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Method 4 – Dividends Model
Dividend ( Div ) equals the earnings times the dividend payout ratio ( PO ); therefore, the growth rate of earnings can be calculated by the difference between the growth rate of dividend and the growth rate of the payout ratio.
6 Stock Market Returns in the Long Run
| EPSt = | Divt | (10) | ||||
| POt | ||||||
| (1+ gREPS ,t ) = | (1+ gRDiv,t ) | (11) | ||||
| (1 | + gPO,t ) | |||||
We substitute dividend growth and payout ratio growth for the earnings growth in equation 8. The equity’s total return in period t can be broken into five components: 1) inflation; 2) the growth rate of the price earnings ratio; 3) the growth rate of the dollar amount of dividend after inflation; 4) the growth rate of the payout ratio; and 5) the dividend yield.
| R | = | (1+CPI | ) ×(1+ g | ) × | (1+ gRDiv,t ) | + Inc | + Rinv | ||||||||
| t | P / E ,t | −1 | t | t | (12) | ||||||||||
| t | (1+ gPO,t ) | ||||||||||||||
Figure 3 shows the annual income return (dividend yield) of U.S. equity from 1926 to 2000. The dividend yield dropped from 5.15% at the beginning of 1926 to only 1.10% at the end of 2000. Figure 4 shows the year-end dividend payout ratio from 1926 to 2000. On average, the dollar amount of dividends grew 1.23% after inflation per year, while the dividend payout ratio decreased 0.51% per year. The dividend payout ratio was 46.68% at the beginning of 1926. It decreases to 31.78% at the end of 2000. The highest dividend payout ratio (929.12%) was recorded in 1932, while the lowest was recorded in 2000. The U.S. equity returns from 1926 and 2000 can be computed according to
| (1+ gRDiv | ) | ||||||||||||||||||||||||||||||
| R = | +CPI ) ×(1+ g | + Inc + Rinv | |||||||||||||||||||||||||||||
| (1 | P / E | ) × | −1 | ||||||||||||||||||||||||||||
| (1 | + gPO ) | ||||||||||||||||||||||||||||||
| (13) | |||||||||||||||||||||||||||||||
| 1+1.23% | |||||||||||||||||||||||||||||||
| + 4.28% | +0.20% | ||||||||||||||||||||||||||||||
| 10.70% = | (1 | +3.08%) | ×(1+1.25%)× | −1 | |||||||||||||||||||||||||||
| 1−0.51% | |||||||||||||||||||||||||||||||
Method 5 – Return on Book Equity Model
7 Stock Market Returns in the Long Run
We can also break the earnings into book value of equity (BV) and return on equity (ROE).
| EPSt = BVt ×ROEt | (14) |
The growth rate of earnings can be calculated by the combined growth rate of BV and ROE.
| (1+ gREPS ,t ) = (1+ gRBV ,t )(1+ gROE,t ) | (15) |
We substitute BV growth and ROE growth for the earnings growth in the equity return decomposition. The equity’s total return in period t can be computed by,
| Rt =[(1+CPIt )×(1+ gP / E,t)×(1+ gRBV ,t)×(1+ gROE,t)−1]+ Inct + Rinvt | (16) |
We estimate that the average growth rate of the book value after inflation is 1.46% from 1926 to 2000.9
The average ROE growth per year is calculated to be 0.31% during the same time period.
| = [(1+ | ) ×(1+ | ) ×(1+ | ) ×(1+ | ) −1]+ | + | |||||||||||
| R | CPI | gP / E | gBV | gROE | Inc | Rinv | (17) | |||||||||
| 10.70% = [(1 +3.08%) ×(1+1.25%)×(1+1.46%) ×(1+0.31%) −1]+ 4.28% +0.20% | ||||||||||||||||
Date: 2016-01-14; view: 697
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