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CFA Level II Exam · Residual Income Valuation

Residual Income Valuation Model Formula and Examples

Updated 7 October 2026 · Fact-checked

The residual income model sets intrinsic equity value equal to current book value plus the present value of expected future residual income. Residual income is net income minus an equity charge, which is required return on equity times beginning book value. Discount each residual income at the cost of equity, then add book value.

Understand Residual Income Valuation Model

Start with a simple idea. A company creates value for shareholders only if it earns more than the return they require. Accounting net income does not show this, because it ignores the cost of equity capital. A firm can report profit and still destroy value.

Residual income fixes this. It is net income minus an equity charge. The equity charge is the cost of equity (r) times the beginning book value of equity (B). If residual income is positive, the firm earns more than investors require. If it is zero, the firm is worth its book value.

This gives the model: intrinsic value = book value today + present value of all expected future residual income. Book value is the starting point because it already holds the capital invested. Residual income adds or subtracts the value created above or below the required return.

Residual income can also be written as (ROE − r) × beginning book value. This form is useful in vignettes that give ROE instead of net income. It shows that value above book depends on ROE exceeding r.

Compared with the dividend discount model, the residual income model puts most of the value in the first term, book value. So less value sits in a distant terminal value. It works for firms that pay no dividends or have negative free cash flow. It depends on reliable accounting, so check for clean surplus violations.

Key formulas to remember

Residual income
RIt = NIt − r × Bt−1
r is the cost of equity. Bt−1 is beginning-of-period book value of equity. The product is the equity charge.
Residual income using ROE
RIt = (ROEt − r) × Bt−1
Equivalent to the first form when ROE = NIt ÷ Bt−1 (beginning equity).
General residual income model
V0 = B0 + Σ [RIt ÷ (1 + r)^t], t = 1 to ∞
V0 is intrinsic value of equity. Per share, use book value per share and EPS-based residual income.
Single-stage (constant growth) model
V0 = B0 + RI1 ÷ (r − g)
Requires g < r. g is the constant growth rate of residual income. RI1 = (ROE − r) × B0 when ROE is applied to beginning equity.
Multistage model with terminal value
V0 = B0 + Σ [RIt ÷ (1 + r)^t] for t = 1 to T + [RIT+1 ÷ (r − g)] ÷ (1 + r)^T
Terminal value at time T equals RIT+1 ÷ (r − g). It is discounted back T periods. With persistence factor ω, RIT+1 ÷ (1 + r − ω) can be used.
Clean surplus relation
Bt = Bt−1 + NIt − Dt
Change in book value equals net income less dividends, with no other items bypassing the income statement.

How to solve Residual Income Valuation Model questions

Use the same sequence for every residual income question. Pull the numbers from the vignette first, then choose the form of the model.

  1. 1Identify the cost of equity r and the beginning book value B0. If r must be built, use CAPM or the figure the vignette gives.
  2. 2Find the earnings forecast or ROE for each year. Check whether the question uses net income or EPS, and total or per-share book value.
  3. 3Compute each year's equity charge: r × beginning book value. Beginning means last year's ending book value.
  4. 4Compute residual income each year: net income minus equity charge, or (ROE − r) × beginning book value.
  5. 5Roll book value forward with the clean surplus relation: ending B = beginning B + NI − dividends.
  6. 6Decide the pattern after the forecast period: constant growth, zero growth, fade with persistence, or a stated terminal value.
  7. 7Discount each residual income at r, discount any terminal value from the right year, then add B0.
  8. 8Sanity check: if ROE is above r throughout, value should exceed book value. If ROE equals r, value equals book.

Quickest way: Shortcut: compute with RI = (ROE − r) × B

When to use it: Use when the vignette gives ROE and book value and the question is single-stage, or a short forecast followed by a growth stage.

  1. Compute RI1 = (ROE − r) × B0 in one line.
  2. If RI grows at g forever, V0 = B0 + RI1 ÷ (r − g). Done.
  3. Before calculating, compare ROE with r. If ROE > r, the answer must exceed B0. Use this to eliminate options.
  4. For a multistage question, discount only the explicit years, then add one discounted terminal value.
  5. Keep unrounded figures until the last step, then match the closest option.

Common mistakes in Residual Income Valuation Model

  • Using ending book value for the equity charge

    Candidates take the book value shown on the latest balance sheet in the year being valued.

    Fix: The charge uses beginning-of-year equity. Year 1 uses B0. Year 2 uses B1, which you must roll forward.

  • Forgetting to add book value

    Candidates treat the present value of residual income as the whole answer, as with a DDM.

    Fix: Always write V0 = B0 + PV(RI). Make B0 the first term in your working.

  • Discounting the terminal value by the wrong number of periods

    The terminal value formula uses RIT+1, which confuses the timing.

    Fix: RIT+1 ÷ (r − g) gives value at time T. Discount it T periods, not T + 1.

  • Ignoring dividends when rolling book value forward

    Candidates add net income to book value and forget payouts.

    Fix: Use Bt = Bt−1 + NIt − Dt. Retained earnings only is the increase in equity under clean surplus.

  • Mixing per-share and total figures

    Vignettes show EPS in one exhibit and total net income in another.

    Fix: Keep the whole calculation in one basis. Use book value per share with EPS, or total equity with total net income.

  • Applying the single-stage formula when g ≥ r or ROE is expected to fade

    Candidates reach for the shortest formula without checking the assumption.

    Fix: Require g < r. If competition erodes excess returns, use a multistage or persistence-factor approach instead of constant growth.

Worked examples

Example 1

Vignette: Altair Ltd has book value of equity of 400 million at the start of Year 1. Cost of equity is 10%. Expected ROE is 14% in Year 1, and residual income is expected to grow at 3% a year forever after Year 1. Questions: (1) What is Year 1 residual income? (2) What is the intrinsic value of equity using the single-stage model? (3) Is the stock worth more or less than book value?

Show the solution
  1. Year 1 residual income = (ROE − r) × B0 = (0.14 − 0.10) × 400 = 16 million.
  2. Single-stage value = B0 + RI1 ÷ (r − g) = 400 + 16 ÷ (0.10 − 0.03).
  3. 16 ÷ 0.07 = 228.57 million.
  4. Intrinsic value = 400 + 228.57 = 628.57 million.
  5. Because residual income is positive, value exceeds book value.

Answer: (1) 16 million. (2) About 628.57 million. (3) More than book value, since ROE exceeds the cost of equity.

Example 2

Vignette: Borealis Inc has equity of 200 million today, cost of equity of 12%, and pays out 25% of net income as dividends. Forecast net income is 30 million in Year 1 and 36 million in Year 2. After Year 2, residual income is expected to be zero. Questions: (1) What is Year 1 residual income? (2) What is book value at the end of Year 1? (3) What is intrinsic value of equity?

Show the solution
  1. Year 1 equity charge = 0.12 × 200 = 24 million. RI1 = 30 − 24 = 6 million.
  2. Dividends in Year 1 = 0.25 × 30 = 7.5 million. B1 = 200 + 30 − 7.5 = 222.5 million.
  3. Year 2 equity charge = 0.12 × 222.5 = 26.7 million. RI2 = 36 − 26.7 = 9.3 million.
  4. PV of RI1 = 6 ÷ 1.12 = 5.357 million.
  5. PV of RI2 = 9.3 ÷ 1.2544 = 7.414 million.
  6. Terminal residual income is zero, so no terminal value is added.
  7. Value = 200 + 5.357 + 7.414 = 212.77 million.

Answer: (1) 6 million. (2) 222.5 million. (3) About 212.77 million.

Exam tips

  • Check the timing words in the vignette. Beginning book value drives the equity charge, and many wrong options come from using ending book value.
  • Compare ROE with r before calculating. This tells you whether the value should be above or below book and removes options fast.
  • When a terminal value is given or implied, write the discount period beside it. Most multistage errors are timing errors.
  • Expect a conceptual question on the model versus the DDM: it suits firms with no dividends or negative free cash flow, but depends on accounting quality and clean surplus.
  • Read the units. Per-share and total figures often both appear in the exhibits.

Residual Income Valuation Model in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Residual Income Valuation Model: frequently asked questions

What is the residual income model formula?

Intrinsic value equals book value of equity today plus the present value of expected residual income, discounted at the cost of equity. Residual income each period is net income minus cost of equity times beginning book value. For constant growth, V0 = B0 + RI1 ÷ (r − g).

How is the residual income model different from the dividend discount model?

The DDM values only expected dividends, so it needs a long forecast or a large terminal value. The residual income model starts from book value, so more of the value is recognised up front. It can value firms that pay no dividends, but it relies on accounting numbers that need checking.

What does zero residual income mean?

It means the firm earns exactly its cost of equity on beginning book value. Net income equals the equity charge. If residual income is expected to stay at zero, intrinsic value equals book value.

Which book value do I use for the equity charge?

Use the beginning-of-period book value for each year. For Year 1 that is B0. For later years, roll book value forward using ending book value equals beginning book value plus net income minus dividends.