Playing with profit levers

Question

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
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%

Answer 1

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

Answer 2

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

Answer 3

Additional Profit required: 30M - 20M = 10M

New Revenue Required: Additional Profit / Contribution margin = 10M / 40% = 25M

Growth in Revenue: 25M / 80M = 31.25%