Question about the math in a practice question.

Math problem practice
New answer on Mar 23, 2020
4 Answers
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Collin asked on Mar 17, 2020

Figured this out: Need to read more carefully.

Hello All,

I am a PhD outside of the business field so maybe I am missing something. I was doing some of the practice questions on this site and came across a question that I belive is incorrect. The question is: If the profit margin of the company in 2013 was 15%, what was the total revenue in the period?​

In case the attached image does not post the total costs of the company in 2013 was $544 million and the solution provided is:

Solution:

Total expenditure of the company in 2013 = $544.44 mn

Profit percentage = 15%

Revenue = 115% of costs = $640 mn

544.44 / 0.85 = 640 mn

However, $544 million x 1.15 is actually $626 million, an answer that was provided as an option but said to be wrong. Is it not correct to get the costs, figure out 15% of the costs, and then add that to the costs to determine the total revenue?

(edited)

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Marcello
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replied on Mar 17, 2020
FREE Coaching tailoring | Active Associate @MonitorDeloitte | Interviewer @Monitor@Altran

Hi Collin!

Hope you are well.

The solution 640 mn is correct. Let me explain:

If something has 15% margin it means that Margin / Sales = 15%

Therefore (Sales - Cost) / Sales = 15%

Also, Cost = (100%-15%)*Sales

Thus, if you know that Cost = 544mn, the equation you want to solve is:

544 = (100%-15%)*Sales; Sales = 544 / 85%; Sales = 640 mn

This way you can validate also that 544 / 640 = 85%; which leads to 15% Margin as you were told on the question.

In the response you show you are calculating an increment which is not correct:

544 / 626 = ~87%, which leads to a Margin of ~13%, which is not correct.

Is then clear? Basically you need to take into account that Margin is part of the sales, not an increment.

Let me know if you need something else!

Regards

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Collin on Mar 17, 2020

Hey Marcello! Thanks for pointing out that the margin is 15%. I read it as the revenue was 15% higher than the costs but clearly the revenues and margins are not going to be the same. Thanks!

(edited)

Francesco
Expert
Content Creator
replied on Mar 18, 2020
#1 Expert for Coaching Sessions (3.700+) | 1.300+ Reviews with 100% Recommendation Rate | Ex BCG | 8+ Years of Coaching

Hi Collin,

the solution you reported has a mistake, as revenues are not 115% of the costs.

Given the information you provided, the formula to apply is the following:

(R-C)/R=15%

<->(R-544.44)/R=15%

<->(R-544.44)=0.15R

<->0.85R=544.44

<->R=544.44/0.85=640

Hope this helps,

Francesco

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Antonello
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replied on Mar 23, 2020
McKinsey | MBA professor for consulting interviews

Hi, 15% is the margin.

Best,
Antonello

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Clara
Expert
Content Creator
updated an answer on Mar 18, 2020
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

In a nutshell: your mistake lays with the margin definition. 15% margin means that margin divided into sales is 15%

Cheers,

Clara.

(edited)

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Marcello gave the best answer

Marcello

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