The Mathematics of Money

in pretty much the same was as markup based on cost. There is a mathematical challenge

here, though. If we know the item’s cost, and if we know our markup percent based on cost,

calculating the selling price is fairly straightforward. Profi t margin, though, is a percent of

the selling price. Obviously we don’t know the selling price before we know the selling

price!

We’ll need to be a bit sneaky to get around this, but we can. Here is the idea: if 35%

of the selling price is gross profi t, we can conclude that the remaining 100%  35% 


65% must be the cost of the item. Before taking this any further, we’ll generalize this to a

formula:

FORMULA 8.2.1

Markup Based on Selling Price

C 
 SP(1  r)

where

C represents the item’s COST

SP represents the SELLING PRICE

and

r represents the gross PROFIT MARGIN

We can now put this formula to work to solve the question at hand.

Example 8.2.7 Determine the selling price of an item costing $45 in order to have

a 35% gross profi t margin.

Applying the formula:

C 
 SP(1  r)

$45 
 SP(1  0.35)

$45 
 SP(0.65)

To fi nd the selling price, we divide both sides by 0.65 to get:

SP 
 $69.23

Notice that the 0.65 that we wound up with on the right side of this equation is the 65% that

we said must be the percent cost of the item. Remember that expressed as a decimal 100%

is 1, and so the (1  r) in this formula serves the purpose of subtracting the gross profi t

margin from 100% to get the percent cost.

Markup based on selling price may also be used even when the idea of gross profi t margin

is not explicitly what is driving the pricing. Another example will serve to illustrate this.

Example 8.2.8 A cooperative market allows its members to place special orders for

items they want to buy in bulk. The price the member pays is based on an 8% markup

on selling price. Lynne ordered a case of protein bars, for which the market’s cost was

$24.17. How much will she pay for this order?

C 
 SP(1  r)

$24.17 
 SP(0.92)

SP 
 $26.27

A Dose of Reality

Before getting too carried away with this method of pricing, a few cautions are in order.

You should absolutely not draw the conclusion from this section that in the real world

prices are set by determining a desired gross profi t margin and then automatically apply-

ing that margin. Whether we think of prices as based on a markup based on cost or based

on a markup based on selling price, the fact of the matter is that a retailer has to deal with

the fact that the prices that they charge must be prices that their customers will pay. Based

on your costs and profi t targets you may calculate that your hardware store should sell a

346 Chapter 8 Mathematics of Pricing