# Estimating Return on Re-Invested Capital

I was thinking about how to calculate the return on re-invested capital, i.e. return on retained earnings.

In reality, the retained earnings can be used for a multitude of purposes, and the returns could be obtained fully in a single year, or perhaps spread over a couple of years (e.g. if i retain \$5 per share and re-invested that, the returns from that might come in at different times and amounts over a period of 10 years). How then do you figure out the return on re-invested capital?

Let’s take a not-too-simple and not-too-difficult case. Say each time you retain a certain amount of earnings, you get back cash inflows in equal amounts across a period of 10 years.

In that situation, when you look at the change in earnings from one period to the next, that “change in earnings” is a result of re-invested earnings from 1 year ago, 2 years ago, 3 years ago ……, 10 years ago (more specifically, a part (about one-tenth) of re-invested earnings from 1 year ago, a part (about one-tenth) of re-invested earnings from 2 years ago, etc.). Naturally the re-invested earnings across the different years would be different, which makes things extremely complicated.

To “un-complify” the situation, a simplification is necessary. One simplification is that the different “parts” across the past 10 years, adds up to the full retained earnings of a single year.  Which single year to choose then?

A lousy simplification would then be to use the most recent year before the “change in earnings” — which is what people typically do when they calculate ratios, they simply take the change divided by the base in the previous year, but i doubt that many people actually know the tons of assumptions/simplifications they are making when they do such a calculation.

To improve the calculation, you can do this across multiple years, i.e. calculate the change in earnings between year 1 and year 10, and then divided by the total retained earnings from year 1 to year 9. This should help a little and by using different lengths of time periods, you can see if the results are stable.