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CFA Institute
Dividends and Share Value Re-RevisitedAuthor(s): Gary SmithSource: Financial Analysts Journal, Vol. 42, No. 1 (Jan. - Feb., 1986), pp. 77-78Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4478905 .
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Lette to the Edito
Dividends and Share Value Re-revisited In their technical note in the May/June 1985 issue, Professors Hoffmeister and Dyl contend that "previous research- ers, including Graham and Dodd, misinterpreted the meaning of a re- gression coefficient, hence reached er- roneous conclusions." (See "Divi- dends and Share Value: Graham and Dodd Revisited.") The interpretation made by these previous researchers is, in fact, appropriate for their intended use, while no apparent purpose is served by the interpretation proposed by Hoffmeister and Dyl.
The equation in question is a cross- section regression of price per share P on dividends per share D and retained earnings per share R:
P =a + M3D + yR + e. (1)
Using annual data on 1,050 firms in 1979, Hoffmeister and Dyl obtained the following ordinary least squares estimates:
P = 7.90 + 7.08 D + 2.58 R.
These estimates are roughly consistent with the findings of earlier research- ers, including Dodd and Graham:
"The weight in the market place of $1 of distributed earnings tended to be about/our times as great as that of $1 of retained earnings."
-Graham and Dodd, Security Analysis, 4th ed., p. 486.
Hoffmeister and Dyl argue that "this conclusion is refuted by the results of a regression run on standardized varia- bles. The standardized variables are centered around a mean of zero and have a unit standard deviation. Any bias due to difference in scale between the independent variables, D, and RP, is thus eliminated."
The results of such a standardiza- tion are easily analyzed; Equation (1) can be rearranged as:
P = (c + ,BD + yR) + (f3SD)D'
+ (ysR)R' + E, (2)
where D and R are the sample means;
SD and SR are the sample standard deviations; and the standardized vari- ables are D' = (D - O)/sD and R' = (R - R)/SR.
Equation (2) shows that the transla- tion to standardized variables has the effect of multiplying each of the origi- nal regression coefficients by the stan- dard deviation of the associated ex- planatory variable. In the Hoffmeister and Dyl data, the standard deviations are apparently SD = 0.743 and SR =
2.085, since they report the following transformed estimates:
P 22.59 + 5.26 D' + 5.38 R' .
Hoffmeister and Dyl infer that "this result does not support the conclusion that investors value dividends more highly than they do retained earnings. On average, firms appear to have divi- dend policies such that the marginal effect of dividends per share on stock price is equal to the marginal effect of retained earnings per share on stock price."
Explanatory variables can be scaled upward or downward freely, without affecting the fit of the model or the predicted values of the dependent variable. All that changes is the inter- pretation of the regression coefficients. If we measure dividends in dollars, then the associated coefficient gauges the effect on price of an extra dollar of dividends, holding constant the other explanatory variables. If we multiply the dividend data by 100, thereby measuring dividends in cents, then the associated coefficient gauges the effect on price of an extra penny of dividends (and is 1/100th the size of the previous coefficient). If we divide the dividend data by its standard devi- ation, then the associated coefficient gauges the effect on price of an in- crease in dividends equal to the stan- dard deviation of dividends, whatever that happens to be, given the data at hand.
Here, with dividends and retained earnings having respective standard deviations of 0.743 and 2.085, the coef- ficient of dividends measures the ef-
fect on share price of an extra 74 cents of dividends, while the coefficient of retained earnings gives the effect of an extra $2.09 of retained earnings. These particular events are not comparable, have no intrinsic interest, and are not relevant to Hoffmeister and Dyl's con- clusion that "firms appear to have established dividend policies such that the marginal effect of dividends per share on stock price is equal to the marginal effect of retained earnings on stock price." That question is an- swered by the original formulation, measuring both dividends and re- tained earnings in dollars, not stan- dard deviations.
If we substitute E = D + R, where E is earnings per share, into Equation I, we obtain the following:
P = a + (f- y)D + yE + E. (3)
The coefficient of D tells how the stock price is affected by an increase in divi- dends, holding earnings constant; i.e., by the diversion of a dollar of profits from retained earnings to dividends. Thus the difference between the two original coefficients, f3 and y, answers the question posed by Hoffmeister and Dyl, as well as earlier researchers: A dollar shifted from retained earnings to dividends raises market price by $7.08 - $2.58 = $4.50.
When Hoffmeister and Dyl instead compare the coefficients of their stan- dardized regression, they are asking whether stock price is affected by in- creasing dividends by 74 cents, while reducing retained earnings by $2.09 (with profits implicitly dropping by $1.35). No one else has asked this question, or is very interested in the answer.
To make the point very concretely, consider the following data set:
earn- divi- re- price ings dends tained
firm P E D R 1 24 6 2 4 2 40 10 3-1/2 6-2/3 3 28.5 6 3 3
The first two firms differ simply in
FINANCIAL ANALYSTS JOURNAL / JANUARY-FEBRUARY 1986 O 77
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scale. Each pays out one-third of earn- ings as dividends and retains two- thirds; but the second firm is two- thirds larger than the first. The third firm provides an answer to the ques- tion of dividends versus retained earn- ings, because it earns the same amount as the first firm but pays out one-half, rather than one-third. Its higher stock value implies that the market values dividends more highly than retained earnings; in fact, a dollar diverted from retained earnings to div- idends raises market value by $4.50.
A least-squares regression yields the following:*
P = 7.0 D + 2.5 R.
The difference between the two coeffi- cients accurately gauges the extra $4.50 in value resulting from a dollar more of dividends and less of retained earnings.
These data were constructed so that SD = 0.694 and SR = 1.90, and the estimates with standardized data are as follows:
P = 30.83 + 4.86 D' + 4.74 R'.
As with the Hoffmeister and Dyl data, the coefficients are roughly equal, con- cealing what these hypothetical data clearly show-that a dollar of divi- dends has more effect on market price than does a dollar of retained earn- ings. What the standardized data show is that 69 cents of dividends and $1.90 of retained earnings have rough- ly the same effect on share price.
There may be problems with the simple stock valuation equation con- sidered here, including a neglect of such other explanatory variables as leverage and rates of return, but mea- suring the data in dollars is not one of them.
-Gary Smith Fletcher Jones Professor of Economics Pomona College
* The intercept for these data is zero; the nonzero intercept estimated by Hoffmeister and Dyl presumably reflects omitted varia- bles and nonlinearities.
FINANCIAL ANALYSTS JOURNAL / JANUARY-FEBRUARY 1986 C 78
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