# 4.3 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. In addition to price inaccuracies having an impact on business finances and customers’ pocketbooks, scanner price inaccuracy may result in violations of Canada’s *Competition Act.* The *Scanner Price Accuracy Volunteer Code* endorsed by Competition Bureau of Canada and managed by the Retail Council of Canada on behalf of participating Canadian retailers may result in even greater impacts to business finances. Under the code, when the scanned price of an item without a price tag is higher than the displayed price, the customer is entitled to receive the item free of charge when it is worth less than $10, or receive a $10 reduction if the correct price is worth more than $10. ^{[1]} Clearly, it is important for you as a consumer and as a business operator 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:

. 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 excess or unwanted inventory**. 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.**Clearing out damaged or discontinued items**. 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.**Increasing sales volumes**. 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.**Promoting add-on purchases**

Markdowns are no different from offering a discount. Recall from Section 4.1 that one of the types of discounts is known as a sale discount. The only difference here lies in choice of language. Both discount and markdown represent reduction in listed price, but discount is the reduction from the consumer’s point of view and markdown is the same reduction, but from the retailer’s point of view. 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. Recall the relationship introduced in Section 4.1 that calculates the net price for a product after it receives a single discount on the listed price:

[latex]N=L\cdot(1-d)[/latex]

This adapts to markdown situations.

#### The sale price of a product

[latex]\text{sale price}=\text{regular selling price}\cdot(1-\text{markdown rate})[/latex]

[latex]N=S(1-d)[/latex]

** [latex]N[/latex]** 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.

** [latex]S[/latex]** 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 Section 4.1 or Section 4.2.

** [latex]d[/latex]** is **markdown rate**: A markdown rate is the same as a sale discount rate. As in formula for a discount rate, 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 the basic formula from above in the same manner that we calculate multiple discounts in trade discounts.

If you are interested in the markdown amount in dollars, recall the two relationships from discussions on trade discounts:

[latex]D=L\cdot d[/latex]

[latex]D=L-N[/latex]

We can adapt these formulas to markdown situations.

#### Markdown amount

[latex]\text{markdown amount}=(\text{regular selling price})\cdot (\text{markdown rate})[/latex]

[latex]D=S\cdot d[/latex]

[latex]\text{markdown amount}=(\text{regular selling price})- (\text{sale price})[/latex]

[latex]D=S-N[/latex]

** [latex]D[/latex]** is **markdown amount**: Markdown amount is the reduction amount from the regular selling price.

** [latex]S[/latex]** is **selling price**: The regular selling price before you apply any markdown percentages.

** [latex]d[/latex]** 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, or 100%.

** [latex]N[/latex]** 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 calculating a markup on selling price percent:

[latex]m_S=\frac{M}{S}[/latex]

This adapts to markdown situations.

#### Markdown rate

[latex]\begin{align*} \text{markdown rate}&=\frac{\text{markdown amount}}{\text{regular selling price}}\\ \\ d&=\frac{D}{S}\\ &=\frac{D}{S}\cdot 100\% \end{align*}[/latex]

** [latex]d[/latex]** is **markdown rate**: Markdown amount represented as a percentage of the selling price. Use the same symbol for a discount rate, since markdown rates are synonymous with sale discounts.

** [latex]D[/latex]** is **markdown amount**: The total dollar amount deducted from the regular selling price.

** [latex]S[/latex]** is **selling price**: The regular selling price of the product before any discounts.

**[latex]\cdot 100\%[/latex]** is **percent conversion**: The markdown is always expressed as a percentage.

Recall from Section 4.2 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 are the sale price and the markdown amount?

Sale price:

[latex]N=(\text{selling price})(1-\text{markdown rate})= 39.99\cdot(1-0.10)=\$ 35.99[/latex]

Markdown amount:

[latex]D=(\text{markdown rate})\cdot (\text{reg. selling price})=0.10\cdot 39.99=\$ 4.00[/latex]

Alternatively, [latex]D=(\text{reg. selling price})-(\text{sale price})=39.99-35.99=\$ 4.00[/latex]

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 Section 4.2, 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.

#### Example 4.3A – 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?

**Answer: **sale price = ?, markdown amount = ?

Conditions: reg. selling price (MSRP) = $189.99, markdown rate = 45%

Sale price:

[latex]\begin{align*} \text{sale price}&=(\text{reg. selling price})(1-\text{markdown rate})\\ &= 189.99(1- 0.45)\\ &=\$104.49 \end{align*}[/latex]

Markdown amount:

[latex]\begin{align*} \text{markdown amount}&=(\text{markdown rate})(\text{reg. selling price})\\ &= 0.45\cdot 189.99\\ &=\$85.50 \end{align*}[/latex]

Therefore 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 4.3B – 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?

**Answer: **sale price = ?, markdown rate = ?

Conditions: cost [latex]C= $650[/latex], expenses [latex]E = 20\% \text{ of cost}[/latex], profits [latex]P= 15\% \text{ of cost}[/latex], markdown amount [latex]D= $100[/latex]

Sale price:

[latex]\begin{align*} \text{sale price}&=(\overset{?}{\text{selling price}})-(\overset{\checkmark}{\text{markdown amount}})\\ \\ &=(C+E+P)-D\\ &=C+0.20C+0.15C-D\\ &=1.35C-D\\ \\ &=1.35(650)-100=\$777.50 \end{align*}[/latex]

Markdown rate:

[latex]\begin{align*} \text{markdown rate}&=\frac{\text{markdown amount}}{\text{selling price}}\\ &=\frac{\text{markdown amount}}{1.35(\text{cost})}\\ &=\frac{100}{1.35(650)}=0.11396=11.396\% \end{align*}[/latex]

Hence, 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.

### Never-Ending Sales

Have you noticed that some companies always seem to have the same item on sale all of the time? This is a common marketing practice. Recall the third and fourth circumstances for markdowns. Everybody loves a sale, so markdowns increase sales volumes for both the marked-down product and other regularly priced items.

For example, Michaels has a product line called the Lemax Village Collection, which has seasonal display villages for Christmas, Halloween, and other occasions. When these seasonal product lines come out, Michaels initially prices them at the regular unit selling price for a short period and then reduces their price. For Michaels, this markdown serves a strategic purpose. The company’s weekly flyers advertising the Lemax Village Collection sale attract consumers who usually leave the store with other regularly priced items.

If an item is on sale all the time, then businesses plan the pricing components with the sale price in mind. Companies using this technique determine the unit profitability of the product at the sale price and not the regular selling price. They adapt the selling price calculation as follows:

[latex]S=C+E+P[/latex]

becomes

[latex]S_{\text{at sale}}=C+E+P_{\text{at sale}}[/latex]

where [latex]P_{\text{at sale}}[/latex] represents the planned profit amount when the product is sold at the sale price. This is not a new formula, just a new application of the selling price calculation.

### How It Works

Under normal circumstances, when businesses set their selling and sale prices they follow a three-step procedure:

- Determine the product’s cost, expenses, and profit amount.
- Set the regular selling price of the product.
- If a markdown is to be applied, determine an appropriate markdown rate or amount and set the sale price.

However, when a product is planned to always be on sale, businesses follow these steps instead to set the sale price and selling price:

**Step 1:** Set the planned markdown rate or markdown dollars. Determine the pricing components such as cost and expenses. Set the profit so that when the product is marked down, the profit amount is achieved. Alternatively, a planned markup on cost, markup on selling price, or even markup dollars may be set for the sale price.

**Step 2:** Calculate the sale price of the product. If cost, expenses, and profit are known, apply the adapted version of selling price calculation. Alternatively, adapt and apply any of the other markup formulas with the understanding that the result is the sale price of the product and not the regular selling price.

**Step 3:** Using the known markdown rate or markdown amount, set the regular selling price by applying any appropriate markdown formula.

Assume for the Michael’s Lemax Village Collection that most of the time these products are on sale for 40% off. A particular village item costs $29.99, expenses are $10.00, and a planned profit of $8.00 is achieved at the sale price. Calculate the sale price and the selling price.

**Step 1:** The known variables at the sale price are

[latex]\begin{align*} C &= $29.99\\ E &= $10.00\\ P &= $8.00\\ d &= 0.40\\ \end{align*}[/latex]

**Step 2:** Adapting selling price calculation, the sale price is

[latex]S_{\text{at sale}}=C+E+P_{\text{at sale}}=$ 29.99+$ 10.00+$ 8.00=$ 47.99[/latex].

This is the price at which Michael’s plans to sell the product.

**Step 3:** However, to be on sale there must be a regular selling price. Therefore, if the 40% off results in a price of $47.99, apply markdown formula and rearrange to get the selling price:

[latex]\begin{align*} \text{sale price}&=(\text{reg. selling price})(1-\text{markdown rate})\\ \\ &\Rightarrow \text{reg. selling price}=\frac{\text{sale price}}{1-\text{markdown rate}}=\frac{47.99}{1-0.40}=\$ 79.98 \end{align*}[/latex]

Therefore, the product’s selling price is $79.98, which, always advertised at 40% off, results in a sale price of $47.99. At this sale price, Michael’s earns the planned $8.00 profit.

You may ask, “If the product is always on sale, what is the importance of establishing the regular price?” While this textbook does not seek to explain the law in depth, it is worth mentioning that pricing decisions in Canada are regulated by the Competition Act. With respect to the discussion of never-ending sales, the Act does require that the product be sold at a regular selling price for a reasonable period of time or in reasonable quantity before it can be advertised as a sale price.

If you revisit the Michael’s example, note in the discussion that the village initially needs to be listed at the regular selling price before being lowered to the sale price.

**Give It Some Thought:**

- If a product has a markup on cost of 40% and a markdown of 40%, will it sell above or below cost?
- What happens to the profit if a product that is always on sale actually sells at the regular selling price?
- Under normal circumstances, arrange from smallest to largest: regular selling price, cost, and sale price.

#### Example 4.3C – Setting the Price in a Never-Ending Sale

An electronics retailer has 16GB USB sticks on sale at 50% off. It initially priced these USB sticks for a short period of time at regular price, but it planned at the outset to sell them at the sale price. The company plans on earning a profit of 20% of the cost when the product is on sale. The unit cost of the USB stick is $22.21, and expenses are 15% of the cost.

a. At what price will the retailer sell the USB stick when it is on sale?

b. To place the USB stick on sale, it must have a regular selling price. Calculate this price.

c. If the USB stick is purchased at the regular selling price during the initial time period, how much profit is earned?

**Answer:**

a. This company plans on always having the product on sale [latex]\Rightarrow S_{\text{at sale}}=?[/latex]

Conditions: markdown rate = 50%, profit at sale = 20% of cost, cost = $22.21, expenses = 15% of cost

[latex]\begin{align*} S_{\text{at sale}}&=C+E+P_{\text{at sale}}\\ &=C+0.15C+0.2C=1.35C\\ &=1.35(22.21)=\$29.98 \end{align*}[/latex]

b. regular selling price = ?

[latex]\begin{align*} \text{sale price}&=(\text{reg. selling price})(1-\text{markdown rate})\\ \\ &\Rightarrow \text{reg. selling price}=\frac{\text{sale price}}{1-\text{markdown rate}}=\frac{29.98}{1-0.5}=\$59.96 \end{align*}[/latex]

c. profit at the regular selling price =?

[latex]\begin{align*} \text{reg. selling price}&=\text{cost}+\text{expenses}+\text{profit}\\ \\ \Rightarrow \text{profit}&=\text{reg. selling price}-\text{cost}-\text{expenses}\\ \\ &=59.96-22.21-0.15(22.21)=\$34.42 \end{align*}[/latex]

Therefore, the USB stick is on sale for $29.98, letting the company achieve its profit of $4.44 per unit. During the initial pricing period, the USB stick sells for $59.96 (its regular selling price). If a consumer actually purchases a USB stick during the initial pricing period, the electronics store earns a profit of $34.42 per unit (which is a total of the $4.44 planned profit plus the planned markdown amount of $29.96).

#### Give It Some Thought Answers

- Below cost, since the 40% markdown is off of the selling price, which is a larger value.
- The profit will be increased by the markdown amount.
- Cost, sale price, regular selling price.

## Section Exercises

Work on section 4.3 exercises in Fundamentals of Business Math Exercises. Discuss your solutions with your peers and/or course instructor.

You may consult answers to select exercises: Fundamentals of Business Math Exercises – Select Answers

- Competition Bureau of Canada. Deceptive marketing practices: Scanner price accuracy. https://www.competitionbureau.gc.ca/eic/site/cb-bc.nsf/eng/03252.html ↵