# 1.4 Markdown

## LEARNING OBJECTIVES

• Calculate the amount of markdown on the selling price of an item.
• Calculate the rate of markdown on the selling price of an item.

Flashy signs in a retail store announce, “40% off, today only!” Excitedly you purchase three tax-free products with regular price tags reading $100,$250, and $150. The cashier processing the transaction informs you that your total is$325. You are about to hand over your credit card when something about the total makes you pause. The regular total of all your items is $500. If they are 40% off, you should receive a$200 deduction and pay only $300. The cashier apologizes for the mistake and corrects your total. A markdown is a reduction from the regular selling price of a product resulting in a lower price. This lower price is called the sale price or reduced selling price to distinguish it from the selling price. Many people perceive markdowns as a sign of bad business management decisions. However, in most situations this is not true. Companies must always attempt to forecast the future. In order to stock products, a reseller must estimate the number of units that might sell in the near future for every product that it carries. This is both an art and a science. While businesses use statistical techniques that predict future sales with a relative degree of accuracy, consumers are fickle and regularly change shopping habits. Markdowns most commonly occur under four circumstances. • Clearing Out Excess or Unwanted Inventory. In these situations, the business thought it could sell 100 units. However, consumers purchased only 20 units. In the case of seasonal inventory, such as Christmas items on Boxing Day, the retailer wishes to avoid packing up and storing the inventory until the next season. • Clearing Out Damaged or Discontinued Items. Selling a damaged product at a discount is better than not selling it at all. When products are discontinued, this leaves shelf space underused, so it is better to clear the item out altogether to make room for profitable items that can keep the shelves fully stocked. • Increasing Sales Volumes. Sales attract customers because almost everyone loves a deal. Though special marketing events such as a 48 hour sale reduce the profitability per unit, by increasing the volume sold these sales can lead to a greater profit overall. • Promoting Add-On Purchases. Having items on sale attracts customers to the store. Many times customers will not only purchase the item on sale but also, as long as they are on the premises, grab a few other items, which are regularly priced and very profitable. Markdowns are no different from offering a discount. Markdowns are common, so you will find it handy to adapt the discount formulas to the application of markdowns, replacing the symbols with ones that are meaningful in merchandising. The sale price or reduced selling price ($S_{red}$) of a product is $\displaystyle{S_{red}=S \times (1-d)}$ where • $S_{red}$ is the sale or reduced selling price. The sale price is the price of the product after reduction by the markdown percent. Conceptually, the sale price is the same as the net price. • $S$ is the regular selling price. The regular selling price of the product before any discounts. • $d$ is the rate of markdown. A markdown rate is the same as a sale discount rate. Therefore, you use the same discount rate symbol ($d$) to represent the percentage (in decimal format) by which you reduce the selling price. Note that you are interested in calculating the sale price and not the amount saved. Thus, you take the markdown rate away from 1 to find out the rate owing. ### NOTES 1. The formula for the reduced selling price is just an application of the $N=L \times (1-d)$ where $S_{red}$ is the net price and $S$ is the list price. 2. In markdown situations, the selling price and the reduced selling price are different variables. The reduced selling price is always less than the selling price. In the event that a regular selling price has more than one markdown percent applied to it, you can extend the formula to apply multiple discounts . ## Markdown The amount of markdown ($D$) is the amount by which the regular selling price ($S$) is reduced to determine the reduced selling price ($S_{red}$). $\displaystyle{D=S-S_{red}}$ where • $D$ is the markdown amount. This is the amount the regular selling price is reduced by to arrive at the reduced selling price. • $S$ is the regular selling price. The regular selling price before you apply any markdown percentages. • $S_{red}$ is the reduced selling price. The price after you have deducted all markdown percentages from the regular selling price. Alternatively, the amount of markdown can be calculated by using the percentage of the of the selling price ($S$) that is deducted to arrive at the reduced selling price ($S_{red}$). $\displaystyle{D=d \times S}$ where • $D$ is the markdown amount. This is the amount the regular selling price is reduced by to arrive at the reduced selling price. • $S$ is the regular selling price. The regular selling price before you apply any markdown percentages. • $d$ is the rate of markdown. The percentage of the selling price to be deducted (in decimal format). ## EXAMPLE A retailer sells an MP3 player for a regular selling price of$39.99. Assume the retailer has excess inventory and places the MP3 player on sale for 10% off. What is the sale price and markdown amount?

Solution:

Step 1:  The given information is

$\begin{eqnarray*} S & = & \39.99 \\ d & = & 10\% \end{eqnarray*}$

Step 2:  Calculate the reduced selling price.

$\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 39.99 \times (1-0.1) \\ & = & 39.99 \times 0.9 \\ & = & \35.99 \end{eqnarray*}$

Step 3:  Calculate the markdown amount.

$\begin{eqnarray*} D & = & S-S_{red}\\ & = & 39.99-35.99 \\ & = & \4.00 \end{eqnarray*}$

The reduced selling price is $35.99. The amount of markdown is$4.00.

A retailer sells a product for $189.99. During a sale the product is marked down by 45%. What is the sale price for the product and what dollar amount is saved? Solution: Step 1: The given information is $\begin{eqnarray*} S & = & \189.99 \\ d & = & 45\% \end{eqnarray*}$ Step 2: Calculate the reduced selling price. $\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 189.99 \times (1-0.45) \\ & = & 189.99 \times 0.55 \\ & = & \104.49 \end{eqnarray*}$ Step 3: Calculate the markdown amount. $\begin{eqnarray*} D & = & S-S_{red}\\ & = & 189.99-104.49 \\ & = & \85.50 \end{eqnarray*}$ The reduced selling price is$104.49.  The amount of markdown is $85.50. ## TRY IT A table lamp regularly sells for$150.  The lamp is marked down by 25%.  What is the amount of markdown?  What is the sale price?

Click to see Solution

$\begin{eqnarray*} D & = & d \times S \\ & = & 0.25 \times 150 \\ & = & \37.50 \end{eqnarray*}$

$\begin{eqnarray*} S_{red} & = & S-D \\ & = & 150 -37.50 \\ & = & \112.50 \end{eqnarray*}$

## Rate of Markdown

Businesses often express markdowns as percentages, facilitating easy comprehension and comparison.  The rate of markdown ($d$) is the percentage of the selling price that is deducted to arrive at the reduced selling price.  The rate of markdown expresses the markdown amount as a percent of the regular selling price.

$\displaystyle{d=\frac{D}{S} \times 100\%}$

where

• $d$ is the rate of markdown. You always deduct a markdown amount from the regular selling price of the product. Therefore, you always express the rate of markdown as a percentage of the selling price. Use the same symbol for a discount rate becasue markdown rates are synonymous with sale discounts.
• $D$ is the markdown amount.  This is the amount the regular selling price is reduced by to arrive at the reduced selling price.
• $S$ is the regular selling price. The regular selling price before you apply any markdown percentages.

## EXAMPLE

A retailer regularly sells USB drives for $79.99 each. During a sale, the USB drives are sold for$58.79.  Calculate the rate of markdown.

Solution:

Step 1:  The given information is

$\begin{eqnarray*} S & = & \79.99 \\ S_{red} & = & \58.79 \end{eqnarray*}$

Step 2:  Calculate the amount of markdown.

$\begin{eqnarray*} D & = & S -S_{red} \\ & = & 79.99-58.79 \\ & = & \21.20 \end{eqnarray*}$

Step 3:  Calculate the rate markdown.

$\begin{eqnarray*} d & = & \frac{D}{S} \times 100\% \\ & = & \frac{21.20}{79.99} \times 100\% \\ & = & 26.50\% \end{eqnarray*}$

The rate of markdown is 26.50%.

### NOTE

Avoid getting bogged down in formulas. Recall that the three formulas for markdowns are not new formulas, just adaptations of three previously introduced concepts. As a consumer, you are very experienced with endless examples of sales, bargains, discounts, blowouts, clearances, and the like. Every day you read ads in the newspaper and watch television commercials advertising percent savings. This section simply crystallizes your existing knowledge. If you are puzzled by questions involving markdowns, make use of your shopping experiences at the mall!

## EXAMPLE

A reseller acquires an Apple iPad for $650. Expenses are planned at 20% of the cost, and profits are set at 15% of the cost. During a special promotion, the iPad is advertised at$100 off. What is the sale price and rate of markdown?

Solution:

Step 1:  The given information is

$\begin{eqnarray*} C & = & \650 \\ E & = & 0.2 \times C \\ P & = & 0.15 \times C \\ D & = & \100 \end{eqnarray*}$

Step 2:  Calculate the expenses.

$\begin{eqnarray*} E & = & 0.2 \times C \\ & = & 0.2 \times 650 \\ & = & \130 \end{eqnarray*}$

Step 3:  Calculate the profit.

$\begin{eqnarray*} P & = & 0.15 \times C \\ & = & 0.15 \times 650 \\ & = & \97.50 \end{eqnarray*}$

Step 4:  Calculate the regular selling price.

$\begin{eqnarray*} S & = & C+E+P \\ & = & 650+130+97.50 \\ & = & \877.50 \end{eqnarray*}$

Step 5:  Calculate the reduced selling price.

$\begin{eqnarray*} S_{red} & = & S-D \\ & = & 877.50-100 \\ & = & \777.50 \end{eqnarray*}$

Step 6:  Calculate the rate markdown.

$\begin{eqnarray*} d & = & \frac{D}{S} \times 100\% \\ & = & \frac{100}{877.50} \times 100\% \\ & = & 11.40\% \end{eqnarray*}$

The reduced selling price is $777.50. The rate of markdown is 11.40%. ## EXAMPLE A clothing retailer purchases shirts for$17.85.  The retailer sells the shirts at a markup of 30% of the selling price.  At the end of the season, the retailer wants to clear the inventory, so sells the shirts for $19.99. Calculate the rate of markdown. Solution: Step 1: The given information is $\begin{eqnarray*} C & = & \17.85 \\ M & = & 0.3 \times S \\ S_{red} & = & \19.99 \end{eqnarray*}$ Step 2: Calculate the regular selling price. $\begin{eqnarray*} S & = & C+M \\ S & = & 17.85+0.3 \times S \\S-0.3 \times S & = & 17.85 \\ 0.7 \times S & = & 17.85 \\ S & = & \frac{17.85}{0.7} \\ S & = & \25.50 \end{eqnarray*}$ Step 3: Calculate the amount of markdown. $\begin{eqnarray*} D & = & S-S_{red} \\ & = & 25.50-19.99 \\ & = & \5.51 \end{eqnarray*}$ Step 4: Calculate the rate markdown. $\begin{eqnarray*} d & = & \frac{D}{S} \times 100\% \\ & = & \frac{5.51}{25.50} \times 100\% \\ & = & 21.61\% \end{eqnarray*}$ The rate of markdown is 21.61%. ## TRY IT A furniture dealer purchases chairs for$500 less a discount of 15%.  The dealer sells the chair with a markup of 30% of the cost.  During a sale, the dealer marks down the price by $100. 1. Calculate the rate of markdown. 2. Calculate the reduced selling price. Click to see Solution $\begin{eqnarray*} C & = & 500 \times (1-0.15) \\ & = & 500 \times 0.85 \\ & = & \425 \end{eqnarray*}$ $\begin{eqnarray*} S & = & C+M \\ & = & 425+0.3 \times 425 \\ & = & \552.50 \end{eqnarray*}$ 1. Rate of markdown. $\begin{eqnarray*} d & = & \frac{D}{S} \times 100\% \\ & = & \frac{100}{552.50} \times 100\% \\ & = & 18.10\% \end{eqnarray*}$ 2. Reduced selling price. $\begin{eqnarray*} S_{red} & = & S-D \\ & = & 552.50-100 \\ & = & \452.50 \end{eqnarray*}$ ## Exercises 1. The regular selling price of an item is$439.85.  The item is put on sale with a rate of markdown of 35%.  Calculate the following:
1. The amount of markdown.
2. The reduced selling price.

a. $153.95; b.$285.90

2. An item is marked down by $100 to a reduced selling price of$199.95. Calculate the following:
1. The regular selling price.
2. The rate of markdown.

a. $299.95 b. 33.3389% 3. The regular selling price of an item is$1,050 and the reduced selling price is $775. Calculate the following: 1. The amount of markdown. 2. The rate of markdown. Click to see Answer a.$275; b.26.1905%

4. The regular selling price of an item is $28,775. During a sale, the item is markdown by$3,250.  Calculate the following:
1. The rate of markdown.
2. The reduced selling price.

a. 11.2945%; b. $25,525 5. The reduced selling price of an item is$13,199.95.  The rate of markdown is 33%.  Calculate the following:
1. The regular selling price.
2. The amount of markdown.

a. $19,701.42; b.$6,501.47

6. An item is marked down by $38.33. The rate of markdown is 12%. Calculate the following: 1. The regular selling price. 2. The reduced selling price. Click to see Answer a.$319.42; b. $281.09 7. A pair of Nike athletic shoes is listed at a regular selling price of$89.99. If the shoes go on sale for 40% off, what is the sale price?

$53.99 8. During its special Bay Days, The Bay advertises a Timex watch for$39.99 with a regular price of $84.99. Calculate the rate of markdown and markdown amount. Click to see Answer$45,  52.9474%

9. For spring break you are thinking about heading to Tulum, Mexico. In planning ahead, you notice that a one-week stay at the Gran Bahia Principe Tulum, regularly priced at $2,349 for air and six nights all inclusive, offers an early-bird booking discount of$350. What rate of markdown is being offered for booking early?

14.9%

10. A Heritage Infusio deep frying pan is advertised at 70% off with a sale price of $39.99. What is the frying pan’s regular selling price, and what markdown amount does this represent? Click to see Answer$133.30, $93.31 11. Quicky Mart regularly sells its Red Bull sports drink for$2.99 per can. Quicky Mart noticed that one of its competitors down the street sells Red Bull for $1.89. What rate of markdown must Quicky Mart advertise if it wants to match its competitor? Click to see Answer 36.7893% 12. A campus food outlet is advertising a “Buy one, get one 25% off” deal. The 25% off comes off the lower-priced item. If you purchase a chicken dinner for$8.99 and your friend gets the burger combo for $6.99, what is the rate of markdown on the total price? Click to see Answer 10.9512% 13. The Brick advertises that when you purchase a queen-size Tempur-Pedic mattress set for$2,499.97 it will give you a 51″ 3-D plasma television with a 3-D starter kit included. The value of this gift is \$1,199.99. What rate of markdown does this represent?

32.4325%