This question was a deal breaker

New answer on May 23, 2022
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Hello everyone,

I had an interview yesterday with a well known consulting firm, but I couldnt solve this question and I think I will be rejected because of this:

The question was:

The client is a smartphone retailer, which will experience a retail-store reduction from 40% to 10% (reduction of 75%).

The client has 3 FTE in every store, they are able to close 1 contract per hour, and the store is 10 hours opened (per day) and 300 days open per year (9k contracts closed per year).

How many stores do the client need?

Can you help me with the logic behind this quesiton? I felt there are missing pieces of information,

Kind regards

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Hello Anonymous, thanks for giving the opportunity to help!

You mention the reduction from 40% to 10%, but I am not sure of what measure exactly? Sounds like it is the share of retail store revenues in overall company revenues. If this is the case, then read on.

Some important questions to ask before solving this case:

• How will the overall revenues of the company evolve between now and the future state?
• Will the average contract sold by the retail workers change in value? Will their productivity (no. of contracts per hour) change?
• What is the goal of store closure?

I will assume that the first answer is “the revenues will be flat”, the second is “no and no”, and the third one is “cutting store lease and human costs with minimal revenue impact”.

Here is the argument: if the overall revenues are flat and there is no change in the average contract, it means that there will be 75% contracts fewer to sell per branch on average. However, you cannot just immeditalely respond that you need to close 75% of the stores. It is important to show that you understand the business implications and limitations of the problem and not just solve it as a maths question. You have the following considerations:

1. If you close a store, is there your company's store near enough that can take the closed store's clients without them going to the competitors? In other words, what % of that store's contracts will remain with you company via a different store
2. What is the distribution of the store's performances? Can we close the worst performing stores in terms of sales? Although it sounds like the question assumes all the stores have the same performance, I would at least ask about this
3. What is the situation with the lease/ownership of the stores and with possibility to optimise headcount? E.g., many stores can be in long-term leases and unavailable for renegotiating. Depending on the country, dismissing a worker can be extremely difficult and painful. All of these things can impact how many stores you can close.
4. Can we change the number of workers in the store, the working hours of the store and can we assume the store's performance will remain the same?

As you collect the answers, you will have a better picture of the possible answer. I am giving one example below:

You have told me that all of our stores are performing equally, that all leases can be ended tomorrow and that dismissing workers is easy in this country. You expect that you can close not more than one in three nearby stores, otherwise you expect a loss of business from that region. You have also told me that we cannot accommodate more than 3 agents in a store and we cannot change the store's working hours. Therefore:

Let's say we have 100 stores today that each sells 9000 contracts per year with 3 FTEs. Over time, if we do nothing, we expect each of the stores to only sign 2250 contracts per year, which would require 0.75 FTEs. Without concern for loss of business, we could close 75% of the stores and navigate the full business of the closed three to the remaining one to restore maximum productivity. However, we can only close each two out of three stores. It is clear then that this is the number that we can close: two thirds or 67 stores. It will mean that each remaining store will be underloaded: each remaining store will receive 2*0.75 FTEs workload from closed stores, therefore in the target you will have 2.25 FTEs worth of work per store. This can be mitigated with part-time work schedules for some employees, if possible.

In this scenario, the calculation is not difficult. It is showing that you understand the implications and limitations of the problem that is important to the interviewer. Speaking from experience, since I conducted 50+ 1st and 2nd round interviews for McKinsey.

Hope this helped, don't hesitate to reach out with further questions!

(edited)

So we need close 1/3 of our stores, did I understand it correctly?

There were some distribution channels, like the following: retail stores 40 % online stores 10% door2door 10% others 40% the distribution changed, now its retail 10% online 30% door2door 30% others 30%

Hi Cornelius The exact answer will depend on the information the case giver would give you during the interview as you ask the questions I higlight above. The information you gave in the problem statement alone is not sufficient. You would need to ask the interviewer smart questions to fish out the extra needed information. Above, I hypothesized some concrete answers to such questions. If those are the answers, then the overall answer to the problem would indeed be to close two thirds of the stores. Hope this helps, don't hesitate to reach out for more help or if you want to practice such problems with me.

Thank you!

I'd just like to weigh in here and point out that percentages and proportions are very commonly featured in difficult quantitative questions.  The math itself is not challenging, but it takes good quantitative sense to do it.  So practice these type of questions!

Best,

Allen

Hey there,

The case cannot be solved with the existing info, especially as framed right now.

What is the reduction for ? e.g., 40% to 10%

Looks like a simple case in which the production per store can be quickly calculated (your 9k) and from the other side, the total production needs to be calculated so that the number of stores is derived (total production over production capacity per store)

I'm guessing the 40% to 10% should be for revenues from which we can derive total volume of contracts needed, to then use to get the stores #

The two missing elements for now are (1) the metric that is being reduced from 40 to 10% (2) the baseline of that metric so that we compute the end state

Mario

Hi there,

There is definitely information missing…you needed to ask for it!

There's not enough here for us to go off of. There are a few clarifying questions I would ask. Then I would setup my equation/formula and ask for the missing pieces of data accordingly.

agree with most of the coaches, we are missing info here, maybe you want to share how did you solve it and what additional info you got to get you feedback.

Lucie

To be honest, it was the last question of the case and I couldnt solve it because I was running out of time and the interviewer dont gave me any hints towards the fact, that there are information missing. I asked him several times if we have any absolute number but he denied.

I don’t understand the question. If you tell me the stores have decreased (I assume you mean number of store), and then you ask me how many stores we need (to achieve what? I am assuming returning to the status quo and break even), then the answer would be to rebuild the amount of stores that were lost. This seems too simple and I am probably misunderstanding your question, so if you can explain it I’ll edit my response and try to solve it.

(edited)