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Break-even units calculation

case math
Neue Antwort am 1. Sept. 2023
7 Antworten
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Anonym A fragte am 23. Feb. 2023

Hi all, 

I used two ways to calculate break-even units and got two different answers! can you help me figure out what went wrong? Thank you!

Our client is a for-profit, specialty college named Chic Cosmetology University (CCU). Founded in 2005, CCU is a program for high school graduates seeking their professional cosmetology license. CCU is currently the market leader for cosmetology education with campuses in ten major metropolitan areas in the US. 

CCU has capital to invest in a new campus and is considering Chicagoland as a location –should they do it?  the investment initial Chicagoland campus cost is $4.5M in initial building costs to renovate its chosen site. These costs can be amortized evenly over a three year period. Assume fixed costs remain flat per year.

How many students will CCU need to break-even in year 1? 

 

Approach 1:  break even units = fixed cost/contributing margin per unit.  fixed cost= 4.8M+1.5M= 6.3M   contributing margin per unit=  15,000(revenue per student) - 8000 (variable cost per student)= 7000. so breakeven units = 6.3M/7000=900

Approach 2:   breakeven units * revenue per student = total costs 

breakeven units*15,000= 4.8M+1.5M+8M, so breakeven units= 953

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Hagen
Experte
Content Creator
antwortete am 24. Feb. 2023
#1 Bain coach | >95% success rate | interviewer for 8+ years | mentor and coach for 7+ years

Hi there,

I would be happy to share my thoughts on it:

  • I feel the whole case study is odd given that if all units are in thousands, then one would have $7m of contribution margin per student, and if one were to ignore the thousands, one would have solely $48k in fixed costs. As such, I would highly advise you to ignore this case study, and maybe the entire case book.
  • Still, I feel you may have misread or overlooked the sentence "assume fixed costs remain flat per year", which means that for this additional investment, there are no fixed costs at all (which seems meaningful given the type of fixed costs). Under the assumption that we ignore the thousands, you would need to solve the formula $1.5m = x * ($15k - $8k) + $0, which would result in ~214 students.

If you would like a more detailed discussion on how to address your specific situation, please don't hesitate to contact me directly.

Best,

Hagen

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Anonym antwortete am 24. Feb. 2023

Hi anonymously,

For breakeven consider all costs, income and discounting. The approach when this happens in an interview is as follows: first come up with your assumption and overall formula, then go through it step by step with the interviewer, then fill the elements with the numbers, and at the end do the combined math. The interviewer can then help you and knows how you are thinking about the question and can see that you are solving it even if the numbers don't work out.  Of course there are other ways, too. But don't just deliver the number answer. Best regards, 

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Jackson
Experte
antwortete am 24. Feb. 2023
BCG| BCG Ambassador On Campus at Kellogg MBA| 50+ mock interviews delivered| Successful placements for McKinsey & BCG

Hello there, 

 

Approach 1 is the corrent way to calculate breakeven unit. 

The reason why your Approach 2 is incorrect is: in the formula, you should also multuply the variable costs with “breakeven units”, since with each addition of breakeven unit your variable costs will increase too. The correct formula should be:

breakeven units*15M= 4.8M+1.5M+(8M*breakeven units), so breakeven units= 0.9 ('000s)

Hope this helps. Let me know if any questions.
 

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Anonym A am 24. Feb. 2023

Thank you so much Jason! Really helpful!

Andi
Experte
antwortete am 26. Feb. 2023
BCG 1st & Final Round interviewer | Personalized prep with >95% success rate | 7yrs coaching | #1 for Experienced Hires

Hi there,

agree with the other coaches: approach 1 is the way to go.
In genreal for BEP calculations, stick to the basics and don't try to re-invent the wheel: 

BE Volume = Fixed Cost / Contribution Margin
Contribution Margin = Price / unit - Var cost / unit. 

All you need to do is to see how the different information maps against that formula and plug in the relevant numbers. As simple as that. As in some examples, the prompt takes into account a specific timeframe, just make sure you account for that.

If you have questions about Finance and Accounting knowledge required to casing, I have a compehensive Cheatsheet that covers all formulae you'll need. 

Feel free to reach out via PM, if you'd like to learn more.

Hope this helps. 


Regards, Andi

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Pedro
Experte
antwortete am 27. Feb. 2023
30% off in April 2024 | Bain | EY-Parthenon | Roland Berger | Market Sizing | DARDEN MBA

It's approach 1, as in 2. you are ignoring the fact that more students also generate more costs. 

You have to multiply the breakeven students times the variable costs on the right side of the equation as well. But if you really think about it, that's exactly what you are doing on 1. (students*contribution margin = students * revenue - students * variable cost).

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Ian
Experte
Content Creator
antwortete am 24. Feb. 2023
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

Hi there,

This one almost got me. Nice work accounting for the “all units in '000s” footnote!

Your approach #1 is the right one. You have to account for the profit per student not the revenue.

When in doubt, check the casebook answer! (Though, admittedly, even those can sometimes be wrong)

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Anonym A am 24. Feb. 2023

I still don't understand why my second approach was wrong. Breakeven means revenue equals cost. Isn't this wrong?

Jackson am 24. Feb. 2023

Hello! I just gave an answer on why your approach 2 is wrong. Let me know if there are further questions!

Clara
Experte
Content Creator
antwortete am 1. Sept. 2023
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

Precisely for the high amount of questions (1) asked by my coachees and students and (2) present in this Q&A, I created the “Economic and Financial concepts for MBB interviews”, recently published in PrepLounge’s shop (https://www.preplounge.com/en/shop/prep-guide/economic_and_financial_concepts_for_mbb_interviews).

After +5 years of candidate coaching and university teaching, and after having seen hundreds of cases, I realized that the economic-related knowledge needed to master case interviews is not much, and not complex. However, you need to know where to focus! Hence, I created the guide that I wish I could have had, summarizing the most important economic and financial concepts needed to solve consulting cases, combining key concepts theorical reviews and a hands-on methodology with examples and ad-hoc practice cases.

It focuses on 4 core topics, divided in chapters (each of them ranked in scale of importance, to help you maximize your time in short preparations):

  • Economic concepts: Profitability equation, Break even, Valuation methods (economic, market and asset), Payback period, NPV and IRR, + 3 practice cases to put it all together in a practical way. 
  • Financial concepts: Balance sheet, Income statement/P&L and Performance ratios (based on sales and based on investment), +1 practice case
  • Market structure & pricing: Market types, Perfect competition markets (demand and supply), Willingness to pay, Pricing approaches, Market segmentation and Price elasticity of demand, +1 practice case
  • Marketing and Customer Acquisition: Sales funnel, Key marketing metrics (CAC and CLV) and Churn, +1 practice case

Feel free to PM me for disccount codes for the guide, and I hope it helps you rock your interviews! 

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Hagen

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