Cum-Dividend Earnings are defined as:

Cum-dividend earnings = Comprehensive Earnings + Cost of Equity Capital*Accounting Dividend_t-1

This in turn permits us to define Abnormal Earnings Growth, as follows.

Abnormal Earnings Growth

This concept is designed to capture the value added from anticipated earnings growth.  In a two stage growth model of intrinsic value, the growth behavior for stage 1 we have referred to as “abnormal growth.”  This is because during stage 1, growth behavior is permitted to exceed economy wide growth bounds.  The interval of time covered by stage 1 is often assumed by analysts to be in the range of 5-7 years, but the exact length is subject to economic considerations.  For example, a software firm may only have 2-years of large growth before competition sets in, whereas a monopolist who is protected by strong barriers to entry such as patents may have 10-years.  As a result, analysts must take into account these economic considerations when deciding how many years to define stage 1 over plus the assumed growth rate for this period of time.  Stage 2 immediately follows stage 1.  For a going concern, stage 2 is assumed to last forever for mathematical convenience and lets us calculate present values as perpetuities.  As a practical note, because the required rate of return is positive, discounting eliminates the “forever part” by applying smaller and smaller present value weightings to cash inflows further out in time.  In this stage growth is referred to as normal and it is bound from above by economy wide growth. 

The abnormal earnings growth refers to earnings growth over time and is defined each year (time = t) to be the difference between dividend protected earnings and earnings that grow at the required rate of return.  This is defined as follows:

And Cum-Dividend Earnings are defined as:

Note:  Both Abnormal Earnings Growth and Residual Earnings approaches to valuation are based upon the clean surplus accounting using “Comprehensive Income” which attempts to measure the total of all operating and financial events that have changed the shareholders’ equity over the period.

To project residual earnings into the future the second important input for this concept is assessed growth behavior of earnings.  This allows earnings to be projected out over time by growing at the assessed growth rates.  Under these projections, if abnormal earnings growth is expected to be positive over time then intrinsic value will exceed the capitalized earnings and vice-versa.

Concept 3 (Cost of Capital):  The cost of capital is the investors’ required rate of return from the investment.  This is the discount rate used to compute the present value of future residual earnings per share.  It is equivalently referred to as the stock’s cost of equity capital.