g=b*ROE是怎么推导出来的？

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算dividend growth rate的公式，一直没想明白为什么

请求指导！

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关键词：ROE Dividend divide Growth Rate growth

不明白呢！！！！！！！！

growth rate g = retention rate b * Return on Equity ROE

image as followings:
year 1: your net income is NI, the portion that is not distributed is:  NI * b; this is the total amount to be invested at the end of year 1
next year: you invested the kept portion of NI*b, the return on it is NI*b*ROE, again you are going to kept some portion, NI*b*ROE*b, which will not be distributed. Considering the amount you already have had in year 1, now totally you have NI*b + NI*b*ROE*b, at the end of year 2 that can be invested in the following year

Thus, the growth rate g is: [(NI*b+NI*b*ROE*b) - NI*b] / NI*b =  b*ROE

说得好！

好的  学习了谢谢

john3721smith 发表于 2011-3-30 01:08
growth rate g = retention rate b * Return on Equity ROE

image as followings:

思路很好，但是好像有点不对。第一年的股利是D0=NI(1-b)，第二年的是D1=(NI*b*roe+NI)*(1-b)，股利增长率g=D1/D0-1=b*roe

1，明年的盈利=今年的盈利+今年的留存收益*留存收益回报率 
NI t+1=NI t + b*NI t*ROE,
2，式子两边除以今年盈利： 明年盈利 / 今年盈利=今年盈利/今年盈利+今年留存收益*留存收益回报率 / 今年盈利
NI t*(1+g)/NI t=1+b*NI t*ROE/NI t
3，约分
1+g=1+b*ROE 两边1抵消g=b*ROE