Help with a simple business math question

Hi Joël,

I would be happy to share my thoughts on it:

• This is indeed a rather simple math question. Given profit margin is the ratio of profit to sales, if profit increases by 15% and sales decrease by 25%, the future profit margin will increase by: ((100%+15%)/(100%-25%))-1=(115%/75%)-1=53.33%.

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Best,

Hagen

This is how I do it mentally. Not sure how much this helps, as this is really about having a lot of mental math training and being able to identify patterns and how to quickly transform numbers into other numbers it is easy to work with. Basically I identified that the 25% reduction in sales is the same as a 33.3% increase in margin (1/0.75 - 1 = 33%)… and then that the 15% increase in GP has to be adjusted to the new sales base that is now 33.3% higher…

Anyway, here's the math. Not sure how easy it is to follow, hope the explanation above helps.

Change = (1 + 15%) / (1 - 25%) - 1
= 115% / 75% - 1 
= 115 / 75 - 1
= 133.3% * 115 / 75 - 1
= (133.3% * 115) / 100 - 1
= (133.3% * (100 + 15) / 100 - 1
= (133.3% + 20) / 100 - 1
= 153 / 100 - 1 = 1.533 - 1 = 53.3%
 

Hello Joel,

To calculate the increase in gross profit margin, you can use the following formula:

Gross Profit Margin = (Gross Profit / Sales) x 100%

First, you need to calculate the change in sales and gross profit:

• Change in Sales = Initial Sales x (-25%) = -0.25 x Initial Sales 
• Change in Gross Profit = Initial Gross Profit x (15%) = 0.15 x Initial Gross Profit

Next, you need to calculate the new values for sales and gross profit after the changes:

• New Sales = Initial Sales + Change in Sales = Initial Sales - 0.25 x Initial Sales = 0.75 x Initial Sales 
• New Gross Profit = Initial Gross Profit + Change in Gross Profit = Initial Gross Profit + 0.15 x Initial Gross Profit = 1.15 x Initial Gross Profit

Finally, you can calculate the new gross profit margin:

• New Gross Profit Margin = (New Gross Profit / New Sales) x 100% = (1.15 x Initial Gross Profit) / (0.75 x Initial Sales) x 100% = 1.533 x (Initial Gross Profit / Initial Sales) x 100%

Therefore, the gross profit margin increased by 53.3%.

Hope it helped!

Best,

Victoria

Hi there, 

whenever you feel a question is too abstract to grasp, as might be the case here, consider using smart numbers to simulate.

For example:

1. Establish starting point: just set let's say sales = 100, gross profit = 20 → initial gross margin would be 20%
2. Plug in new scenario: sales down 25% → now 75, gross profit up 15% → now 23; new gross margin is 23/75 = 30.67%
3. Compare old vs new: 30.67% / 20% - 1 = 53.33% increase 
    

Hope this helps.

Cheers, Andi

Hello,

Have a look at the picture below. I assumed Sales = 100 and Gross Profit Margin (GPM) as 10%. After a 25% decrease in sales and a 15% increase in Gross Profit, I got Sales of 75 and GP of 11.5. To get the GPM, divide 11.5 by 75, to get 15%. 

Thus the GPM increased from 10% to 15.33% i.e. by 53.33% or 5.33 percentage points. 

Hope this helps!

Rushabh

Hi Joel,

The other coaches have it exactly right!

Now, remember, it is critical that you know all your major formulas and how to use them. 

Make sure you learn margin, markup, breakeven, ROI, NPV, etc.