# Residual Income Valuation: Book Value Plus Economic Profit

The residual income model values equity as current book value plus discounted earnings above the required return on beginning equity, subject to clean-surplus accounting and careful adjustments.

Canonical: https://wiki.fcontext.com/stocks/residual-income-model/
Fact checked: 2026-07-21

> For educational purposes only; not investment advice.

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## Direct answer

The **residual income model (RIM)** values common equity as current common book value plus the present value of future earnings above the shareholders' required return:

`V₀ = B₀ + Σ[RIₜ / (1 + rₑ)ᵗ]`

`RIₜ = NIₜ - rₑ × Bₜ₋₁ = (ROEₜ - rₑ) × Bₜ₋₁`

Here `B₀` is book value attributable to common shareholders, `NIₜ` is comprehensive earnings available to common, and `rₑ` is the cost of equity. Positive accounting profit is not necessarily positive residual income: earnings must exceed the capital charge on beginning book value.

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## Why the model works

Under the **clean-surplus relation**, ending common book value equals beginning book value plus comprehensive income available to common minus common dividends and other owner distributions, after separately tracking share issuance and repurchases. Combining that relation with a dividend-discount model yields the residual-income identity when assumptions and accounting are consistent.

RIM can be useful when dividends do not reflect capacity to distribute cash or when free cash flow is difficult to define, including some financial institutions. It does not make bank valuation automatic: credit losses, regulatory capital, other comprehensive income, preferred claims, and asset marks still require analysis. It is less reliable when book value is negative, accounting recognition is severely delayed, or large unrecorded intangible assets make book value hard to interpret.

Forecast ROE and book value together. Competitive returns generally fade; assuming a permanent `ROE > cost of equity` embeds lasting economic rents. A continuing-value form is `CVₜ = RIₜ₊₁ / (rₑ - g)` only when `rₑ > g` and the growth, payout, ROE, and book-value path are mutually consistent.

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## Three-year example

Assume beginning common book value per share is `$20`, cost of equity is `10%`, and forecasts are:

| Year | Beginning book | Net income | Dividend | Ending book | Residual income |
| --- | ---: | ---: | ---: | ---: | ---: |
| 1 | $20.00 | $3.00 | $1.00 | $22.00 | $1.00 |
| 2 | $22.00 | $3.30 | $1.10 | $24.20 | $1.10 |
| 3 | $24.20 | $3.63 | $1.21 | $26.62 | $1.21 |

If year-four residual income is assumed to grow `3%` to `$1.2463`, continuing value at year three is `$1.2463 / (10% - 3%) = $17.80`. Discounting the three explicit residual incomes and continuing value gives about `$16.10`; adding current book value gives an estimated `$36.10` per share.

This is conditional, not a target-price fact. If excess ROE fades faster, credit losses rise, the cost of equity changes, or clean-surplus adjustments were omitted, value changes materially.

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## Model checklist

- Use common equity attributable to current common shareholders; remove preferred and noncontrolling claims consistently.
- Reconcile beginning to ending book value, including comprehensive income, dividends, issuance, repurchases, and accounting reclassifications.
- Normalize earnings for credit cycles, asset sales, restructuring, litigation, tax items, and acquisition accounting.
- Examine whether research, brands, customer acquisition, and internally developed software are expensed while acquired intangibles are capitalized.
- Match nominal earnings with a nominal cost of equity in the same currency.
- Apply the capital charge to beginning, not ending, book value unless timing is modeled explicitly.
- Forecast payout, growth, ROE, and book value as one linked system.
- Test competitive fade and terminal assumptions; terminal value often dominates.
- Cross-check with dividend, cash-flow, price-to-book, and scenario analysis using consistent claims.

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## Common misconceptions

- “Residual income means leftover cash.” It is accounting earnings minus an imputed equity capital charge.
- “ROE above zero creates value.” ROE must exceed the cost of equity.
- “Book value is liquidation value.” It is an accounting measure shaped by recognition and measurement rules.
- “RIM avoids terminal value.” It merely expresses continuing value through future residual income.
- “High current ROE can continue forever.” Competition, regulation, mean reversion, and changing leverage can erode it.
- “RIM and DCF should produce different true values.” With consistent forecasts and accounting, they are alternative expressions of the same equity economics.

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## Related topics

- [Discounted Cash Flow](/stocks/discounted-cash-flow/)
- [Cost of Equity](/stocks/cost-of-equity/)
- [Return on Equity](/stocks/return-on-equity/)

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## Authoritative sources

- [Earnings, Book Values, and Dividends in Equity Valuation](https://doi.org/10.1111/j.1911-3846.1995.tb00461.x) - The Accounting Review
- [Conceptual Framework](https://www.fasb.org/standards/accounting-standards-codification/conceptual-framework) - FASB
- [Beginners' Guide to Financial Statements](https://www.sec.gov/about/reports-publications/investorpubsbegfinstmtguide) - SEC