Dividends And Stock Valuation: A Study From The Nineteenth To The Twenty-First Century Page 11
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45Our next model relaxes the assumption of perfect foresight of dividends. The GGM contains
several simplifying assumptions relative to the previous model. Namely it is based on the assumption of a
growing perpetuity, that the dividend growth rate is constant and the discount rate will remain stable over
time. The model is as follows:
E
[P2
] = E
[D
/ (r
– g
)]
(5)
t
t
t
t+1
t
t
where r
is the discount rate at time t and g
is the anticipated constant dividend growth rate at time t. The
t
t
dividend for year t+1, D
, is the perfect foresight dividend, the discount rate is estimated using the
t+1
CAPM from equation (3) and the anticipated growth rate is estimated using past information. Since a
standard assumption in corporate finance is that dividends can grow, at most, at the expected growth rate
of the economy, we use the nominal growth rate in the economy using the historical GNP to estimate the
growth rate of the dividends paid by the firms in the S&P Composite Index over time. The argument is
that firms’ growth rate is constrained by the growth rate of the economy and long-term dividend payouts
should grow at a rate similar to or lower than the growth rate of the economy.
The theoretical prices obtained using equations (3) and (5) are then compared to the actual price
at each time t to get a “pricing error” or the unexpected portion of the current price:
( (E
UP2
[P2
] - P
) / P
(6)
t
t
t
t
t
where UP2
is the unexpected portion of the price in period t, P
is the actual price and E
[P2
] is the
t
t
t
t
expected valuation based on an estimated constant growth rate. This gives rise to the following
hypothesis:
Hypothesis 3: There is no difference in the actual price series, P
, and the estimated price series
t
based on estimates using the constant growth or Gordon growth model, E
[P2
].
t
t
Because hypothesis 2 can be considered to be a measure of the mis-estimation of the discount rate
and hypothesis 3 a measure of the mis-estimation of both the discount rate and the growth rate, we also
consider the relative performance of the two different models by investigating the differences between
their pricing errors:
( UP1
UP3
– UP2
(7)
t
t
t
9
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