Dividends And Stock Valuation: A Study From The Nineteenth To The Twenty-First Century (Page 12 of 45) in pdf

Dividends And Stock Valuation: A Study From The Nineteenth To The Twenty-First Century Page 12

UP3 can loosely be interpreted as an investigation of the mis-estimation of “g”, the annual dividend

growth rate. In this representation, as our forecasted growth rate for dividends falls below the actual

growth rate (e.g., we are under-estimating the value for g), we expect to see smaller (or possibly more

negative) pricing errors for UP2 than for UP1 and therefore an increase in UP3. Thus our hypothesis is:

Hypothesis 4: There is no difference between the two estimated price series, E

[P1

] and E

[P2

3.2 Cost of Equity

Since both of these valuation methods require us to make certain assumptions to estimate the

value of equity, we need to consider the quality of our estimates for these inputs and thus the legitimacy

of our assumptions. The future dividends and terminal value we use in our fundamental valuation models

are the actual dividends between time t and the end of our sample, T or 2003. The assumption of perfect

foresight means that we assume investors are able to rationally forecast what actually happened. For the

cost of equity, we estimate the value using both the rolling average of the difference between the total

return in the U.S. market and a long-term government bond over the past 30 years and the overall average

differences since the start of our sample (referred to as the cumulative technique). Both of these methods

provide us with estimates for the cost of equity based on historical information that would have been

available to investors at a given point in time.

As a source of comparison we use the observed prices to back out the implied discount rate being

used by investors. Specifically, the implied cost of equity is obtained as the discount rate that equates the

actual current price with i) the discounted value of the actual future dividends from that time until the end

of the sample plus the terminal price (e.g., equation (2)) and ii) the discounted value of the next period’s

dividend and the actual growth rate in dividends observed from that time until the end of the sample (e.g.,

equation (5)). The implied discount rates are determined assuming our investors are perfectly rational and

therefore would have accurately forecasted the future dividends and terminal price.

Dividends And Stock Valuation: A Study From The Nineteenth To The Twenty-First Century Page 12