4.4: Markdown: Setting the Sale Price
Formula & Symbol Hub
For this section you will need the following:
Symbols Used
- [latex]C[/latex] = Cost
- [latex]d[/latex] = Markdown rate, discount rate
- [latex]D\$[/latex] = Markdown amount, discount amount
- [latex]E[/latex] = Expenses
- [latex]L[/latex] = List price
- [latex]N[/latex] = Net price
- [latex]P[/latex] = Profit
- [latex]P_{onsale}[/latex] = Planned profit amount
- [latex]S[/latex] = Selling price
- [latex]S_{onsale}[/latex] = Sale price
Formulas Used
-
Formula 4.2a – Single Discount
[latex]\begin{eqnarray*}N&=&L\times(1-d)\end{eqnarray*}[/latex]
-
Formula 4.2b – Discount Amount
[latex]\begin{eqnarray*}D\$&=&L\times d\end{eqnarray*}[/latex]
-
Formula 4.2c – Discount Amount
[latex]\begin{eqnarray*}D\$&=&L-N\end{eqnarray*}[/latex]
-
Formula 4.4a – The Sale Price of a Product
[latex]\begin{eqnarray*}S_{onsale}&=&S\times (1-d)\end{eqnarray*}[/latex]
-
Formula 4.4b – Markdown Amount
[latex]\begin{eqnarray*}D\$&=&S\times d\end{eqnarray*}[/latex]
-
Formula 4.4c – Markdown Amount
[latex]\begin{eqnarray*}D\$&=&S-S_{onsale}\end{eqnarray*}[/latex]
-
Formula 4.4d – Markdown Percentage
[latex]\begin{eqnarray*}d&=&\frac{D\$}{S}\times 100\end{eqnarray*}[/latex]
-
Formula 4.4e – The Selling Price of a Product Adapted
[latex]S_{onsale}=C+E+P_{onsale}[/latex]
Introduction
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 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 4.1a[latex]N=L\times(1−d)[/latex], introduced in Section 4.1, calculates the net price for a product after it receives a single discount:
[latex]\boxed{4.1\text{a}}[/latex] [latex]\text{Single Discount:}\;{\color{red}{N}}\;=\;{\color{green}{L}}\;\times\;(1\;-\;{\color{blue}{d}})[/latex]
Formula 4.4a adapts this formula for use in markdown situations.
[latex]\boxed{4.4\text{a}}[/latex] The Sale Price Of A Product
[latex]{\color{chocolate}{S}}_{\color{chocolate}{{onsale}}}\;\text{is Sale Price:}[/latex] 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]{\color{green}S}\;\text{is Selling Price:}[/latex] 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 4.2 or Section 4.3.
[latex]{\color{blue}{d}}\;\text{is Markdown Rate:}[/latex] A markdown rate is the same as a sale discount rate. Therefore, you use the same discount rate symbol ([latex]d[/latex]) 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.
—
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 4.4a to calculate multiple discounts.
If you are interested in the markdown amount in dollars, recall that Formula 4.1b[latex]D\$=L\times d[/latex] calculates the discount amount in dollars. Depending on what information is known, the formula has two variations:
[latex]\boxed{4.1\text{b}}[/latex] [latex]\text{Discount Amount:}\;{\color{red}{D}}{\color{red}{\$}}={\color{green}{L}}\times{\color{blue}{d}}[/latex]
[latex]\boxed{4.1\text{c}}[/latex] [latex]\text{Discount Amount:}\;{\color{red}{D}}{\color{red}{\$}}={\color{green}{L}}{\color{black}{-}}{\color{purple}{N}}[/latex]
—
Formula 4.4b and Formula 4.4c adapt these formulas to markdown situations.
[latex]\boxed{4.4\text{b}}[/latex] Markdown Amount
[latex]{\color{red}{D}}{\color{red}{\$}}\;\text{is Markdown Amount:}[/latex] 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 4.4b. If you know the selling price and sale price, apply Formula 4.4c.
[latex]{\color{green}{S}}\;\text{is Selling Price:}[/latex] The regular selling price before you apply any markdown percentages.
[latex]{\color{blue}{d}}\;\text{is Markdown Rate:}[/latex] 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 4.4a[latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex].
[latex]\boxed{4.4\text{c}}[/latex] Markdown Amount
[latex]{\color{red}{D}}{\color{red}{\$}}\;\text{is Markdown Amount:}[/latex] 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 4.4b. If you know the selling price and sale price, apply Formula 4.4c.
[latex]{\color{green}{S}}\;\text{is Selling Price:}[/latex] The regular selling price before you apply any markdown percentages.
[latex]{\color{chocolate}{S}}_{\color{chocolate}{{onsale}}}\;\text{is Sale Price:}[/latex] 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 the formula which calculated a markup on selling price percent: [latex]MoS\%=\frac{M\$}S\times100[/latex]
Formula 4.4d adapts this formula to markdown situations.
[latex]\boxed{4.4\text{d}}[/latex] Markdown Percentage
[latex]{\color{blue}{d}}\;\text{is Markdown Percentage:}[/latex] 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.
[latex]{\color{red}{D}}{\color{red}{\$}}\;\text{is Markdown Amount:}[/latex] The total dollar amount deducted from the regular selling price.
[latex]{\color{green}{S}}\;\text{is Selling Price:}[/latex] The regular selling price of the product before any discounts.
[latex]{\color{purple}{\times}}{\;}{\color{purple}{100}}\;\text{is Percent Conversion:}[/latex] The markdown is always expressed as a percentage.
HOW TO
Calculate a Markdown
Step 1: Across all three markdown formulas, the four variables consist of the selling price ([latex]S[/latex]), sale price ([latex]S_{onsale}[/latex]), markdown dollars ([latex]D\$[/latex]), and markdown rate ([latex]d[/latex]). 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 Formula 4.4a[latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex], Formula 4.4b[latex]\text{D}\$=\text{S}\times d[/latex], Formula 4.4c[latex]\text{D}\$=\text{S}−\text{S}_\textrm{onsale}[/latex], and Formula 4.4d[latex]\begin{align*}d=\frac{\text{D}\$}{\text{S}}\times 100\end{align*}[/latex] to calculate the unknown variable(s). In the event that multiple markdown rates apply, extend Formula 4.4a[latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex] to accommodate as many markdown rates as required.
Recal the example of the MP3 player with a regular selling price of [latex]\$39.99[/latex]. Assume the retailer has excess inventory and places the MP3 player on sale for [latex]10\%[/latex] off. What is the sale price and markdown amount?
Step 1: The selling price and markdown percent are [latex]S=\$39.99[/latex] and [latex]d=0.10[/latex], respectively.
Step 2: Apply Formula 4.4a[latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex] to calculate the sale price, resulting in:
[latex]\begin{eqnarray*}S_{onsale}&=&\$39.99\times(1–0.10)\;\\S_{onsale}&=&\$35.99\end{eqnarray*}[/latex]
Step 3: You could use either of Formula 4.4b[latex]\text{D}\$=\text{S}\times d[/latex] or Formula 4.4c[latex]\text{D}\$=\text{S}−\text{S}_\textrm{onsale}[/latex] to calculate the markdown amount since the selling price, sale price, and markdown percent are all known. Arbitrarily choosing Formula 4.4b[latex]\text{D}\$=\text{S}\times d[/latex], you calculate a markdown amount of:
[latex]\begin{eqnarray*}D\$&=&\$39.99\times0.10\;\\D\$&=&\$4.00\end{eqnarray*}[/latex]
Therefore, if the retailer has a [latex]10\%[/latex] off sale on the MP3 players, it marks down the product by [latex]\$4.00[/latex] and retails it at a sale price of [latex]\$35.99[/latex].
Key Takeaways
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!
Paths To Success
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.
Example 4.4.1
The MSRP for the “Guitar Hero: World Tour” video game is [latex]\$189.99[/latex]. 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 [latex]45\%[/latex] off. What is the sale price for the video game and what dollar amount is saved?
Solution
Step 1: Write what we know from the question.
The regular selling price for the video game and the markdown rate are known:
[latex]\begin{eqnarray*}S&=&\$189.99\\d&=&0.45\end{eqnarray*}[/latex]
Step 2: Calculate the sale price by applying Formula 4.4a.[latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex]
[latex]\begin{eqnarray*}S_{onsale}&=&\$189.99\times(1\;–\;0.45)\;\;\\S_{onsale}&=&\$189.99\times0.55\;\\S_{onsale}&=&\$104.49\end{eqnarray*}[/latex]
Step 3: Calculate the markdown amount by applying Formula 4.4c.[latex]\text{D}\$=\text{S}−\text{S}_\textrm{onsale}[/latex]
[latex]\begin{eqnarray*}D\$&=&\$189.99-\$104.49\;\\D\$&=&\$85.50\end{eqnarray*}[/latex]
Step 4: Write as a statement.
The sale price for the video game is [latex]\$104.49[/latex]. When purchased on sale, “Guitar Hero: World Tour” is [latex]\$85.50[/latex] off of its regular price.
Example 4.4.2
A reseller acquires an Apple iPad for [latex]\$650[/latex]. Expenses are planned at [latex]20\%[/latex] of the cost, and profits are set at [latex]15\%[/latex]of the cost. During a special promotion, the iPad is advertised at [latex]\$100[/latex] off. What is the sale price and markdown percent?
Solution
Step 1: Write what you know from the question.
The pricing elements of the iPad along with the markdown dollars are known:
[latex]\begin{eqnarray*}C&=&\$650\\E&=&0.2C\\P&=&0.15C\\D\$&=&\$100\end{eqnarray*}[/latex]
Step 2: Calculate the selling price of the product by applying Formula 4.3a.[latex]\text{S}=\text{C}+\text{E}+\text{P}[/latex]
[latex]\begin{eqnarray*}S&=&\$650+0.2(\$650)+0.15(\$650)\\S&=&\$877.50\end{eqnarray*}[/latex]
Step 3: Calculate the markdown percent by applying Formula 4.4d.[latex]\begin{align*}d=\frac{\text{D}\$}{\text{S}}\times 100\end{align*}[/latex]
[latex]\begin{eqnarray*}d&=&\frac{\$100}{\$877.50}\times100\\[1ex]d&=&11.396\%\end{eqnarray*}[/latex]
Step 4: Calculate the sale price by applying Formula 4.4c.[latex]\text{D}\$=\text{S}−\text{S}_\textrm{onsale}[/latex].
[latex]\begin{eqnarray*}\$100&=&\$877.50-S_{onsale}\;\;\\S_{onsale}&=&\$777.50\end{eqnarray*}[/latex]
Step 5: Write as a statement.
When the iPad is advertised at [latex]\$100[/latex] off, it receives an [latex]11.396\%[/latex] markdown and it will retail at a sale price of [latex]\$777.50[/latex].
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.
[latex]\boxed{4.4\text{e}}[/latex] The Selling Price of a Product Adapted
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 Formula 4.3a[latex]\text{S}=\text{C}+\text{E}+\text{P}[/latex] as follows:
Where [latex]P_{onsale}[/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 Formula 4.3a[latex]\text{S}=\text{C}+\text{E}+\text{P}[/latex].
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Under normal circumstances, when businesses set their selling and sale prices they follow a three-step procedure:
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- 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:
HOW 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 Formula 4.4e[latex]S_{onsale}=C+E+P_{onsale}[/latex], the adapted version of Formula 4.3a[latex]\text{S}=\text{C}+\text{E}+\text{P}[/latex]. Alternatively, adapt and apply any of the other markup formulas (Formula 4.3b[latex]\text{M}\$=\text{E}+\text{P}[/latex] through Formula 4.3e[latex]\begin{align*}\text{MoS}\%=\frac{\text{M}\$}{\text{S}}\times 100\end{align*}[/latex]) 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 (Formula 4.4a[latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex] through Formula 4.4d[latex]\begin{align*}d=\frac{\text{D}\$}{\text{S}}\times 100\end{align*}[/latex]).
Assume for the Michael’s Lemax Village Collection that most of the time these products are on sale for [latex]40\%[/latex] off. A particular village item costs [latex]\$29.99[/latex], expenses are [latex]\$10.00[/latex], and a planned profit of [latex]\$8.00[/latex] 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{eqnarray*}C&=&\$29.99\\E&=&\$10.00\\P&=&\$8.00\\d&=&0.40\end{eqnarray*}[/latex]
Step 2: Adapting Formula 4.3a[latex]\text{S}=\text{C}+\text{E}+\text{P}[/latex], the sale price is:
[latex]\begin{eqnarray*}S_{onsale}&=&C+\;E+P_{onsale}\;\\S_{onsale}&=&\$29.99+\$10.00+\$8.00\;\\S_{onsale}&=&\$47.99\end{eqnarray*}[/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 [latex]40\%[/latex] off results in a price of [latex]\$47.99[/latex], apply Formula 4.4a[latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex] and rearrange to get the selling price:
[latex]\begin{eqnarray*}S&=&\$47.99\;\div(1\;–\;0.40)\;\\S&=&\$79.98\end{eqnarray*}[/latex]
Therefore, the product’s selling price is [latex]\$79.98[/latex], which, always advertised at [latex]40\%[/latex] off, results in a sale price of [latex]\$47.99[/latex]. At this sale price, Michael’s earns the planned [latex]\$8.00[/latex] profit.
Key Takeaways
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.
Try It
1) Answer the following questions:
- If a product has a markup on cost of [latex]40\%[/latex] and a markdown of [latex]40\%[/latex], 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.
Solution
- Below cost, since the [latex]40\%[/latex] 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.
Example 4.4.3
An electronics retailer has 16GB USB sticks on sale at [latex]50\%[/latex] 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 [latex]20\%[/latex] of the cost when the product is on sale. The unit cost of the USB stick is [latex]\$22.21[/latex], and expenses are [latex]15\%[/latex] 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?
Solution
Step 1: Write what you know from the question.
You know the unit cost, the retailer’s associated expenses, its planned profit at the sale price, and the markdown rate:
[latex]\begin{eqnarray*}d&=&0.50\;\\C&=&\$22.21\;\;\\E&=&\;0.15C\\P_{onsale}&=&0.2C\end{eqnarray*}[/latex]
Step 2: To solve part a. apply Formula 4.4e.
[latex]\begin{eqnarray*}S_{onsale}&=&C+E+P_{onsale}\\S_{onsale}\;&=&\$22.21+0.15(\$22.21)+0.2(\$22.21)\;\;\\S_{onsale}&=&\$22.21+\$3.33+\$4.44\;\\S_{onsale}&=&\$29.98\\\end{eqnarray*}[/latex]
Step 3: After you know the sale price, solve part b. by applying Formula 4.4a.[latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex]
[latex]\begin{eqnarray*}\$29.99&=&S\times(1\;–\;0.5)\\\$29.98&=&S\times0.5\\\$59.96&=&S\end{eqnarray*}[/latex]
Step 4: Solving part c. requires applying Formula 4.3a.[latex]\text{S}=\text{C}+\text{E}+\text{P}[/latex]
[latex]\begin{eqnarray*}\$59.96&=&\$22.21+\$3.33+P\;\;\\\$59.96&=&\$25.54+P\;\;\\\$34.42&=&P\end{eqnarray*}[/latex]
Step 5: Write as a statement.
The USB stick is on sale for [latex]\$29.98[/latex], letting the company achieve its profit of [latex]\$4.44[/latex] per unit. During the initial pricing period, the USB stick sells for [latex]\$59.96[/latex] (its regular selling price). If a consumer actually purchases a USB stick during the initial pricing period, the electronics store earns a profit of [latex]\$34.42[/latex] per unit (which is a total of the [latex]\$4.44[/latex] planned profit plus the planned markdown amount of [latex]\$29.96[/latex]).
Section 4.4 Exercises
Round all money to two decimals and percentages to four decimals for each of the following exercises.
Mechanics
For questions 1–6, solve for the unknown variables (identified with a ?) based on the information provided.
|
|
Regular Selling Price |
Markdown Amount |
Markdown Percent |
Sale Price |
|
1. |
[latex]\$439.85[/latex] |
? |
[latex]35\%[/latex] |
? |
|
2. |
? |
[latex]\$100.00[/latex] |
? |
[latex]\$199.95[/latex] |
|
3. |
[latex]\$1,050.00[/latex] |
? |
? |
[latex]\$775.00[/latex] |
|
4. |
[latex]\$28,775.00[/latex] |
[latex]\$3,250.00[/latex] |
? |
? |
|
5. |
? |
? |
[latex]33\%[/latex] |
[latex]\$13,199.95[/latex] |
|
6. |
? |
[latex]\$38.33[/latex] |
[latex]12\%[/latex] |
? |
Solutions
- .[latex]D\$ = \$153.95[/latex]; [latex]S_{onsale} = \$285.90[/latex]
- [latex]S = \$299.95[/latex]; [latex]d = 33.3389\%[/latex]
- [latex]D\$ = \$275[/latex]; [latex]d = 26.1905\%[/latex]
- [latex]S_{onsale} = \$25,525[/latex]; [latex]d = 11.2945\%[/latex]
- [latex]S = \$19,701.42[/latex]; [latex]D\$ = \$6,501.47[/latex]
- [latex]S = \$319.42[/latex]; [latex]S{onsale} = \$281.09[/latex]
Applications
- A pair of Nike athletic shoes is listed at a regular selling price of [latex]\$89.99[/latex]. If the shoes go on sale for [latex]40\%[/latex] off, what is the sale price?
- During its special Bay Days, The Bay advertises a Timex watch for [latex]\$39.99[/latex] with a regular price of [latex]\$84.99[/latex]. Calculate the markdown percent and markdown amount.
- 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 [latex]\$2,349[/latex] for air and six nights all inclusive, offers an early-bird booking discount of [latex]\$350[/latex]. What markdown percentage is being offered for booking early?
- A Heritage Infusio deep frying pan is advertised at [latex]70\%[/latex] off with a sale price of [latex]\$39.99[/latex]. What is the frying pan’s regular selling price, and what markdown amount does this represent?
- A mass merchandiser uses its Lagostina cookware product line as a marketing tool. The cookware is always on sale at an advertised price of [latex]45\%[/latex] off. The cost of the cookware is [latex]\$199.99[/latex], expenses are [latex]\$75[/latex], and the planned profit at the sale price is [latex]\$110[/latex]. Calculate the sale price and selling price for the cookware.
- Quicky Mart regularly sells its Red Bull sports drink for [latex]\$2.99[/latex] per can. Quicky Mart noticed that one of its competitors down the street sells Red Bull for [latex]\$1.89[/latex]. What markdown percentage must Quicky Mart advertise if it wants to match its competitor?
- A hardware store always advertises a Masterdesigner 75-piece screwdriver set at [latex]80\%[/latex] off for a sale price of [latex]\$17.99[/latex].
- If the cost of the set is [latex]\$10[/latex] and expenses are [latex]30\%[/latex] of the sale price, what is the planned profit when the product is on sale?
- What profit is earned if the product actually sells at its regular selling price?
- A campus food outlet is advertising a “Buy one, get one [latex]25\%[/latex] off” deal. The [latex]25\%[/latex] off comes off the lower-priced item. If you purchase a chicken dinner for [latex]\$8.99[/latex] and your friend gets the burger combo for [latex]\$6.99[/latex], what is the markdown percentage on the total price?
- Blast’em Stereos purchases a stereo system for [latex]\$1,900[/latex] less two discounts of [latex]40\%[/latex] and [latex]18\%[/latex]. The store uses this product to draw customers to the store and always offers the stereo on sale at [latex]25\%[/latex] off. When the stereo is on sale, it plans on expenses equalling [latex]30\%[/latex] of the cost and a profit of [latex]20\%[/latex] of the sale price.
- What is the sale price for the stereo?
- How much profit does Blast’em make when the stereo sells at the sale price?
- By law, this stereo must sell at the regular selling price for a period of time before going on sale. What is the regular selling price?
- What profit does Blast’em earn if a customer purchases the stereo during this initial period?
Solutions
- [latex]S_{onsale} = \$53.99[/latex]
- [latex]D\$ = \$45[/latex]; [latex]d = 52.9474\%[/latex]
- [latex]d = 14.9\%[/latex]
- [latex]S = \$133.30[/latex]; [latex]D\$ = \$93.31[/latex]
- [latex]S_{onsale} = \$384.99[/latex]; [latex]S = \$699.98[/latex]
- [latex]d = 36.7893[/latex]
- a. [latex]P_{onsale} = \$2.59[/latex]; b. [latex]P = \$74.55[/latex]
- [latex]d = 10.9512\%[/latex]
- a. [latex]S_{onsale} = \$1,519.05[/latex]; b. [latex]P_{onsale} = \$303.81[/latex]; c. [latex]S = \$2,025.40[/latex]; d. [latex]P = \$810.16[/latex]
Challenge, Critical Thinking, & Other Applications
- Frigid Boards purchases one of its snowboards for [latex]\$395[/latex] less a retail trade discount of [latex]15\%[/latex] and a loyalty discount of [latex]4\%[/latex]. Its markup on selling price percentage on all snowboards is [latex]21\%[/latex]. At the end of the season, any leftover snowboards are marked down by [latex]10\%[/latex]. What is the sale price for the snowboard?
- An HP LaserJet printer has an MSRP of [latex]\$399.95[/latex]. It is subject to trade discounts of [latex]30\%[/latex] and [latex]23\%[/latex]. The LaserJet is a featured item for a computer store and is always on sale. The store plans to sell the LaserJet for a sale price that allows it to cover expenses equalling [latex]15\%[/latex] of cost and realize a profit of [latex]\$35.00[/latex].
- What is the sale price?
- If the MSRP is the regular unit price of the printer, what rate of markdown can the computer store advertise?
- What markup on selling price percentage is realized at the sale price?
- The Brick advertises that when you purchase a queen-size Tempur-Pedic mattress set for [latex]\$2,499.97[/latex] it will give you a 51″ 3-D plasma television with a 3-D starter kit included. The value of this gift is [latex]\$1,199.99[/latex]. What markdown percent does this represent?
- A Maytag 27 cubic foot refrigerator retails for [latex]\$2,400.00[/latex] at Landover Appliance Centre. The company, which is celebrating its 30th anniversary this coming weekend, features the fridge for [latex]30\%[/latex] off. The markup on selling price percentage on the fridge at the regular unit selling price is [latex]53\%[/latex].
- What is the sale price?
- At the sale price, what is the markup on selling price percentage?
- If the expenses are [latex]15\%[/latex] of the regular selling price, what is the profit when the fridge is on sale?
- Dreger Jewellers is selling a diamond bracelet. It uses this bracelet in its promotions and almost always has it on sale. The cost of the bracelet is [latex]\$2,135[/latex] less discounts of [latex]20\%[/latex] and [latex]30\%[/latex]. When the bracelet is on sale for [latex]25\%[/latex] off, the expenses are [latex]15\%[/latex] of cost and the profit is [latex]20\%[/latex] of cost.
- What is the sale price?
- What is the bracelet’s regular selling price?
- If the bracelet sells at the regular selling price, what are the markup amount and the markup on cost percent?
Solutions
- [latex]S_{onsale} = \$367.20[/latex]
- a. [latex]S_{onsale} = \$282.91[/latex]; b. [latex]d = 29.2637\%[/latex]; c. [latex]MoS\% = 23.8026\%[/latex]
- [latex]D = 32.4325\%[/latex]
- a. [latex]S_{onsale} = \$1,680[/latex]; b. [latex]MoS\%[/latex] when on sale = [latex]32.8571\%[/latex]; c. [latex]P_{onsale} = \$192.00[/latex]
- a. [latex]S_{onsale} = \$1,614.06[/latex]; b. [latex]S = \$2,152.08[/latex]; c. [latex]M\$ = \$956.48[/latex]; [latex]MoC\% = 80\%[/latex]
THE FOLLOWING LATEX CODE IS FOR FORMULA TOOLTIP ACCESSIBILITY. NEITHER THE CODE NOR THIS MESSAGE WILL DISPLAY IN BROWSER.[latex]S_{onsale}=C+E+P_{onsale}[/latex][latex]N=L\times(1−d)[/latex][latex]\text{D}\$=\text{S}\times d[/latex][latex]D\$=L\times d[/latex][latex]S_\textrm{onsale}=\text{S}\times(1 − d)[/latex][latex]\text{D}\$=\text{S}−\text{S}_\textrm{onsale}[/latex][latex]\begin{align*}d=\frac{\text{D}\$}{\text{S}}\times 100\end{align*}[/latex][latex]\text{S}=\text{C}+\text{E}+\text{P}[/latex][latex]\text{M}\$=\text{E}+\text{P}[/latex][latex]\begin{align\text{MoS}\%=\frac{\text{M}\$}{\text{S}}\times 100\end{align*}[/latex]
Attribution
“6.3 Markdown: Setting the Sale Price” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.
