The Mathematics of Money

336 Chapter 8 Mathematics of Pricing

Example 8.1.6 At the end of the summer, a backyard play set that usually sells for

$599.95 is marked down to $450. What is the markdown percent?

Working from the formula, we get:

MP 
 OP(1  d)

$450 
 $599.95(1  d)

Dividing both sides by $599.95 gives:

0.7500625 
 1  d

Since the d is subtracted on the right side, while we want a positive d, we add d to both sides

to get:

0.7500625  d 
 1

Then we subtract 0.7500625 from both sides and rewrite d as a percent to get:

d 
 0.2499374


 24.99%

An alternative approach to the solution is the following. The markdown is $599.95  $450 


$149.95. As a percent of the original price this is $149.95/$599.95 
 0.2499374 


24.99%.

Again we need to repeat a caution here. The markdown is 24.99% of the original $599.95

price. It is not 24.99% of the marked-down price of $450.

The amount, or percent, that a price is marked down is also commonly called discount.

The retailer selling the play set in Example 8.1.6 might describe this offer as a 24.99% (or,

more likely, rounded to 25%), or $149.95 discount. This is quite common phrasing, and

probably phrasing that you are already quite familiar with. Be careful, though, not to con-

fuse this with simple discount as discussed in Chapter 2. While the two ideas are similar,

they are not exactly the same thing.

Comparing Markup Based on Cost with Markdown

There are many cases where markup and markdown are both involved, and it is important

to exercise care with the calculations. When both markup and markdown are involved,

sometimes “obvious” things are not nearly as obvious as they seem. The following exam-

ple will illustrate.

Example 8.1.7 Gemma’s Gemstone Gewelry bought a necklace for $375. In the

store, Gemma marked up this price by 20%. Several months later, when the necklace

still had not sold, she decided to mark down the price by 20%. What was the marked-

down price?

The “obvious” answer is $375; she marked it up by 20% and then down by 20%, so it seems

to be common sense that the markup and markdown would cancel each other out. However,

when we work it through, we see that this is not correct.

Markup:

P 
 C(1  r)

P 
 $375(1.20)

P 
 $450.00

Markdown:

MP 
 OP(1  d)

MP 
 $450(0.80)

MP 
 $360.00

The marked-down price was $360, not $375!