Question

Find both the arithmetic growth rate and the geometric growth rate of the dividends for Brantley's Service Centers.

 What is the arithmetic growth rate of the dividends for Brantley's Service Centers?

Answer 1

Let dividend in year n be denoted by D_n

Growth in dividend = (D_n - D_n-1)/D_n-1

Let us first find the growth rate for each year -

Year(n)	Dividend(Dn)	Growth Rate (gn)
2001	1.48	-
2002	2.38	0.6081
2003	3.09	0.2983
2004	4.21	0.3625
2005	5.61	0.3325
2006	6.94	0.2371
2007	7.29	0.0504
2008	8.04	0.1029
2009	7.72	-0.0398
2010	7.49	-0.0298
	Average	0.2136

Arithmetic Growth rate = average growth rate = 0.2136 = 21.36%

Geometric Growth Rate = [(1+g₁)(1+g₂).....(1+g_n)]^1/n - 1
= [(1+0.6081)(1+0.2983)(1+0.3625)(1+0.3325)(1+0.2371)(1+0.0504)(1+0.1029)(1-0.0398)(1-0.0298)]^1/9 - 1
= 0.1974 = 19.74%