How do you value a stock using the residual income model, and when is it better than DCF?

The residual income (RI) model is a powerful valuation tool, and it's especially useful when dividends are unpredictable or free cash flow is negative. Let me give you a thorough walkthrough. ## The Core Idea Residual income is the earnings a company generates **above and beyond** what investors require on their equity capital: **RI_t = EPS_t - (r_e x B_{t-1})** Where: - EPS_t = Earnings per share in period t - r_e = Required return on equity (cost of equity) - B_{t-1} = Book value per share at start of period The intrinsic value is: **V_0 = B_0 + Sum of [RI_t / (1 + r_e)^t] + Continuing Value** ## Worked Example: Calderon Biotech **Given data:** - Current book value per share (B_0): $24.50 - Cost of equity (r_e): 11% - Forecast EPS for years 1-3: $4.20, $4.75, $5.10 - ROE forecast: Year 1 = 17.1%, Year 2 = 18.2%, Year 3 = 18.5% - Dividend payout ratio: 40% each year - After Year 3, residual income fades to zero over time (persistence factor w = 0.60) **Step 1 — Project book values and residual income:** | Year | Beginning BV | EPS | Equity Charge (11% x BV) | Residual Income | Dividends | Ending BV | |---|---|---|---|---|---|---| | 1 | $24.50 | $4.20 | $2.70 | $1.51 | $1.68 | $27.02 | | 2 | $27.02 | $4.75 | $2.97 | $1.78 | $1.90 | $29.87 | | 3 | $29.87 | $5.10 | $3.29 | $1.81 | $2.04 | $32.93 | **Step 2 — Calculate PV of residual income:** - PV(RI_1) = $1.51 / 1.11 = $1.36 - PV(RI_2) = $1.78 / 1.11^2 = $1.44 - PV(RI_3) = $1.81 / 1.11^3 = $1.32 **Step 3 — Continuing value (using persistence factor):** Continuing value at end of Year 3 = RI_3 x w / (1 + r_e - w) = $1.81 x 0.60 / (1.11 - 0.60) = $1.086 / 0.51 = **$2.13** PV of continuing value = $2.13 / 1.11^3 = **$1.56** **Step 4 — Intrinsic value:** V_0 = $24.50 + $1.36 + $1.44 + $1.32 + $1.56 = **$30.18** ## When to Use RI Over DCF 1. **Negative free cash flow** — Growth companies reinvesting heavily may have negative FCFE for years, making DCF awkward. RI anchors on book value, which is observable. 2. **No dividends** — The RI model works without dividend forecasts. 3. **Accounting transparency** — Works best when financial statements are clean and book value is meaningful (e.g., financial institutions). ## Watch Out For - **Clean surplus violations**: The RI model assumes all gains and losses flow through the income statement. If large items bypass income and go directly to equity (OCI items like foreign currency translation), the model's accuracy degrades. - **Continuing value assumptions**: Whether you assume RI persists, fades, or drops to zero has a major impact on the final value. For more equity valuation models with side-by-side comparisons, explore our CFA Level II Equity module on AcadiFi.