Question

Please proof the internal growth rate when ROE is defiend as NI/ending total assets

Answer 1

Internal growth can be defined as the maximum growth that could be obtained by applying internal sources of finance only, that is without applying external sources of finance. The said statement can be formulated as follows:

Internal Growth Rate = Reinvested Earnings/Ending Total Assets ........1

In the above equation, numerator and denominator of Right Hand Side to be multiplied with Net Income

Internal Growth Rate =Reinvested Earnings/Net Income X Net Income/EndingTotal Assets ..........2

We know that,

Retention rate = Reinvested Earnings/Net Income ...........3

and Return on Equity= Net Income/Ending Total Assets given in question

Substituting the equations 3 & 4 in equation 2, we get

Internal Growth Rate =Retention Rate X Return on Equity

Retention ratio= 1-Dividend Payout ratio, so

Internal Growth Rate=(1-Dividend Payout ratio) X Return on Equity .............5

As we know that,

Sustainable Growth Rate= (1-Dividend Payout ratio) X Return on Equity ..............6

from Equations 5 and 6, we can conclude that

Internal Growth Rate = Sustainable Growth Rate

Hence, we can conclude that when Return on Equity equals to Return on assets, or in other words Shareholders Equity = closing Total Assets value, the firm will have sustainable internal growth rate.