Data processing in the USA: By clicking on "I accept", you also consent, in accordance with article 49 paragraph 1 sentence 1 lit. GDPR, to your data being processed in the USA (by Google LLC, Facebook Inc., LinkedIn Inc., Stripe, Paypal).

expert

Clara

100% Recommendation Rate

55 Meetings

USD 229 / Coaching

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?

• Date ascending
• Date descending

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

Hi there,

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,

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.

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)

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

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

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

Good luck!

Best,

Anton

## Related case(s)

### MBB Final Round Case - Smart Education

Solved 16.5k times
MBB Final Round Case - Smart Education Our client is SmartBridge, a nonprofit educational institution offering face-to-face tutoring services. The client operates in the US. The mission of SmartBridge is to help as many students as possible to complete studies and prevent that they drop from the school system, in particular in disadvantaged areas. The client is considering starting operations for its services in the Chicago area. They hired us to understand if that makes sense. Due to the nonprofit regulation, SmartBridge should operate on its own in the market, without any partnership. How would you help our client?
| Rating: (4.6 / 5.0)

Our client is SmartBridge, a nonprofit educational institution offering face-to-face tutoring services. The client operates in the US. The mission of SmartBridge is to help as many students as possible to complete studies and prevent that they drop from the school system, in particular in disadvant ... Open whole case

### Airline Economics

Solved 16.1k times
Airline Economics We are an airline major operating out of India. We want to increase the number of passengers on all our flights. Could you please calculate the financial return of adding one more passenger per flight?
| Rating: (4.3 / 5.0)

We are an airline major operating out of India. We want to increase the number of passengers on all our flights. Could you please calculate the financial return of adding one more passenger per flight? Open whole case

### REA Reinsurance

Solved 11.8k times
REA Reinsurance Your client, REA, is a reinsurance company. REA recently acquired another reinsurance company (approximatively same size): the choice of this company was notably based on its product portfolio as well as its market presence which appeared complement with REA. However, the acquisition is not well received by the market. The acquisition price is considered too high and the transaction has not been well graded. REA management asks you to evaluate the transaction.
| Rating: (4.1 / 5.0)

Your client, REA, is a reinsurance company. REA recently acquired another reinsurance company (approximatively same size): the choice of this company was notably based on its product portfolio as well as its market presence which appeared complement with REA. However, the acquisition is not well r ... Open whole case

### Cutting Carbs - Divestiture in the Electrical Power Market

Solved 1.5k times
Cutting Carbs - Divestiture in the Electrical Power Market Our client is Energy England, one of northern England’s largest electric utility companies. They were created over the past decade through an aggressive series of mergers of existing utility companies each specializing in a single energy generation source. Recently, the CEO has embarked on an initiative to return to the core of the business. She is looking to increase free cash flow and cash reserves in order to prepare the business for evolving future trends.   The following can be verbally provided to interviewee if asked: Energy England is made up of assets across the energy-generation space. These include coal, gas, nuclear, and wind We are looking to divest from just one of our previous acquisitions (i.e one target is sufficient) There are no specific goals/metrics – the client trusts our judgement
| Rating: (4.3 / 5.0)

Our client is Energy England, one of northern England’s largest electric utility companies. They were created over the past decade through an aggressive series of mergers of existing utility companies each specializing in a single energy generation source. Recently, the CEO has embarked on an initi ... Open whole case

### Bain 1st Round Case – BlissOttica

Solved 1.4k times
Bain 1st Round Case – BlissOttica Our client is a BlissOttica, an Eyewear Manufacturer that is looking to reach a 10% increase in profits. How would you help our client?
| Rating: (4.5 / 5.0)

Our client is a BlissOttica, an Eyewear Manufacturer that is looking to reach a 10% increase in profits. How would you help our client? Open whole case