Question

Suppose that a company's annual sales were $1,200,000 in 1999. The annual growth rate of sales from 1999 to 2000 was 16 percent, from 2000 to 2001 it was ?5 percent, and from 2001 to 2002 it was 22 percent. The geometric mean growth rate of sales over this three-year period is calculated as 10.37 percent. Use the geometric mean growth rate and determine the forecasted sales for 2004.

Answer 1

$ 1,965,334

Explanation:

Annual sales of company in 1999 = $ 1,200,000

Geometric mean growth rate = 10.37 % = 0.1037

In order to forecast we have to use the concept of Geometric sequence. The annual sales of company in 1999 constitute the first term of the sequence, so:

`a_(1)=1,200,000`

The growth rate is 10.37% more, this means compared to previous year the growth factor will be

r =1 + 0.1037 = 1.1037

We have to forecast the sales in 2004 which will be the 6th term of the sequence with 1999 being the first term. The general formula for n-th term of the sequence is given as:

`a_(n)=a_(1)(r)^(n-1)`

So, for 6th term or the year 2004, the forecast will be:

`a_(6)=1,200,000(1.1037)^(6-1)\\\\ a_(6)=1,965,334`

Thus, the forecasted sales for 2004 are $ 1,965,334