Ex BCG | MBB Specialist | #1 Expert for meetings done (900+) and recommendation rate (100%)
Book a coaching

Math prep : CAGR without excel - any tips?

Anonymous A

Hi,

How do you approach CAGR calculations during the interview without excel?

Any tips?

Ex1: Your client revenue has grown from 100 to 150 in 5 years, how would you estimate the average annual growth manually (1,5)^(1/5)-1?

Thank you in advance!

  • Upvotes
  • Date ascending
  • Date descending
Francesco replied on 07/29/2017
Ex BCG | MBB Specialist | #1 Expert for meetings done (900+) and recommendation rate (100%)

Hi Anonymous,

basically here you have to compute

(1+x)^a=V

where you don’t know x and where a=5 and V=1,5.

For relative low interest rates and periods, the simpler process for precise results is the following:

1) Calculate what would be the solution with simple interest – in this case, 10%; the real result will always be lower than that

2) Decrease by 1 percentage point – in this case, 9%

3) Apply Taylor series till the third element. To do so, you would have to learn by art the following formula:

1+ax+1/2*a*(a-1)*x^2

Given point 2, x=9%

1+0,45+1/2*5*4*0,09^2=

=1,45+10*0,0081=

=1,531

4) Repeat decreasing till when you find a value below V=1.5

Given x=8%

1+0,4+1/2*5*4*0,08^2=

=1,4+10*0,064=

=1,464

Thus the result is between 8% and 9%.

Hope this helps,

Francesco

Hemant
Expert
replied on 07/28/2017
Ex-Mckinsey, current strategy guy at Google.

Easiest is the rule of 72 (if you divide 72 by the interest rate in question, you'll get the number of years it will take your money to double at that interest rate). So if interest rate were 12%, it'll take 5yrs to double 100 to 200. You are at 150 after 5 years, so, you know that it will take more than 5yrs to double, so the interest rate has to be <12%. At 6%, it'll take 12yrs to double, which means at year 6 it is at least 150, so 6% is too low. You can likely guess it's not exactly 9% because compound interest grows faster with each year, so you can estimate somewhere closer to 8%. If you practice more, you can get better at this.

SR replied on 07/28/2017

Hello,

You can use binomial appriximation but may have to iterate depending; works best with low value of r as noted below.

150/100 = (1+r)^5

Binomial approximation: means, set the right side to 1+ 5*r .... and ignore higher power terms in r for now..

Solving will give you r=0.1. Now this is equivanent to 10% simple ineterest. So compound rate will be smaller than 10%.

Also plug back and check how far off are we. (1.1)^5 = [(1.1*1.1)^2 ] *1.1 = (1.21^2) *1.1

~ 1.44*1.1 = 1.44+.14 = 1.58. Now 158 is pretty close to 150. You can stop here.

OR you can try 9% and see if that works. Now calculate 1.09^5 in bite size steps.

1.09^2 = 1+ 0.18+ 0.0081 ~1.19 ----- use (a+b)^2

Repeat again with (1.19)^2 = 1.38 + 0.19^2 ~ 1.38 + 0.04 ~ 1.40. ------ By now you have 1.09^4 approxiately

Last step 1.4*1.1 = 1.54.

So still higher than 1.5. Repeat with 8%

Regards,

SR

Related BootCamp article(s)

Typical Question Types in Written Tests

Questions among all tests can be categorized in math, GMAT-style, chart reading and brain teaser questions. Each type needs to be approached differently.

4 Comment(s)

Which companies are currently using written tests ?

All major firms like McKinsey, BCG and Bain use tests to assess a candidate's analytical skills. However the design of those tests can differ a lot.

11 Comment(s)

Interviewer-Led vs Candidate-Led cases

Case Interviews can be led by the candidate or by the interviewer: In Candidate-led cases the main challenge is the structure. In Interviewer-led cases the main challenge is to adapt quickly

0 Comment(s)

Guide to Improving Speed in Written Tests such as the PST

Follow these instructions to significantly improve your performance and speed in solving problem solving tests used at McKinsey, BCG and Bain.

4 Comment(s)

Getting Up to Speed

In order to repeatedly demonstrate prerequisite skills under the pressure of a real case interview, you need to learn the basics and practice cases.

2 Comment(s)

Related case(s)

McKinsey Questions

Solved 14.1k times | Rating: (4.6 / 5.0)
Difficulty: Intermediate | Style: Fit interview | Topics: Personal fit

Tell me of a situation where you had an opinion and no one seemed to agree with you. What was your goal when you decided to join university / work / clubs / a sports team? Did you have a goal that you were not able to reach? What did you do? What do you want to be remembered for and how are ... Open whole case

REA Reinsurance

Solved 1.8k times | Rating: (4.3 / 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 we ... Open whole case

AirService

Solved 1.1k times | Rating: (3.7 / 5.0)

Your client AirService is the service provider for a number of airports. The management realized a decrease in profits that is linked to increasing costs. How would you help them? Open whole case