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Clara

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5

Big Compounding Estimations

Hi,

I've been looking around for rules to help estimate compound growth for >10% CAGRs.

I know the binomial rule and the rule of 72/114/144/168. Those only work well for small annual growth.

Does anyone know any method to approximate compound growth for large CAGRs for multiple years apart from sequential multiplication?

Hi,

I've been looking around for rules to help estimate compound growth for >10% CAGRs.

I know the binomial rule and the rule of 72/114/144/168. Those only work well for small annual growth.

Does anyone know any method to approximate compound growth for large CAGRs for multiple years apart from sequential multiplication?

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Book a coaching with Clara

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Hello !

Don´t worry, never in my life -as a candidate, coach, professor, etc.- have I seen someone being asked about CAGRs in an oral case.

Cheers,

Clara

Hello !

Don´t worry, never in my life -as a candidate, coach, professor, etc.- have I seen someone being asked about CAGRs in an oral case.

Cheers,

Clara

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Hi there,

You don't need to worry about this with casing!

Learn NPV into perpituity and NPV out 1-2 years (no more than squared).

Any other growth, you will only either have to apply linear growth (i.e. multiply CAGR by years) OR rule of 72.

Hi there,

You don't need to worry about this with casing!

Learn NPV into perpituity and NPV out 1-2 years (no more than squared).

Any other growth, you will only either have to apply linear growth (i.e. multiply CAGR by years) OR rule of 72.

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No sorry, I don't. But tbh I feel the number of cases where that would be needed for more than 2 years out is so limited, that there is little value in spending a lot of time in preparing for that. If you have reached the level of mental math, where you start worrying about such nieche skills, you should focus your energy on other aspects of the case delivery ;)

No sorry, I don't. But tbh I feel the number of cases where that would be needed for more than 2 years out is so limited, that there is little value in spending a lot of time in preparing for that. If you have reached the level of mental math, where you start worrying about such nieche skills, you should focus your energy on other aspects of the case delivery ;)

Well for growth above 10% it's indeed tricky mathematically and there is no easy trick as most approximation fall short once you're not close to zero anymore but let's think about it logically will you.

If i call x the CAGR and n the number of year i consider I have to compute (1+x)^n.
To first order it is roughly equal to 1+n*x and to second order to 1+n*x+n*(n-1)/2*x^2.

Let's go with five years (so n=5).
For a CAGR of 5% by using the first approximation you'll do an error of 2.0%. And an error of 0.1% by using the second one.

For a CAGR of 10% the error will be 6.9% and 0.6%
For a CAGR of 20% it will be 19.6% and 3.5%.

This is perfectly fine to have an error of 3.5%. So if you ran into such a question during an actual interview (only happened to me twice once in a prep case and once in actual interview) just go with the first order approximation and do the second order one once the CAGR is above 10%. This seems to be something you can run into during cases for companies that do a lot of due dill.

And if the interviewer ask what is the error will be (which will never happen) it's easy as it will be on the order of the next leading term.

Well for growth above 10% it's indeed tricky mathematically and there is no easy trick as most approximation fall short once you're not close to zero anymore but let's think about it logically will you.

If i call x the CAGR and n the number of year i consider I have to compute (1+x)^n.
To first order it is roughly equal to 1+n*x and to second order to 1+n*x+n*(n-1)/2*x^2.

Let's go with five years (so n=5).
For a CAGR of 5% by using the first approximation you'll do an error of 2.0%. And an error of 0.1% by using the second one.

For a CAGR of 10% the error will be 6.9% and 0.6%
For a CAGR of 20% it will be 19.6% and 3.5%.

This is perfectly fine to have an error of 3.5%. So if you ran into such a question during an actual interview (only happened to me twice once in a prep case and once in actual interview) just go with the first order approximation and do the second order one once the CAGR is above 10%. This seems to be something you can run into during cases for companies that do a lot of due dill.

And if the interviewer ask what is the error will be (which will never happen) it's easy as it will be on the order of the next leading term.

(edited)

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Hi,

Please take into account that you will never have to do complex maths problems during your interviews.

A lot of people spend tremendous effort on oral maths while the key is to focus on your analytical skills:

  1. your ability to quickly understand the problem, what you are asked to calculate/ analyze
  2. your ability to read different types of graphs and draw relevant insights
  3. your ability to define calculating strategy/ algorithms and execute it
  4. your ability to clearly communicate your reasoning behind the calculations

I suggest that you should invest your time and energy in building this skillset.

Good luck!

Best,

Anton

Hi,

Please take into account that you will never have to do complex maths problems during your interviews.

A lot of people spend tremendous effort on oral maths while the key is to focus on your analytical skills:

  1. your ability to quickly understand the problem, what you are asked to calculate/ analyze
  2. your ability to read different types of graphs and draw relevant insights
  3. your ability to define calculating strategy/ algorithms and execute it
  4. your ability to clearly communicate your reasoning behind the calculations

I suggest that you should invest your time and energy in building this skillset.

Good luck!

Best,

Anton

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