8.7
Residual Income: Constant Growth Model
Recall in
chapter 5 we considered the simplest form of the basic dividend
model, the constant dividend growth model.
In this model, dt = d*(1+g)t so the
current dividend, d, grows for every at rate g.
Note that dt is a forecast of the dividend at time
t. Mathematically this
has a nice implied simplification which can be expressed as follows:
This simplifies
to:
An immediate
practical problem with this model was that it was applicable only to
dividend paying stocks.
However, under clean surplus accounting a1 = CI1
– (BV1 – BV0), where CI1 is
comprehensive income for the next period, BV1 is end of
period book value per share and 0 denotes the present, we can
interpret a1 as the dividend paid out next period (d1).
As a result, we can extend the basic constant growth model to
all firms, irrespective of whether they pay dividends or not, by
invoking the clean surplus accounting assumption.
Under constant
growth the change in the book value equals CI1*RR (the
retention ratio) = ROE*RR*BV0 when ROE (Return on Equity
is measured using Comprehensive Income).
In the beginning of chapter 3 we developed accounting or
fundamental growth as ROE*RR = g.
Extending this definition to measuring ROE using
Comprehensive Income the change in the book value from time 0 to
time 1 equals BV0*g which provides the constant dividend
growth model extended to all firms by substituting for d1
as follows:
The advantage of the latter form is that it is applicable to all stocks irrespective of whether or not they pay dividends.