344 Chapter 8 Mathematics of Pricing
Example 8.2.1 Sally’s Fashion Paradise sells a dress that cost $45 for $65. Find
the gross profi t margin from this sale.The gross profi t from the sale of the dress is $65 $45 $20. Since gross profi t is a percent
of the selling price, the gross profi t margin from this sale is $20/$65 0.3077 30.77%.It should be apparent that, whenever we know both the selling price and cost, we can fi nd the
gross profi t margin in this way. Likewise, if we know the gross profi t margin and the selling
price, we can determine the gross profi t by multiplying.Example 8.2.2 Sally’s Fashion Paradise sells women’s purses, pricing them with a
35% gross profi t margin. If a purse is priced at $72, what is the gross profi t in that price?The gross profi t is (35%)($72) $25.20. The question did not ask for it, but we can also fi nd
that the purse’s cost is $72.00 $25.20 $46.80.While a gross profi t margin can be calculated for a single item, it can also be calculated for
a business as a whole:Example 8.2.3 Last year, sales at Sally’s Fashion Paradise totaled $219,540.
The cost of the items sold was $147,470. What was the business’s overall gross
profi t margin for the year?Total gross profi t is $219,540 $147,470 $72,070. As a percent of sales,
$72,070/$219,540 32.83%, so that is the gross profi t margin.Note that this is an overall percent. It does not mean that every single item sold was priced
with a 32.83% gross profit margin. Some items undoubtedly would have been sold at a
higher gross profit margin, others a lower one. The 32.83% overall margin can be thought
of as an average of the gross margins on all the store’s sales for the year.Net Profit Margin
How good is a 32.83% gross profi t margin? The answer to this question really depends on
how much overhead the dress shop has to cover. If expenses run at 20% of overall sales,
a 32.83% gross margin is more than enough to cover that and provide a healthy net profi t.
On the other hand, if expenses run at 40% of sales, this would not be enough to cover
costs.
As discussed earlier in this section, the net profi t margin, which takes expenses into
account, is a better measure of the business’s actual profi tability.Example 8.2.4 Last year, Sally’s Fashion Paradise had overhead expenses totaling
$63,073. Find (a) the expenses as a percent of sales, and (b) the net profi t margin.(a) $63,073/$219,540 28.73%(b) The gross profi t was $72,070. Subtracting expenses from this leaves a net profi t of
$72,070 $63,073 $8,997. As a percent of sales $8,997/$219,540 4.10%, so that is
the net profi t margin.Notice that we could also have gotten the net profi t margin by taking the gross margin and
subtracting the expenses percent: 32.83% 28.73% 4.10%.Before moving on, let’s work through another example.Example 8.2.5 Tw o years ago, Sally’s shop had sales totaling $153,670. The cost
of the goods sold was $118,945, and her expenses totaled $57,950. Find her overall
(a) gross profi t margin and (b) net profi t margin for that year.(a) Gross profi t $153,670 $118,945 $34,725.Then $34,725/$153,670 22.60%; that is the gross profi t margin.(b) We can calculate the net profi t margin in either of two ways.