Understanding the Residual Income and Abnormal Earnings Growth Model through practical, numerical case studies.
Abnormal earnings, also known as residual income, measure the profit a company generates above the minimum return required by its equity investors. Unlike accounting net income, which treats all profit as value creation, abnormal earnings deduct a charge for the cost of equity capital. This concept is central to the Residual Income Valuation Model (RIV) and the Abnormal Earnings Growth (AEG) Model.
Where NIt is net income in period t, re is the cost of equity, and BVt−1 is the book value of equity at the beginning of the period.
Traditional valuation metrics like P/E ratios ignore the cost of equity. A company can show positive net income while destroying shareholder value if it fails to earn its cost of capital. Abnormal earnings directly address this by asking: Did the company earn more than what investors could have earned elsewhere at the same risk?
The model is particularly valuable for:
Let us begin with a simple case. Company Alpha has the following data for the fiscal year:
Beginning Book Value of Equity (BV0): $500 million
Net Income (NI): $65 million
Cost of Equity (re): 10%
Step 1: Compute the required return on equity:
Required Return = 10% × $500M = $50 million
Step 2: Subtract from net income:
Abnormal Earnings = $65M − $50M = $15 million
Company Alpha generated $15 million of value beyond investor expectations. This positive abnormal earnings suggests the firm has a competitive advantage that allows it to earn above its cost of capital.
Now consider Company Beta over a three-year forecast period with a terminal value. This illustrates the full Residual Income Valuation approach.
Assumptions: Cost of equity = 12%. Beginning BV = $800M.
Forecast:
Year 1:
Abnormal Earnings = $120M − (12% × $800M) = $120M − $96M = $24M
Ending BV = $800M + $120M − $40M = $880M
Year 2:
Abnormal Earnings = $130M − (12% × $880M) = $130M − $105.6M = $24.4M
Ending BV = $880M + $130M − $45M = $965M
Year 3:
Abnormal Earnings = $140M − (12% × $965M) = $140M − $115.8M = $24.2M
Ending BV = $965M + $140M − $50M = $1,055M
Terminal Value: TV = $24.2M × 1.03 / (0.12 − 0.03) = $276.9M
Present Value of Abnormal Earnings:
PV = $24M/1.12 + $24.4M/1.122 + $24.2M/1.123 + $276.9M/1.123
PV = $21.4M + $19.4M + $17.2M + $197.1M = $255.1M
Total Equity Value = Beginning BV + PV of Abnormal Earnings
= $800M + $255.1M = $1,055.1M
The Residual Income Model arrives at the same value as a DCF if consistent assumptions are used, but it has the advantage of anchoring value in the current book value and only adding value for expected outperformance.
Not all companies create value. Company Gamma illustrates persistent value destruction.
Beginning Book Value: $300M
Cost of Equity: 11%
Net Income: $25M
Required Return: 11% × $300M = $33M
Abnormal Earnings: $25M − $33M = −$8M
Despite reporting $25M in net income, Company Gamma destroyed $8M of shareholder value. The firm earned 8.3% on equity while investors required 11%. If this persists, the stock will trade below book value.
This example explains why many unprofitable-but-growing tech firms can still have positive valuations: investors expect future abnormal earnings to offset current negative ones. The AEG model formalizes this by projecting the entire path of abnormal earnings.
The AEG model takes a slightly different perspective. Instead of anchoring on book value, it focuses on how abnormal earnings themselves grow over time.
Where AEGt = (Abnormal Earningst − Abnormal Earningst−1). This formulation separates the base earnings capitalization from the present value of abnormal earnings growth.
Cost of Equity: 10%
Year 1 Earnings: $50M
Year 2 Earnings: $56M
Year 3 Earnings: $61M
Dividend Payout: 30% of earnings
Step 1: Calculate abnormal earnings for each year:
AE1 = $50M − (10% × prior BV) = need prior BV
Instead, the AEG model works with the change in abnormal earnings directly.
Simplified AEG Calculation:
Capitalized base earnings = $50M / 0.10 = $500M
Present value of AEG = (growth above cost of capital) / r
If abnormal earnings grow at 4% per year after Year 1:
AEG in Year 2 = $50M × (10% − 4%) / 0.10 = ...
For a full derivation and calculator, visit the Abnormal Earnings Growth Model guide.
Finance professionals use abnormal earnings analysis for:
While powerful, the abnormal earnings model relies on accounting book values, which can be affected by accounting policies, write-offs, and intangible assets not recorded on the balance sheet. Analysts should adjust for these distortions and always cross-check with market-based valuations.
For a complete theoretical treatment, including derivations and sensitivity analysis, refer to the Financial Wiki article on the Abnormal Earnings Growth Model.