Growth Rate

[Native]

Hello: Apologizes for this is probably more of a math question, but
since this is such a great group wanted to try.

Here is my issue. I'm performing a growth rate calculation and then
applying that growth to project a full-year estimate. Everything looks
good. However, if I try to add up the parts, I get a different answer
than if I do the calculation against the whole. Any thoughts?

Example Data Below:

Neighborhood A
Year 1 105YTD 245Full-Year
Year 2 120 ?
YTD Growth = (120/105)-1 = 14%
Applying the 14% to 245 I get 280 for a full-year estimate.

Neighborhood B
Year 1 73YTD 197Full-Year
Year 2 112 ?
YTD Growth (112/73)-1=53%
Applying the 53% I get a full-year estimate of 302

TOTAL
Year 1 178YTD 442
Year 2 232 ?
YTD Growth (232/178)-1=30%
Applying the 30% to 442 I get 575.

My issue is 280 + 302 does not equal 575. Any thoughts?

 

[Bernard Liengme]

It's all math! The A data increased at 14%, the B at 53%
Since they involve different starting amounts, you cannot use the sum of the
two to compute the total rate of combined amounts.

 

[joeu2004]

Neighborhood A
Year 1 105YTD 245Full-Year
Year 2 120 ?
YTD Growth = (120/105)-1 = 14%
Applying the 14% to 245 I get 280 for a full-year estimate.

Neighborhood B
Year 1 73YTD 197Full-Year
Year 2 112 ?
YTD Growth (112/73)-1=53%
Applying the 53% I get a full-year estimate of 302

TOTAL
Year 1 178YTD 442
Year 2 232 ?
YTD Growth (232/178)-1=30%
Applying the 30% to 442 I get 575.

My issue is 280 + 302 does not equal 575. Any thoughts?

You want to solve for z in the following formula:

A*x + B*y = (A+B)*z

z =(A*x + B*y) / (A + B)

where A=245, B=197, x=120/105 and y=112/73.

In other words, z, the growth rate for the whole, is the weighted
average of the growth rates of the parts. By the way, in this case,
you need to compute z to at least one decimal place (i.e. 31.7%) in
order to get the correct integer answer, namely 582.

As to why your approach does not work, you are assuming:

A*x1/x0 + B*y1/y0 = (A+B)*(x1+y1)/(x0+y0)

= A*(x1+y1)/(x0+y0) + B*(x1+y1)/(x0+y0)

where x1=120, x0=105, y1=112, y0=73.

In that form, hopefully it is obvious that that would be true only if
the two growth rates, x1/x0 and y1/y0, are the same.