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Population density

Reine asked on Jun 05, 2018

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.


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An (Jack)
updated his answer on Jun 06, 2018
Google Strategy Manager | Ex- BCG Consultant | References Available
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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!


Thank you An. How will you then calculate the area? — Reine on Jun 06, 2018

I think one safe way is to use your own city as a proxy - I live in San Francisco which is 50 square miles with population of 800K. So a city of 2m population will be 2.5 x 50 sqr miles = ~125 sqr miles.. Your population density is 2m / 125 sqr miles = 16K people per sqr mile — An (Jack) on Jun 06, 2018

Awesome. Thank you An — Reine on Jun 06, 2018

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

Hello Hemant. Thank you for answering. How will you calculate the area? — Reine on Jun 06, 2018

Vlad updated his answer on Jun 05, 2018
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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)



Thank you Vlad. How will you then calculate the area? — Reine on Jun 06, 2018

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