Equity Valuation & Accounting Theory
Ohlson Linear Information Dynamics Valuation Formula
Calculate James Ohlson’s (1995) closed-form equity value P_t = B_t + alpha_1 * x_t^a + alpha_2 * v_t combining clean-surplus book value, abnormal earnings persistence omega, and forward information v_t.
Bridge dividend discounting, clean-surplus book value, and analyst forward surprises!
James Ohlson (1995) revolutionized modern financial statement valuation by combining Clean-Surplus Accounting (B_t = B_{t-1} + NI_t - Div_t) with autoregressive Linear Information Dynamics (LID): next-year Abnormal Earnings x_{t+1}^a = omega * x_t^a + v_t + eps_1 and forward non-accounting "Other Information" v_{t+1} = gamma * v_t + eps_2 (with persistence parameters 0 <= omega < 1 and 0 <= gamma < 1)! Summing discounted expected abnormal earnings to infinity collapses the entire infinite-horizon DCF/Residual-Income series into one exact closed-form price equation: P_t = B_t + alpha_1 * x_t^a + alpha_2 * v_t, where alpha_1 = omega / (1 + r - omega) and alpha_2 = (1 + r) / ((1 + r - omega) * (1 + r - gamma))!
Verify on Current_Book_Value B_t = $50.00/sh (B2), Prior_Book_Value B_{t-1} = $45.00/sh (B3), Current_EPS NI_t = $9.50/sh (B4), Cost_of_Equity r = 0.10 (10.0%, B5 -> Current Abnormal Earnings x_t^a = 9.50 - 0.10 * 45.00 = $5.00/sh), Abnormal_Earnings_Persistence omega = 0.60 (B6), Forward_Information_Shock v_t = $1.50/sh (B7, e.g. FDA approval or backlog surprise not yet in current GAAP earnings), and Forward_Shock_Persistence gamma = 0.55 (B8): Multiplier alpha_1 is 0.60 / (1.10 - 0.60) = 1.2000; Multiplier alpha_2 is 1.10 / ((1.10 - 0.60) * (1.10 - 0.55)) = 1.10 / 0.275 = 4.0000; and Intrinsic Equity Value is P_t = 50.00 + 1.20 * 5.00 + 4.00 * 1.50 = $62.00/sh (Justified P/B = 1.24x)!
| Ohlson (1995) LID Valuation Metric (B_t=$50, x_t^a=$5, r=10%, om=0.6, gm=0.55) | Formula | Verified Output |
|---|---|---|
| Current Abnormal Earnings (x_t^a) | NI_t - r * B_{t-1} | $5.00 / share |
| Abnormal Earnings Multiplier (alpha_1) | omega / (1 + r - omega) | 1.2000x (+$6.00 Goodwill) |
| Other-Information Multiplier (alpha_2) | (1 + r) / ((1 + r - omega) * (1 + r - gamma)) | 4.0000x (+$6.00 Forward Value) |
| Intrinsic Share Price (P_t) | B_t + alpha_1 * x_t^a + alpha_2 * v_t | $62.00 / share (P/B = 1.24x) |
Ohlson (1995) Closed-Form Intrinsic Equity Price P_t Formula
Test competitive mean-reversion omega = 0 and v_t = 0 in cells B6 and B7: alpha_1 = 0, so P_t = B_t = $50.00 even when current ROE is 9.50 / 45.00 = 21.1% — because one-off abnormal profits without persistence add zero future economic goodwill beyond today’s book value B_t!
=LET(bt_cr, B2, bt_pr, B3, ni_ps, B4, r_eq, B5, om_ae, B6, vt_fw, B7, gm_fw, B8, IF(OR(bt_cr <= 0, bt_pr <= 0, r_eq <= 0, om_ae < 0, om_ae >= 1, gm_fw < 0, gm_fw >= 1), "Invalid Ohlson LID Input", LET(xa_t, ni_ps - r_eq * bt_pr, al_1, om_ae / (1 + r_eq - om_ae), al_2, (1 + r_eq) / ((1 + r_eq - om_ae) * (1 + r_eq - gm_fw)), ROUND(bt_cr + al_1 * xa_t + al_2 * vt_fw, 2))))Multiplier alpha_1 & alpha_2 Verification Formula
Validate 0 <= omega < 1, 0 <= gamma < 1, r > 0, and positive clean-surplus book equity.
=IF(ISTEXT(E5), E5, ROUND((1 + B5) / ((1 + B5 - B6) * (1 + B5 - B8)), 4))Try the example
Use the original values or change them to test your understanding.