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!