11.13 Markdown

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11.13 Markdown

Markdown

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.

Although most retail stores use automated checkout systems, these systems are ultimately programmed by human beings. A computer system is only as accurate as the person keying in the data. A study by the Competition Bureau revealed that 6.3% of items at various retail stores scanned incorrectly. The average error spread is up to 13% around the actual product’s price!^[1] Clearly, it is important for you as a consumer to be able to calculate markdowns.

Businesses must also thoroughly understand markdowns so that customers are charged accurately for their purchases. Businesses must always comply with the Competition Act of Canada, which specifically defines legal pricing practices. If your business violates this law, it faces severe penalties.

The Importance of Markdowns

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 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. Like many others, you may have walked into Target to buy one item but left with five instead.

Markdowns are no different from offering a discount. Recall from Appendix A that one of the types of discounts is known as a sale discount. The only difference here lies in choice of language. 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. Formula 1.1, introduced in Appendix A, calculates the net price for a product after it receives a single discount:

$N=L\times(1-d)$

Formula 1.10 adapts this formula for use in markdown situations.

Formula 1.10 – The Sale Price Of A Product

$S_o_n_s_a_l_e=S\times(1-d)$

$S_o_n_s_a_l_e$ is Sale 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 Selling Price: The regular selling price of the product before any discounts. The higher price is the list price. In merchandising questions, this dollar amount may or may not be a known variable. If the selling price is unknown, you must calculate it using an appropriate formula or combination of formulas from either Appendix A or Appendix B.

$d$ is Markdown Rate: A markdown rate is the same as a sale discount rate. Therefore you use the same discount rate symbol from Appendix A to represent the percentage (in decimal format) by which you reduce the selling price. As in Formula 1.1, 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.

In markdown situations, the selling price and the sale price are different variables. The sale 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 Formula 1.10 in the same manner that Formula 1.3 calculated multiple discounts.

If you are interested in the markdown amount in dollars, recall that Formula 1.2 calculates the discount amount in dollars. Depending on what information is known, the formula has two variations:

Formula 1.2a: $D\char36=L\times d$
Formula 1.2b: $D\char36=L-N$

Formulas 1.11a and 1.11b adapt these formulas to markdown situations.

Formula 1.11a and 1.11b – Markdown Amount

Formula 1.11a

$D\char36=S\times d$

Formula 1.11b

$D\char36=S-S_o_n_s_a_l_e$

$D\char36$ is Markdown Amount: You determine the markdown amount using either formula depending on what information is known. If you know the selling price and markdown percent, apply Formula 1.11a. If you know the selling price and sale price, apply Formula 1.11b.

$S$ is Selling Price: The regular selling price before you apply any markdown percentages.

$d$ is Markdown Rate: the percentage of the selling price to be deducted (in decimal format). In this case, because you are interested in figuring out how much the percentage is worth, you do not take it away from 1 as in Formula 1.10.

$S_o_n_s_a_l_e$ is Sale Price: The price after you have deducted all markdown percentages from the regular selling price.

The final markdown formula reflects the tendency of businesses to express markdowns as percentages, facilitating easy comprehension and comparison. Recall Formula 1.9 from Appendix B, which calculated a markup on selling price percent:

$MoS\%=\frac{M\char36}{S}\times100$

Formula 1.12 adapts this formula to markdown situations.

Formula 1.12 – Markdown Percentage

$d=\frac{D\char36}{S}\times100$

$d$ is Markdown Percentage: You always deduct a markdown amount from the regular selling price of the product. Therefore, you always express the markdown percent as a percentage of the selling price. Use the same symbol for a discount rate, since markdown rates are synonymous with sale discounts.

$D\char36$ is Markdown Amount: The total dollar amount deducted from the regular selling price.

$S$ is Selling Price: The regular selling price of the product before any discounts.

100 is Percent Conversion: The markdown is always expressed as a percentage.

How It Works

Follow these steps to calculate a markdown:

Step 1: Across all three markdown formulas, the four variables consist of the selling price ( $S$ ), sale price ( $S_o_n_s_a_l_e$ ), markdown dollars ( $D\char36$ ), and markdown rate ( $d$ ). Identify which variables are known. Depending on the known information, you may have to calculate the selling price using a combination of discount and markup formulas.

Step 2: Apply one or more of Formulas 1.10, 1.11a, 1.11b, and 1.12 to calculate the unknown variable(s). In the event that multiple markdown rates apply, extend Formula 1.10 to accommodate as many markdown rates as required.

Recall from Appendix B the example of the MP3 player with 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?

Step 1: The selling price and markdown percent are $S$ = $39.99 and $d$ = 0.10, respectively.

Step 2: Apply Formula 1.10 to calculate the sale price, resulting in

$S_o_n_s_a_l_e=\char36 39.99\times(1-0.10)=\char36 35.99$ .

You could use either of Formulas 1.11a or 1.11b to calculate the markdown amount since the selling price, sale price, and markdown percent are all known. Arbitrarily choosing Formula 1.11a, you calculate a markdown amount of

$D\char36=\char36 39.99\times0.10=\char36 4.00$

Therefore, if the retailer has a 10% off sale on the MP3 players, it marks down the product by $4.00 and retails it at a sale price of $35.99.

Just as in Appendix B, 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!

Three of the formulas introduced in this section can be solved for any variable through algebraic manipulation when any two variables are known. Recall that the triangle technique helps you remember how to rearrange these formulas, as illustrated here.

Two triangle diagrams demonstrating how to rearrange formulas. The triangle on the left illustrates formula 4.10: the sale price of a product. The top sector of the triangle represents S(onsale). The left sector represents S. The right sector represents (1-d.) The triangle on the right illustrates both Formulas 4.11a and 4.12: markdown amount and rate. The top sector of the triangle represents D$. The left sector represents S. The right sector represents d.

Example 1.3A – Determining the Sale Price and Markdown Amount

The MSRP for the “Guitar Hero: World Tour” video game is $189.99. Most retail stores sell this product at a price in line with the MSRP. You have just learned that a local electronics retailer is selling the game for 45% off. What is the sale price for the video game and what dollar amount is saved?

Plan:
There are two unknown variables. The first is the video game’s sale price ( $S_o_n_s_a_l_e$ ). The second is the markdown amount ( $D\char36$ ) that is realized at that sale price.

Understand:
Step 1: The regular selling price for the video game and the markdown rate are known:

$S$ = $189.99
$d$ = 0.45

Step 2: Calculate the sale price by applying Formula 1.10.

Calculate the markdown amount by applying Formula 1.11b.

Perform:
Step 2:

$S_o_n_s_a_l_e=\char36 189.99\times(1-0.45)$
$=\char36 189.99\times0.55=\char36 104.49$

$D\char36=\char36 189.99-\char36 104.49=\char36 85.50$

Present:
The sale price for the video game is $104.49. When purchased on sale, “Guitar Hero: World Tour” is $85.50 off of its regular price.

Example 1.3B – Markdown Requiring Selling Price Calculation

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 markdown percent?

Plan:
The unknown variables for the iPad are the sale price ( $S_o_n_s_a_l_e$ ) and the markdown rate ( $d$ ).

Understand:
Step 1: The pricing elements of the iPad along with the markdown dollars are known:

$C$ = $650
$E = 0.2C$
$P = 0.15C$
$D\char36$ = $100

Calculate the selling price of the product by applying Formula 1.5.

Step 2: Calculate the markdown percent by applying Formula 1.12.

Calculate the sale price by applying Formula 1.11b, rearranging for $S_o_n_s_a_l_e$ .

Perform:
Step 1:

$S=\char36 650+0.2(\char36 650)+0.15(\char36 650)=\char36 877.50$

Step 2:

$d=\frac{\char36 100}{\char36 877.50}\times100=11.396\%$

$\char36 100=\char36 877.50-S_o_n_s_a_l_e$
$S_o_n_s_a_l_e=\char36 777.50$

Present:
When the iPad is advertised at $100 off, it receives an 11.396% markdown and it will retail at a sale price of $777.50.

The section is reproduced from Chapter 4.3 in Fundamentals of Business Mathematics by OER Lab licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

competition Bureau, Fair Business Practices Branch, Price Scanning Report, Table B, page 5, 1999, www.competitionbureau.gc.ca/epic/site/cb-bc.nsf/en/01288e.html ↵

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