# I need help!!

• Sep 3rd 2008, 07:57 AM
kat22
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?
• Sep 3rd 2008, 12:56 PM
tcRom
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
• Sep 3rd 2008, 01:25 PM
kat22
another question...
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.
• Sep 3rd 2008, 03:34 PM
tcRom
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! (Cool)
• Sep 4th 2008, 05:19 AM
kat22
another
how do you subtract x from both sides and get -.505?
• Sep 4th 2008, 06:01 AM
tcRom
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.