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?
- Revenue (R) = $80M
- Profit (P) = $20M
- Total Costs (TC) = $80M – $20M = $60M
- Contribution Margin Rate (CMR) = 0.4 = CM/R
- Contribution Margin (CM) = CMR * R = 0.4 * Revenue = $32M
- Variable Costs (VC) = R – CM = $80M - $32M = $48M
- Fixed Costs (FC) = TC – VC = $60M – $48M = $12M
- New Profit (NP) = $30M = New CM – FC
- New CM = NP + FC = $30M + $12M = $42M
- New Revenue = New CM/CMR = $42M/0.4 = $105M
- % Increase in Volume = % Increase in Revenue, since Price is constant = ($105M - $80M)/$80M = $25M/$80M = 5/16 = 31.25%