# 1.3 Markup

## LEARNING OBJECTIVES

- Calculate the selling price, cost, expenses, or profit of an item.
- Calculate the amount of markup of an item.
- Calculate the rates of markup on an item.

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 does not cost anywhere near that much. But then gazing around the café, you notice the carefully applied color 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 Selling Price

Before you learn to calculate markup, you first have to understand the various components of a selling price. 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.

Most people think that marking up a product must be a fairly complex process. The relationship between the three components of cost ([latex]C[/latex]), expenses ([latex]E[/latex]), and profits ([latex]P[/latex]) and the selling price ([latex]S[/latex]) is given by the following formula

[latex]\displaystyle{S=C+E+P}[/latex]

where

**[latex]S[/latex] is the selling price.**Once you calculate what the business paid for the product (cost), the bills it needs to cover (expenses), and how much money it needs to earn (profit), you arrive at a selling price by summing the three components.**[latex]C[/latex] is the cost.**The cost is the amount of money that the business must pay to purchase or manufacture the product. If manufactured, the cost represents all costs incurred to make the product. If purchased, this number results from applying an appropriate discount, as we learned in a previous section. There is a list price from which the business will deduct discounts to arrive at the net price. The net price paid for the product equals the cost of the product. If a business purchases or manufactures a product for $10 then it must sell the product for at least $10. Otherwise, it fails to recover what was paid to acquire or make the product in the first place—a path to sheer disaster!**[latex]E[/latex] is the expenses.**Expenses are the financial outlays involved in selling the product. Beyond just purchasing the product, the business has many more bills to pay, including wages, taxes, leases, equipment, electronics, insurance, utilities, fixtures, décor, and many more.**[latex]P[/latex] is the profit.**Profit is the amount of money that remains after a business pays all of its costs and expenses. A business needs to add an amount above its costs and expenses to allow it to grow. If it adds too much profit, though, the product’s price will be too high, in which case the customer may refuse to purchase it. If it adds too little profit, the product’s price may be too low, in which case the customer may perceive the product as shoddy and once again refuse to purchase it. Many businesses set general guidelines on how much profit to add to various products.

### NOTES

- The expenses must be recovered and may be calculated as:
- A fixed dollar amount per unit.
- A percentage of the product cost. For example, if a business forecasts total merchandise costs of $100,000 for the coming year and total business expenses of $50,000, then it may set a general guideline of adding 50% ($50,000÷$100,000) to the cost of a product to cover expenses.
- A percentage of the product selling price based on a forecast of future sales. For example, if a business forecasts total sales of $250,000 and total business expenses of $50,000, then it may set a general guideline of adding 20% ($50,000÷$250,000) of the selling price to the cost of a product to cover expenses.

- As with expenses, the profit may be expressed as:
- A fixed dollar amount per unit.
- A percentage of the product cost.
- A percentage of the selling price.

## EXAMPLE

Suppose a business pays $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.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$75 \\ E & = & \$25 \\ P & = & \$50 \end{eqnarray*}[/latex]

**Step 2:** Calculate the selling price per unit.

[latex]\begin{eqnarray*} S & = & C + E + P \\ & = & 75+25+50 \\ & = & \$100 \end{eqnarray*}[/latex]

The selling price per unit is $100.

### NOTE

The most common mistake in working with pricing components occurs in identifying and labeling the information correctly. 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.

## EXAMPLE

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: **

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$23.67 \\ E & = & \$5.42 \\ P & = & \$6.90 \end{eqnarray*}[/latex]

**Step 2:** Calculate the selling price per unit.

[latex]\begin{eqnarray*} S & = & C + E + P \\ & = & 23.97+5.42+6.90 \\ & = & \$35.99 \end{eqnarray*}[/latex]

The selling price of the dress is $35.99.

## EXAMPLE

John’s Discount Store just completed a financial analysis. The company purchases a product for $19.99 less a trade discount of 45%. The company determined that expenses average 20% of the product cost and profit averages 15% of the product cost. What will be the regular selling price for the product?

**Solution: **

**Step 1: ** The given information is

[latex]\begin{eqnarray*} L & = & \$19.99 \\ d & = & 45\% \\ E & = & 20\% \mbox{ of cost} \\ & = & 0.2 \times C\\ P & = & 15\% \mbox{ of cost} \\ & = & 0.15 \times C \end{eqnarray*}[/latex]

**Step 2:** Calculate the cost per unit. The cost equals the net price.

[latex]\begin{eqnarray*} C & = & L \times (1-d) \\ & = & 19.99 \times (1-0.45) \\ & = & 19.99 \times 0.55 \\ & = & \$10.99 \end{eqnarray*}[/latex]

**Step 3:** Calculate the expenses.

[latex]\begin{eqnarray*} E & = & 0.2 \times C \\ & = & 0.2 \times 10.99 \\ & = & \$2.20 \end{eqnarray*}[/latex]

**Step 4:** Calculate the profit.

[latex]\begin{eqnarray*} P & = & 0.15 \times C \\ & = & 0.15 \times 10.99 \\ & = & \$1.65 \end{eqnarray*}[/latex]

**Step 5:** Calculate the selling price per unit.

[latex]\begin{eqnarray*} S & = & C + E + P \\ & = & 10.99+2.20+1.65 \\ & = & \$14.84 \end{eqnarray*}[/latex]

The selling price of the product is $14.84.

## EXAMPLE

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: **

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$1,200 \\ E & = & 30\% \mbox{ of selling price} \\ & = & 0.3 \times S\\ P & = & 25\% \mbox{ of selling price} \\ & = & 0.25 \times S \end{eqnarray*}[/latex]

**Step 2:** Calculate the selling price per unit.

[latex]\begin{eqnarray*} S & = & C + E + P \\ S & = & 1,200+0.3 \times S+0.25 \times S \\ S & = & 1,200+(0.3+0.25) \times S \\ S & = & 1,200+0.55 \times S \\ S-0.55 \times S & = & 1,200 \\ (1-0.55) \times S & = & 1,200 \\ 0.45 \times S & = & 1,200 \\ S & = & \frac{1,200}{0.45} \\ S & = & \$2,666.67 \end{eqnarray*}[/latex]

The selling price of the fridge is $2,666.67.

## EXAMPLE

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: **

**Step 1: ** The given information is

[latex]\begin{eqnarray*} S & = & \$39.99 \\ E & = & 30\% \mbox{ of cost} \\ & = & 0.3 \times C\\ P & = & 15\% \mbox{ of selling price} \\ & = & 0.15 \times S \end{eqnarray*}[/latex]

**Step 2:** Calculate the profit.

[latex]\begin{eqnarray*} P & = & 0.15 \times S \\ & = & 0.15 \times 39.99 \\ & = & \$6.00 \end{eqnarray*}[/latex]

**Step 3:** Calculate the cost per unit.

[latex]\begin{eqnarray*} S & = & C + E + P \\ 39.99 & = & C+0.3 \times C+6 \\ 39.99 & = & (1+0.3) \times C+6 \\ 39.99 & = & 1.3 \times C+6 \\ 39.99-6 & = & 1.3 \times C\\ 33.99 & = & 1.3 \times C \\ \frac{33.99}{1.3} & = & C \\ \$26.15 & = & C \end{eqnarray*}[/latex]

The cost of the MP3 player is $26.15.

## TRY IT

A company purchases a product to sell in its stores for $50. The company has expenses that are 27% of the selling price and profit that is 13% of the selling price. What is the selling price of the product?

**Click to see Solution**

[latex]\begin{eqnarray*} S & = & C + E + P \\ S & = & 50+0.27 \times S+0.13 \times S \\ S & = & 50 +(0.27+0.13) \times S \\ S & = & 50 +0.4 \times S \\ S-0.4 \times S & = & 50 \\ (1-0.4) \times S & = & 50 \\ 0.6 \times S & = & 50 \\ S & = & \frac{50}{0.6} \\ S & = & \$83.33 \end{eqnarray*}[/latex]

## TRY IT

A retailer sells a pair of shoes for $75. The retailer’s expenses are 40% of cost and profit is 25% of cost. What is the cost of the shoes?

**Click to see Solution**

[latex]\begin{eqnarray*} S & = & C + E + P \\ 75 & = & C+0.4 \times C+0.25 \times C \\ 75 & = & (1+0.4+0.25) \times C \\ 75 & = & 1.65 \times C \\ \frac{75}{1.65} & = & C \\ \$45.45 & = & C \end{eqnarray*}[/latex]

## Markup

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, called the **markup** ([latex]M[/latex]).

One of the most basic ways a business simplifies its merchandising is by combining the dollar amounts of its expenses and profits together into the markup. The amount of markup is

[latex]\displaystyle{M=E+P}[/latex]

where

**[latex]M[/latex] is the markup amount.**Markup is taking the cost of a product and converting it into a selling price. The markup amount represents the dollar amount difference between the cost and the selling price.**[latex]E[/latex] is the expenses.**The expenses associated with the product.**[latex]P[/latex] is the profit.**The profit earned when the product sells.

Because the markup amount represents the expenses and profit combined, you can substitute [latex]M[/latex] into the selling price formula.

[latex]\displaystyle{S=C+M}[/latex]

where

**[latex]S[/latex] is the selling price.**The regular selling price of the product.**[latex]C[/latex] is the cost.**The amount of money needed to acquire or manufacture the product. If the product is being acquired, the cost is the same amount as the net price paid.**[latex]M[/latex] is the markup.**The markup is the single number that represents the total of the expenses and profit.

## EXAMPLE

Recall from the MP3 player example above, that the expenses are $7.84, the profit is $6.00 and the cost is $26.15. Calculate the markup and the selling price.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$26.15 \\ E & = & \$7.84 \\ P & = & \$6.00 \end{eqnarray*}[/latex]

**Step 2:** Calculate the markup.

[latex]\begin{eqnarray*} M & = & E+P\\ & = & 7.84+6 \\ & = & \$13.84 \end{eqnarray*}[/latex]

**Step 3:** Calculate the selling price.

[latex]\begin{eqnarray*} S & = & C + M \\ & = & 26.15+13.84 \\ & = & \$39.99 \end{eqnarray*}[/latex]

The MP3 player is marked up by $13.84 and the selling price is $39.99.

## EXAMPLE

A cellular retail store purchases an iPhone with a list price of $779 less a trade discount of 35% and volume discount of 8%. The store sells the phone at the list price.

- What is the markup amount?
- If the store knows that its expenses are 20% of the cost, what is the store’s profit?

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} L & = & \$779 \\ d_1& = & 35\% \\ d_2 & = & 8\% \\ S & = & \$779 \\ E & = & 20\% \mbox{ of cost} \\ & = & 0.2 \times C \end{eqnarray*}[/latex]

**Step 2:** Calculate the cost per unit. The cost is the net price.

[latex]\begin{eqnarray*} C & = & L \times (1-d_1) \times (1-d_2) \\ & = & 779 \times (1-0.35) \times (1-0.08)\\ & = & 779 \times 0.65 \times 0.92 \\ & = & \$465.84 \end{eqnarray*}[/latex]

**Step 3:** Calculate the markup.

[latex]\begin{eqnarray*} S & = & C + M \\ 779 & = & 465.84+M \\ 779-465.84 & = & M \\ \$313.16 & = & M \end{eqnarray*}[/latex]

**Step 4: ** Calculate the expenses.

[latex]\begin{eqnarray*} E & = & 0.2 \times C \\ & = & 0.2 \times 465.84 \\ & = & \$93.17 \end{eqnarray*}[/latex]

**Step 5: ** Calculate the profit.

[latex]\begin{eqnarray*} M & =& E+P \\ 313.16 & = & 93.17 +P \\ 313.16-93.17 & = & P \\ \$219.99 & = & P \end{eqnarray*}[/latex]

The markup amount on the iPhone is $313.16. When the store sells the iPhone for $779, the profit is $219.99.

## EXAMPLE

An office supply store purchases a desk chair to sell in its store. The store marks up the chair by $250. The store’s expenses are 25% of the cost and the profit is 13% of the cost. Calculate the cost of the chair and the selling price of the chair.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} M & = & \$250 \\ E & = & 25\% \mbox{ of cost} \\ & = & 0.5 \times C \\ P & =& 13\% \mbox{ of cost} \\ & = & 0.13 \times C \end{eqnarray*}[/latex]

**Step 2:** Calculate the cost of the chair.

[latex]\begin{eqnarray*} M & = & E+P \\250 & = & 0.25 \times C+0.13 \times C\\ 250 & = & (0.25 +0.13) \times C \\ 250 & = & 0.38 \times C \\ \frac{250}{0.38} & = & C \\ \$657.89 & = & C \end{eqnarray*}[/latex]

**Step 3:** Calculate the selling price.

[latex]\begin{eqnarray*} S & = & C + M \\ & = & 657.89+250\\ & = & \$907.89 \end{eqnarray*}[/latex]

The cost of the chair is $657.89. The selling price of the chair is $907.89.

## TRY IT

An office supply store sells a desk lamp in its store. The store marked up the price of the lamp by $35. The store’s operating expenses are 17% of the selling price and the profit is 10% of the selling price. What is the selling price of the chair?

**Click to see Solution**

[latex]\begin{eqnarray*} M & =& E+P \\ 35 & = & 0.17 \times S+0.1 \times S \\ 35 & = & (0.17+0.1) \times S \\ 35 & =& 0.27 \times S \\ \frac{35}{0.27} & = & S \\ \$129.63 & = & S \end{eqnarray*}[/latex]

## Rates of Markup

Although it is important to understand markup in terms of the actual dollar amount, it is more common in business practice to calculate the markup as a percentage, of either the cost or the selling price. 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 $0.50 markup included in a selling price of $1 but 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. But if these numbers were expressed as a percentage of the selling price, the chocolate bar has a 50% markup and the car has a 5% markup. In this case 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.

The **rate of markup on cost** expresses the markup as a percent of the cost of the item. Many companies use this technique internally because most accounting is based on cost information. The rate of markup on cost allows a reseller to convert easily from a product’s cost to its regular unit selling price.

The rate of markup on cost is

[latex]\displaystyle{ROM_C=\frac{M}{C} \times 100\%}[/latex]

where

**[latex]ROM_C[/latex] is the rate of markup on cost.**This is the percentage by which the cost of the product needs to be increased to arrive at the selling price for the product.**[latex]M[/latex] is the markup amount.**The total dollars of the expenses and the profits. This total is the difference between the cost and the selling price.**[latex]C[/latex] is the cost.**The amount of money needed to acquire or manufacture the product. If the product is being acquired, the cost is the same amount as the net price paid.

The rate of markup on selling price expresses the markup as a percent of the selling price of the item. Many other companies use this method because 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 rate of markup on selling price is

[latex]\displaystyle{ROM_S=\frac{M}{S} \times 100\%}[/latex]

where

**[latex]ROM_S[/latex] is the rate of markup on selling price.**This is the percentage of the selling price that remains available as list profits after the cost of the product is recovered.**[latex]M[/latex] is the markup amount.**The total dollars of the expenses and the profits. This total is the difference between the cost and the selling price.**[latex]S[/latex] is the selling price.**The regular selling price of the product.

## EXAMPLE

Recall from the MP3 player example above that the cost is $26.15, the selling price is $39.99 and the markup is $13.84. Calculate the rate of markup on cost and the rate of markup on selling price.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$26.15 \\ S & = & \$39.99 \\ M & = & \$13.84 \end{eqnarray*}[/latex]

**Step 2:** Calculate the rate of markup on cost.

[latex]\begin{eqnarray*} ROM_C & = & \frac{M}{C} \times 100\%\\ & = & \frac{13.84}{26.15} \times 100\% \\ & = & 52.93\% \end{eqnarray*}[/latex]

**Step 3:** Calculate the rate of markup on selling price.

[latex]\begin{eqnarray*} ROM_S & = & \frac{M}{S} \times 100\% \\ & = & \frac{13.84}{39.99} \times 100\% \\ & = & 34.61\% \end{eqnarray*}[/latex]

The rate of markup on cost is 52.93%. This means that you must add 52.93% of the cost of MP3 player to the cost to arrive at the selling price.

The rate of markup on selling price is 34.61%. This means that you must add 34.61% of the selling price of MP3 player to the cost to arrive at the selling price. In other words, 34.61% of the selling price represents list profits after the business recovers the $26.15 cost of the MP3 player.

### NOTE

Merchandising involves many variables. Several 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. 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.

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?”

## EXAMPLE

A large national retailer wants to price a calculator for $39.99. The retailer can acquire the calculator for $17.23.

- What is the rate of markup on cost?
- What is the rate of markup on selling price?

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$17.23 \\ S & = & \$39.99 \end{eqnarray*}[/latex]

**Step 2:** Calculate the markup.

[latex]\begin{eqnarray*} S & = & C+M \\ 39.99 & = & 17.23+M \\ 39.99-17.23 & = & M \\ \$22.76 & = & M \end{eqnarray*}[/latex]

**Step 3:** Calculate the rate of markup on cost.

[latex]\begin{eqnarray*} ROM_C & = & \frac{M}{C} \times 100\%\\ & = & \frac{22.76}{17.23} \times 100\% \\ & = & 132.10\% \end{eqnarray*}[/latex]

**Step 4:** Calculate the rate of markup on selling price.

[latex]\begin{eqnarray*} ROM_S & = & \frac{M}{S} \times 100\% \\ & = & \frac{22.76}{39.99} \times 100\% \\ & = & 56.91\% \end{eqnarray*}[/latex]

The rate of markup on cost is 132.10%. The rate of markup on selling price is 56.91%.

## EXAMPLE

A retailer purchases a product for $500. The retailer has a rate of markup on selling price of 35%. Calculate the selling price of the product and the amount of markup.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$500 \\ M & = & 35\% \mbox{ of selling price} \\ & = & 0.35 \times S \end{eqnarray*}[/latex]

**Step 2:** Calculate the selling price.

[latex]\begin{eqnarray*} S & = & C+M \\ S & = & 500+0.35 \times S \\ S-0.35 \times S & = & 500 \\ (1-0.35) \times S & = & 500 \\ 0.65 \times S & = & 500 \\ S& =& \frac{500}{0.65} \\ S & = & \$769.23 \end{eqnarray*}[/latex]

**Step 3:** Calculate the amount of markup.

[latex]\begin{eqnarray*} M & = & 0.35 \times S\\ & = & 0.35 \times 769.23 \\ & = & \$369.23 \end{eqnarray*}[/latex]

The selling price of the product is $769.23. The amount of markup is $369.23.

## EXAMPLE

An electronics store sells a laptop for $2,500. The store has a rate of markup on cost of 27%. What is the cost to the store to purchase the laptop?

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} S & = & \$2,500 \\ M & = & 27\% \mbox{ of cost} \\ & = & 0.27 \times C \end{eqnarray*}[/latex]

**Step 2:** Calculate the cost.

[latex]\begin{eqnarray*} S & = & C+M \\ 2,500 & = & C+0.27 \times C \\ 2,500 & = & (1+0.27) \times C \\ 2,500 & = & 1.27 \times C \\ \frac{2,500}{1.27} & = & C \\ $1,968.50 & =& C \end{eqnarray*}[/latex]

The cost of the laptop is $1,968.50.

## TRY IT

A furniture manufacturer sells a table for $470. They have a 37% rate of markup on the cost of the table. What is the cost to the manufacturer to produce the table?

**Click to see Solution**

[latex]\begin{eqnarray*} S & = & C+M \\ 470 & = & C+0.37 \times C \\ 470 & = & (1+0.37) \times C \\ 470 & = & 1.37 \times C \\ \frac{470}{1.37} & = & C \\ $343.07 & =& C \end{eqnarray*}[/latex]

## TRY IT

A retailer purchases a product for $350.29 less a trade discount of 15%. They have a 20% rate of markup on the selling price. At what price does the retailer sell the product? What is the markup on the product?

**Click to see Solution**

[latex]\begin{eqnarray*} C & = & 350.29 \times (1-0.15) \\ & = & 350.29 \times 0.85 \\ & = & \$297.75 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} S & = & C+M \\ S & = & 297.75 +0.2 \times S \\ S-0.2 \times S & = & 297.75 \\ (1-0.2) \times S & =& 297.75 \\ 0.8 \times S & = & 297.75 \\ S & = & \frac{297.75}{0.8} \\ S & = & \$372.19 \end{eqnarray*}[/latex]

\begin{eqnarray*} S & = & C+M \\ 372.19& =& 297.75 +M \\ 372.19-297.75 & = & M \\ \$74.44 & = & M \end{eqnarray*}

## Break-Even Price

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! With your understanding of markup, you now know what it takes to break even in your business. **Break-even** means that you are earning no profit, but you are not losing money either because your profit is zero.

If the regular unit selling price must cover three elements—cost, expenses, and profit—then the break-even price ([latex]BE[/latex]) is the selling price when profit is zero.

[latex]\displaystyle{BE=C+E}[/latex]

This is not a new formula. It summarizes that at break-even there is no profit or loss, so the profit is eliminated from the formula.

## EXAMPLE

Recall from the MP3 player example above, that the expenses are $7.84 and the cost is $26.15. Calculate the break-even price.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$26.15 \\ E & = & \$7.84 \end{eqnarray*}[/latex]

**Step 2:** Calculate the break-even price.

[latex]\begin{eqnarray*} BE & = & C+E\\ & = & 26.15+7.84 \\ & = & \$33.99 \end{eqnarray*}[/latex]

The break-even price is $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.

## EXAMPLE

A jewelry store purchases a necklace for $300 less discounts of 12% and 5%. The store sells the necklace for $425 so that the profit on each necklace is 27% of the cost. What is minimum price the store has to sell the necklace at in order to break-even?

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} L & = & \$300 \\ d_1 & = & 12\% \\ d_2 & = & 5\% \\ S & = & \$425 \\ P & =& 27\% \mbox{ of cost} \\ & = & 0.27 \times C \\ \end{eqnarray*}[/latex]

**Step 2:** Calculate the cost. The cost is the net price.

[latex]\begin{eqnarray*} C & = & L \times (1-d_1) \times (1-d_2) \\ & = & 300 \times (1-0.12) \times (1-0.05) \\ & = & 300 \times 0.88 \times 0.95 \\ & = & \$250.80\end{eqnarray*}[/latex]

**Step 3:** Calculate the profit.

[latex]\begin{eqnarray*} P & = & 0.27 \times C \\ & = & 0.27 \times 250.80 \\ & = & \$67.72 \end{eqnarray*}[/latex]

**Step 4:** Calculate the break-even price.

[latex]\begin{eqnarray*} BE & = & S-P \\ BE & = & 425-67.72 \\ BE & = & \$357.28 \end{eqnarray*}[/latex]

The break-even price for the necklace is $357.28.

## EXAMPLE

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:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$100 \\ E & = & 40+2+2.19+0.035 \times (BE-25) \\ & = & 44.19+0.035 \times BE-0.88 \\ & = & 43.31 +0.035 \times BE \end{eqnarray*}[/latex]

**Step 2:** Calculate the break-even price.

[latex]\begin{eqnarray*} BE & = & C+E \\ BE & = & 100+43.31+0.035 \times BE \\ BE-0.035 \times BE & = & 143.31 \\ (1-0.035) \times BE & = & 143.31 \\ 0.965 \times BE & = & 143.31 \\ BE& =& \frac{143.31}{0.965} \\ BE & = & \$148.51 \end{eqnarray*}[/latex]

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.

## TRY IT

A retailer sells an item for $10. The expenses are 30% of the cost and the profit is 17% of costs. What is the break-even price?

**Click to see Solution**

[latex]\begin{eqnarray*} S & = & C+E+P \\ 10 & = & C+0.3 \times C+0.17 \times C \\ 10 & = & (1+0.3+0.17) \times C \\ 10 & = & 1.47 \times C \\ \frac{10}{1.47} & = & C \\ \$6.80 & = & C \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} E & = & 0.3 \times C \\ & = & 0.3 \times 6.80 \\& = & \$2.04 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} BE & = & C+E \\ & = & 6.80+2.04 \\ & = & \$8.84 \end{eqnarray*}[/latex]

**Exercises**

- The cost of an item is $188.42. The expenses are $48.53. The profit is $85.00. Calculate the following:
- The selling price.
- The markup amount.
- The break-even price.
- The rate of markup on cost.
- The rate of markup on selling price.

**Click to see Answer**a. $321.95; b. $133.53; c. $236.95; d. 70.8683%; e. 41.4754%

- The selling price of an item is $999.99. The expenses are 30% of cost and the profit is 23% of cost. Calculate the following:
- The cost.
- The amount of markup.
- The break-even price.
- The rate of markup on cost.
- The rate of markup on selling price.

**Click to see Answer**a. $653.59; b. $346.41; c. $849.67; d. 53.0011%; e. 34.6413%

- The profit on an item is 10% of the selling price. The amount of markup is $183.28. The rate of markup on cost is 155%. Calculate the following:
- The selling price.
- The cost.
- The expenses.
- The break-even price.
- The rate of markup on selling price.

**Click to see Answer**a. $301.53; b. $118.25; c. $153.13; d. $271.38; e. 60.7833%

- The selling price of an item is $274.99. The expenses are 20% of the selling price. The rate of markup on selling price is 35%. Calculate the following:
- The cost.
- The profit.
- The amount of markup.
- The break-even price.
- The rate of markup on cost.

**Click to see Answer**a. $178.74; b. $41.25; c. $96.25; d. $223.74; e. 53.8492%

- The expenses on an item are 45% of cost. The markup amount is $540. The break-even price is $1,080. Calculate the following:
- The selling price.
- The cost.
- The profit.
- The rate of markup on cost.
- The rate of markup on selling price.

**Click to see Answer**a. $1, 284.83; b. $744.83; c. $204.83; d. 72.4998%; e. 42.0289%

- The cost of an item is $200 less a discount of 40%. The profit is 15% of the selling price. The rate of markup on cost is 68%. Calculate the following:
- The selling price.
- The expenses.
- The markup amount.
- The break-even price.
- The rate of markup on selling price.

**Click to see Answer**a. $201.60; b. $51.36; c. $81.60; d. $171.36; e. 40.4762%

- An item is marked up by $275. The expenses are $100. The rate of markup on selling price is 19%. Calculate the following:
- The selling price.
- The cost.
- The profit.
- The break-even price.
- The rate of markup on cost.

**Click to see Answer**a. $1,447.37; b. $1,172.37; c. $175; d. $1,272.37; e. 23.4568%

- The break-even price of an item is $253. The expenses on an item are 15% of cost. The profit is 12% of the (regular) selling price. Calculate the following:
- The selling price.
- The cost.
- The amount of markup.
- The rate of markup on cost.
- The rate of markup on selling price.

**Click to see Answer**a. $287.50; b. $220; c. $67.50; d. 30.6818%; e. 23.4783\%

- If a pair of sunglasses sells at a regular unit selling price of $249.99 and the markup is always 55% of the regular unit selling price, what is the cost of the sunglasses?

**Click to see Answer**$112.50

- A transit company wants to establish an easy way to calculate its transit fares. It has determined that the cost of a transit ride is $1.00, with expenses of 50% of cost. It requires $0.75 profit per ride. What is the rate of markup on cost?

**Click to see Answer**125%

- Daisy is trying to figure out how much negotiating room she has in purchasing a new car. The car has a list price of $34,995.99. She has learned from an industry insider that most car dealerships have a 20% markup on selling price. What does she estimate the dealership paid for the car?

**Click to see Answer**$27,996.79

- The markup amount on an eMachines desktop computer is $131.64. If the machine regularly retails for $497.25 and expenses average 15% of the selling price, what profit will be earned?

**Click to see Answer**$57.05

- Manitoba Telecom Services (MTS) purchases an iPhone for $749.99 less discounts of 25% and 15%. MTS’s expenses are known to average 30% of the regular unit selling price.
- What is the regular unit selling price if a profit of $35 per iPhone is required?
- What are the expenses?
- What is the rate of markup on cost?
- What is the break-even selling price?

**Click to see Answer**a. $733.03; b. $219.91; c. 53.3151%; d. $698.03

- A snowboard has a cost of $79.10, expenses of $22.85, and profit of $18.00.
- What is the regular unit selling price?
- What is the markup amount?
- What is the rate of markup on cost?
- What is the rate of markup on selling price?
- What is the break-even selling price? What is the rate of markup on cost at this break-even price?

**Click to see Answer**a. $119.95; b. $40.85; c. 51.6435%; d. 34.0559%; e. $101.95, 28.8887%

- A waterpark wants to understand its pricing better. If the regular price of admission is $49.95, expenses are 20% of cost, and the profit is 30% of the regular unit selling price, what is the markup amount?

**Click to see Answer**$20.82

- Sally works for a skateboard shop. The company just purchased a skateboard for $89.00 less discounts of 22%, 15%, and 5%. The company has standard expenses of 37% of cost and desires a profit of 25% of the regular unit selling price. What regular unit selling price should Sally set for the skateboard?

**Click to see Answer**$102.40

- If an item has a 75% markup on cost, what is its rate of markup on selling price?

**Click to see Answer**42.8571%

- A product received discounts of 33%, 25%, and 5%. A markup on cost of 50% was then applied to arrive at the regular unit selling price of $349.50. What was the original list price for the product?

**Click to see Answer**$488.09

- Mountain Equipment Co-op (MEC) wants to price a new backpack. The backpack can be purchased for a list price of $59.95 less a trade discount of 25% and a quantity discount of 10%. MEC estimates expenses to be 18% of cost and it must maintain a markup on selling price of 35%.
- What is the cost of backpack?
- What is the markup amount?
- What is the regular unit selling price for the backpack?
- What profit will Mountain Equipment Co-op realize?
- What happens to the profits if it sells the backpack at the list price instead?

**Click to see Answer**a. $40.47; b. $21.79; c. $62.26; d. $14.51; e. $12.20, $2.31 reduction

- Costco can purchase a bag of Starbucks coffee for $20.00 less discounts of 20%, 15%, and 7%. It then adds a 40% markup on cost. Expenses are known to be 25% of the regular unit selling price.
- What is the cost of the coffee?
- What is the regular unit selling price?
- How much profit will Costco make on a bag of Starbucks coffee?
- What rate of markup on selling price does this represent?
- Repeat questions (a) through (d) if the list price changes to $24.00.

**Click to see Answer**a. $12.65; b. $17.71; c. $0.63; d. 28.5714%; e. $15.18, $21.25, $0.76, 28.5647%

#### Attribution

“4.3: Markup: Setting the Regular Price” from Introduction to Business Math by Margaret Dancy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

“6.2: Markup – Setting the Regular 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.