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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: 570

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