Copyright © 2008, The McGraw-Hill Companies, Inc.
First approach: As a percent of sales, the expenses were $57,950/$153,670 37.71%.22.60% 37.71% 15.11%Alternative approach: Net profi ts were $34,725 $57,950 $23,225.$23,225/$153,670 15.11%A negative net profi t margin indicates that the business lost money, unfortunately not an
uncommon occurrence for many businesses. Gross profi t margins can also be negative.
A negative gross margin would indicate that things were being sold for less than cost.
In both of these examples of net profi t margin, we have calculated the margin for the
business as a whole. Calculating a net profi t margin for an individual item is far less
straightforward. The problem here is that there is no absolute way of determining just
how much of a business’s overhead expenses should be attributed to any given item.
How much of Sally’s electric bill, or rent, or insurance should be attributed to the dress
she sold for $65?
One simple method of doing this is proportionate allocation. This assumes that expenses
should be attributed to each item sold in proportion to the overall sales. The following
example will illustrate how this can be done.Example 8.2.6 In the year in which the dress sold for $65, the total sales were
$219,540 and expenses were $63,073. If expenses are allocated in proportion to sales,
how much of the store’s expenses is attributable to that dress?We fi rst look at this dress in relation to the overall sales for the year. $65/$219,540
0.02961%. (We take this out to more than two decimal places because it is such a small per-
cent.) Since the dress was 0.02961% of sales, we attribute to it 0.02961% of the expenses.
Then (0.0002961)($63,073) $18.67.We could avoid the trouble of the small percentage by avoiding explicitly writing it out. We
obtained this percent by dividing the dress sale by total sales; then we multiplied it by the
overall expenses. Rather than write out the percent itself, we could simply have eliminated
that intermediate step and gone directly to the multiplication:($65/$219,540)($63,073) $18.67.A third option may be the most appealing. We previously calculated that the shop’s over-
all expense percent was 28.73%. Proportionate allocation assumes that this same percent
applies to all sales, so (28.73%)($65) $18.67.While this sort of allocation is attractively straightforward, it is probably overly simplistic
for most business situations. Some items account for more overhead than others. A grocery
store might think it entirely appropriate to attribute more of its utility bills to refrigerated and
frozen foods than canned goods, for example. A department store might fi nd it appropriate to
attribute a larger percentage of its rent to appliances, which take up a lot of fl oor space, than
to jewelry. And so on and so forth. Realistically speaking, the determination of net profi t margin
on any given item mainly depends on how the business’s management deems it appropriate to
allocate expenses. While this is an interesting subject to investigate, it is primarily a matter of
accounting rather than mathematics and so we will not address it further here.Markup Based on Selling Price
However a business determines that expenses should allocated, once the expenses as a per-
cent of sales are known management can determine a gross margin which will be adequate
to meet expenses and profi tability goals. Suppose, for example, that Sally determines that
she needs to set her dress prices by using a 35% gross margin. Of course, it is too late to fi t
that target on the dress from our fi rst example, but we can look ahead and ask what price
she would need to charge for a dress costing $45 to reach this target.
Determining a price by using a target gross margin is called markup based on selling
price, in contrast to markup based on cost. It may seem at fi rst as though this will work8.2 Profit Margin 345