Math question during interview. Please help

case math
New answer on Nov 10, 2021
3 Answers
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Anonymous A asked on Nov 10, 2021

Hi everyone,

I encountered this math question during one of my interviews and apparently I got it wrong. I asked the interviewer but she didn't tell me what the correct answer was. It's still bugging me. Can someone please help to solve the question below:

An e-commerce website tries to improve its revenue by sending out recommendations for next purchase based on historical data of a customer's previous purchases. The website sends recommendations to 1.5 million customers at the cost of $2/message. The recommendation system costs $2 million/year to maintain. Each customer spends $600/year on average on the site. The site targets to have $3 in revenue for every $1 cost -→ How many recommendations need to result in 1 purchase to achieve the target above? 

Thanks everyone so much for helping!

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Ian
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Content Creator
replied on Nov 10, 2021
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

Hi there,

I'll just add to the other comments by flagging that this is a classic breakeven! It's super important that you get exposed to all of the different breakeven types and get quite comfortable with setting them up no matter the format :)

Breakeven

Breakeven is tough as there are so many scenarios! Just remember, all breakeven is, is solving for x, where x is some number to figure out how much of something we need.

The formula you create is specific to the case. So, we may say: We make $20 profit per shoe, and we spent $1,000 to create the shoe stand. How many shoes do we need to breakeven?

In this case, the formula is 1,000 = $20 x ====> x = 50 shoes

Understood? Feel free to message if you'd like to go through multiple examples/scenarios!

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Derek
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updated an answer on Nov 10, 2021
BCG & Rocket Internet | Used authenticity to land offers at McK, BCG and Bain - will help you do the same

Interesting question, let's dive in:

 

Target cost per customer per year

A 3:1 revenue-to-cost ratio at an average revenue if $600/year, means the company needs to arrive at a cost of $200/year per customer.

 

Total cost of the personalized messages:

$2*1.5M (variable) + $2M (fixed) = $5M

 

Dividing the total amount with the cost target gives:

$5M/$200 = 25.000 recommendations will have to result in a purchase

 

Note: for this to be true we will need to assume that a converted customer will indeed spend the average $600 in the first year of being a customer and was not a customer already.

(edited)

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Anonymous A on Dec 07, 2021

Hi there, just wondering if this 25k means 25k customers (or purchases) instead of recommendations? Because each customer generates a profit of $200, you need 25k customers to cover the $5M cost. I'm still not sure how to solve this...

Pedro
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replied on Nov 10, 2021
30% off in March 2024 | Bain | EY-Parthenon | Roland Berger | Market Sizing | DARDEN MBA

X is Number of Purchases

Revenue = 3 * Costs

600X  = 3* (2M + 2 * 1.5M)

600 * X = 15M

X = 15M / 600 = 25,000 Purchases

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Ian gave the best answer

Ian

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