# Calculating Operating Costs to give a fixed profit margin

We are importing sales data from a company we just purchased. We want to calculate the logistics value so that the profit margin is 13%.

We have the following rules in our system:

Profit = SalesValue - OriginalPrice - LogisticsValue
CostValue = OriginalPrice + LogisticsValue

ProfitMargin = Profit/CostValue * 100
= (SalesValue - OriginalPrice - LogisticsValue) / (OriginalPrice + LogisticsValue) * 100


If SalesValue = $1000, OriginalPrice =$750 and ProfitMargin = 13 and LogisitcsValue = LV then

             13 = ((1000-750-LV)/(750+LV)) * 100
= (250 - LV) / (750+LV) * 100
0.13 * (750+LV) = (250 - LV)
0.13LV + LV = 250


How can I find the value of LV?

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Here is a formula you can use generally.

LV = ( 100*(SV - OP) - PM*OP )/ (100 + PM)

In your example, you would get 134.96.

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You have an error in your last step there. It should read:

$0.13(750+LV)=250-LV \Rightarrow 0.13(750)+0.13LV=250-LV \Rightarrow 1.13LV=250-0.13(750) \Rightarrow LV \approx 134.955$.

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Thanks. Typo when putting it into the site. 134.96 was the answer I got –  Greg Sep 10 '12 at 2:00

Just worked out what I was missing.

0.13LV + LV = 1.13LV


So

0.13LV + LV = 250
1.13LV = 250
LV = 250/1.13
LV = 134.96 (to 2 decimal places)

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