How do you calculate residual income continuing value and what assumptions drive it?

Question

AcadiFi · Accepted Answer

Residual income (RI) valuation is a powerful alternative to DDM and FCF models, especially for companies that don't pay dividends. The continuing value (CV) captures the value of residual income beyond the explicit forecast period.

**Residual Income Basics:**

$$
RI_t = NI_t - (r 	imes B_{t-1})
$$

Where:
- NI = Net income
- r = Required return on equity
- B = Book value of equity
- The equity charge (r x B) is the minimum return shareholders require

**Full RI Valuation:**

$$
V_0 = B_0 + \sum_{t=1}^{T} \frac{RI_t}{(1+r)^t} + \frac{CV_T}{(1+r)^T}
$$

**Three Approaches to Continuing Value:**

**Approach 1: RI Drops to Zero After Year T**
CV = 0 (no residual income beyond the forecast period)

This assumes ROE = r eventually — the company earns exactly its cost of equity with no excess returns.

**Approach 2: RI Persists at Current Level Forever**

$$
CV_T = \frac{RI_T}{r}
$$

Assumes competitive advantage lasts indefinitely.

**Approach 3: RI Decays with Persistence Factor (omega)**

$$
CV_T = \frac{RI_T}{1 + r - \omega}
$$

Where omega (0 to 1) represents the persistence of abnormal earnings:
- omega = 0: RI drops to zero immediately (same as Approach 1)
- omega = 1: RI persists forever (same as Approach 2)
- omega = 0.4-0.6: Typical for most industries

**Worked Example: Alderton Financial Services**

- Current book value B0 = $42/share
- Required return r = 10%
- Forecast period: 3 years

| Year | EPS | Book Value (Begin) | Equity Charge | RI |
|---|---|---|---|---|
| 1 | $6.30 | $42.00 | $4.20 | $2.10 |
| 2 | $6.80 | $45.30 | $4.53 | $2.27 |
| 3 | $7.15 | $48.77 | $4.88 | $2.27 |

(Book value grows by retained earnings: B1 = 42 + 6.30 - 3.00 dividend = $45.30)

**Valuation with Persistence Factor omega = 0.5:**

CV3 = $2.27 / (1 + 0.10 - 0.50) = $2.27 / 0.60 = **$3.78**

$$
V_0 = 42 + \frac{2.10}{1.10} + \frac{2.27}{1.21} + \frac{2.27}{1.331} + \frac{3.78}{1.331}
$$

$$V_0 = 42 + 1.91 + 1.88 + 1.71 + 2.84 = \$50.33$$

```mermaid
flowchart TD
    V["V0 = $50.33"] --> BV["Book Value
$42.00"]
    V --> PV["PV of Residual Income
$5.50"]
    V --> CV["PV of Continuing Value
$2.84"]
    PV --> Y1["Year 1 RI: $2.10"]
    PV --> Y2["Year 2 RI: $2.27"]
    PV --> Y3["Year 3 RI: $2.27"]
    CV --> OM["Persistence ω = 0.5
RI gradually fades"]
    style V fill:#c9a84c,color:#0a0a0f,stroke:#c9a84c
    style BV fill:#1a1a2e,color:#fff,stroke:#c9a84c
    style PV fill:#1a1a2e,color:#fff,stroke:#c9a84c
    style CV fill:#1a1a2e,color:#fff,stroke:#c9a84c
```

**Choosing the Persistence Factor:**

| Industry | Typical omega | Rationale |
|---|---|---|
| Utilities | 0.3-0.4 | Regulated returns ≈ cost of equity |
| Consumer brands | 0.5-0.7 | Brand value sustains some excess return |
| Technology | 0.2-0.4 | Competitive advantages erode quickly |
| Pharma (patented) | 0.3-0.5 | Patent protection fades |

**Exam Tip:** If the question says the company will earn its cost of equity in the long run, set CV = 0. If it says competitive advantages are sustainable, use omega close to 1. Most exam questions specify the assumption.

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How do you calculate residual income continuing value and what assumptions drive it?

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