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| Math Central | Quandaries & Queries |
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Question from Roxane: I'm trying to figure out the formula for the following, I have a product that I want to receive a certain profit margin, but with this product I also have to pay a percentage of commission to someone. I need to know how to calculate my new selling price taking into account the markup percentage, but I don't want my gross margin to be lowered. I have calculated the markup percentage to get my new selling price with the commission, but it lowers my profit margin once I pay the commission and I don't want it to do that. |
Ho Roxane,
Suppose S is the selling price in dollars. Your cost is composed of two parts, the cost C before the commission and the commission D, both in dollars. I expect you calculate your profit margin M as a percent by
M = [[S - (C + D)]/S] × 100
Again I expect the commission D is a percentage of S, say E% then
D = E/100 × S
Hence
MS/100 = S - (C + E/100 × S)
Thus
S - MS/100 - ES/100 = C or
S(1 - M/100 - E/100) = C
Finally if M is the margin and E is the commission, both as percentages then the selling price S is
S = C/(1 - M/100 - E/100)
If I have misinterpreted what you mean by margin or commission let me know.
Penny
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