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Case Math Question

case math profitability
New answer on Jan 15, 2024
3 Answers
Anonymous A asked on Jan 14, 2024


I was hoping someone could help me figure out how to solve these problems without using 100 or 1000 as an arbitrary value for revenue. Could you please explain an assumptions in your calculation and how you would go about solving this. 

Problem #1

  • Clients Profitability is (10%)
  • Competitors Costs are 20% less than the client.
  • Competitors Price is 10% less than the client.

-------- What is the competitors Profitability?

Problem #2

Cost Structure of the Client 

  • 70% Raw Materials
  • 20% manufacturing/automation
  • 10% personnel 

------- By how much should raw materials decrease for our client’s profitability to be the same as the competitors?

Thank you! 

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Best answer
replied on Jan 14, 2024
Business Dev. @Multiversity | MBA @ Columbia | Ex-Bain & VC Investor| MSc @ MIT, BSc @ Bocconi

Sure, see below my solution to this, and happy to walk you through some tips on how to solve these kind of cases in a dedicated session together!

In the case provided, we have to reason in terms of unitary revenues & margins as we have no info on competitor volume sales. 

So in detail, I would proceed as follows:

Problem 1:

  1. Define our client's price ad an arbitrary amount (e.g. 100€). From there we know the competitor's price is 10% less, i.e. 90€.
  2. From the case we know our client's margin is 10% (i.e. costs are 90%), therefore unitary costs are 90€. From this we know the competitor's costs are 20% less, i.e. 90€ x (1-20%) = 72€
  3. Now we can compute the competitor's absolute unitary margin as 90€ - 72€ = 18€, and in percentage terms as 18€ / 90€ = 20%


Problem 2:

I assume this is a follow up from problem 1. If this is the case, then you know the client's As is cost structure is as follows:

  • Raw mat. 70% x 90€ = 63€
  • Manufacturing / Autom = 20% x 90€ = 18€
  • Personnel 10% x 90€ = 9€

Keep in mind the case asks us to reach a target profitability equal to our competitor's (i.e. 20%) by reducing Raw mat. costs only. In this case we know that in order to reach a target profitability of 20€, assuming  a constant price at 100€, we need costs to add up to 80€ in total. 
This implies reducing overall costs by 10€ from 90€ (as is) to 80€ (to be) by only saving on raw material.

Therefore raw materials need to drop from 63€ to 53€, equal to a -16% reduction in raw material costs.

Here a downloadable excel for clarity, showing all the passages mentioned above. 

Hope this helps!

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Anonymous A on Jan 14, 2024

Thank you for your response. I was wondering if there would be a way to calculate this without taking an arbitrary price, just using the percentages?

Gabriele on Jan 14, 2024

Yes: notice that I chose 100 as an arbitrary price both because of your initial request and to show you this is possible to do with percentages only: with price = 100 percentages are the same figure (just add % to those numbers and you find the % version of this solution)!

Content Creator
replied on Jan 14, 2024
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

Hi there,

You're overcomplicating this a bit. Why do you want to do this? (and, more importantly, why is this where you're focusing your energy/thinking? Of alllll the other things you need to learn/work on!)

The exact same calculation would occur except you're using 100% (PERCENT) rather than $100.

Regardless, do the approach that is easiest for you (I would argue just picking $100 is going to make life easier for you…% is just weird)

Problem #1

Comp Price = 90%

Client Cost = 90%

Comp Cost = 72%

Comp Profit = 90% - 72% = 18%

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Content Creator
replied on Jan 15, 2024
#1 rated MBB & McKinsey Coach

Hi there!

I see you received really good answers already, so I am dropping an additional resource that you might find helpful. It's a collection of the most common terms that you're likely to come across during case interviews:

Good luck!

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