Hong Life CalculatorsUnderstanding the residual income valuation calculator — concept and principle
The residual income model values a share as its book value plus the present value of the profits it is expected to earn above shareholders' required return. This calculator applies the model with a forecast period and a fade-out afterwards, and also shows the S-RIM shortcut popular among Korean investors.
How it is calculated
- Residual income: RIt = (ROE − r) × Bt−1.
- Book value grows by retained earnings: Bt = Bt−1 × (1 + ROE × (1 − payout)).
- Value: V0 = B0 + Σ RIt ÷ (1 + r)^t over the forecast years.
- After the forecast, residual income fades by the persistence factor ω each year; its value at year N is RIN × ω ÷ (1 + r − ω), discounted to today.
- S-RIM: B0 + B0 × (ROE − r) × ω ÷ (1 + r − ω), with book value held constant.
The principle
Book value is the capital shareholders have in the company. If the company earns exactly its cost of equity on that capital, it is worth its book value. Only returns above the cost of equity, the residual income, add value. Because high returns tend to be competed away, the model lets residual income fade after the forecast. If ROE is below r, residual income is negative and the value falls below book.
Worked example
Default inputs: B0 = 25 USD, ROE 14%, required return 9%, payout 30%, 5 forecast years, ω = 0.8, price 30 USD.
- Book value grows by 1 + 0.14 × 0.7 = 1.098 a year. RI1 = 0.05 × 25 = 1.25 USD; RI5 = 0.05 × 36.34 ≈ 1.82 USD.
- PV of residual income in years 1–5 ≈ 5.82 USD.
- Fade value at year 5 = 1.82 × 0.8 ÷ 0.29 ≈ 5.01 USD; PV ≈ 3.26 USD.
- Intrinsic value = 25.00 + 5.82 + 3.26 ≈ 34.08 USD; justified price-to-book = 1.36×.
- Price ÷ value = 30 ÷ 34.08 ≈ 88%. S-RIM value = 25 + 25 × 0.05 × 0.8 ÷ 0.29 ≈ 28.45 USD. Book value at year 5 ≈ 39.90 USD.
| Book value per share now (B₀) | Intrinsic value per share |
|---|---|
| 6.25 | $8.52 |
| 12.5 | $17.04 |
| 18.8 | $25.56 |
| 25 | $34.08 |
| 31.2 | $42.60 |
| 37.5 | $51.11 |
| 50 | $68.15 |
How to read the result
A price below intrinsic value suggests the market expects less than your assumptions, or the stock is undervalued. The result is very sensitive to ROE, r and ω, so test a range. The model works well for banks and other firms where book value is meaningful.
Common mistakes
- Using a peak-year ROE as if it will last.
- Setting the required return too low.
- Using ω = 1 (permanent excess returns) without good reason.
- Applying the model to companies with negative or distorted book value.
Frequently asked questions
What is residual income?
Profit above the return shareholders require on the book value of equity.
What is S-RIM?
A simplified residual income model widely used in Korea that keeps book value constant and fades excess returns with ω.
What persistence factor should I use?
Values between 0 and 1; lower values mean excess returns fade faster. Many users try 0.8, 0.9 and 1 to see a range.
Sources: Ohlson, J. A. (1995). Earnings, Book Values, and Dividends in Equity Valuation. Contemporary Accounting Research, 11(2). · CFA Institute, Equity Valuation: Residual Income Valuation (CFA Program curriculum)