Re: growth rates not totalling

Native wrote:
New to this group so any help appreciated.

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:

YTD = year to date

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?

Do it symbolically. Use lower case for YTD, upper for FullYear.

Neighborhood A:
YTD FullYear
Year 1 a1 A1
Year 2 a2 estimated A2 = A1*(a2/a1)

Neighborhood B:
YTD FullYear
Year 1 b1 B1
Year 2 b2 estimated B2 = B1*(b2/b1)

Total:
YTD FullYear
Year 1 t1 = a1+b1 T1 = A1+B1
Year 2 t2 = a2+b2 estimated T2 = T1*t2/t1
= (A1+B1)*((a2+b2)/(a1+b1))

To have est.A2 + est.B2 = est.T2, you must have

A1*(a2/a1) + B1*(b2/b1) = (A1+B1)*((a2+b2)/(a1+b1)).

However, that equation will not hold in general, but only under
special conditions. One such condition is that the FullYear/YTD
ratio for Year 1 be the same in both neighborhoods;
i.e., that A1 = c*a1 and B1 = c*b1 for some constant c.
Then T1 = c(a1+b1), and the critical equation becomes

c*a1*(a2/a1) + c*b1*(b2/b1) = c(a1+b1)*((a2+b2)/(a1+b1)),

which always holds. So one reason that 280 + 302 does not equal 575
is that the FullYear/YTD ratio for Year 1 is not the same in both
neighborhoods.

.

Relevant Pages

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    ... I'm performing a growth rate calculation and then ... applying that growth to project a full-year estimate. ... Neighborhood B ... YTD Growth -1=30% ...
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  • Re: Growth Rate
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