How does the persistence factor work in the residual income model's continuing value, and what drives it?
CFA Level II residual income valuation. I understand that residual income = NI - equity charge, but the continuing value after the explicit forecast period confuses me. My textbook mentions a 'persistence factor' (omega) between 0 and 1 that drives the terminal value. What determines omega and how does it affect valuation?
The persistence factor is one of the more nuanced concepts in CFA Level II equity valuation. It addresses a fundamental economic question: how long can a company sustain abnormal profitability?
Residual Income Basics
Residual Income (RI) = Net Income - (Equity Charge)
RI = NI - (r_e x B_{t-1})
Where r_e is the cost of equity and B is book value. Positive RI means the company earns more than its cost of equity -- it creates economic value.
The Continuing Value Problem
After your explicit forecast period (say, 5 years), you need to estimate the present value of all future residual income. The persistence factor model handles this:
CV_T = (omega x RI_T) / (1 + r_e - omega)
Where omega ranges from 0 to 1:
| Omega | Meaning | Economic Interpretation |
|---|---|---|
| 0 | RI drops to zero immediately | Perfectly competitive market, no moat |
| 0.3-0.5 | RI decays quickly | Weak competitive position, easily replicated |
| 0.6-0.8 | RI persists partially | Moderate moat, brand, or scale advantages |
| 1.0 | RI persists forever | Permanent monopoly (theoretical extreme) |
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Worked Example: Prestwick Luxury Holdings (fictional)
| Input | Value |
|---|---|
| Book value at year 5 (B5) | $40 per share |
| ROE in year 5 | 14% |
| Cost of equity (r_e) | 10% |
| Persistence factor (omega) | 0.60 |
RI_5 = (0.14 - 0.10) x 40 = $1.60
CV_5 = (0.60 x 0.96 / 0.50 = $1.92
If omega were 0 instead: CV_5 = $0 (all excess returns evaporate)
If omega were 1.0 instead: CV_5 = 16.00** (ten times larger!)
What Drives Omega in Practice?
- Brand strength: A luxury brand with 200 years of heritage has high omega
- Regulatory barriers: A licensed utility or pharma patent holder has structurally protected returns
- Network effects: Platform businesses where value grows with users
- Switching costs: Enterprise software with deep integration into client workflows
- Commoditized industry: Low barriers, easy replication means omega near zero
Exam Strategy: The CFA exam won't ask you to estimate omega from scratch. Instead, it will give you omega and test whether you can compute the continuing value and interpret the economic meaning. Be prepared for sensitivity analysis -- 'if omega changes from 0.4 to 0.7, how does intrinsic value change?'
Practice residual income problems in our CFA equity question bank.
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