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 $155.
My question is: is there a general formula that could be used to identify the share of growth attributable to different growth factors? Here I have used two growth factors, but I would like to generalise this to n growth factors.
I hope this makes sense, and thank you so much for taking the time to read my question!
Steve
Please bear with me while I try to articulate my problem!
I am multiplying a number by two growth rates (call these "Factor A" and "Factor B").
I can calculate overall growth, but I was wondering if there is a way to calculate the average contribution of each factor to the overall growth? In other words, I would like to say "$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