CAGR Growth Rate Formula

[antonyice2]

Hello experts,

I need some help in finding solution to below problem.This question is basically about finding CAGR growth rates.

For example lets say that price of an asset was 100$ in Year 2012 & its price was appreciated to 1000$ in 3 years time ie by 2015.So the CAGR rate for asset's price appreciation was 115.44% in 3 years.Now Lets assume items if X,Y & Z are the factors influencing the price appreciation or depreciation of the asset.

That is Asset Price formula is , Price = X * Y * Z

In 2012 Value of X,Y & Z are as given - X = 10 Y = 5 & Z = 2

So in 2012 - Asset Price = 10*5*2 = 100$

In 2015 Value of X,Y & Z are as given - X = 15 Y = 16.66 & Z = 4

So in 2012 - Asset Price = 15*16.66*4 = 1000$

I need some formula which I can use to decide how much CAGR growth is required for each components X,Y & Z for the asset price to move from 100$ to 1000$.I mean is there a formula I can use to find out how much CAGR growth each component X,Y & Z is required to collectively grow at 115.44%.

 

[Ishuda]

Hello experts,

I need some help in finding solution to below problem.This question is basically about finding CAGR growth rates.

For example lets say that price of an asset was 100$ in Year 2012 & its price was appreciated to 1000$ in 3 years time ie by 2015.So the CAGR rate for asset's price appreciation was 115.44% in 3 years.Now Lets assume items if X,Y & Z are the factors influencing the price appreciation or depreciation of the asset.

That is Asset Price formula is , Price = X * Y * Z

In 2012 Value of X,Y & Z are as given - X = 10 Y = 5 & Z = 2

So in 2012 - Asset Price = 10*5*2 = 100$

In 2015 Value of X,Y & Z are as given - X = 15 Y = 16.66 & Z = 4

So in 2012 - Asset Price = 15*16.66*4 = 1000$

I need some formula which I can use to decide how much CAGR growth is required for each components X,Y & Z for the asset price to move from 100$ to 1000$.I mean is there a formula I can use to find out how much CAGR growth each component X,Y & Z is required to collectively grow at 115.44%.

First, the red 115.44% above is an 'interest rate', not the appreciation percentage which is 1000/100=10=1000%

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

HINT: Do you know what the Future Value formula is? For example suppose you had a present amount PV [=100$ in the case at hand] and an interest rate i per period [the 115.44% in your example]. The rate of growth would be r=1+i/100 [=2.1544]. The future value FV after n periods for compounded interest [3 in your case] would be
FV = PV * rⁿ
So you would have
1000 = 100 * 2.1544^3
which is close. Using 115.443469% would get you even closer. In any case, can you see how to solve for r if you are given FV, PV, and n? Does this tell you anything about the relationship between X, Y, and Z.