Playing with profit levers pt. 2

Question

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!

Answer 1

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.

Answer 2

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

Answer 3

Hey there,

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

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

Cheers,

Florian

Answer 4

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