Thread: I need help!!

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?

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

that helps alot thank you. but i have one more question can you give me the step by step in the equation 49.5% =( x-486000)/x

im having trouble coming up with the number you got.

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!

how do you subtract x from both sides and get -.505?

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.