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Playing with profit levers

I solved the question below but my method seems way too complicated for an actual case. As such, I'm looking for a more intuitive way to solve questions like these. Ideally, I'd get to a place where I can see the levers in my mind's eye (hope that makes sense) so I can put pen to paper in a more confident, less time-consuming manner. This helps me internalize math more efficiently. Any help here would be greatly appreciated!

BoilerCo has revenue of $80M, profit of $20M and contribution margin of 40%. The new CEO wants to make a profit of $30M. How much more volume (%) does he have to sell if prices stay stable?

  1. Revenue (R) = $80M
    1. Profit (P) = $20M
    2. Total Costs (TC) = $80M – $20M = $60M
    3. Contribution Margin Rate (CMR) = 0.4 = CM/R
    4. Contribution Margin (CM) = CMR * R = 0.4 * Revenue = $32M
    5. Variable Costs (VC) = R – CM = $80M - $32M = $48M
    6. Fixed Costs (FC) = TC – VC = $60M – $48M = $12M
    7. New Profit (NP) = $30M = New CM – FC
    8. New CM = NP + FC = $30M + $12M = $42M
    9. New Revenue = New CM/CMR = $42M/0.4 = $105M
    10. % Increase in Volume = % Increase in Revenue, since Price is constant = ($105M - $80M)/$80M = $25M/$80M = 5/16 = 31.25%
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Top answer
Mariana
Coach
edited on Mar 07, 2025
You CAN make it! | xMckinsey | 1.5h session | +200 sessions |Free 15-Minute Call

Hi there!

Good job trying to find a more elegant/efficient way to tackle the problem. Often case math tests this ability.

Let’s see: for every extra $1 in revenue (R), $0.4 is the profit generated (based on the CM). If it is required to increase profits (P) by 10 (target profit - current profit), we should calculate the additional revenue (AR) as: 

  • AR * CM = P
  • AR * 0,4 = 10  —> 10/0.4 =25.
  • AR/R = % increase
  • 25/80 —> we need an increase of 31.25%.

Best,

Mari

on Mar 07, 2025
THAT'S what I'm talking about. Thank you!! Super helpful and intuitive.
Mariana
Coach
on Mar 07, 2025
You CAN make it! | xMckinsey | 1.5h session | +200 sessions |Free 15-Minute Call
My pleasure! 👍
Florian
Coach
on Mar 07, 2025
1400 5-star reviews across platforms | 600+ offers | Highest-rated case book on Amazon | Uni lecturer in US, Asia, EU

Hi Charles,

That thinking is what MBB interviewers are looking for. ;-)

BoilerCo's current contribution margin is 40%, meaning 40% of each additional dollar in revenue contributes to profit. So, to increase profit from $20M to $30M, the company needs an additional $10M in profit.

Since 40% of revenue contributes to profit, the extra revenue required is: 10M/0.40=25M

BoilerCo's current revenue is $80M, so the required percentage increase in volume is: 25M/80M=31.25% 

To make this even easier, in an actual case you would round the numbers (directionally correct and swift > slow and perfectionist):

  • Round 25M to 24M (a multiple of 8) →

    24M/80M=30% 

    (Very close to 31.25%, easier mental math)

  • Round 80M to 75M (a cleaner denominator) →

    25M/75M=33%

    (Slightly overestimates, but very simple)

All the best,

Florian

on Mar 07, 2025
Thank you! Super helpful. Cheers
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