Calculating Percentage Markup Versus Profit
Date: 01/23/2004 at 15:57:26 From: Lisa Subject: Explanation of profit percentage In order to figure a profit of 10% I would normally take the amount and then multiply by 1.1 to find the selling price. For example, 800 x 1.1 = 880 so I say we should charge $880 to make a 10% profit. However my employer tells me that in order to find a 10% profit I should divide by .9 to get 800/.9 = $888.89. I do not understand how this is 10%. Can you please explain? Thank you very much.
Date: 01/23/2004 at 23:34:22 From: Doctor Peterson Subject: Re: Explanation of profit percentage Hi, Lisa. You and your employer are calculating two subtly different things: a markup versus a profit. Your calculation is correct when you are given the cost and want to find a sale price that will give you a profit of 10% OF THE COST TO YOU. If the cost to you is C and you sell it for 1.1C, your profit is 1.1C - C = 0.1C, or 10% of C. which is 10% of what you paid for the item, or a 10% markup. But your employer is calculating the price that will give you a profit of 10% OF THE SELLING PRICE. If you sell the item for C/0.9, then your profit is C/0.9 - C = (C - 0.9C)/0.9 = 0.1 * C/0.9, or 10% of C/0.9. which is 10% of the selling price, C/0.9. What he is doing is solving the equation P - C = 0.1P which says the profit (price minus cost) is 10% of the price, this way: P - 0.1P = C 0.9P = C P = C/0.9 You method solves the equation P - C = 0.1C Your employer's method is correct for what he is calling it, a 10% profit on the sale. Your method is correct for a 10% markup over the cost. It's all a matter of words. You can see similar issues here: Duelling Percentages http://mathforum.org/library/drmath/view/60803.html Markups and Discounts http://mathforum.org/library/drmath/view/58077.html If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 01/24/2004 at 09:03:22 From: Lisa Subject: Explanation of profit percentage Thanks! I can follow this now that I see the mathematical equations written out. This has been a great help. I have another similar question for you, if I could, again involving us buying and then selling an item, but now figuring tax in as well. For example, the price we pay is $250.00 (tax not included). We would then figure in 7% tax (250 * 1.07 = 267.50) to find our total cost. We then proceed to figure out our selling price by calculating 267.50/0.9 = 297.22. This selling price will give us 10% profit. Other people believe that we should do it the following way. Take 250.00 (our cost)/0.93 = 268.82 (price with tax) and then calculate 268.82/0.9 = 298.69 for the selling price with 10% profit. I have always figured sales tax as a multiplication factor but then again I had never thought about the difference between a markup of 10% and a selling price with a 10% profit either, so I wanted to verify that I truly am understanding everything correctly.
Date: 01/25/2004 at 22:28:15 From: Doctor Peterson Subject: Re: Explanation of profit percentage Hi, Lisa. There could be tax issues that are beyond my knowledge, but the math aspect seems straightforward. You would divide by 0.93 if, as in the case of the profit, you wanted 7% of the price you charge to go for tax. But that isn't how tax works. The tax part of the transaction, as I understand it, is simply your payment when you buy the item, based on the amount charged to you, so your calculation is clearly correct, and the fact that the other version gives a different answer shows that it is wrong. You can always check something like this (assuming you have defined clearly what you want to do) by seeing how much the actual tax and profit are based on the number you calculate. If you charge $297.22; 10% of that is $29.72, which leaves $267.50. That is $250 plus the 7% tax. The other number will not check out this way. To put it simply, you multiply by 1.07 because the tax is calculated forward, from the cost to you; you divide by 0.9 because the profit is calculated backward, from the price to your customer. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 01/27/2004 at 14:31:12 From: Lisa Subject: Thank you (Explanation of profit percentage) Thank you so much for all your help. All of this actually makes sense to me now! I appreciate it very much.
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