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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 .

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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 coefficients by previous researchers had led to incorrect inferences regarding the relative contributions of dividends and retained earnings to share price valuation. After standardizing the independent variables, they demonstrated that the coefficients on the standardized 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 dividend relevance question.

Hoffmeister and Dyl used the following basis regression 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 earnings 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 specification. 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 coefficients.

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 appropriate valuation model, it does overcome the misspecification problem discussed above.4 The test for dividend 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 estimated 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 variables 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 dividends 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



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 unstandardized variable. It is easy to show that the coefficient 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 coefficients 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 standardized 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 variables 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) investors 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 retention 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, respectively-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 power, most research has shown that investors do not appear to use such adjustments.9

Even if the joint assumption of model validity and investor use of inflation adjustments were sustained, however, the analyst must be careful about drawing inferences from the equality of the coefficients on the dividend and retention variables. Although this result is consistent with an "optimal" dividend policy, it is also consistent with dividend irrelevance. That is, investors may be indifferent to the division by the firm between dividends and retained earnings. The issue of dividend relevance is still not resolved, but the results of this note at least add reliability to those of Hoffmeister and Dyl.

Footnotes

1. J. R. Hoffmeister and E. A. Dyl, "Dividends and Share Value: Graham and Dodd Revisited," Finan- cial Analysts Journal, May/June 1985, pp. 77-78.

2. Firm subscripts are suppressed for ease of nota- tion.

3. Results reported here actually used year-end prices, but these are qualitatively similar to results using average prices for the year.

4. See, e.g., L. D. Johnson, "Inflation and Stock Prices" (Doctoral dissertation, University of To- ronto, 1984) for a discussion of functional forms for valuation models.

5. The discount rate was computed using both the long-term bond rate and the Treasury bill rate. As the results are similar, only those using the long- term rate are reported here.

6. See, e.g., T. Mirer, Economic Statistics and Economet- rics (New York: Macmillan, 1983), pp. 84-86.

7. The March/April 1983 issue of this journal was dedicated to a discussion of this issue.

8. F. Modigliani and R. Cohn, "Inflation, Rational Valuation and the Market," Financial Analyst Jour- nal, March/April 1979, pp. 24-44.

9. See, e.g., R. Berliner, "Do Analysts Use Inflation- Adjusted Information? Results of a Survey," Fi- nancial Analysts Journal, March/April 1983, pp. 65- 72.

FINANCIAL ANALYSTS JOURNAL / SEPTEMBER-OCTOBER 1985 O 80

