This question was a deal breaker

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)