9.6  Implied Equivalence Relationship:  IBM Example

As discussed in the introduction to this chapter there is an implied relationship between Residual Income and Abnormal Earnings Growth under clean surplus accounting.  Next section discusses and demonstrates this relation for the current example.

Equivalence Relationship between AEG and the Change in RI under Clean Surplus Accounting

The clean surplus accounting relationship implies a direct relationship between the AEG and RIV models.  This is because we can re-express AEG for a particular year, as the difference between Residual Income for that year and the previous year.  Recall, we measure Residual Income in terms of the dollar earnings over and above what investors’ require relative to the book value of shareholders’ equity.  In the current IBM example context this applies as follows:

AEG₂₀₁₀ = C. Earn₂₀₁₀ + k_eDiv₂₀₀₉ – (1+ke)C. Earn₂₀₀₉

              =  C. Earn_2010­ – C. Earn₂₀₀₉ – k_e (C. Earn₂₀₀₉ – Div₂₀₀₉)

From the clean surplus relationship and comprehensive earnings

Book Value₂₀₀₉ = Book value₂₀₀₈ + C. Earn₂₀₀₉ – Div₂₀₀₉

Substituting in:

AEG₂₀₁₀ = C. Earn_2010­ – C. Earn₂₀₀₉ – k_e ( Book Value₂₀₀₉ - Book value₂₀₀₈)

Rearranging we express as the differences between two residual incomes

AEG₂₀₁₀ = C. Earn_2010­ – k_e( Book Value₂₀₀₉ ) – (C. Earn2009 – k_e(Book value₂₀₀₈))

Verification of Equivalence

So given current growth forecasts we expect IBM to return to positive Abnormal earnings growth.