Abnormal Earnings Growth and Model Reconciliation
The residual income model needs a clean-surplus balance sheet; the abnormal earnings growth (AEG) model needs only forecast earnings per share — exactly what analysts produce. This lesson builds the AEG model, weighs it against residual income, shows how accounting choices "wash out" under clean surplus, and then tackles the central practical puzzle: why do the DDM, DCF, RIVM and AEG models appear to disagree? — and how to make them reconcile.
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The RIVM builds on the DDM and the clean-surplus relation (CSR), assuming "comprehensive" earnings — but in practice analysts use net income. Ohlson & Juettner-Nauroth (2005) develop a model that needs neither book value nor CSR, working with the notion of abnormal earnings growth rather than abnormal earnings.
Learning outcomes
- Define abnormal earnings growth and relate it to residual income.
- Value equity with the AEG model (perpetuity, constant-growth, two-stage).
- Weigh residual income against AEG, and explain how accounting washes out.
- Diagnose why practical forecasts fail to reconcile (Lundholm & O'Keefe).
- Avoid growth-timing, WACC and dirty-surplus inconsistencies.
The abnormal earnings growth model
If a firm reinvested its dividend at \(r_e\), next year's "normal" earnings would be \((1+r_e)e_0\). Abnormal earnings growth is the excess of actual over normal earnings growth:
Computing AEG
\(r_e=10\%\), \(e_0=10\text{p}\), \(d_0=4\text{p}\), \(e_1=12\text{p}\).
Show solution
\(AEG_1=12+(0.1\times4)-(1.10\times10)=\textbf{1.4p}\). If clean surplus holds, \(AEG_t=RI_t-RI_{t-1}\) — AEG is simply the change in residual income.
12 + 0.4 − 11 = 1.4p (= the change in residual income under CSR)AEG valuation
A no-growth firm is worth capitalised next-year earnings, \(e_1/r_e\). A going concern adds the compounded stream of future AEG:
A two-stage version forecasts AEG explicitly for \(n\) years then applies terminal growth. Because the model is built on changes rather than levels, you must be careful exactly when terminal growth begins (see below). Even a negative PV of AEG is valid — it just means the price is worth less than capitalised one-year-ahead EPS.
Residual income vs AEG — for and against
RI and AEG advantages: easier when dividends are hard to forecast and FCF is negative for years; they recognise value earlier via the book-value (\(b_0\)) or capitalised-earnings (\(e_1/r_e\)) anchor, so the uncertain "continuing value" is a smaller share — reducing error. But it is still all future cash flows that matter (for most firms \(P_0>B_0\) and \(P_0>e_1/r_e\)), and both rest on accounting that can be manipulated. RIVM equals the DDM only if CSR holds (comprehensive earnings, watching off-balance-sheet items). AEG focuses on EPS (what analysts forecast) and needs no clean surplus — but that is also its weakness: creative accounting can paint a misleading earnings-growth picture.
How accounting choices wash out
Consider an all-equity firm earning 30% on £1m of tangible assets, spending 10% of assets on R&D each year (5-year life), cost of capital 10%. Capitalising vs expensing R&D changes the reported ROE and residual income in the early years (capitalising makes early ROE look high — 28% falling to a steady 16.7% once capitalisation = amortisation; RI falls from 180 to 80) — yet FCF is identical. In the long-run steady state the effect disappears: lower RI is offset by higher book value (the balance sheet and income statement act jointly), so accounting does not change equity value. The danger is the short term — a naïve analyst may over-value the capitalising firm early on (the general problem of "aggressive" accounting). Treat non-recurring "exceptionals" with care, since the aim is to predict future RI.
Why models disagree in practice
Some studies (Penman, 2001) find RI-based models predict prices "better" than DCF — which can't be right in theory, since all models give the same answer under consistent assumptions. Lundholm & O'Keefe (2001) identify why practical forecasts fail to reconcile:
- Inconsistent growth — cash-flow, dividend, asset and RI growth rates don't agree.
- Inconsistent cost of capital.
- Clean surplus assumed but violated.
All are fixable — and the central remedy is to forecast the balance sheet and income statement jointly.
Growth-timing errors
The subtle trap is naïvely multiplying the final forecast value by \((1+g)\). Under CSR, if dividends and book value grow at \(g\) from year \(t\), then earnings and RI grow at \(g\) only from \(t+1\) (one year later), and AEG grows at \(g\) from \(t+2\) (one year later still — two years after dividends and book values):
So if you truncate RI in the same period as dividends (or AEG in the same period as RI), the models will generate different equity values. The true steady state — where dividends, RI and AEG all grow at the same rate — begins at \(n+2\). Mind the lagged variable.
WACC and dirty-surplus consistency
WACC. The leverage weights must be at market value. If \(r_e\) is held constant (as in the DDM), then for a given \(r_d\) the WACC must change with leverage — you cannot hold both \(r_e\) and WACC constant unless leverage is constant (MM Proposition 2). And calculating WACC needs MVE, which is exactly what the indirect approach is trying to estimate — a real consistency bind at high leverage.
Dirty surplus. The other trap is forgetting clean surplus: items in comprehensive earnings but not net income — unrealised gains/losses on available-for-sale securities, foreign-currency translation, gains/losses on derivatives, employee stock options. What matters for valuation is the present value of these dirty-surplus items.
Morrisons plc (a FTSE 100 supermarket until Oct 2021) was taken private by Clayton, Dubilier & Rice in a ~£7bn deal, its shares bid from ~180p to 286p. Building a consistent model from the balance sheet and income statement (e.g. debt = 60% of book equity, 4% pre-tax interest, 20% tax) shows all the methods — DDM, DCF, RIVM, AEG — converge to the same value. Reconciliation is a test of consistency, not of which model is "right".
The AEG model values equity as capitalised next-year earnings plus the PV of future abnormal earnings growth — needing only EPS forecasts and no clean surplus (\(AEG=RI_t-RI_{t-1}\) when CSR holds). RI/AEG models recognise value earlier and suit negative-FCF growth firms, but rest on accounting that only washes out in the long run. Apparent disagreement between DDM, DCF, RIVM and AEG comes from inconsistent growth, cost of capital, or broken clean surplus (Lundholm & O'Keefe) — and from growth-timing lags (RI lags dividends by a year, AEG by two). Forecast the balance sheet and income statement jointly, keep the WACC compatible with the implied leverage each period, and respect clean surplus — and every model reconciles, as the Morrisons case shows.