Revisiting P/E10: Dividends

I did not start out assuming that P/E10 was a good measure of valuation. I checked a variety of measures and found that P/E10 is the best so far.

This time, I have examined variations on the number of years in the denominator. I looked at P/E1, P/E5, P/E10, P/E15, P/E20, P/E25 and P/E30.

Valuations have less relevance when estimating dividend amounts than prices. But they are relevant.

I checked a variety of measures. Even with dividends, P/E10 is best.

Year 5 Regression Equations

Year 5 100E1/P = x.
Y = 0.0058x + 1.057
R-squared = 0.0032.
Confidence interval = 1.7 to -0.5.

Year 5 100E5/P = x.
Y = 0.0056x + 1.0613
R-squared = 0.002.
Confidence interval = 1.7 to -0.5.

Year 5 100E10/P = x.
Y = 0.0485x + 0.7427
R-squared = 0.159.
Confidence interval = 0.5 to -0.5.

Year 5 100E15/P = x.
Y = 0.0374x + 0.8319
R-squared = 0.1.
Confidence interval = 0.6 to -0.5.

Year 5 100E20/P = x.
Y = 0.0432x + 0.7952
R-squared = 0.1479.
Confidence interval = 0.5 to -0.5.

Year 5 100E25/P = x.
Y = 0.0394x + 0.8269
R-squared = 0.1289.
Confidence interval = 0.5 to -0.5.

Year 5 100E30/P = x.
Y = 0.0367x + 0.8517
R-squared = 0.1105.
Confidence interval = 0.6 to -0.6.

Year 5 Largest slope (the term multiplied by x): 0.0485x from 100E10/P. [100E20/P is similar.]

Year 5 Largest value of R-squared: 0.159 from 100E10/P. [100E15/P, 100E20/P, 100E25/P and 100E30/P have similar values of R-squared.]

Year 5 Smallest confidence interval: 1.0 (covering 0.5 to -0.5) from 100E10/P, 100E20/P and 100E25/P. [100E15/P and 100E30/P are similar.]

Year 5 Smallest downside (negative portion of the confidence interval): -0.5 from 100E1/P, 100E10/P, 100E15/P, 100E20/P and 100E25/P. [100E30/P is similar.]

Year 10 Regression Equations

Year 10 100E1/P = x.
Y = 0.0265x + 0.9244
R-squared = 0.0693.
Confidence interval = 1.0 to -0.5.

Year 10 100E5/P = x.
Y = 0.0376x + 0.8521
R-squared = 0.0963.
Confidence interval = 0.6 to -0.4.

Year 10 100E10/P = x.
Y = 0.0355x + 0.8718
R-squared = 0.0895.
Confidence interval = 0.5 to -0.5.

Year 10 100E15/P = x.
Y = 0.0271x + 0.9395
R-squared = 0.0549.
Confidence interval = 0.6 to -0.5.

Year 10 100E20/P = x.
Y = 0.0266x + 0.9465
R-squared = 0.0586.
Confidence interval = 0.6 to -0.5.

Year 10 100E25/P = x.
Y = 0.0225x + 0.9782
R-squared = 0.044.
Confidence interval = 0.6 to -0.5.

Year 10 100E30/P = x.
Y = 0.0256x + 0.9601
R-squared = 0.0566.
Confidence interval = 0.5 to -0.5.

Year 10 Largest slope (the term multiplied by x): 0.0376 from 100E5/P. [100E10/P is similar.]

Year 10 Largest value of R-squared: 0.0963 from 100E5/P. [100E10/P is similar.]

Year 10 Smallest confidence interval: 1.0 (covering 0.6 to -0.4 or covering 0.5 to -0.5) from 100E5/P, 100E10/P and 100E30/P. [100E15/P, 100E20/P and 100E25/P are similar.]

Year 10 Smallest downside (negative portion of the confidence interval): -0.4 from 100E5/P. [100E1/P, 100E10/P, 100E15/P, 100E20/P, 100E25/P and 100E30/P are similar.]

Year 15 Regression Equations

Year 15 100E1/P = x.
Y = 0.0529x + 0.8175
R-squared = 0.1622.
Confidence interval = 0.6 to -0.5.

Year 15 100E5/P = x.
Y = 0.0561x + 0.8161
R-squared = 0.1259.
Confidence interval = 0.7 to -0.5.

Year 15 100E10/P = x.
Y = 0.074x + 0.6896
R-squared = 0.2279.
Confidence interval = 0.6 to -0.5.

Year 15 100E15/P = x.
Y = 0.0634x + 0.7799
R-squared = 0.1798.
Confidence interval = 0.7 to -0.5.

Year 15 100E20/P = x.
Y = 0.0608x + 0.8068
R-squared = 0.1798.
Confidence interval = 0.6 to -0.5.

Year 15 100E25/P = x.
Y = 0.0577x + 0.8348
R-squared = 0.1704.Confidence interval = 0.6 to -0.5.

Year 15 100E30/P = x.
Y = 0.0611x + 0.8207
R-squared = 0.1889.
Confidence interval = 0.6 to -0.6.

Year 15 Largest slope (the term multiplied by x): 0.074 from 100E10/P.

Year 15 Largest value of R-squared: 0.2279 from 100E10/P.

Year 15 Smallest confidence interval: 1.1 (covering 0.6 to -0.5) from 100E1/P, 100E10/P, 100E20/P and 100E25/P. [100E5/P, 100E15/P and 100E30/P are similar.]

Year 15 Smallest downside (negative portion of the confidence interval): -0.5 from 100E1/P, 100E5/P, 100E10/P, 100E15/P, 100E20/P and 100E25/P. [100E30/P is similar.]

Year 20 Regression Equations

Year 20 100E1/P = x.
Y = 0.038x + 1.0202
R-squared = 0.0587.
Confidence interval = 1.0 to -0.5.

Year 20 100E5/P = x.
Y = 0.0656x + 0.8281
R-squared = 0.1208.
Confidence interval = 1.0 to -0.5.

Year 20 100E10/P = x.
Y = 0.0737x + 0.7753
R-squared = 0.1589.
Confidence interval = 0.9 to -0.5.

Year 20 100E15/P = x.
Y = 0.0581x + 0.9018
R-squared = 0.1043.
Confidence interval = 1.0 to -0.5.

Year 20 100E20/P = x.
Y = 0.0622x + 0.8804
R-squared = 0.1322.
Confidence interval = 1.0 to -0.6.

Year 20 100E25/P = x.
Y = 0.0603x + 0.9003
R-squared = 0.1307.
Confidence interval = 0.9 to -0.5.

Year 20 100E30/P = x.
Y = 0.07x + 0.843
R-squared = 0.1742.
Confidence interval = 0.9 to -0.5.

Year 20 Largest slope (the term multiplied by x): 0.0737 from 100E10/P. [100E30/P is similar.]

Year 20 Largest value of R-squared: 0.1742 from 100E30/P. [100E10/P next highest at 0.1589.]

Year 20 Smallest confidence interval: 1.4 (covering 0.9 to -0.5) from 100E10/P, 100E25/P and 100E30/P. [100E1/P, 100E5/P and 100E15/P are similar.]

Year 20 Smallest downside (negative portion of the confidence interval): -0.5 from 100E1/P, 100E5/P, 100E10/P, 100E15/P, 100E25/P and 100E30/P. [100E20/P is similar.]

Comparisons

At years 5, 15 and 20, percentage earnings yield 100E10/P (the inverse of P/E10 expressed as a percentage) has the biggest slope. This means that changes in 100E10/P cause the biggest changes.

At year 10, percentage earnings yield 100E5/P has a slightly higher slope than 100E10/P.

At years 5 and 15, percentage earnings yield 100E10/P has the largest R-squared. It explains the greatest percentage of the variance (a measure of scatter). At year 10, 100E5/P has a slightly higher value of R-squared than 100E10/P. At year 20, 100E30/P has a slightly higher value of R-squared than 100E10/P.

The confidence intervals, including the downside component, were similar for all variations in the percentage earnings yield.

Overall, P/E10 (or 100E10/P in the equations) was the best measure of value.

Overall Sensitivity to Valuations

Here are the slopes of the percentage earnings yield for 100E10/P.

Year 5: 0.0485.
Year 10: 0.0355.
Year 15: 0.074.
Year 20: 0.0737.

In year 10, 100E5/P had a larger slope than 100E10/P. It was 0.0376.

Here are the R-squared values using 100E10/P.

Year 5: 0.159.
Year 10: 0.0895.
Year 15: 0.2279.
Year 20: 0.1589.

In year 10, 100E5/P had a larger value of R-squared than 100E10/P. It was 0.0963.

In year 20, 100E30/P had a larger value of R-squared than 100E10/P. It was 0.1742.

Remember that correlation coefficients are the square root of R-squared. These correlations are in the neighborhood of 40% (since 0.40^2=0.16).

Analysis

The dividend yield of a stock depends upon its price. The amount of a dividend does not. Or, at least, the amount is not directly related to the price. We would expect dividend amounts of the overall stock market to grow with earnings and track the growth of the Gross Domestic Product.

It is interesting that dividend growth is related to price (in terms of percentage earnings yields).

Looking at the graphs, the dividend ratio at years 5, 10, 15 and 20 was always close to 1.0 when the percentage earnings yield was close to 4%. That is, dividends have kept up with inflation but have not grown (on average) when P/Ex = 25 for all values of x using 1, 5, 10, 15, 20, 25 and 30 years.

Today’s valuations are in the range that we would not expect to see dividends grow faster than inflation.

[Separately from this study, I have found that dividend growth is sensitive to the payout ratio when expressed in terms of smoothed earnings (i.e., combining dividend yield and P/E10). Because of today’s low payout ratio, the outlook for dividend growth is much better than indicated. A low payout ratio means that a dividend cut is unlikely.]

Typically, dividend amounts increase by 50% (plus inflation), a ratio of 1.5, over 20 years when stocks are at bargain prices (e.g., P/E10 = 8).

These growth numbers assume that none of the dividends are reinvested. Reinvestment improves returns substantially.

Conclusion

Valuations have less relevance when estimating dividend amounts than prices. But they are relevant.

I checked a variety of measures. Even with dividends, P/E10 remains the best measure of valuation that I have found so far.

[There is a stronger effect related to the quality of earnings. To see this, examine the payout ratio based on smoothed earnings and average the dividend income over several years. Today’s dividend outlook is favorable in spite of today’s valuations.]

Have fun.

John Walter Russell
April 23, 2006