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Dividends and Share Value: Graham and Dodd Revisited, AgainAuthor(s): Lewis D. JohnsonSource: Financial Analysts Journal, Vol. 41, No. 5 (Sep. - Oct., 1985), pp. 79-80Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4478875 .Accessed: 13/06/2014 04:07

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Tchnical Note

Dividends and Share Value: Graham and Dodd Revisited, Again

by Lewis D. Johnson, Assistant Professor of Finance, Queen's University, Kingston, Canada*

A recent technical note by Hoffmeister and Dyl argued that incorrect interpretation of regression co- efficients by previous researchers had led to incorrect inferences regarding the relative contributions of div- idends and retained earnings to share price valua- tion. After standardizing the independent variables, they demonstrated that the coefficients on the stan- dardized dividend and retention variables were ap- proximately identical. From this they concluded that the marginal effect on price of dividends and retained earnings was equivalent and that firms on average were following "optimal" dividend policies.

Their evidence is more suggestive than conclusive, however, because of model specification errors and other problems. The purpose of this note is to repli- cate the Hoffmeister and Dyl tests using a more correct methodology. The results obtained are similar but more reliable, and the inferences drawn from the results are somewhat different in terms of the divi- dend relevance question.

Hoffmeister and Dyl used the following basis re- gression model:2

P = a + bX + u, (1)

where P = average share price for the year, X = contemporaneous earnings per share,

a,b = regression coefficients, and u = an error term.

Hoffmeister and Dyl ran cross-sectional regressions on 1,050 firms, using 1979 data. The first problem with this procedure is its use of contemporaneous earnings rather then expected earnings. Although contemporaneous price-earnings relations (such as the P/E ratio) are somfetimes used as rules of thumb, investment decisions should be based on the earn- ings expected in the future, not on current earnings (although current earnings may be one indicator of future earnings). The widespread phenomenon dur- ing the recent recession of negative earnings and positive share prices is evidence enough of this. However, the use of the average share price for the year mitigates this problem somewhat, so, in the interests of consistency, the same procedure will be used in this replication.

A more basic problem has to do with model specifi- cation. The use of Equation (1) requires cross-section-

al stability of the regression coefficients a and b. In the context of this study, that means that the earnings of AT&T are being capitalized at the same rate as those of, say, Mesa Petroleum. This misspecification results in regression coefficients that are biased and inconsistent; accordingly, inferences cannot be drawn on the relative magnitudes of these coeffi- cients.

The implicit model underlying Equation (1) is a perpetuity valuation model:

P = a + bX/k, (2)

where k is an appropriate firm-specific discount rate. Although Equation (2) may not be the most appropri- ate valuation model, it does overcome the misspecifi- cation problem discussed above.4 The test for divi- dend relevance, then, may be conducted using the following equation:

P = a + bD/k + cR/k + e, (3)

where D = dividends per share, R = retained earnings per share,

a,b,c = regression coefficients, and e = an error term.

Examination of the relative magnitudes of estimates of b and c would be equivalent to Hoffmeister and Dyl's tests of dividend relevance.

The replication tests were conducted using 1981 data for 213 large industrials trading on the New York Stock Exchange and listed in the Value Line Investment Survey. Firms had to have positive earnings and dividends to be included. Although not as large as the Hoffmeister and Dyl sample, the companies are from a broad range of industries, and the results should be qualitatively comparable. Betas were esti- mated from the CRSP returns tape, and discount rates computed with the Capital Asset Pricing Model.

Equations (2) and (3) were first run using nonstan- dardized variables. The result for Equation (2) (t- statistic in brackets) was:

P = 17.67 + 0.68 X/k. (4) (12.03)

The coefficient on X/k is highly significant, and the coefficient of determination of 0.41 indicates a high degree of explanatory power in this form of the model. The results from estimation of Equation (3) are:

P = 16.71 + 0.9 D/k + 0.6 RIk. (5) (5.06) (7.33)

The coefficients on the dividend and retention varia- bles are significant and, as with the Hoffmeister and Dyl study, the coefficient of determination has in- creased, but only by 1 per cent. Similar qualitative results on the relative explanatory power of divi- dends and retained earnings are also achieved, with

* The authors thanks Robin MacLean for research assistance and Canadian Pacific Limited and the D.I. McLeod Fund for financial support.

FINANCIAL ANALYSTS JOURNAL / SEPTEMBER-OCTOBER 1985 O 79

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the former having 50 per cent more weight. The variables were then standardized to remove

scale effects by subtracting the mean of the variable and dividing by its standard deviation. The results for Equation (2) are:

P = 35.28 + 10.78 (X/K)'. (6) (12.03)

Notice that, in contrast to Hoffmeister and Dyl's Equations (1) and (3), which were identical, the regression coefficients are not the same using the standardized income variable as in using the unstan- dardized variable. It is easy to show that the coeffi- cient on the standardized income variable is equal to the coefficient on the unstandardized income variable divided by the standard deviation of income.6 Simi- larly, the constant term in the standardized model is equal to that of the unstandardized form plus the product of the mean of the sample and the coefficient on the unstandardized income variable. The coeffi- cients of determination are identical, however, and, as the standard errors are similarly transformed, so are the t-statistics.

The results of running Equation (3) on the stan- dardized dividend and retention variables are:

P = 35.28 + 5.13 (D/k)' + 7.45 (R/k)'. (7) (5.06) (7.33)

The estimated coefficients on the standardized varia- bles suggest that the Hoffmeister and Dyl result of equality between the marginal effects of dividends and retention on valuation are not sustained. Howev- er, the story does not stop here.

There is an ongoing empirical controversy over which measure of earnings (hence retention) inves- tors use in the valuation process when there is secular inflation.7 Many researchers (and regulatory powers such as the SEC and FASB) promote the use of income adjusted for the effects of inflation on the assets of the firm, primarily inventory and fixed assets. In addition, Modigliani and Cohn have shown that income should be further adjusted for the effects of inflation on the fixed liabilities of the firm.8

Equation (3) was thus reestimated using retention rates based on two alternative income measures-X2, constant dollar income as reported in the Value Line Investment Survey, and X3, income further adjusted to account for the effects of inflation on the debt of the firm. The results for the standardized models are as follows:

P 35.28 + 8.8 (D/k)' + 8.61 (R2/k)', (8) (10.9) (10.68)

P = 35.28 + 7.23 (D/k)' + 7.94 (R3/k)', (9) (9.12) (9.38)

where R2 and R3 are retention rates based on X2 and X3, respectively.

Equations (8) and (9) support the equality of the coefficients on the standardized dividend and reten- tion variables as found by Hoffmeister and Dyl. The t-

statistics are higher in the alternative income forms than in the basic historical cost income form (Equa- tion (7)). In addition, the coefficients of determination for Equations (8) and (9)-0.52 and 0.48, respective- ly-are higher than the 0.42 of Equation (7). This evidence, taken at face value, should lead to the same conclusion drawn by Hoffmeister and Dyl-that is, firms are following "optimal" dividend policies.

This conclusion still cannot be made unequivocally, however. The first problem is the use of a perpetuity valuation formula, which may not be appropriate for most firms. The second problem is the issue of which income measure is appropriate in a valuation context. Although the results above appear to indicate that inflation-adjusted income has more explanatory pow- er, most resear

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