Approach to increasing margin calculation

Question

Can someone please help me with the best logic to approach this question? The answer I am arriving at isn't making sense to me as it is over 100%. A firm with a 90% margin is planning to increase revenue by 10% and decrease cost by 10%, what will its new margin be?

No further information is available *

Answer 1

The answer is ~91.8%, corresponding to ~1.8% margin increase.

Please consider the following, where r is revenue, c is cost, and x is the new margin:

Current: (r - c) / r = 90% → (100 - 10) / 100 = 90%
Proposed: (r*1.1 - c*0.9) / (r*1.1) = x → (100*1.1 - 10*0.9) / (100*1.1) = (110-9) / (110) = 91.8%

Hope this helps!

Answer 2

Hi there,

The best way to solve this kind of problem is to use numerical examples:

Let's assume the following:

Initial Revenue = 100
Initial Cost = 10
Initial Margin = (Revenue - Cost) / Revenue = (100-10)/100 = 90%

This is your current state now the company wants to increase revenues by 10% and reduce costs by 10% so your new values would be the following:

New Revenue = Initial Revenue * 1.1 (or * 110% to show increase of 10%) = 100 *1.1 = 110
New Cost = Initial Cost * 0.9 (or 90% to show decrease of 10%) = 10 * 0.9 = 9
New Margin = (New Revenue - New Cost) / New Revenue = (110 - 9)/110 = ~92% or you can integrate the initial values but since it was already calculated no need to complicate the math

If the firm manages to increase revenues by 10% and decrease costs by 10% it will have an incremental 2% in the margin with a net margin of 92%

Hope this was helpful!

Answer 3

Hi there,

Hani and Mortiz are exactly right!

Make sure that you fully understand the major math concepts (Margin, Markup, ROI, Breakeven, NPV, etc.) and how to apply them in multiple scenarios!