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