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CHARLES
on Mar 13, 2025
USA
I want to receive updates regarding this question via email.

Playing with profit levers pt. 2

Would love a faster way to solve the following question (my laborious steps are below):

PackageCo has revenue of $135M, profit of $27M and contribution margin of 60%. The new CEO wants to increase the profit margin to 30% by reducing marketing and sales expenses (part of fixed costs), which currently make up 15% of total costs. How much does the company need to reduce marketing and sales expenses (in %) in order to achieve the new profit margin?

  • Old profit margin = $27M / $135M = 20%
  • Change in PM = New PM - Old PM = 30% - 20% = 10% ==> Q: what can I do with this info?
  • Gross Profit = $135M * 60% = $81M
  • Total Costs = $135M - $27M = $108M
  • VC = $135M - $81M = $54M
  • M&S FC = $108M * 15% = $16.2M = ~$16M
  • Other FC = $38M
  • Target Profit = Revenue * 30% = $40.5M
  • New M&S = Gross Profit - (New Profit + Other FC) = $81M - $40.5M - $38M = $2.5M
  • % Change in M&S = ($2.5M - $16M) / $16M = ~ -$13M / $16M = ~ -81%
    • Quick calc: 13/16 is between 12/16 = 75% and 14/16 = 7/8 = 87.5% ==> Slightly larger than 80%

I'm not seeing the faster way to do this but I'm sure there is. Any help would be greatly appreciated!

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Deleted user
on Mar 14, 2025

Here's a cleaner approach:

Given:

  • Revenue = $135M
  • Current profit margin = 20% = $27M
  • Target profit margin = 30% = $40.5M
  • Contribution margin = 60%
  • M&S = 15% of total costs

Step 1: Calculate the additional profit needed

  • Additional profit = $40.5M - $27M = $13.5M

Step 2: Since contribution margin is fixed, this additional profit must come entirely from reducing M&S expenses.

Step 3: Calculate current M&S expenses

  • Total costs = $135M - $27M = $108M
  • M&S = 15% of $108M = $16.2M

Step 4: Calculate required reduction

  • Required reduction = $13.5M
  • As percentage of current M&S: $13.5M/$16.2M = 83.3%

This approach is faster because it focuses directly on the gap in profit that needs to be closed through M&S reduction.

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1 comment
CHARLES
on Mar 14, 2025
This is great. Thanks so much!
Sebastian
Coach
on Mar 13, 2025
Ex-BCG Principal & Senior Recruiter in Germany | 300+ real recruiting interviews at BCG | Free 15min intro call

Hi Charles, 

below a way to simplify it a bit by omitting some calcs that are not necessary:

Step 1 - Calculate new profit required: $135M x 30% = $40.5M

Step 2 - Calculate change in profit required: $40.5M -$27M = $13.5M

Step 3 - Calculate M&S costs: ($135M - $27M) x 15% = ~$16M

Step 4 - Calculate required reduction in M&S costs: -$13.5M / $16M = ~-85%

Hope that helps. 

Best, 
Sebastian

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CHARLES
on Mar 14, 2025
Super helpful. Thank you!
Pedro
Coach
on Mar 14, 2025
Bain | EY-Parthenon | Former Principal | 1.5h session | 30% discount 1st session

Already some good answers above, just wanted to point out that you don't need the contribution margin information to solve this question.

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Florian
Coach
on Mar 14, 2025
1400 5-star reviews across platforms | 600+ offers | Highest-rated case book on Amazon | Uni lecturer in US, Asia, EU

Hey there,

Think of it this way -> Instead of calculating all intermediate cost elements, you can jump to:

  1. Required cost reduction = Profit increase needed ($13.5m)
  2. Only M&S costs can be cut → Reduce from $16m
  3. % Reduction = $13.5m / $16m ≈ 84%

Cheers,

Florian

11
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