# Residual Income Model => RI growth = Earnings growth ??

I have been lagging on the residual model;

In a double stage valuation model I began addiing the retined earnings for each hight growth period to the begining book value.

This to get the next period expenditures on capital.

It was false I just had to apply the growth rate to the first period RI calculated.

I didn’t wan to put to much time on it, but seems to me implying the RI will grow at the grownth rate of earnings need some assumptions, no?

Thanks a lot for the help,

Not always, no.

In clean surplus accounting, a growing net income would also see the ROE diverging on the stable growth rate going into perpetuity. Keeping, the required rate of return constant, the divergent (and in a perpetuity state, stable) ROE at g would also make the RI grow at g.

So it depends on the time frame you’re looking at. A growing net income would see the ROE and RI approach g.

I was actually wandering the same thing as I got tripped up by this on the CFAI mock… AM #47 asks to calculated terminal value in perpetuity. It is given that there is a 0 growth rate beyond 2023, yet in the soluation we still forecast next years RI by 1+g derived from (ROE*retention ratio) as the numerator for terminal value.

The lesson learned is that even given a zero earnings growth rate, we can still expect RI to grow at (ROE*retention ratio) into perpetuity. Is this correct? A little intuition would be much appreciated.

No it’s not.

If net income doesn’t grow, then where would the additional excess return over the one from the previous period come from?

Think about it, if net income is the same every year, and the retained earnings is growing every year by a certain amount less than net income, then your residual income contracts and eventually reaches zero when the ROE equals the r, at that point, you will even have negative RI’s, and a declining market value for equity.

ROE and g need to converge keeping r the same, for RI to grow at the same pace as net income, in clean surplus accounting.

Thank you sir… makes a lot of sense now