“Average” by definition is a standard or level that is considered to be “typical” or “usual” (https://dictionary.cambridge.org/dictionary/english/average). In statistics, simple average can be computed by summing up a series of values in say, a sample population and divided by the sample size. “Simple Average” is also known as Simple Mean or Arithmetic Mean, written in formula below:
Simple Average is commonly used in analyzing the financials of companies, for eg: in calculating average annual turnover of a company, analysing GP margin, level of staff strength by average no. of employees etc. By “standardizing” and “centralizing” the sales turnover amounts of a group of companies within a specific period of time, it gives readers an overview of how a subject company fares in comparison to its peers, taken on an average basis. One pre-requisite to apply simple average or arithmetic mean is that the data analysed are to be clear of outliers.
Many would have already been aware of limitations of applying simple average method in financial analysis. And one of the common mistakes would be using simple average to interpret a company revenue trend over a period of time.
Exhibit AA shows the revenue trend of Company A over the last 10 years, from 2014 to 2024.
(Exhibit AA)
Assuming that there is no outlier, that is the revenue trend of Company A is in line with that of the industry players; the average annual revenue growth of Company shows an increase of 1.90% on average basis, with median at 1.32%., indicating the location at which highest density/frequency revenue growth rates recorded by Company A over the last 10 years. Readers would therefore interpret that revenue of Company A has been growing on an average rate of 1.90% in the last 10 years.
However, one with a closer look at the table, would realise that revenue of Company A has been trending down from $100mil in 2014 to $79mil to 2024. And this calls to the question – why growth rate computed using simple average method and median suggest otherwise?
This newsletter seeks to explain the use of Geometric Mean as a more appropriate way to analyse the financial information in situation above.
Geometric Mean (G-Mean) is written as follows:
Where:
X = value of an observation
n = number of observations
(One condition for G-Mean to work meaningfully is that all value (X) in each observation must be > 0.)
Referring back to the earlier Exhibit AA – As Company A registered negative revenue growths between 2014 and 2024, to calculate G-Mean, 1 is to be added to nullify these negative growths. This gives G-Mean of revenue growth of Company A at rate of -2.33% (a decline rate) in Exhibit AA.1 below.
(Exhibit AA.1)
Therefore it is interpreted that Company A’s revenue has been trending down at a consistent declining rate at -2.33% from $100 mil in 2014 to $79 mil in 2024. Intuitively, this negative growth rate gives more accurate analysis about Company A’s revenue performance over the last 10 years, as opposed to revenue growth at 1.90% calculated using simple average method. In addition, it is noted that G-Mean in this situation also achieves the same revenue growth rate calculated using CAGR formula with the starting revenue base of $100mil in 2014 and the recent revenue at $79mil in 2024 (Exhibit AA.2).
(Exhibit AA.2)
Another instance where G-Mean is more accurately applied would be on the analysis of return on investment. This is especially so as the formula is capable of dealing with negative returns. See Exhibit BB below - a simple arithmetic average gives investors an impression that the investment portfolio offers a positive annual return of 15.61% . On the other hand, G-Mean indicates a negative investment return of 3.06% given that NAV of the investment has declined from the initial investment sum of $100mil (at t=0) to $78mil (at t=5). In such situation, using simple average method will give misleading analysis about the performance of an investment portfolio.
(Exhibit BB)
Exhibit CC below, illustrates that all three methods (simple average, G-mean and median) appear to work well in handling absolute values | x |, such as revenue, number of headcount etc and where the data observed are independent of each other. Where such conditions established, the information can be analysed and interpreted with small differences.
(Exhibit CC)
Nonetheless, if the data observed are expressed in the form of quantitative relations which involve ratio, rate, a fraction of a base value or in connection with time-series data compounding on the earlier data point - under these circumstances, care should be taken that one may want to consider apply G-Mean (instead of Simple Average or Median) as a more appropriate way to analyze the information to arrive at the right conclusion.
We assist companies to build financial models and review cash flow forecast & projections for potential projects or investments; as for the accounting firms, we assist in the review process on impairment assessment for non-financial assets.
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