# Various ways how to calculate growth rate

Last updated: 11.11.2016

This series provides the basic ways to determine the growth rate of certain variables (e.g. costs, GDP etc.) in the period. The series discusses these methods:

• average annual growth rate (AAGR)
• straight-line growth rate (i.e. % change of final and beginning figure)
• compound annual growth rate (CAGR)
• Gordon growth model

## Growth rate

Growth rate is the rate by which the considered variable (revenues, expenses, dividends, investment, GDP etc.) increase either annually or over the considered period of time. It is usually derived from past data and can be calculated by a number of methods. None of the calculation methods is correct or incorrect, but it is important to know that a presented growth rates does not necessarily need to be fully comparable as the result of using different methods. The calculation models can include:

## Average annual growth rate (AAGR)

Average annual growth rate (AAGR) calculates average annual growth rate from time series based on the formula:

(grow rate during period 1 + grow rate during period 2 + grow rate during period 3 + …………+ grow rate during period n ) / number of periods of grow

## Be careful:

in the denominator is not the number of periods covered but number of periods of grow!

→ 4 periods, but 3 periods of grow

## Example:

Average annual growth rate (AAGR) between 2015 and 2010 is thus calculated as (0,13 + 0,06 + 0,00 + 0,11 + 0,05) / 5 = 0,07 (7%).

AAGR therefore considers also the movements within the considered time series. This may cause problems if the values inside the time range fluctuate. In this case, straight-line growth rate may be more appropriate.

## Straight-line growth rate

Straight-line growth rate (also called as relative change, relative variance, relative difference or % change) method calculates growth rate during the considered periods of time based on the formula:

(ending value – beginning value) / beginning value

## Example:

2-years grow rate between 2012 and 2010 is calculated as (18-15)/15 = 0,2 (20%)

5-years grow rate between 2015 and 2010 is calculated as (21-15)/15 = 0,4 (40%)

Straight-line growth rate method is advantageous when the values inside the time series fluctuate.

The disadvantages may include the facts that it considers just ending and beginning value and therefore can show high growth rates even though the reason for such grow is just due to very low beginning value.

## Compound annual growth rate (CAGR)

Compound annual growth rate (CAGR) is method used to calculate annual grow rate from time series.

The result of CAGR is interpreted as the smoothed annualized growth rate achieved during the considered time horizon. It therefore represents the rate at which the variable would have grown if the rate of growth was constant during the considered period. (40)

## CAGR formula

n = number of periods of grow

## Problems with CAGR

• as it considers just ending and beginning value, CAGR may show high growth rates even if the reason for such grow is just due to very low beginning value
• CAGR assumes that rate of grow was constant during the considered period which is in fact unrealistic

CAGR is often used to calculate annual grow rate of investment (using present value as beginning value and future value as ending value).

## Example

….7%  smoothed annualized grow rate

## Gordon growth model (Dividend discount model)

Gordon growth model (Dividend discount model) uses the assumed relationship of the constantly growing dividend amount received in perpetuity and the share price and is used to (39):

• calculate market value of share (equity) = present value of future dividends

P0 = D1 / (Ke – g)

Ke = (D1/P0) + g

where:

D1 = expected annual dividend per share in year 1 (D1 = D0 * (1 + g))

P0 = ex-dividend share price = market value

g = constant annual growth rate (39)

## Example:

The last dividend per share was € 0,15; current share price is € 0,89; annual growth rate is 3%.

D1 = 0,15 * (1 + 0,03) = 0,1545

Ke = (0,1545 / 0,89) + 0,03 = 0,204 (= 20,4%)

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Used sources:

39. Dividend growth model (online). Citation date: 30.1.2016. Available from www:  https://wiki.treasurers.org/wiki/Dividend_growth_model

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