Enter Values

$
Current book value of equity per share
%
Forward normalized ROE (not trailing reported)
%
Required return from CAPM or factor model
%
% of earnings paid as dividends (b = 1 - payout)
years
Years of explicit RI forecast (1-20)
%
Long-term RI growth rate (must be < cost of equity)
Residual Income Formula
V0 = B0 + Σ PV(RIt) + PV(TV)
RIt = (ROE - k) × Bt-1 | TV = RIT+1 / (k - g) | b = 1 - payout
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Intrinsic Value

Intrinsic Value Per Share $56.04 Value Creator
Book Value (B0) $30.00
PV of Explicit RI $6.70
PV of Terminal Value $19.35
Value Creation +$26.04 (+86.81%)
ROE Spread +5.00%
Implied P/B Ratio 1.87x

Year-by-Year RI Breakdown

Year Beg. Book Value EPS Dividends End Book Value Residual Income PV Factor PV(RI)

Formula Breakdown

V0 = B0 + Σ PV(RIt) + PV(TV)
Where RIt = (ROE - k) × Bt-1 and TV = RIT+1 / (k - g)

Value Creation Interpretation

Scenario Condition Implication
Value Creator ROE > k (positive spread) Stock should trade above book value
Value Destroyer ROE < k (negative spread) Stock should trade below book value
Fair Value ROE ≈ k (spread ≈ 0) Stock should trade at book value

Understanding the Residual Income Model

What is Residual Income?

Residual income (also called Economic Value Added or EVA) measures the dollar value of earnings above the cost of equity capital. A firm generates positive residual income only when its return on equity exceeds what investors require for bearing that level of risk.

The return on equity spread (ROE - k) determines whether a firm creates or destroys value. This concept is central to intrinsic value analysis.

Residual Income Model
RIt = (ROE - k) × Bt-1
V0 = B0 + Σ PV(RIt) + PV(TV)
Where TV = RIT+1 / (k - g) and b (retention ratio) = 1 - payout ratio

Residual Income vs. Dividend Discount Model

Residual Income Model

Anchored to book value
Values excess returns above cost of equity. Works well for non-dividend-paying firms and financial institutions where book value is meaningful.

Dividend Discount Model

Based on cash distributions
Values expected future dividends. Requires firms to pay dividends and forecast distant cash flows. See also DCF and free cash flow approaches.

Clean Surplus Accounting

The residual income model relies on the clean surplus relation: all changes in book value must flow through the income statement. Mathematically: Bt = Bt-1 + Earningst - Dividendst. This ensures consistency between earnings, dividends, and book value growth, and is a key assumption underlying the model's equivalence to the DDM.

Key Insight: Under clean surplus accounting and consistent assumptions, the residual income model and the dividend discount model produce identical valuations. The RI model simply repackages the same information using book value and ROE rather than dividends.
Model Assumptions
  • Constant ROE over the explicit forecast period (simplified from multi-stage)
  • Clean surplus accounting: Bt = Bt-1 + Earnings - Dividends
  • Terminal residual income grows at a constant rate g in perpetuity
  • Cost of equity is constant over all periods
  • No share buybacks or equity issuances affect book value
  • Accounting book value is a meaningful measure of invested capital
  • Terminal growth uses exogenous g applied to RI (not derived from ROE × b)

For educational purposes. Not financial advice. Market conventions simplified.

Frequently Asked Questions

The residual income model values a stock by adding the current book value of equity to the present value of expected future residual income. Residual income (RI) equals the excess earnings above the required return: RI = (ROE - k) × Book Value. If a firm's ROE exceeds its cost of equity, it creates value above book value; if ROE falls below the cost of equity, the stock should trade below book value. The model is grounded in BKM Chapter 18 (Equity Valuation Models) and Chapter 19 (Financial Statement Analysis).

Under consistent assumptions (clean surplus accounting), the residual income model and dividend discount model produce identical valuations. However, the RI model is more practical for firms that pay low or no dividends, since it values the firm based on book value and ROE rather than dividend payments. The RI model also converges faster because book value anchors the valuation, while DDM requires forecasting distant dividends.

Economic Value Added (EVA), a concept popularized by Stern Stewart & Co., is the firm-level analog of residual income. EVA = (Return on Capital - WACC) × Invested Capital. While residual income uses equity measures (ROE, cost of equity, book value of equity), EVA uses total capital measures. Both capture the same idea: a firm creates value only when its returns exceed the opportunity cost of capital.

Use the residual income model when the firm has stable, predictable book value and ROE but uncertain free cash flows. It is especially useful for financial institutions (banks, insurers) where book value is economically meaningful, for mature firms with stable accounting, and when the firm pays minimal dividends. DCF is preferred when free cash flows are more predictable than accounting earnings.

Negative residual income means the firm's ROE is below its cost of equity (the required return). The firm is earning less than investors could earn elsewhere at the same risk level. This implies the stock should trade below its book value (P/B < 1). Persistent negative residual income suggests the firm is destroying shareholder value, even if it reports positive accounting profits.

Clean surplus accounting requires that all changes in book value flow through the income statement: Book Value(t) = Book Value(t-1) + Earnings - Dividends. This means no "dirty surplus" items bypass the income statement (such as unrealized gains posted directly to equity). The residual income model depends on this assumption to link earnings, dividends, and book value consistently.
Disclaimer

This calculator is for educational purposes only and uses simplified assumptions including constant ROE, clean surplus accounting, and a single-stage terminal value. Actual equity valuation requires detailed financial analysis, multi-stage models, and professional judgment. This tool should not be used for investment decisions.

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