Key Concept in Calculating Returns on the Investments -> CAGR

What Does Compound Annual Growth Rate – CAGR Mean?

The Compounded Annual Growth Rate (CAGR) is the rate at which something (e.g., Revenues, Savings, Population) grows over a period of years, taking into account the effect of Annual Compounding.

A Compound is composed of two or more parts. In the case of compound growth, the two parts are Principal and the Amount of change in the principal over a certain time period, which is called “interest” in some circumstances.

This is sometimes called “growth on growth” because it measures periodic growth of a value, that is itself growing periodically. If we are calculating the annual compound growth rate, then each year the new basis, is the previous basis plus the growth over the previous period.

Thus, a Compound Annual Growth Rate (CAGR) measures the rate of return for an investment — such as a Mutual Fund or Bond — over an Investment period or Horizon, such as 5 or 10 years.

The CAGR is also called a “Smoothed” rate of return, because it measures the growth of an investment, as if , it had grown at a steady rate on an annually compounded basis.

It’s Significance & Importance :

In looking at an Investment, the CAGR is a measure that is commonly used to show how quickly the investment, or certain aspects of it, such as gross sales, have been growing.

Investment analysts often look at 5 year periods to discern a trend. A specific company’s rate of growth is often then compared with that of competitors or with the industry as a whole.

For example, Company A had a revenue CAGR of 8.5% over the past 5 years. One of its direct competitors has grown by 9.4% and two others have seen slower growth. The industry as a whole has seen revenues grow by 7.3% per year, compounded annually.

On this basis, one would conclude that Company A is doing well and in fact might be gaining market share. Of course, other factors need to be looked at, such as debt and the outlook for the industry.

                                            Formula for Calculating CAGR :

The formula for Compound Annual Growth Rate is:

((Ending Value/Beginning Value)^(1/# of Years))-1

There are five variables in a compound growth rate calculation:

Beginning value
Ending value
Length of time between the values
Periodic scale (days?, months? years?)
Periodic rate of change

You need to know four of these values to make the calculation of the fifth.

For example, Company A had revenues of $1.35 billion in 2002. Revenues grew by a CAGR of 8.5% through 2007, a period of five years. We know the beginning value, the length of time, the periodic scale (years) and the periodic rate of change. Now we can determine what the revenue was in 2007.

CAGR (Compounded Annual Growth Rate) is growth rate annualized over a period of time. This is not actual growth year on year, but it shows the annualized growth, if the same Investment would have experienced a steady growth rate over the period. Let’s understand it with an example:

Year ->                                                                       0              1            2            3                 4               5                    6

Growth Rate (%)  ->                                                          20         -8           11               -5             35                   5

Value of Investment (Principal) ->    100       120    110.4      122.54     116.42    157.16       165.02

CAGR will be calculated based on the evidence that an Investment of Rs 100 turned out to be Rs 165.02 in 6 Years.
CAGR will be (165.02/100)^(1/6)-1 = 0.0871=8.71%

1 More Example :

Say the sales of a Company 4 years back was 100. Today, after 4 years, it is 200. A simple conclusion is that sales has increases by 100% in 4 years. But does it mean that it has increased by 25% each year?

That would not be correct, as simply dividing 100% by 4 doesn’t take into consideration the compounding effect.

So, to find out the per year growth rate of a company, we use the compound interest formula.

A = P * ( ( 1 + r ) ^ n )   Same as above formula, but in a Simplified Notation for better Understanding

Where
A = Final Amount
P = Principal amount
r = Rate of interest, expressed in %
n = Number of years

In our example,

A = 200
P = 100
r = The annual growth rate (that we want to find out)
n = 4 years

From this formula, we find out that r is around 19%.

How do we interpret this?

It means that the average growth of the company over these 4 years, taking into account the impact of compounding, is 19%.

In the first year, the company grew from 100 to 119. In the second year, it grew 119 to 142. In the third year, it grew by 19% from 142 to 168.5, and in the fourth year, it grew from 168.5 to 200.

This principle is very important to understand, because it is used at many places.

For example, it is looked at while examining at returns generated by mutual funds (MFs). Whenever one sees returns for more than 1 year, they are expressed in terms of CAGR. If they are not expressed in CAGR terms, the returns are not accurate!

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