354 Chapter 8 Mathematics of Pricing
$6.63 LP(0.725)
LP $9.14
Markdown and trade discounts are not, however, entirely the same thing. It is worthwhile
to compare trade discounts to gross profi t margins and markup based on cost.Example 8.3.6 A manufacturer offers a 30% trade discount. If the merchant sells
items at a 10% discount to list, what is the gross profi t margin? What is the markup
based on cost?Since we are working with percents, we can assume any list price that we want. We will use
$100 in this case for convenience as we have in the past.The cost would be (70%)($100) $70.00
The selling price would be (90%)($100) $90.00.
To fi nd the gross profi t margin:C SP(1 r)
$70 $90(1 r)
0.7777777 1 r
0.7777777 r 1
r 0.2222223 22.22%To fi nd the markup based on cost:$90 $70(1 r)
1.2857143 1 r
r 0.2857143 28.57%Note that if the items were sold for list price, the trade discount would be the same as
the gross profi t margin. It is not unusual, though, for a manufacturer to set list prices that
are higher than most retailers will actually charge; this practice enables retailers to make
their usual prices sound more attractive by describing them as discounted below the list
price.Series Discounts
Series discounts are multiple discounts applied to a price in succession. Sometimes, a
manufacturer may offer multiple trade discounts. For example, a company might normally
offer a 25% trade discount, but, during a special promotion or to match a competitor’s
pricing, might offer an additional 15% discount. This series discount might be denoted as
“25%, 15%,” or sometimes as “25/15” (though that second notation can be confusing since
the “/ ” looks like division).
As we have seen before, despite appearances it is incorrect to conclude that successive
discounts of 25% and 15% are equivalent to a single discount of 40%. In fact, they are not.Example 8.3.7 The list price for a herbal weight loss supplement is $39.95. The
manufacturer normally offers a 25% trade discount, but during a special promotion it
offers an additional 15% discount. Find the net price for this item.The fi rst, 25% discount, reduces the price to (75%)($39.95) $29.96. The second discount
further reduces the price to (85%)($29.96) $25.47.This could also be calculated more simply as (75%)(85%)($39.95) $25.47.The single discount equivalent to a series of discounts is referred to as the single equivalent
discount.Example 8.3.8 Find the single equivalent discount for successive 25% and 15%
discounts.For convenience, we will work from an assumed price of $100. These discounts would reduce
that price to (75%)(85%)($100) $63.75. This is a total discount of $100 $63.75
$36.25. As a percent of the list price, this works out to $36.25/$100 36.25%.