6.2: Markup- Setting the Regular Price (Need to Stay in Business)
- Page ID
- 22098
As you wait in line to purchase your Iced Caramel Macchiato at Starbucks, you look at the pricing menu and think that $4.99 seems like an awful lot of money for a frozen coffee beverage. Clearly, the coffee itself doesn’t cost anywhere near that much. But then gazing around the café, you notice the carefully applied colour scheme, the comfortable seating, the high-end machinery behind the counter, and a seemingly well-trained barista who answers customer questions knowledgeably. Where did the money to pay for all of this come from? You smile as you realize your $4.99 pays not just for the macchiato, but for everything else that comes with it.
The process of taking a product’s cost and increasing it by some amount to arrive at a selling price is called markup. This process is critical to business success because every business must ensure that it does not lose money when it makes a sale. From the consumer perspective, the concept of markup helps you make sense of the prices that businesses charge for their products or services. This in turn helps you to judge how reasonable some prices are (and hopefully to find better deals).
The Components in a Selling Price
Before you learn to calculate markup, you first have to understand the various components of a selling price. Then, in the next section, markup and its various methods of calculation will become much clearer.
When your business acquires merchandise for resale, this is a monetary outlay representing a cost. When you then resell the product, the price you charge must recover more than just the product cost. You must also recover all the selling and operating expenses associated with the product. Ultimately, you also need to make some money, or profit, as a result of the whole process.
The Formula
Most people think that marking up a product must be a fairly complex process. It is not. Formula 6.5 illustrates the relationship between the three components of cost, expenses, and profits in calculating the selling price.
How It Works
Follow these steps to solve pricing scenarios involving the three components:
Step 1: Four variables are involved in Formula 6.5. Identify the known variables. Note that you may have to calculate the product’s cost by applying the single or multiple discount formulas (Formula 6.1 and Formula 6.3, respectively). Pay careful attention to expenses and profits to capture how you calculate these amounts.
Step 2: Apply Formula 6.5 and solve for the unknown variable.
Assume a business pays a net price of $75 to acquire a product. Through analyzing its finances, the business estimates expenses at $25 per unit, and it figures it can add $50 in profit. Calculate the selling price.
Step 1: The net price paid for the product is the product cost. The known variables are \(C\) = $75, \(E\) = $25, and \(P\) = $50.
Step 2: According to Formula 6.5, the unit selling price is \(S = C + E + P\) = $75 + $25 + $50 = $150.
Important Notes
In applying Formula 6.5 you must adhere to the basic rule of linear equations requiring all terms to be in the same unit. That is, you could use Formula 6.5 to solve for the selling price of an individual product, where the three components are the unit cost, unit expenses, and unit profit. When you add these, you calculate the unit selling price. Alternatively, you could use Formula 6.5 in an aggregate form where the three components are total cost, total expenses, and total profit. In this case, the selling price is a total selling price, which is more commonly known as total revenue. But you cannot mix individual components with aggregate components.
Things To Watch Out For
The most common mistake in working with pricing components occurs in the "Understand" portion of the PUPP model. It is critical to identify and label information correctly. You have to pay attention to details such as whether you are expressing the expenses in dollar format or as a percentage of either cost or selling price. Systematically work your way through the information provided piece by piece to ensure that you do not miss an important detail.
- What is the relationship between net price and cost?
- Answer
-
- Cost, expenses, and profit. They are expressed either per unit or as a total.
- A specific dollar amount, a percentage of cost, or a percentage of the selling price.
- The net price paid for a product is the same as the cost of the product.
Mary’s Boutique purchases a dress for resale at a cost of $23.67. The owner determines that each dress must contribute $5.42 to the expenses of the store. The owner also wants this dress to earn $6.90 toward profit. What is the regular selling price for the dress?
Solution
You are looking for the regular selling price for the dress, or \(S\).
What You Already Know
Step 1:
The unit cost of the dress and the unit expense and the unit profit are all known: \(C=\$ 23.67, E=\$ 5.42, P=\$ 6.90\)
How You Will Get There
Step 2:
Apply Formula 6.5.
Perform
Step 2:
\(S=\$ 23.67+\$ 5.42+\$ 6.90=\$ 35.99\)
Mary’s Boutique will set the regular price of the dress at $35.99.
John’s Discount Store just completed a financial analysis. The company determined that expenses average 20% of the product cost and profit averages 15% of the product cost. John’s Discount Store purchases Chia Pets from its supplier for an MSRP of $19.99 less a trade discount of 45%. What will be the regular selling price for the Chia Pets?
Solution
You are looking for the regular selling price for the Chia pets, or \(S\).
What You Already Know
Step 1:
The list price, discount rate, expenses, and profit are known:
\(L\)=$ 19.99, \(d\)=0.45
\(E\) = 20% of cost, or \(0.20C\)
\(P\) = 15% of cost, or \(0.15C\)
How You Will Get There
Step 1 (continued):
Although the cost of the Chia Pets is not directly known, you do know the MSRP (list price) and the trade discount. The cost is equal to the net price. Apply Formula 6.1.
Step 2:
To calculate the selling price, apply Formula 6.5.
Perform
Step 1:
\(N=\$ 19.99 \times(1-0.45)=\$ 19.99 \times 0.55=\$ 10.99=C\)
Step 2:
\[\begin{align*} S &= \$ 10.99+0.20 C+0.15 C\\ S &= \$ 10.99+0.20(\$ 10.99)+0.15(\$ 10.99)\\ S &= \$ 10.99+\$ 2.20+\$ 1.65=\$ 14.84 \end{align*} \nonumber \]
John’s Discount Store will sell the Chia Pet for $14.84.
Based on last year’s results, Benthal Appliance learned that its expenses average 30% of the regular selling price. It wants a 25% profit based on the selling price. If Benthal Appliance purchases a fridge for $1,200, what is the regular unit selling price?
Solution
You are looking for the regular unit selling price for the fridge, or \(S\).
What You Already Know
Step 1:
The cost, expenses, and profit for the fridge are known:
\(E\) = 30% of \(S\), or \(0.3S\)
\(P\) = 25% of \(S\), or \(0.25S\)
\(C\) = $1,200.00
How You Will Get There
Step 2:
Apply Formula 6.5.
Perform
Step 2:
\[\begin{align*} S &= \$1,200.00+0.3S+0.25S\\ S &= \$1,200.00+0.55S\\ S-0.55S &= \$ 1,200.00\\ 0.45S&=\$1,200.00\\ S&=\$2,666.67 \end{align*} \nonumber \]
Benthal Appliance should set the regular selling price of the fridge at $2,666.67.
If a company knows that its profits are 15% of the selling price and expenses are 30% of cost, what is the cost of an MP3 player that has a regular selling price of $39.99?
Solution
You are looking for the cost of the MP3 player, or \(C\).
What You Already Know
Step 1:
The expenses, profits, and the regular unit selling price are as follows:
\(S\) = $39.99, \(P\) = 15% of \(S\), or \(0.15S\)
\(E\) = 30% of cost, or \(0.3C\)
How You Will Get There
Step 2:
Apply Formula 6.5, rearranging for \(C\).
Perform
Step 2:
\[\begin{align*} \$ 39.99&=C+0.3C+0.15(\$ 39.99)\\ \$ 39.99&=1.3C+\$ 6.00\\ \$ 33.99&=1.3C\\ \$ 26.15&=C \end{align*} \nonumber \]
The cost of the MP3 Player is $26.15.
Peak of the Market considers setting the regular unit selling price of its strawberries at $3.99 per kilogram. If it purchases these strawberries from the farmer for $2.99 per kilogram and expenses average 40% of product cost, does Peak of the Market make any money?
Solution
In asking whether Peak of the Market makes money, you are looking for the profit, or \(P\).
What You Already Know
Step 1:
The cost, expenses, and proposed regular unit selling price for the strawberries are as follows:
\(S\) = $3.99, \(C\) = $2.99, \(E\) = 40% of cost, or \(0.4C\)
How You Will Get There
Step 2:
Apply Formula 6.5, rearranging for \(P\).
Perform
Step 2:
\[\begin{align*} \$ 3.99&=\$ 2.99+0.4(\$ 2.99)+P\\ \$ 3.99&=\$ 4.19+P\\ -\$ 0.20&=P \end{align*} \nonumber \]
The negative sign on the profit means that Peak of the Market would take a loss of $0.20 per kilogram if it sells the strawberries at $3.99. Unless Peak of the Market has a marketing reason or sound business strategy for doing this, the company should reconsider its pricing.
Calculating the Markup Dollars
Most companies sell more than one product, each of which has different price components with varying costs, expenses, and profits. Can you imagine trying to compare 50 different products, each with three different components? You would have to juggle 150 numbers! To make merchandising decisions more manageable and comparable, many companies combine expenses and profit together into a single quantity, either as a dollar amount or a percentage. This section focuses on the markup as a dollar amount.
The Formula
One of the most basic ways a business simplifies its merchandising is by combining the dollar amounts of its expenses and profits together as expressed in Formula 6.6.
Note that since the markup amount (\(M\$\)) represents the expenses (\(E\)) and profit (\(P\)) combined, you can substitute the variable for markup amount into Formula 6.5 to create Formula 6.7, which calculates the regular selling price.
How It Works
Follow these steps when you work with calculations involving the markup amount:
Step 1: You require three variables in either Formula 6.6 or Formula 6.7. At least two of the variables must be known. If the amounts are not directly provided, you may need to calculate these amounts by applying other discount or markup formulas.
Step 2: Solve either Formula 6.6 or Formula 6.7 for the unknown variable.
Recall from Example \(\PageIndex{4}\) that the MP3 player’s expenses are $7.84, the profit is $6.00, and the cost is $26.15. Calculate the markup amount and the selling price.
Step 1: The known variables are \(E\) = $7.84, \(P\) = $6.00, and \(C\) = $26.15.
Step 2: According to Formula 6.6, the markup amount is the sum of the expenses and profit, or \(M \$ F=\$ 7.84+\$ 6.00=\$ 13.84\).
Step 2 (continued): Applying Formula 6.7, add the markup amount to the cost to arrive at the regular selling price, resulting in \(S=\$ 26.15+\$ 13.84=\$ 39.99\)
Paths To Success
You might have already noticed that many of the formulas in this chapter are interrelated. The same variables appear numerous times but in different ways. To help visualize the relationship between the various formulas and variables, many students have found it helpful to create a markup chart, as shown to the right.
This chart demonstrates the relationships between Formula 6.5, Formula 6.6, and Formula 6.7. It is evident that the selling price (the green line) consists of cost, expenses, and profit (the red line representing Formula 6.5); or it can consist of cost and the markup amount (the blue line representing Formula 6.7). The markup amount on the blue line consists of the expenses and profit on the red line (Formula 6.6).
A cellular retail store purchases an iPhone with an MSRP of $779 less a trade discount of 35% and volume discount of 8%. The store sells the phone at the MSRP.
- What is the markup amount?
- If the store knows that its expenses are 20% of the cost, what is the store’s profit?
Solution
First of all, you need to calculate the markup amount (\(M\$\)). You also want to find the store’s profit (\(P\)).
What You Already Know
Step 1:
The smartphone MSRP and the two discounts are known, along with the expenses and selling price:
\(L =\$270, d_{1}=0.35, d_{2}=0.08\)
\(E\) = 20% of cost, or \(0.2C\), \(S\) = $779
How You Will Get There
Step 1 (continued):
Calculate the cost of the iPhone by applying Formula 6.3.
Step 2:
Calculate the markup amount using Formula 6.7.
Step 2 (continued):
Calculate the profit by applying Formula 6.6, rearranging for \(P\).
Perform
Step 1 (continued):
\[\begin{array}{l}{N=\$ 779.00 \times(1-0.35) \times(1-0.08)} \\ {N=\$ 779.00 \times 0.65 \times 0.92=\$ 465.84=C}\end{array}\nonumber \]
Step 2:
\[\begin{array}{l}{\$ 779.00=\$ 465.84+M\$} \\ {\$ 313.16=M\$}\end{array}\nonumber \]
Step 2 (continued):
\[\begin{array}{l}{\$ 313.16=0.2(\$ 465.84)+P} \\ {\$ 313.16=\$ 93.17+P} \\ {\$ 219.99=P}\end{array}\nonumber \]
The markup amount for the iPhone is $313.16. When the store sells the phone for $779.00, its profit is $219.99.
Calculating the Markup Percent
It is important to understand markup in terms of the actual dollar amount; however, it is more common in business practice to calculate the markup as a percentage. There are three benefits to converting the markup dollar amount into a percentage:
- Easy comparison of different products having vastly different price levels and costs, to help you see how each product contributes toward the financial success of the company. For example, if a chocolate bar has a 50¢ markup included in a selling price of $1, while a car has a $1,000 markup included in a selling price of $20,000, it is difficult to compare the profitability of these items. If these numbers were expressed as a percentage of the selling price such that the chocolate bar has a 50% markup and the car has a 5% markup, it is clear that more of every dollar sold for chocolate bars goes toward list profitability.
- Simplified translation of costs into a regular selling price—a task that must be done for each product, making it helpful to have an easy formula, especially when a company carries hundreds, thousands, or even tens of thousands of products. For example, if all products are to be marked up by 50% of cost, an item with a $100 cost can be quickly converted into a selling price of $150.
- An increased understanding of the relationship between costs, selling prices, and the list profitability for any given product. For example, if an item selling for $25 includes a markup on selling price of 40% (which is $10), then you can determine that the cost is 60% of the selling price ($15) and that $10 of every $25 item sold goes toward list profits.
You can translate the markup dollars into a percentage using two methods, which express the amount either as a percentage of cost or as a percentage of selling price:
- Method 1: Markup as a Percentage of Cost. This method expresses the markup rate using cost as the base. Many companies use this technique internally because most accounting is based on cost information. The result, known as the markup on cost percentage, allows a reseller to convert easily from a product's cost to its regular unit selling price.
- Method 2: Markup as a Percentage of Selling Price. This method expresses the markup rate using the regular selling price as the base. Many other companies use this method, known as the markup on selling price percentage, since it allows for quick understanding of the portion of the selling price that remains after the cost of the product has been recovered. This percentage represents the list profits before the deduction of expenses and therefore is also referred to as the list profit margin.
The Formula
Both formulas are versions of Formula 2.2 on rate, portion, and base. The markup on cost percentage is expressed in Formula 6.8, while the markup on selling price percentage is expressed in Formula 6.9.
How It Works
Refer back to the steps in calculating markup. The steps you must follow for calculations involving markup percent are almost identical to those for working with markup dollars:
Step 1: Three variables are required in either Formula 6.8 or Formula 6.9. For either formula, at least two of the variables must be known. If the amounts are not directly provided, you may need to calculate these amounts by applying other discount or markup formulas.
Step 2: Solve either Formula 6.8 or Formula 6.9 for the unknown variable.
Continuing to work with Example \(\PageIndex{4}\), recall that the cost of the MP3 player is $26.15, the markup amount is $13.84, and the selling price is $39.99. Calculate both markup percentages.
Step 1: The known variables are \(C\) = $26.15, \(M\$\) = $13.84, and \(S\) = $39.99.
Step 2: To calculate the markup on cost percentage, apply Formula 6.8:
\[MoC \%=\dfrac{\$ 13.84}{\$ 26.15} \times 100=52.9254 \%\nonumber \]
In other words, you must add 52.9254% of the cost on top of the unit cost to arrive at the regular unit selling price of $39.99.
Step 2 (continued): To calculate the markup on selling price percentage, apply Formula 6.9:
\[MoS \%=\dfrac{\$ 13.84}{\$ 39.99} \times 100=34.6087 \%\nonumber \]
In other words, 34.6087% of the selling price represents list profits after the business recovers the $26.15 cost of the MP3 player.
Important Notes
Businesses are very focused on profitability. Your Texas Instruments BAII Plus calculator is programmed with the markup on selling price percentage. The function is located on the second shelf above the number three. To use this function, open the window by pressing 2nd 3. You can scroll between lines using your ↑ and ↓ arrows. There are three variables:
- CST is the cost. Use the symbol \(C\).
- SEL is the selling price. Use the symbol \(S\).
- MAR is the markup on selling price percentage. Use the symbol MoS%.
As long as you know any two of the variables, you can solve for the third. Enter any two of the three variables (you need to press ENTER after each), making sure the window shows the output you are seeking, and press CPT.
Things To Watch Out For
Merchandising involves many variables. Nine formulas have been established so far, and a few more are yet to be introduced. Though you may feel bogged down by all of these formulas, just remember that you have encountered most of these merchandising concepts since you were very young and that you interact with retailers and pricing every day. This chapter merely formalizes calculations you already perform on a daily basis, whether at work or at home. The calculation of discounts is no different than going to Walmart and finding your favorite CD on sale. You know that when a business sells a product, it has to recoup the cost of the product, pay its bills, and make some money. And you have worked with percentages since elementary school.
Do not get stuck in the formulas. Think about the concept presented in the question. Change the scenario of the question and put it in the context of something more familiar. Ultimately, if you really have difficulties then look at the variables provided and cross-reference them to the merchandising formulas. Your goal is to find formulas in which only one variable is unknown. These formulas are solvable. Then ask yourself, “How does knowing that new variable help solve any other formula?”
You do not need to get frustrated. Just be systematic and relate the question to what you already know.
Paths To Success
The triangle method simplifies rearranging both Formula 6.8 and Formula 6.9 to solve for other unknown variables as illustrated in the figure above.
Sometimes you need to convert the markup on cost percentage to a markup on selling price percentage, or vice versa. Two shortcuts allow you to convert easily from one to the other:
\[MoC \%=\dfrac{MoS\%}{1-MoS\%} \quad \quad MoS\%=\dfrac{MoC \%}{1+MoC \%}\nonumber \]
Notice that these formulas are very similar. How do you remember whether to add or subtract in the denominator? In normal business situations, the \(MoC\%\) is always larger than the \(MoS\%\). Therefore, if you are converting one to the other you need to identify whether you want the percentage to become larger or smaller.
- To calculate \(MoC\%\), you want a larger percentage. Therefore, make the denominator smaller by subtracting \(MoS\%\) from 1.
- To calculate \(MoS\%\), you want a smaller percentage. Therefore, make the denominator larger by adding \(MoC\%\) to 1.
Answer the following true/false questions.
- If you know the markup on selling price percentage and the cost, you can calculate a selling price.
- Answer
-
- False. The markup amount is a portion of the selling price and therefore is less than 100%.
- False. The markup amount plus the cost equals the selling price. It must be less than the selling price.
- True. A cost can be doubled or tripled (or increased even more) to reach the price.
- True. The base for markup on cost percentage is smaller, which produces a larger percentage.
- True. You could combine Formula 6.7 and Formula 6.8 to arrive at the selling price.
- True. You could convert the \(MoS\%\) to a \(MoC\%\) and solve as in the previous question.
A large national retailer wants to price a Texas Instruments BAII Plus calculator at the MSRP of $39.99. The retailer can acquire the calculator for $17.23.
- What is the markup on cost percentage?
- What is the markup on selling price percentage?
Solution
You have been asked to solve for the markup on cost percentage (\(MoC\%\)) and the markup on selling price percentage (\(MoS\%\)).
What You Already Know
Step 1:
The regular unit selling price and the cost are provided:
\(S\) = $39.99, \(C\) = $17.23
How You Will Get There
Step 1 (continued):
You need the markup dollars. Apply Formula 6.7, rearranging for \(M\$\).
Step 2:
To calculate markup on cost percentage, apply Formula 6.8.
Step 2 (continued):
To calculate markup on selling price percentage, apply Formula 6.9.
Perform
Step 1 (continued):
\[\begin{array}{l}{\$ 39.99=\$ 17.23+M \$} \\ {\$ 22.76=MS}\end{array}\nonumber \]
Step 2:
\[MoC \%=\dfrac{\$ 22.76}{\$ 17.23} \times 100=132.0952 \%\nonumber \]
Step 2 (continued):
\[MoS \%=\dfrac{\$ 22.76}{\$ 39.99} \times 100=56.9142 \%\nonumber \]
Calculator Instructions
| CST | SEL | MAR |
|---|---|---|
| 17.23 | 39.99 | Answer: 56.9142 |
The markup on cost percentage is 132.0952%. The markup on selling price percentage is 56.9142%.
Break-Even Pricing
In running a business, you must never forget the “bottom line.” In other words, if you fully understand how your products are priced, you will know when you are making or losing money. Remember, if you keep losing money you will not stay in business for long! As revealed in Chapter 5, 15% of new businesses will not make it past their first year, and 49% fail in their first five years. This number becomes even more staggering with an 80% failure rate within the first decade.[1] Do not be one of these statistics! With your understanding of markup, you now know what it takes to break even in your business. Recall from Chapter 5 that break-even means that you are earning no profit, but you are not losing money either. Your profit is zero.
The Formula
If the regular unit selling price must cover three elements—cost, expenses, and profit—then the regular unit selling price must exactly cover your costs and expenses when the profit is zero. In other words, if Formula 6.5 is modified to calculate the selling price at the break-even point (\(S_{BE}\)) with \(P=0\), then
\[S_{BE}=C+E\nonumber \]
This is not a new formula. It just summarizes that at break-even there is no profit or loss, so the profit (\(P\)) is eliminated from the formula.
How It Works
The steps you need to calculate the break-even point are no different from those you used to calculate the regular selling price. The only difference is that the profit is always set to zero.
Recall Example \(\PageIndex{4}\) that the cost of the MP3 player is $26.15 and expenses are $7.84. The break-even price (\(S_{BE}\)) is $26.15 + $7.84 = $33.99. This means that if the MP3 player is sold for anything more than $33.99, it is profitable; if it is sold for less, then the business does not cover its costs and expenses and takes a loss on the sale.
John is trying to run an eBay business. His strategy has been to shop at local garage sales and find items of interest at a great price. He then resells these items on eBay. On John’s last garage sale shopping spree, he only found one item—a Nintendo Wii that was sold to him for $100. John’s vehicle expenses (for gas, oil, wear/tear, and time) amounted to $40. eBay charges a $2.00 insertion fee, a flat fee of $2.19, and a commission of 3.5% based on the selling price less $25. What is John’s minimum list price for his Nintendo Wii to ensure that he at least covers his expenses?
Solution
You are trying to find John’s break-even selling price (\(S_{BE}\)).
What You Already Know
Step 1:
John’s cost for the Nintendo Wii and all of his associated expenses are as follows:
\(C\) = $100.00, \(E\) (vehicle) = $40.00
\(E \text { (insertion})=\$ 2.00\)
\(E(\text {flat})=\$ 2.19\)
\(E \text { (commission })=3.5 \%\left(S_{BE}-\$ 25.00\right)\)
How You Will Get There
Step 1 (continued):
You have four expenses to add together that make up the \(E\) in the formula.
Step 2:
Formula 6.5 states \(S = C + E + P\). Since you are looking for the break-even point, then \(P\) is set to zero and \(S_{BE} = C + E\).
Perform
Step 1 (continued):
\[\begin{aligned}
E&=\$ 40.00+52.00+52.19+3.5 \%\left(S_{BE}-\$25.00\right)\\
E&=\$ 44.19+0.035\left(S_{BE}-\$25.00\right)\\
&=\$44.19+0.035 S_{BE}-\$ 0.875\\
E&=\$ 43.315+0.0355 S_{BE}
\end{aligned} \nonumber \]
Step 2:
\[\begin{aligned}
S_{B E}&=\$ 100.00+\$ 43.315+0.035 S_{B E} \\
S_{B E}&=\$ 143.315+0.035 S_{B E} \\
S_{B E}-0.035 S_{B E}&=\$ 143.315 \\
0.965 S_{B E}&=\$ 143.315 \\
S_{B E}&=\$ 148.51
\end{aligned} \nonumber \]
At a price of $148.51 John would cover all of his costs and expenses but realize no profit or loss. Therefore, $148.51 is his minimum price.
References
- Statistics Canada, “Failure Rates for New Firms,” The Daily, February 16, 2000, www.statcan.gc.ca/daily-quotidien/000216/dq000216b-eng.htm.