Finance
Residual Income (RI) Equity Valuation & Justified Price-to-Book (P/B)
Value banks, insurers, and non-dividend companies using the Edwards-Bell-Ohlson Residual Income Model V_0 = BV_0 + ((ROE - r_e) * BV_0) / (r_e - g) and Justified P/B = 1 + (ROE - r_e) / (r_e - g).
Anchor intrinsic equity value in clean-surplus book equity rather than terminal multiples!
Traditional DCF and Dividend Discount Models struggle with commercial banks, insurers, and capital-reinvesting firms whose free cash flow is distorted by loan-book growth or zero dividends! Under Clean-Surplus Accounting, the Edwards-Bell-Ohlson Residual Income (RI) Model starts directly from current Book Value per Share (BV_0) and adds the present value of future excess equity returns above the Cost of Equity (r_e): RI_1 = (ROE - r_e) * BV_0!
Assuming constant sustainable Return on Equity (ROE) and book-value growth g < r_e, intrinsic share value collapses to V_0 = BV_0 + ((ROE - r_e) * BV_0) / (r_e - g)! Dividing both sides by BV_0 immediately explains why high-ROE franchises trade above book while sub-hurdle banks trade below book: Justified P/B = 1 + (ROE - r_e) / (r_e - g)!
| Bank / Franchise Scenario (BV_0 = $40, r_e = 10%, g = 4%) | Sustainable ROE | Year-1 Residual Income RI_1 | Intrinsic V_0 & Justified P/B |
|---|---|---|---|
| High-ROE Wealth Franchise | 16.0% | (16% - 10%) * $40 = +$2.40 | $80.00 / sh | 2.00x Book |
| Cost-of-Equity Earner | 10.0% (= r_e) | $0.00 / sh | $40.00 / sh | 1.00x Book |
| Sub-Hurdle Regional Bank | 8.0% (< r_e!) | (8% - 10%) * $40 = -$0.80 | $26.67 / sh | 0.67x Book! |
Single-Stage Residual Income Intrinsic Share Value V_0 ($)
Enforces BV_0 > 0 and r_e > g, then computes BV_0 + ((ROE - r_e) * BV_0) / (r_e - g).
=IF(OR(B2 <= 0, B4 <= B5), "Invalid Book Value or Growth g >= r_e", ROUND(B2 + (((B3 - B4) * B2) / (B4 - B5)), 2))Justified Price-to-Book Multiple P/B = 1 + (ROE - r_e) / (r_e - g)
Computes the fundamental P/B multiple implied by ROE, cost of equity, and sustainable growth.
=IF(B4 <= B5, "Invalid Growth g >= r_e", ROUND(1 + ((B3 - B4) / (B4 - B5)), 2))Try the example
Use the original values or change them to test your understanding.