# ROE vs Earnings Growth Rate

Some simple calculations relating Earnings Growth Rate to ROE:

Case 1: No dividends
E1 = SE1*ROE

SE2 = SE1*(1+ROE)
E2 = SE2*ROE = SE1*(1+ROE)*ROE
E2/E1 = (1+ROE)

=> Earnings Growth Rate = ROE

Case 2: With dividends
E1 = SE1*ROE

SE2 = SE1*(1+ROE) – D1
E2 = SE2*ROE = (SE1*(1+ROE) – D1)*ROE
E2/E1 = (1+ROE) – D1/SE1

SE3 = SE2*(1+ROE) – D2 = (SE1*(1+ROE) – D1)*(1+ROE) – D2
E3 = SE3*ROE = ((SE1*(1+ROE) – D1)*(1+ROE) – D2)*ROE
E3/E2 = (1+ROE) – D2/SE2

Check: If D2 = E2, then E3/E2 = (1+ROE) – E2/SE2 = (1+ROE) – ROE = 1, i.e. E3 = E2

payout ratio = D2/E2 = D2 / (SE2*ROE)
=> payout ratio * ROE = D2 / SE2
=> E3/E2 = (1+ROE) – (payout ratio*ROE)

=> Earnings Growth Rate = ROE – payout ratio*ROE = ROE*(1-payout ratio)

[Note: In Rule #1 by Phil Town, the advice is to use the growth rate of equity to project future earnings.

In Case 1: No dividends, Growth rate of equity = SE2/SE1 – 1 = ROE
In Case 2: With dividends, Growth rate of equity = SE3/SE2 – 1 = (1+ROE) – (D2/SE2) – 1 = ROE – (payout ratio*ROE) = ROE*(1-payout ratio)

In both cases, Growth rate of equity = Earnings Growth Rate as calculated before. Hence Phil Town is fine using the Growth rate of equity.]

[Note: The above calculations is applicable with other bases: e.g. if SE means Net Tangible Assets, then ROE becomes the Return on Net Tangible Assets (i.e. FCF/Net Tangible Assets). Some bases are not applicable though, e.g. tangible capital employed minus excess cash. If excess cash is not included, then the definition of this base does not follow the rule of SE2 = SE1*(1+ROE) – D1, so that wouldn’t work out. But wouldn’t a redefinition of the base change the Earnings Growth Rate? seems like it does…..]