ROI / IRR / CAGR - Finance Industry ?

[cinderblock]

Since ROI (simple interest) is return with no reinvestment and CAGR with re-investment and g (<1) being the rate at which more vehicles are added,

CAGR = ROI + ROI*g + ROI*g^2 + ROI*g^3 + .......to infinity
CAGR = ROI (1+g + g^2 + g^3 +.....)

The sum in the bracket is sum of infinite geometric series = 1 / (1-g)

CAGR = ROI / (1-g)

So, CAGR with complete reinvestment corresponding to 50% growth in vehicles is

15 / (1-0.5) = 30

For 30% growth in vehicles,

15 / (1-0.3) = 21.5%

And so on...

 

[aces27]

Since ROI (simple interest) is return with no reinvestment and CAGR with re-investment and g (<1) being the rate at which more vehicles are added,

CAGR = ROI + ROI*g + ROI*g^2 + ROI*g^3 + .......to infinity
CAGR = ROI (1+g + g^2 + g^3 +.....)

The sum in the bracket is sum of infinite geometric series = 1 / (1-g)

CAGR = ROI / (1-g)

So, CAGR with complete reinvestment corresponding to 50% growth in vehicles is

15 / (1-0.5) = 30

For 30% growth in vehicles,

15 / (1-0.3) = 21.5%

And so on...

Alright , So our ROI is going to remain 14% always , is it possible to determine the highest g that can be acheived.
ie all proceeds reinvested , no additional capital from pocket. Other than Initial Investment.

Can we make a list in excel , showing the increase in number of vehicle per month or per year.

 

[UberMachine]

So, as I was reading the previous message by Uber, I just had a mini Eureka moment.

There is a one line answer to your problem: CAGR = ROI / (1-g)

g is the growth rate.

If you are mathematically inclined, I will be happy to derive the equation for you. The proof itself is 3 lines

You could even turn it into a perpetuity
But I have own reservations about the g estimations in practice. If my memory is right, g is way too much during the dotcom boom with infinte growth predictions and people believed it
@aces27
Would implement it in Excel.
But for real business, need to add some senstivity though.