I'm working on a simple forecast model that uses Cumulative Annual Growth Rate (CAGR) to project future growth, and I've run into an apparent paradox.
The model includes multiple lines of business that change at different rates. I'm ultimately concerned with the projected total of all the lines combined. However I'd also like to project the growth of the individual lines to show how they contribute to the total.
Issue: the sum of individual line projections does not equal the projection of the total.
2011 2012 2013 2014 | CAGR 2015(P) Line A 100 200 300 400 | 59% 634.96 Line B 100 100 200 300 | 44% 432.67 Line C 200 800 1500 2500 | 132% 5,801.99 TOTAL 400 1100 2000 3200 | 100% 6,400.00
CAGR is 2014/2011^(1/3). Projected values 2015(P) are found by multiplying the previous year by 1+CAGR.
2015(P) Line A + Line B + Line C = 6,869.62
2015(P) TOTAL = 3200 * (1 + 100%) = 6400
What accounts for the difference? Is there a way to reconcile the growth rates of the individual lines and the total, or do I just need to pick a level of detail and stick with it? Been banging my head against a wall on this one for a while and any help is appreciated.