Case Interview Questions (Part 1: Estimation)
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This is a follow-up piece to the article I wrote earlier about Case Interview Basics. Part 1 of a three-part series, this article focuses on questions of estimation that are found in case interviews.
Estimation questions cover the guesstimate and market sizing form of questions and are some of the most unnerving (and fun) interview questions you will come across. Simply put, estimation questions are meant to test your composure in the face of a very bizarre line of questioning. Indeed, as a management consultant you may very well have to answer such unusual client questions, and so the interviewer is trying to see whether you will “crack” under the pressure, or maintain your professionalism while answering the question in a logical manner.
In this article I will look at two estimation questions and the approach you may take when answering them:
- Question 1: What is the market size for bowling balls?
- Question 2: How many pounds of rice is consumed in China each day?
- Before we dive right in, let’s familiarize ourselves with the following tips that are helpful when answering questions of estimation:
Do not panic: Recall the interviewer is expecting to get a reaction from you, so the best way to show you’re still very much in control of the interview is to welcome the question and in the process buy some time to collect your thoughts (e.g. “That’s a very interesting question; may I be allowed a few moments to gather my thoughts?”)
- Make (and state) assumptions: As you can imagine, without assumptions the above questions go from just plain bizarre to absolutely ludicrous. As you think through the question, make a list of assumptions you will need to arrive at an answer and state the reasoning behind each assumption to the interviewer.
- Don’t be too specific with your answer: Specificity hints at some highly-scientific calculation; clearly not what you would call an estimate. In fact, being overly-specific with numerical questions will raise the interviewer’s suspicion and invite unnecessary questions challenging your thinking. Generalization / simplification is fine as long as you state your assumption (e.g. dividing an answer by 500 for ease of calculation vs. 490)
Sample Estimation Questions:
Question 1: You have just received a call from a colleague asking you to attend a meeting with a client that that manufactures bowling balls. Not having had the time to do any background research, you wonder what the U.S. market size is for bowling balls. The client meeting is scheduled to begin in 10 minutes.
Approach: A fairly typical market sizing question, you should immediately realize you will need to make assumptions (while keeping the interviewer informed of your thought process). Start broad and slowly narrow your focus using qualifying assumptions.
Bowling ball sales are driven by end-consumers. You could argue that bowling alleys purchase bowling balls as well, however we could assume their demand is captured by the end-consumers. Don’t get too hung up on the accuracy of your assumption as long as it isn’t completely off track. To identify the market size, you can simplify the formula as:
Number of end-consumers x Number of bowling ball purchases
Total number of possible end-consumers is approximately 300 million - the U.S. population. Of this group, you can assume that those between 12 and 50 years of age bowl (about half the population), so that brings your end-consumers to 150 million. Next, estimate that a fifth of this total figure will take the next step and learn to bowl professionally (thus requiring their own bowling ball). This reduces the pool of possible candidates to 30 million. This is the first half of your equation above.
Next, estimate the number of purchases per end-consumer. We can assume each player will go through one initial purchase. Let’s further assume that 3/4 of these end-consumers (3/4 x 30 million = approximately 23 million) will later “upgrade” to another bowling ball. This gives you all the information you need to solve the equation above:
Number of end-consumers x Number of bowling ball purchases
= (30 million x one initial bowling ball purchase) +
(23 million x second bowling ball purchase)
= 53 million
Based on the calculation above, you can estimate the market size for bowling balls in the U.S. as a 53 million ball market. Notice how qualifying assumptions help you go from an initial broad view (300 million end-consumers) to a narrow more focused end-consumer market. Also note how setting up the information gathering with a simple formula at the outset allows you to focus on the data you need without wasting time.
Question 2: How many pounds of rice is consumed in China each day?
Note: Thanks to Tom Spencer for pointing out an error in this post that has now been corrected.
Approach: We will take the same approach as in the question above and 1) put together a simple formula to gather the information, and 2) make assumptions to help narrow the focus.
The daily Chinese rice consumption is dependent on the number and average weight of rice servings consumed each day. So, the formula would be:
Number of daily rice servings x
Average weight of one serving of rice
In order to calculate the number of daily rice servings, let’s look at the total Chinese population size of 1 billion and work from there. Let’s assume that children under the age of three do not have rice and that this demographic constitutes 20% of the population, leaving us with 800 million consumers of rice. Let’s further assume that due to taste preferences, another 20% prefer to substitute rice with some other food staple. This then leaves us with 640 million rice lovers (80% x 800 million).
For simplicity, we will assume the average weight of one serving of rice is 0.5 pounds for lunch and 0.75 pounds at dinner.
This gives you all the information you need to solve the equation above:
Number of daily rice servings x
Average weight of one serving of rice
= (640 million x 0.5 pounds) + (640 million x 0.75 pounds)
= 800 million pounds
Based on the calculation above, you can estimate the daily Chinese rice consumption to be 800 million pounds. Again, note we set up a basic formula and went from broad to narrow using simple assumptions.
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Comments
Tom,
You’re absolutely correct - good catch. The 640 million is the daily number of rice eaters and reducing this by a third doesn’t make sense. I clearly need to proofread my work prior to publishing!
I will make the edit now to reflect the correction.
Zeeshan
Great post. Well done.
Also, are you using wordpress and if so where did you find the theme if you don’t mind me asking ?
ZS,
I was thinking of writing a similar article, nicely done. In Question 2, you make an assumption that gives you a total rice-eating population of 420 million. Query whether this makes sense. If you had said, assume people eat rice in two out of every three days then the assumption works. In your example, I think the total rice-eating population should just be 640 million.
Am I right?
Tom