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A math question, please help out!

break-even analysis
New answer on Nov 11, 2023
6 Answers
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Anonymous A asked on Apr 13, 2023

Dear all, I believe this is a very simple math question to all of you, but I still don't know if I did it correctly. Can you help to take a quick look? 

A burger company is planning to do a promotion. They will add free fries to each burger order. They want to know how many extra burgers they need to sell to make this promotion profitable. they currently sell 10,000 burgers each day. burgers are $5 each, and costs are $ 2 each. Fries are $2 each, costs are $0.5 each. 40% burger orders include fries.

This is how I did. 

1. Find out current profit - 10,000*3 + 4000*1.5= 36,000

2. To make the promotion profitable, which means the profit should be higher than 36,000.  Suppose we need to sell additional x burgers.  (10,000+x)*5 - (10,000+x)*2.5= 36,000   x=4400 

so, they should sell 4400 more burgers. 

Is this correct? I know the formula for break even unit is:  breakeven units= fixed cost/contribution margin. In this case, what's the fixed cost? Thanks!

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Hagen
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updated an answer on Apr 13, 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:

  • Yes, your calculation is correct.
  • Generally speaking, with promotions, you first need to understand current profitability level, adjust the profitability formula for the promotion, and solve for the new volume.
  • Lastly, in this situation, while there are no fixed costs indicated, typical fixed costs for a burger company would be rent or depreciation on real estate, personnel costs, depreciation and amortization expenses for equipment, furniture, and fixtures, marketing and advertising costs aso.

If you would like a more detailed discussion on how to best prepare for your upcoming interviews, please don't hesitate to contact me directly.

Best,

Hagen

(edited)

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Cristian
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replied on Apr 13, 2023
#1 rated MBB & McKinsey Coach

Hi there,

Your calculation looks correct. You correctly found the current profit per day and then found the number of extra burgers they need to sell to make the promotion profitable.

In this case, the fixed cost would be the cost of running the burger company, such as rent, salaries, utilities, etc. However, the question doesn't provide this information, so we cannot calculate the exact fixed cost.

If you had the fixed cost information, you could use the formula you mentioned to find the breakeven units:

breakeven units = fixed cost / contribution margin

where the contribution margin is the difference between the price and variable cost per unit. In this case, the contribution margin per burger is $5 - $2 = $3, and the contribution margin per order with fries is $7 - $2.5 = $4.5.

Hope this helps!

Best,

Cristian

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Ian
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replied on Apr 14, 2023
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

Hi,

I’m sorry but this calculation is not correct. You need to subtract out the losses from offering our existing fries sales for free.

You need 6,000 burger sales not 4,400.

Let's break it down step by step.

Find out lost profit from offering fries: 

  1. Current fries profit: 40% of burger orders include fries, so 0.4 * 10,000 = 4,000 orders. Profit from these orders is 4,000 * ($2 - $0.5) = 4,000 * $1.5 = $6,000 lost profits from offering fries for free
  2. Adding fries to existing orders cost: 10,000 *.6 = 6000 orders at a cost of $.5 need to be added to all current orders. That costs us $3,000 in extra costs

To make the promotion profitable, we need to make more than $9,000 in new profits from additional burger sales.

Find out burgers needed

Each new burger sale brings $5 in revenue - $3 burger cost - $.5 fries cost = $1.5 profit per burger.

$9,000 = $1.5 x Number of Burgers

6,000 = Extra Burgers Needed

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Francesco
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replied on Apr 13, 2023
#1 Coach for Sessions (4.500+) | 1.500+ 5-Star Reviews | Proven Success (➡ interviewoffers.com) | Ex BCG | 10Y+ Coaching

Hi there,

1) Is this correct? 

Yes, good job! The steps can be summarized as follows:

1) Calculate current profits

  • Current profits from Burgers: 10k*3 = 30k
  • Current profits from Fries: 4k*1,5 = 6k
  • Total: 36k

2) Calculate burgers to match current profits

  • New margin for burgers: 2.5 (5-2-0,5)
  • Burgers to match current profits: 36k/2.5 = 14.400

3) Calculate the difference

  • Extra burgers = 4.400

2) I know the formula for break even unit is:  breakeven units= fixed cost/contribution margin. In this case, what's the fixed cost? Thanks!

In this case there is no fixed cost. Given you want to do more than current profits (instead of more than fixed cost), the numerator in the formula is the old profit amount.

Best,

Francesco

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Pedro
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replied on Apr 14, 2023
Bain | Roland Berger | EY-Parthenon | Mentoring Approach | 30% off first 10 sessions in May| Market Sizing | DARDEN MBA

There's no fixed cost here.

Current profit: you got it right ($36000)

New margin of the bundle: $2.5

To make $36000 you need to sell $2.5 * X bundles. So

36000 = 2.5X

X = 14400.

That's 4400 more than what you sell right now. 

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Clara
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replied on Nov 11, 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 “Math & Formulas - 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).

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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
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Hagen gave the best answer

Hagen

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