Uber Strategy Manager | BCG Consultant, Interviewer
Book a coaching

Population density


Hello, how would you solve this case...

Your client is a superstore and they want to open a store in Lagos (any city would do). What is the minimum population density the city should have.

I thought about approaching it by using the following steps:

1. Population density first which is population/area.

2. Calculate the area of the city (honestly struggling with this, will need some help)

3. Then detemine the minimum population needed for the client to Breakeven taking into consideration market penetration, competition, and purchase power.

4. To determine the population to breakeven, I will then have to estimate the cost of the store both fixed and variable costs as well as contribution margin to get the volume that has to be sold.

5. Next step will be to determine the average frequency of purchase/person/month.

6. I should be able to determine how many people on average should come to my store and buy/ month.

7. Making the assumption that the client will have 50% of the 80% or so of the population that will shop in a superstore, we should be able to reach a reasonable answer.

8. Plug it into the initial equation and we should have answer.

I'd love to know how others will solve this.


  • Upvotes
  • Date ascending
  • Date descending
replied on 06/06/2018
Uber Strategy Manager | BCG Consultant, Interviewer

Hey there,

You need to work out the breakeven volume of baskets for the store (including making some assumptions about payback period), and then extrapolate the purchase volume into population (by making some assumptions about conversion rates between the population size and their rate of purchase at the store).

Here is an illustration with some sample numbers

Let breakeven volume of baskets = B

Breakeven is when:

  • Avg price of basket x B = Fixed Costs of Setting Up Store + Variable cost per basket x B
  • Or, B = Fixed Costs / (Avg price per basket - Variable cost per basket)


  • Fixed Cost of Setting up the Store = 10 million
  • Average Price per Basket = $100
  • Average variable cost per Basket = $50

Therefore B = $10m / ($100-$50) = 200,000 baskets to breakeven

Now, assume

  • you need to payback the store in 1 year.
  • on average, each customer of superstore shops 10 times per year there (~once per month)
  • that in this city, 1% of the population will become customers of superstore

Hence, you need

  • 200K baskets per year = 20K customers (each shops there 10 times per year) = 2m population (1% of people in the city will become customers)

Hope that is helpful!


replied on 06/06/2018
Current partner @ Andreessen Horowitz (VC firm). Ex-Mckinsey, ex- strategy guy at Google.

Do it in reverse:

Revenue = price * vol

At break even: total revenue = total costs.

=> Price * x = FC + UVC*x (UVC is unit var cost)

=> x = FC / (Price - UVC)

now you need to assume avg prices for the product and avg UVC. It could also be a blended / weighted avg based on product mix.

Once you have x == no# of "purchases". Now a few things:

- what was this over: 1yr, 2? 10? -- depends on your expectations for returns

- how does this translate to no# of people -- do people buy once a year, twice?

Say people buy from the superstore 12 times per year and we want BEven in 5 yrs.

So, actual population needed to achieve this = x / (12*5) = x/60

Now you have x. Assume an area, and get the pop density.

Vlad replied on 06/05/2018
McKinsey / Accenture / Got all BIG3 offers / More than 300 real MBB cases / Harvard Business School


I would also take into account several macro factors:

  1. Demand seasonality (e.g. tourists, climate, etc)
  2. Roads and infrastructure availability (public transportation, cars, etc)
  3. Consumer salaries and willingness to spend (since it drives frequency)



Related BootCamp article(s)

Market Sizing

Market Sizing Cases are used to test your quantitative and reasoning skills. The interviewer evaluates your structure, numbers-handling and business sense.

14 Comment(s)

Important Facts

It's essential to know some key figures regarding geographies, population, economies for your case interviews. We summarized them for you here.

9 Comment(s)

Related case(s)

Your client, large automotive OEM WyCar, has developed its first fully electric vehicle (EV) and introduced it as a pilot on the Austrian market last year. However, sales have been far below the expected numbers. The management has engaged you to support them in understanding the reasons and advise ... Open whole case


Solved 34.3k times
4.5 5 991
| Rating: (4.5 / 5.0) |

Nutripremium is a very well-known premium nutrition food company in Europe (€1 billion revenue last year). It is based in Spain and has an excellent market share not only in its home country but also in Portugal, France, Italy and Germany. Nutripremium has two main lines of products: Vitam ... Open whole case

Children vaccine

Solved 31.8k times
4.4 5 923
| Rating: (4.4 / 5.0) |

Beyer, one of the biggest pharmaceutical companies in the world, just invented a very reliable vaccine against Chickenpox, a disease that affects children in the age from 2 to 16 years. Beyer came to you wondering what their potential sales in Europe in the first year would be if they launched th ... Open whole case

Gas station

Solved 22.8k times
4.3 5 439
| Rating: (4.3 / 5.0) |

How many gas stations are there in Paris? Suppose a friend of yours wants to open a gas station in Paris. What aspects should he consider? Open whole case

Airport taxi

Solved 14.1k times
4.7 5 1168
| Rating: (4.7 / 5.0)

Dubai Airport has decided to counter the chaos in the airport taxi service by commencing a bidding process to assign airport taxi services to 3 operators only. After years of cheating passengers, black-market drivers and unlicensed cabs, the airport has had enough of the problems and is now taking a ... Open whole case