Calculationformula
Annualaveragegrowthrate=[Ntimesundertherootsign(lastyear/firstyear)]-1,N=numberofyears-1,thecalculatedresultcanonlybeappliedtothefirstyearasthelastyear,ifthemiddleyeariscalculated,itisnotequaltotheoriginalvalue.
Thatism=.WhereBisthelastyearandAisthefirstyear.Infact,considerB=A(1+m)n,thenitisaprocessofsolvingm.
Formulaexplanation
Thecurrentperiod/previousNyears
Itshouldbetheendofthecurrentyear/previousNyears,where,beforeTheendofyearNreferstotheendoftheNthyearfromthebottomofthecurrentyear.Forexample,tocalculatethefour-yearassetgrowthrateattheendof2005,thecalculationperiodshouldbe2005,2004,2003,and2002,buttheendofthefirstfouryearsshouldbe2001Theendoftheyear.ThebracketscalculatethecomprehensivegrowthindexforNyears,notthegrowthrate.
^{1/(n-1)}
isthesquarerootoftheN-yeartotalassetgrowthindexinparentheses,thatis,indexaveraging.BecausethevalueinbracketscontainsthecumulativegrowthofNyears,whichisequivalenttocompoundinterestcalculation,itisnecessarytosquareandaverage.ItshouldbenotedthatthenumberofsquarerootsshouldbeN,notN-1,unlesstheendofthepreviousNyearsischangedtothebeginningofthepreviousNyears.Inshort,thenumberofsquarerootsmustmatchthenumberofperiodscorrespondingtothecomprehensivegrowthindexinparentheses.Howtodefinetheformulacanbeunderstoodbytheuser.
[()^1/(n-1)]-1
Subtract1becausethecomprehensivegrowthindexcalculatedinbracketsincludesthebaseperiodAfterthesquarerootistheaverageannualgrowthindex,itisstillgreaterthan1,andwhatweneedistheaverageannualgrowthrate,thatis,onlytheincrementalpartisinspected.Therefore,1mustberemovedfromthebaseperiod,so1mustbesubtracted.