The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

8.1 Markup and Markdown 337

Why didn’t things work out here as “common sense” would have suggested? The markup

is a percent of the cost, the markdown is a percent of the marked-up selling price. Since

those two 20%’s are not 20% of the same thing, they are not really the same at all. This can

be confusing. It is important to not make assumptions off the cuff when comparing markup

and markdown percents. Be careful and work things through!

Suppose we know a markup percent, and we want to mark things back down to cost. We

can determine what the percent should be, as the next example will show.

Example 8.1.8 If prices are calculated with a 35% markup based on cost, what

is the percent that those prices should be marked down to get back to their original

cost?

We don’t know what sort of things we are pricing here, much less what the dollar amount

of those prices would be. Fortunately, though, since we are working with percents the actual

dollar amounts don’t matter. We can work the problem out with whatever dollar amounts

we like; the percent answer will be the same regardless of the price we assume. Following

what we did to calculate effective interest rates back in Chapter 3, we choose a convenient

cost of $100.

P 
 C(1  r)

P 
 $100(1.35)

P 
 $135.00

MP 
 OP(1  d)

$100.00 
 $135.00(1  d)

0.7407407 
 1  d

d 
 25.93%

So a 25.93% discount “undoes” a 35% markup.

When “Prices” Aren’t Really Prices

Even though we’ve approached this chapter from the point of view of retail prices, the

mathematics we’ve developed here can be applied to other related situations. Whenever we

have something that increases as a percent of the original amount, we can mathematically

look at this as “markup.” Likewise, whenever something decreases as a percent of some

starting value, we can look at this as “markdown.” The exercises provide several examples

of this; the following example is just one of many possibilities.

Example 8.1.9 In 2004, 184 students graduated from Central City Business College.

The graduating class of 2005 increased by 10.3% over 2004, but then the 2006 class

decreased 9.8% versus 2005. How many students graduated in 2006?

The size of the 2005 class can be thought of as a “markup” over the size of the 2004 class.

Using this idea we get:

P 
 C(1  r)

P 
 184(1.103)

P 
 203

(We round to the nearest whole number, since we are talking about a number of people.)

The 2006 class is given as a percent decrease from the 2005 class, so we can look at this

decrease as a “markdown” from the 2005 class size.

MP 
 OP(1  d)

MP 
 203(0.902)

MP 
 183

So there were 183 students in the 2006 graduating class.