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CAGR Compound Annual Growth Rate (investing)
CAGR Compound Annual Growth Rate
CAGR Casa Grande Ruins National Monument (US National Park Service)
CAGR Cumulative Average Growth Rate (less common)
CAGR Compounded Average Growth Rate
CAGR Colored Angora Goat Registry
CAGR Citizens Against Government Rule

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Sort results: alphabetical | rank ?

Rank Abbr.Meaning
CAGR Compound Annual Growth Rate (investing)
CAGR Compound Annual Growth Rate
CAGR Casa Grande Ruins National Monument (US National Park Service)
CAGR Cumulative Average Growth Rate (less common)
CAGR Compounded Average Growth Rate
CAGR Colored Angora Goat Registry
CAGR Citizens Against Government Rule

Note: We have 4 other definitions for CAGR in our Acronym Attic

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Search for CAGR in Online Dictionary Encyclopedia

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  • CAGMAGS
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  • CAGN
  • CAGNO
  • CAGNY
  • CAGO
  • CAGP
  • CAGPC
  • CAGPO
  • CAGPT
  • CAGRD
  • CAGRE
  • CAGRH
  • CAGRS
  • CAGS
  • CAGSD
  • CAGSE
  • CAGSL
  • CAGSR
  • CAGT
 

Compound annual growth rate

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Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. [1] [2] CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry. [3]

CAGR is equivalent to the more generic exponential growth rate when the exponential growth interval is one year.

Contents

  • 1 Formula
  • 2 Example
  • 3 Applications
  • 4 See also
  • 5 References

Formula[ edit ]





C
A
G
R

(

t

0


,

t

n


)
=


(



V
(

t

n


)


V
(

t

0


)



)



1


t

n




t

0







1


\displaystyle \mathrm CAGR (t_0,t_n)=\left(\frac V(t_n)V(t_0)\right)^\frac 1t_n-t_0-1





  • V
    (

    t

    0


    )


    \displaystyle V(t_0)

     : start value,




    V
    (

    t

    n


    )


    \displaystyle V(t_n)

     : finish value,





    t

    n




    t

    0




    \displaystyle t_n-t_0

     : number of years.

  • Actual or normalized values may be used for calculation as long as they retain the same mathematical proportion.

Example[ edit ]

In this example, we will compute the CAGR over three periods. Assume that the year-end revenues of a business for four years, V(t) in above formula, have been:

Year-End12/31/200412/31/2007
Year-End Revenue9,00013,000






t

n




t

0





\displaystyle t_n-t_0

= 2007 – 2004 = 3

Therefore, to calculate the CAGR of the revenues over the three-year period spanning the “end” of 2004 to the “end” of 2007 is:






C
A
G
R


(
0
,
3
)
=


(


13000
9000


)



1
3




1
=
0.13
=
13
%


\displaystyle \rm CAGR(0,3)=\left(\frac 130009000\right)^\frac 13-1=0.13=13\%

– it’s a smoothed growth rate per year. This rate of growth would take you to the ending value, from the starting value, in the number of years given, if growth had been at the same rate every year. (In reality, growth is seldom constant.)

Verification:

Multiply the initial value (2004 year-end revenue) by (1 + CAGR) three times (because we calculated for 3 years). The product will equal the year-end revenue for 2007. This shows the compound growth rate:




V
(

t

n


)
=
V
(

t

0


)
×
(
1
+


C
A
G
R



)

n




\displaystyle V(t_n)=V(t_0)\times (1+\rm CAGR)^n

For n = 3:




=
V
(

t

0


)
×
(
1
+


C
A
G
R


)
×
(
1
+


C
A
G
R


)
×
(
1
+


C
A
G
R


)


\displaystyle =V(t_0)\times (1+\rm CAGR)\times (1+\rm CAGR)\times (1+\rm CAGR)




=
9000
×
1.1304
×
1.1304
×
1.1304
=
13000


\displaystyle =9000\times 1.1304\times 1.1304\times 1.1304=13000

For comparison:

  • the Arithmetic Mean Return (AMR) would be the sum of annual revenue changes (compared with the previous year) divided by number of years, or:





AMR

=



x
¯



=


1
n





i
=
1


n



x

i


=


1
n


(

x

1


+

+

x

n


)
=



11.11
%
+
10
%
+
8.33
%

3


=
9.81
%
.


\displaystyle \textAMR=\bar x=\frac 1n\sum _i=1^nx_i=\frac 1n(x_1+\cdots +x_n)=\frac 11.11\%+10\%+8.33\%3=9.81\%.

In contrast to CAGR, you cannot obtain




V
(

t

n


)


\displaystyle V(t_n)

by multiplying the initial value,




V
(

t

0


)


\displaystyle V(t_0)

, three times by (1 + AMR) (unless all annual growth rates are the same).

  • the Arithmetic Return (AR) or simple return would be the ending value minus beginning value divided by the beginning value:





AR

=



V
(

t

1


)

V
(

t

0


)


V
(

t

0


)



=



13000

9000

9000


=
44.44
%
.


\displaystyle \textAR=\frac V(t_1)-V(t_0)V(t_0)=\frac 13000-90009000=44.44\%.

Applications[ edit ]

These are some of the common CAGR applications:

  • Calculating and communicating the average returns of investment funds [4]
  • Demonstrating and comparing the performance of investment advisors [4]
  • Comparing the historical returns of stocks with bonds or with a savings account [4]
  • Forecasting future values based on the CAGR of a data series (you find future values by multiplying the last datum of the series by (1 + CAGR) as many times as years required). As every forecasting method, this method has a calculation error associated.
  • Analyzing and communicating the behavior, over a series of years, of different business measures such as sales, market share, costs, customer satisfaction, and performance.

See also[ edit ]

  • Annual growth %
  • Arithmetic mean
  • Average annual return
  • Continuous compounding
  • Geometric mean
  • Exponential growth

References[ edit ]

  1. ^ Mark J. P. Anson; Frank J. Fabozzi; Frank J. Jones (3 December 2010). The Handbook of Traditional and Alternative Investment Vehicles: Investment Characteristics and Strategies . John Wiley & Sons. pp. 489–. ISBN   978-1-118-00869-0 .

  2. ^ root. “Compound Annual Growth Rate (CAGR) Definition | Investopedia” . Investopedia. Retrieved 2016-03-04.
  3. ^ Emily Chan (27 November 2012). Harvard Business School Confidential: Secrets of Success . John Wiley & Sons. pp. 185–. ISBN   978-1-118-58344-9 .
  4. ^ a b c http://www.12manage.com/methods_cagr.html
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