Hi guys,

I heard that one of my friends got this question during her interview. How would you approach this: **Calculate the number of divorces/year.**

expert

Expert with best answer

Hi guys,

I heard that one of my friends got this question during her interview. How would you approach this: **Calculate the number of divorces/year.**

3 answers

Hey Ana-Maria,

Let's hear from you first and we can provide feedback!

To start, do you think it makes more sense to do **top-down** (i.e. # of people in the country, # married, divorce rate, and so on) or **bottom-up** (i.e I know x people married, x divorced, in x demographic, and extrapolate)?

Hi Ana,

That is an interesting market sizing exercise. My suggestion would be to always try to solve those cases yourself first. This will help to sharpen your case solving skills (especially breaking down the market sizing and making the right assumptions).

What always helps is after you solved it to sanity check your answer with the actual answer and the assumptions that you have taken.

Back of the envelop approach that I would use is as follows:

**Population**of the country (let's take as example the Netherlands): 17million**Age**at which you can legally get married: 18+- Since average life expectancy is ¬80, we can assume that 25% of the Dutch population is not eglible (4.25million)
- What would probably give you bonus points is explaining that your answer is a simplification because in reality it will depend on how fast the population is aging e.g. in the Netherlands we have an aging population with relatively low number of children per household and late marriages therefore less then 25% (let's say ¬22%), while in fast growing countries like Turkey you have a lot younger demographic break-down (due to more children per household / earlier marriage), which would mean more than 25% (let's say ¬28%) with the same life expectancy. However, given it is easier to work with rounded number my recommendation is to highlight such assumptions, but indicate that you will work with the 25% for simplicity of the calculations.

**People that won't get married**(probably need to make an assmption about what % of people never get married, especially in the Netherlands some people don't get married, or there might be other reasons such as health reasons, religious etc): 5-10% of the population that is left which is 0.5-1mm- Another important factor is the
**age at which people get married**, which is overall probably around 30 years, while in the Netherlands probably slightly later let's assume 35: Therefore on average people between 18-35 are not yet married, which is another 3.5million people not yet married - In total you will probably have 8-9 million not married while 8-9 that were once married. Important to then understand the potential categories i.e. married, divorced, widowed. This will allow you to estimate some kind of % of people that get divorced. Let's say 1/8 then you have approximately 1million people divorced. 6/8 still married, which is 6million married. 1/8 widowed.
- Not that I did not even look into
**multiple marriages and multiple divorces**, but no need to make the problem larger than it is, but important to highlight that you are aware of such points. - You can then estimate the number of divorces in two ways:
- (1)
**Based on the number of married people**+ number of new marriages - assumption of people of those getting divorced. - (2)
**Based on "renew rate" of divorced people**to keep that at 1million i.e. dividing by 20 years or 30 years, which will give you a range of 33-50k divorces per year

- (1)

Looked up the actual divorce rate, which is between 30-35k in the Netherlands based on the national statistical agencies.

However, it is __ NOT__ about finding the answer it is about how you break-down the problem, the way you think, the assumptions you make and the ease of your math calculations

Thank you Ian and Sadik for the answers. I was thinking also about a different approach: let's say the population of US is 300 mil, life expectancy is 80. That would mean that each year 4 mil people die. We know that the majority of the people that die are married so let's assume 90%*4 mil=3,6 mil are married, this would result in 1,8 mil marriages each year. I assume also a divorce rate of 40%, that would mean that 720k of those marriages would end up in a divorce. This is a simplistic approach not considering remarriages ( that can maybe result in a second divorce), however when I Google the correct answer which is 827k my approach yields a close number :) . — Ana-Maria on May 29, 2019 (edited)

Interesting approach. As indicated in my answer it is not about the actual answer, rather your way of thinking. The key advice I would give is try capture as many relevant elements as you can and add some reasonable assumptions to those. — Sadik Cevik on May 29, 2019

Hi, first of all thank you for elaborating your approach. I'd like to ask about the estimating number of divorces per year using the "renew rate". What's the reasoning behind dividing the 1 million by 20 years or 30 years? I didn't quite get it why it was 20 or 30 years. What does this number represent and where we can derive that number? Thank you in advance! — on Oct 29, 2020 (edited)

Hi Ana,

I would keep it simple. Let's say the population is 80M. Average marriage age is 30 and life expectancy is 80. Average marriage number is 1. Almost all above 30 married at least once. So roughly 50M people are a candidate for divorce or they already divorced. They live 50 years after they marry. Let's say 50% of them will divorce at any year in those 50 years. It means that on average every year 1% (50%/50) of them will divorce. The answer is roughly 1M divorce a year.

Cheers

Serhat