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## The Gory Details: When is AADGR the same as DGR? 0 comments

When is the Average Annual Dividend Growth Rate (

AADGR) the same as the Dividend Growth Rate (DGR) for the entire time period?In other words, when is:

AVERAGE(divt

_{n}/divt_{n-1}-1;divt

_{n-1}/divt_{n-2}-1;…;

divt

_{0+1}/divt_{0}-1) =(divt

_{n}/divt_{0})^(1/(t_{n}-t_{0}))-1Where divt

_{m}is the dividend payment for time period m.Answer:AVERAGE(a; b; c; d; …; z)

is a shorthand notation for:

(a + b + c + d + … + z)

/ (number_of_terms)

But if the individual terms, a, b, c, …, z are all equal, then:

(a + b + c + d + … + z)

/ (number_of_terms) =

(a + a + a + a + … + a)

/ (number_of_terms)

And

(a + a + a + a + … + a)

/ (number_of_terms) = a

Thus,

divt

_{n}/divt_{n-1}-1 =divt

_{n-1}/divt_{n-2}-1 =… =

divt

_{0+1}/divt_{0}-1 =(divt

_{n}/divt_{0})^(1/(t_{n}-t_{0}))-1Or for any sequential dividend payments, divt

_{m}and divt_{m-1}divt

_{m}/divt_{m-1}-1 =(divt

_{n}/divt_{0}) ^(1/(t_{n}-t_{0})) -1Summary: If the AADGR is composed of a series of exactly equal annual DGRs, then the AADGR for the time period is the same as any individual annual DGR which is also the same as the DGR for the entire time period.Instablogsare blogs which are instantly set up and networked within the Seeking Alpha community. Instablog posts are not selected, edited or screened by Seeking Alpha editors, in contrast to contributors' articles.## Share this Instablog with a colleague

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