Estimate intrinsic equity value, equity capital charges, and justified P/B multiples using Clean Surplus Accounting and competitive persistence decay.
Key Valuation Principle: Unlike DCF models where 70%–85% of total value sits in uncertain terminal cash flows, the Residual Income model anchors directly on current audited book value ($B_0$), with residual income representing only the incremental premium created above capital charges.
Year-by-year decomposition of economic profits, discount factors, and discounted present values under Ohlson autoregressive decay.
| Period | Residual Income (RI) ($/sh) | Discount Factor (1+r)^t | Discounted PV of RI | Cumulative PV of RI |
|---|
Intrinsic share price ($) and Margin of Safety across varied operating profitability and investor hurdle rates.
| ROE \ Hurdle (Ke) | 6.5% Ke | 7.5% Ke | 8.5% Ke | 9.5% Ke | 10.5% Ke |
|---|
Under Clean Surplus Accounting, intrinsic equity value is identically equal to initial book value plus the present value of future economic residual income:
Where \(RI_t = \text{Net Income}_t - (r \times B_{t-1}) = B_{t-1} \times (\text{ROE}_t - r)\).
Clean Surplus Accounting requires that all balance sheet changes in equity book value flow through the income statement (no direct-to-equity bypass items like dirty OCI gains/losses):
In competitive markets, extraordinary economic profits are eroded by industry entry and technological disruption. James Ohlson formulated this as an autoregressive process with persistence parameter \(\omega\):
Dividing the infinite-horizon residual income formula by initial book value (\(B_0\)) reveals why corporate valuation multiples expand or contract:
Test your mastery of Clean Surplus Accounting, equity charges, and Edwards-Bell-Ohlson valuation dynamics.
1. What accounting relationship is strictly required for the Residual Income model to be mathematically equivalent to the Dividend Discount Model?
2. How is the fundamental Equity Capital Charge calculated in Year 1?
3. If a company's Expected Return on Equity (ROE) exactly equals its Cost of Equity ($r$), what is its Justified Price-to-Book (P/B) ratio?
4. Under James Ohlson's competitive fade model, what does an omega (ω) persistence factor of 1.0 signify?
The Residual Income Valuation Model, formalized by James Ohlson and Edwards & Bell (the EBO model), values a company's equity as the sum of its current book value plus the present value of all expected future residual income. Residual income is defined as accounting net income minus a charge for the cost of equity capital (Equity Charge = Book Value * Cost of Equity).
The Clean Surplus Relation (CSR) states that the ending book value of equity equals beginning book value plus net income minus net dividends (Bt = Bt-1 + Et - Dt). It guarantees that all changes in equity book value pass through the income statement, ensuring mathematical equivalence between the Residual Income Model and the Dividend Discount Model.
The persistence parameter (omega, where 0 ≤ omega ≤ 1) captures how quickly abnormal economic profits decay toward zero due to market competition. An omega of 1.0 means residual income persists indefinitely, while an omega near 0 means residual income drops to zero immediately after the discrete forecast window.
When ROE exceeds the cost of equity (r), the company earns an economic spread (ROE - r > 0), generating positive residual income. This positive residual income adds premium value above the initial equity investment, justifying a Price-to-Book (P/B) ratio greater than 1.0.
Yes. You can export complete discrete annual residual income projections, discount factors, terminal continuing values, and the 5x5 ROE vs. Cost of Equity sensitivity table as a formula-protected CSV spreadsheet.