book value; and when ROE < r_e, the stock is worth less than book value — it is a value destroyer.
The strength of the residual income model relative to dividend discount models and FCF models is its explicit connection to accounting data. Rather than forecasting dividends or free cash flows (which can be unstable or obscured by investment cycles), the RI model starts from book value and adds the PV of future economic profits. For companies that pay no dividends and have lumpy FCF, the RI model can be more tractable. It is also particularly useful for financial sector companies (banks, insurance companies) where FCFF and FCFE are difficult to estimate because financing and investing activities are intertwined with core operations. The key disadvantage is that the model is sensitive to accounting quality — if book value or earnings are manipulated, the residual income estimates are correspondingly distorted.
Practical considerations in applying the RI model include: (1) Clean surplus accounting — the RI model requires that all changes in book value flow through the income statement; items recorded directly to OCI (foreign currency translation adjustments, unrealized pension gains/losses, hedging gains/losses) violate clean surplus and require adjustment. (2) Convergence of RI — if a firm's ROE converges to r_e over time, its RI converges to zero, and the stock value converges to book value. This is a reasonable long-run assumption for competitive industries. (3) Terminal value in RI models — instead of projecting residual income in perpetuity, analysts often use a terminal year adjustment: terminal value = premium (or discount) to book at the end of the forecast period, using a persistence factor that reflects how long above-normal ROE is expected to continue.
Economic Value Added (EVA) is the corporate application of the residual income concept at the total firm level: EVA = NOPAT - (WACC * Total Capital), where NOPAT = Net Operating Profit After Tax = EBIT*(1-t) and Total Capital = debt + equity (invested capital). EVA is positive when the firm earns more than its total cost of capital (ROIC > WACC). Market Value Added (MVA) = Market Value of Firm - Total Capital = PV of all future EVAs, discounted at WACC. Companies with consistently positive EVA (ROIC > WACC) create shareholder value; companies with negative EVA destroy value even if they show positive GAAP net income. EVA analysis is widely used for internal performance measurement, compensation systems (economic bonus plans tied to EVA improvement), and external equity research.
Key Terms:
Quiz Questions:
Q1. Stellar Corp has book value per share of $20.00, expected EPS of $3.00, and a required return on equity of 12%. Residual income per share for the upcoming year is:
A) $3.00 - 0.12 * $20.00 = $3.00 - $2.40 = $0.60 per share. B) $3.00 / 0.12 = $25.00 per share. C) $3.00 - $20.00 = -$17.00 per share. D) $3.00 * 0.12 = $0.36 per share.
Answer: A — Residual Income = Net Income - Equity Capital Charge = EPS - (r_e * Beginning Book Value) = $3.00 - (0.12 * $20.00) = $3.00 - $2.40 = $0.60 per share. This $0.60 is the economic profit per share above and beyond the minimum required return for equity investors. Stellar earns ROE = $3.00/$20.00 = 15%, which exceeds r_e = 12%, generating positive residual income.
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Q2. Using the residual income model, what is the intrinsic value of Stellar Corp from Q1 if residual income is expected to persist at $0.60 per share indefinitely (zero growth)?
A) V0 = B0 + RI / r_e = $20.00 + $0.60 / 0.12 = $20.00 + $5.00 = $25.00. B) V0 = RI / r_e = $0.60 / 0.12 = $5.00. C) V0 = EPS / r_e = $3.00 / 0.12 = $25.00 (DDM with zero growth). D) V0 = B0 + RI / (r_e - g) = $20.00 + $0.60 / 0.12 = $25.00 — same as A.
Answer: A — V0 = B0 + PV(future RI). With constant RI of $0.60 per share in perpetuity at zero growth: PV(RI) = $0.60 / 0.12 = $5.00. V0 = $20.00 + $5.00 = $25.00. Note that this equals the DDM no-growth value (EPS/r = $3.00/0.12 = $25.00), as it should — both models give equivalent results when consistently applied. Options C and D are both technically correct but express the same answer differently.
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Q3. A company has ROE of 18% and is expected to grow at 7% per year indefinitely. Required return on equity is 11%. Current book value per share is $25. Using the justified P/B approach, what is the intrinsic value per share?
A) P/B = (ROE - g)/(r - g) = (0.18 - 0.07)/(0.11 - 0.07) = 0.11/0.04 = 2.75x; V0 = 2.75 * $25 = $68.75. B) P/B = ROE/r = 0.18/0.11 = 1.64x; V0 = 1.64 * $25 = $41.0. C) P/B = (r - g)/(ROE - g) = (0.11-0.07)/(0.18-0.07) = 0.36x; V0 = $9.0. D) P/B = 1 + (ROE - r)/(r - g) = 1 + (0.07)/(0.04) = 2.75x; same as A.
Answer: A — Justified P/B = (ROE - g) / (r - g) = (0.18 - 0.07) / (0.11 - 0.07) = 0.11 / 0.04 = 2.75. Intrinsic value = 2.75 * $25 = $68.75 per share. This company earns significantly above its cost of equity (ROE 18% vs. r 11%), justifying a substantial premium to book value. The formula is equivalent to V0 = B0 + (ROE - r)*B0/(r - g) = $25 + (0.07)*$25/0.04 = $25 + $43.75 = $68.75 — consistent.
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Q4. Continental Bank reports the following: NOPAT = $300M; Total Invested Capital = $2,000M; WACC = 10%. What is the bank's EVA and what does it imply about value creation?
A) EVA = $300M - 0.10 * $2,000M = $300M - $200M = $100M; the bank creates $100M of economic value above and beyond the cost of its capital, implying ROIC (15%) exceeds WACC (10%). B) EVA = $300M / $2,000M = 15%; the bank creates 15% EVA. C) EVA = $300M - $2,000M = -$1,700M; value destroying. D) EVA = $300M * 0.10 = $30M; this is the value added per dollar of capital.
Answer: A — EVA = NOPAT - (WACC * Total Capital) = $300M - (0.10 * $2,000M) = $300M - $200M = $100M. ROIC = $300M / $2,000M = 15%, which exceeds WACC of 10%. The $100M EVA represents true economic value created for all capital providers above their required return. MVA (market value added) = PV of all future EVAs, so consistently positive EVA firms should trade above their book value of invested capital.
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Q5. A technology company reports net income of $50M. During the year, $15M of unrealized gains on available-for-sale securities were recognized directly in OCI (not through the income statement). Book value rose from $200M to $265M: $200M + $50M net income + $15M OCI = $265M. Why does the OCI item require adjustment when applying the residual income model?
A) OCI items are tax-free and therefore need no adjustment. B) The residual income model requires clean surplus accounting — all changes in book value must flow through net income. The $15M OCI item increases book value without flowing through income, violating clean surplus; the analyst must add it to net income (or reduce the book value increase) to correctly compute RI. C) OCI items always reduce residual income and should be excluded. D) There is no adjustment needed; OCI does not affect the RI calculation because it is not cash.
Answer: B — Clean surplus accounting is a requirement of the RI model. When book value changes through OCI rather than through net income, the accounting violates clean surplus. In this case, book value increased by $65M ($50M NI + $15M OCI) but only $50M flowed through income. If the analyst uses the standard RI formula with reported net income, the income underestimates the true return because the $15M unrealized gain added to book value is not captured. The correct adjustment is to add the $15M to comprehensive income (total comprehensive income = $65M) when computing RI, so that all increases in book value are matched by income.
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