a store has a cost of goods of 486,000 the expected gross margin is 49.50% operating expenses are 225,000 what will be the percent profit?

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- September 3rd 2008, 08:57 AM #1

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- September 3rd 2008, 01:56 PM #2

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Gross Profit Margin = (Sales - Cost of Goods Sold) / Sales

We need to know sales, while we already know CoGS and the GPM. Thus, Sales becomes x in the equation above and we solve for it.

49.50% = ( x - $486,000)/ x

x = $ 962,376.24 = Sales

Net Profit Margin = Net Income / Sales

Net Income = Sales - Expenses

Where expenses include operating exp and CoGS.

So, we now have all the pieces to plug in:

NPM = ($962,376.24 - $486,000 - $225,000)/$962,376.24

NPM = $251,376.24/$962,376.24

NPM = 26.12%

Be careful when dealing with Net Profit and Net Profit Margin. Net Profit Margin is expressed as a percent, as seen above, while Net Profit is the actual dollar amount of profit ($251,376.24 in this problem). A good way to check if you're in the ballpark on this type of problem is to know that Gross Profit Margin is greater than Net Profit Margin. 26.12% is less than 49.50% so it's likely that we're on the right track.

~TC

- September 3rd 2008, 02:25 PM #3

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- September 3rd 2008, 04:34 PM #4

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Our initial equation:

49.50% = ( x - $486,000)/ x

Rewrite without the percent:

.495 = ( x - $486,000)/ x

Multiply both sides by x:

.495x = x - $486,000

Subtract x from both sides:

(.495x - x) = -$486,000

-.505x = -$486,000

Divide both sides by -.505:

x = $962,376.2376

And of course, I just rounded to the nearest cent:

x = $962,376.24

There ya go!

- September 4th 2008, 06:19 AM #5

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- September 4th 2008, 07:01 AM #6

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The coefficient in front of the x on the left is .495 while the coefficient in front of the x on the right is implied as 1. Below, I show it as if you were to factor out x, subtract the one, then multiply the result by x.

Subtract x from both sides:

(.495x - 1x) = -$486,000

x(.495 - 1) = -$486,000

x(-.505) = -$486,000

-.505x = -$486,000

Another way to think of it is that you have .495 x's and you need to subtract from that one x. Which results in a x in the amount of -.505.