Identify the contribution of various growth rates to overall growth?

SteveRD

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Jan 28, 2015
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Hi,

Please bear with me while I try to articulate my problem!

I am multiplying a number by two growth rates (call these "Factor A" and "Factor B").

I can calculate overall growth, but I was wondering if there is a way to calculate the average contribution of each factor to the overall growth? In other words, I would like to say "$x worth of growth was due to Factor A and $y worth of growth was due to Factor B."

To give a concrete example, say my principle amount is $1000.

At the end of the year, this amount is increased by two growth factors:
Growth Factor A = 5%
Growth Factor B = 10%

These factors apply simultaneously. So the total value after applying these two growth factors is = $1155, i.e. $1000 x (1.05) x (1.10). This gives total growth of $155.

The issue is that the contribution of each Growth Factor (which I would like to identify) depends on the order in which you calculate it. So, for example:

Impact of A before B= $50
Impact of A after B = $55

Impact of B before A = $100
Impact of B after A = $105

One option is to take the average contribution under either scenario. In this case, the average contribution of Factor A would be $52.50 and the average contribution of Factor B would be $102.50, which sums to the total growth of $155.

My question is: is there a general formula that could be used to identify the share of growth attributable to different growth factors? Here I have used two growth factors, but I would like to generalise this to n growth factors.

I hope this makes sense, and thank you so much for taking the time to read my question!

Steve
 
u = rate1 (.05)
v = rate2 (.10)
k = invested (1000)
a = rate1 portion(?)
b = rate2 portion(?)

General case formula:
a = cu / (u+v)
b = c - a
where c = k(1 + u)(1 + v) - k

For above example (your problem):
c will = 155
a will = 51.67
b will = 103.33

Denis,

Great, thank you! I think that will be a very good approach. Many thanks for your time,

Steve
 
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