Investors Extrapolate Historic Growth Towards The Future
In the valuation of a company, investors often extrapolate historic growth towards the future. The reason is that growth in the past is a predictor of a good sector, capable management or a competitively strong position. This is especially the case if this growth remains consistent over time. Uncle Stock offers different ways of extrapolating past growth towards the future, some methods being more sophisticated as others. This article gives some deeper understanding on the more advanced growth calculations Uncle Stock uses to deal with growth.
Growth Calculations In Uncle Stock
To give a first impression on the growth calculations offered by Uncle Stock, take a look at the image taken from the revenue of Apple over past 6 years. We see a lot of growth calculations in the evolution tab, and we will discuss the following three: CAGR, rCAGR and rCAGR 67.
CAGR: Compound Annual Growth Rate
| CAGR | Compound Annual Growth Rate (CAGR), calculated by taking the geometric mean annual growth rate over a multi-year period |
The most basic growth calculation in Uncle Stock is the CAGR (Compound Annual Growth Rate). This growth calculation method is widely used for tracking growth of a financial number (e.g. revenue ) or the return of an asset portfolio that reinvests profits and does not replenish losses. It takes the geometric mean annual growth rate over the past X years. To determine CAGR, one needs a start value, and end value and the amount of time between these values and can be calculated as follows: “To calculate compound annual growth rate, divide the value of an investment at the end of the period in question by its value at the beginning of that period, raise the result to the power of one divided by the period length, and subtract one from the subsequent result.”
By taking CAGR instead of arithmetic mean (just counting the growth rates and divide that sum by the number of points in time), we make sure the effect of compounding gets included. For example if the revenue of a company drops 50 percent between year 1 and year 2 and increases 50 percent between year 2 and year 3, the revenue in year 3 will be lower than the revenue in year 1. The reason is that the principal grows 50 percent in the first period and only half the principal drops 50 percent in the second period. arithmetic growth would give a mean growth of 0 percent in this situation, whereas CAGR would give a negative growth being in line with reality.
But CAGR has some serious disadvantages. The main problem is that it only looks at two values: the start value and the end value. This means that a lot of information gets lost, leading into two main problems with extrapolating CAGR towards the future:
1) What if a boundary point of your measurements is exceptional?
2) Can we come up with a growth estimate that is reliable in case growth numbers deviating a lot from the mean (punishing volatility)?
Both problems caused by CAGR are solved in Uncle Stock by using more advanced measurements of growth: rCAGR and rCAGR 67
rCAGR: Compound Annual Growth Rate Using Regression
| rCAGR | Compound Annual Growth Rate (CAGR) over a maximum multi-year period, calculated using the slope as result of log-linear regression. |
1) What if a boundary point of your measurements is exceptional?
As CAGR only looks at two points, an exceptionality in one of these points would have a huge impact and lead towards wrong conclusions. To solve this issue, Uncle Stock has defined rCAGR, which uses logarithmic linear regression of a financial number. Technically a log linear regression is created by taking the logarithm of all values, drawing the linear regression, and taking the exponent of the slope. As we can only take the logarithm of positive numbers, Uncle Stock makes some transformations to make this algorithm possible. This growth metric can be found by drawing the regression line with the best fit between all the yearly values over a time period. The most important reason for using regression is that it takes into account all the points between the first point and the last point, which protects us from those boundary points being exceptional. We can define rCAGR as the expected yearly growth taking into account all past observantion points. rCAGR equals the slope of the regression that we have created. We have solved the problem of not taking into account all the observations between the first and last one.
rCAGR is a great growth estimate, but it gives no punishment for volatility. It does not benefit companies with a very stable growth over companies that have minor reliability of results.
rCAGR 67: Conservative Compound Annual Growth Rate
| rCAGR 67% | Conservative Compound Annual Growth Rate, based on rCAGR and GSD, with 67% probability to be better. |
| GSD% | Geometric Standard Deviation is a measure of spread of yearly growth numbers (using geometric mean). |
2) Can we come up with a growth estimate that is reliable in case growth numbers deviating a lot from the mean (punishing volatility)?
Most investors try to avoid volatility and even rCAGR does not take this into account. If a company has a growth that fluctuates all the time, it becomes much more dangerous extrapolating this growth towards the future. To deal with this problem, Uncle Stock has introduced rCAGR 67 (Conservative Compound Annual Growth Rate) based on rCAGR, a student T distribution and GSD, with 67% probability to be better.
A student T distribution is chosen over a standard normal distribution because it remain accurate even if only a small sample of input values are available, which is often the case for one financial number on one specific company. For rCAGR 67, Uncle Stock takes the growth rate for which the distribution gives statistically a 67 percent chance of outperforming. This technique is more conservative than rCAGR, as we need that 67 percent chance. The more volatile yearly growth numbers we find, the more conservative rCAGR 67 becomes as the T distribution gets flattened out. That is why I think this is the best way of extrapolating growth into the future.
Acknowledgement
We thank Philip Kurtin for his meaningful input on the creation of these concepts.
If you need additional information on our financial numbers in general, our Glossary could help.
