Published: May 30, 2017

Welcome back to our series on preparing for the mental math portion of your consulting case interviews! Previously, we specifically looked at how to handle multiplication and division with large numbers and break even analysis. In this post, we’re going to do a deeper dive on growth rates.

A little good news before we get started, if you remember the Placeholders technique from Part I, you’ll be able to utilize that for growth rate problems, as well as market sizing, which I'll cover in an upcoming post. Which is great—it means that your toolbox for solving mental math problems is starting to compound.

Now, let’s jump into the problem type at hand:

**Calculating Growth Rates**

Consulting cases are full of various types of growth rate calculations. Revenue growth rates. Cost growth rates. Consultants love to drill candidates on CAGRs, compounded annual growth rates.

Why?

Well, it’s not because they’re going out of their way to be mean or tough and just want to see candidates sweat for the sport of it, but rather because CAGRs show up constantly on the job itself.

Let’s look at a sample problem:

*Your client has revenues of $500,000,000 annually and is currently growing at three percent annually. If that growth rate remains constant, how much will annual revenues be five years from now?*

The obvious way to solve this problem is start calculating how much revenue will grow each year manually and then repeating the process for five years. While this will lead to the correct answer, there are three challenges with this:

- You’ll have to perform a lot of calculations, which will eat up precious interview time
- The likelihood of an error will compound with each additional calculation
- By aiming for an exact answer, you’re doing more work than necessary, since most consulting scenarios typically only need an accurate estimate.

You should ask yourself: is there a better way to solve this problem and get an accurate estimate?

The answer: Yes!

The key technique to keep in mind is to precompute all the growth and then apply it in a lump sum instead of doing each growth calculation serially (i.e. one after the other). In this case, we’d take a three percent CAGR and multiply it times five, since we want to see growth after five years, which gives us 15%. Calculating 15% of $500M (again, using placeholder techniques!) gives us $75M, so our answer is going to be around $575M.

Now, one drawback to this approach is that it ignores the compounding effect. So, a final touch is to acknowledge the number is an underestimate and, if you want, you can even correct slightly for it. For example, knowing we left out the impact of compounding we could round up to $580M. As it turns out, the exact answer is $579.6M. Thus, this approach provides us with a great estimate that was significantly quicker to calculate!

One final word of caution: if you’re working with large CAGRs, say 10% or larger, the compounding effect becomes significantly harder to estimate for. For example, say we tackle the same exact problem as above but the CAGR is 10%. Our approach will yield a growth rate of 50% and an answer of $750M, before rounding up. However, the exact answer is $805.2M. While our estimate is still pretty good, it’s important to be cognizant that the amount the estimate undershoots will go up as compounding gets higher.

As I mentioned, my next post will tackle market sizing tips, so be sure to check back in for those. Until then, good luck with your interview preparation!

*Kenton Kivestu is the Founder and CEO of RocketBlocks, an online platform that helps students prepare for case interviews. Prior to RocketBlocks, he worked as a strategy consultant in BCG's San Francisco Office, launched online ad platforms at Google and led the Zynga mobile poker franchise. He has successfully navigated hundreds of case interviews himself and believes that the case interview is an important recruiting tool that helps simulate the on the job experience. He started RocketBlocks to help candidates hone their analytical skills so they can put their best foot forward on interview day. Kenton graduated as an Echols Scholar with distinction from the University of Virginia and holds an MBA from the Tuck School of Business at Dartmouth. *

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