Finance textbooks state that g = plowback ratio x ROE. (ROE = net income / (S/E))

I want to know if this formula is realistic in determining g. At first glance, it seems to but after a year accepting it as truth, I was thinking now that it might not.

Say for example, you have a company that has a net income of $5, stock price of 100, and theoretcially no debt. You retain a dollar for growth and 4 dollars is given out in dividend. According to the above formula, g = 20% x (5/100) = 1%.

The basic assumption of this model is that money you put back into the company grows at the same rate as ROE, or the net income relative S/E. But is this realistic at all? Does money you put back into the company have any predictive value with respects to net income relative to S/E?