Mathematics of Merchandising
7.3 Markup
A. Introduction to Markup
Each member of the supply chain adds costs to the product, from production, handling, and transportation to storage and marketing. As a product moves through the supply chain, these costs accumulate, and each member, except the consumer, adds a markup to cover their costs and earn a profit. The markup amount must be carefully calculated to be high enough to cover all these expenses while remaining competitive in the market. In this section, we will delve deeper into the nuances of markup, explore how it’s calculated, and understand its critical role in merchandising.
B. Markup Calculation
Let’s consider an example to understand markup calculation. A retailer buys a USB flash drive from a manufacturer for $5. The retailer incurs an operating expense of $3 on each USB and aims to make a profit of $2 per unit. Consequently, the retailer sets the selling price at $10. Here, the markup of $5 is the sum of the operating expenses and the desired profit added to the cost price to arrive at the selling price of $10.
Figure 7.3.1: The relationship among selling price, markup, expenses, and profit
Markup is essentially the amount added to the cost price of a product to establish its selling price. This can be represented by
[asciimath]S=C+M[/asciimath] Formula 7.6
Where S is the selling price, C is the cost of purchasing or producing a product, and M represents the amount of markup.
The markup includes overhead expenses or operating expenses (E), which are expenses associated with running a business, and operating profit or simply profit (P).
[asciimath]M=E+P[/asciimath] Formula 7.7
Combining Formulas 7.6 and 7.7, the selling price can be expressed as the sum of cost, expenses, and profit.
[asciimath]S=C+E+P[/asciimath] Formula 7.8
A retailer purchases printers for $110 each. The overhead expenses on each printer are $85 and the profit on each printer is $130 a) Calculate the amount of markup. b) Determine the selling price.
Show/Hide Solution
- The cost of purchasing each camera is $110, so [asciimath]C=110[/asciimath]
- The operating expenses on each camera are $85, so [asciimath]E=85[/asciimath]
- The operating profit is $130 so [asciimath]P=130[/asciimath]
a) [asciimath]M=?[/asciimath]
The amount of markup is the sum of expenses and profit.
[asciimath]M=E+P[/asciimath]
[asciimath]M=85+130[/asciimath]
[asciimath]=$215[/asciimath]
b) [asciimath]S=?[/asciimath]
The selling price can be found using either Formula 7.6 or 7.8:
[asciimath]S=C+M[/asciimath]
[asciimath]S=110+215[/asciimath]
[asciimath]=$325[/asciimath]
Try an Example
C. Markup Rate
Markup can also be expressed in percentage terms, either as a percentage of the cost (Markup on Cost) or as a percentage of the selling price (Markup on Selling Price):
[asciimath]"Rate of Markup on Cost"\ (MoC)[/asciimath][asciimath]=M/Cxx100%[/asciimath] Formula 7.9
and
[asciimath]"Rate of Markup on Selling Price"\ (MoS)[/asciimath][asciimath]=M/Sxx100%[/asciimath] Formula 7.10
A retailer purchases cameras for $1020 each and wants to sell them each for a profit of $300. The overhead expenses on each camera are $250. a) Calculate the amount of markup. b) Determine the selling price. c) What is the rate of markup on cost? d) What is the rate of markup on selling price? Round your answers to two decimal places where needed.
Show/Hide Solution
- The cost of purchasing each camera is $1020, so [asciimath]C=1020[/asciimath]
- The operating expenses on each camera is $250, so [asciimath]E=250[/asciimath]
- The operating profit is $300, so [asciimath]P=300[/asciimath]
a) [asciimath]M=?[/asciimath]
The amount of markup is the sum of expenses and profit.
[asciimath]M=E+P[/asciimath]
[asciimath]M=250+300[/asciimath]
[asciimath]=$550[/asciimath]
b) [asciimath]S=?[/asciimath]
The selling price can be found using either Formula 7.6 or 7.8:
[asciimath]S=C+M[/asciimath]
[asciimath]S=1020+550[/asciimath]
[asciimath]=$1570[/asciimath]
c) [asciimath]"MoC Rate"=?[/asciimath]
The rate of markup on cost can be determined using Formula 7.9:
[asciimath]"MoC Rate"=M/Cxx100%[/asciimath]
[asciimath]"MoC Rate" =550/1020xx100%[/asciimath]
[asciimath]~~53.92%[/asciimath]
d) [asciimath]"MoS Rate"=?[/asciimath]
The rate of markup on the selling price can be calculated using Formula 7.10:
[asciimath]"MoS Rate"=M/Sxx100%[/asciimath]
[asciimath]"MoS Rate" =550/1570xx100%[/asciimath]
[asciimath]~~35.03%[/asciimath]
Try an Example
A wholesaler purchases snowboards for $130 each and has a markup rate of 20% on the cost. The wholesaler’s overhead expenses are 10% of the cost. a) Calculate the amount of markup. b) Determine the selling price. c) What is the rate of markup on cost? d) What is the rate of markup on selling price? e) What are the operating expenses? f) What is the operating profit? Round your answers to two decimal places where needed.
Show/Hide Solution
- The cost of each snowboard is $130, so [asciimath]C=130[/asciimath]
- The markup is 20% of the cost, so [asciimath]M=20%*C[/asciimath]
- The operating expenses are 10% of the cost, so [asciimath]E=10%*C[/asciimath]
a) [asciimath]M=?[/asciimath]
[asciimath]M=20%*C[/asciimath]
[asciimath]=20%(130)[/asciimath]
[asciimath]=$26[/asciimath]
b) [asciimath]S=?[/asciimath]
The selling price can be found using either Formula 7.6:
[asciimath]S=C+M[/asciimath]
[asciimath]S=130+26[/asciimath]
[asciimath]=$156[/asciimath]
c) [asciimath]"MoC Rate"=?[/asciimath]
The rate of markup on cost can be determined using Formula 7.9:
[asciimath]"MoC Rate"=M/Cxx100%[/asciimath]
[asciimath]"MoC Rate" =26/130xx100%[/asciimath]
[asciimath]=20%[/asciimath]
d) [asciimath]"MoS Rate"=?[/asciimath]
The rate of markup on selling price can be calculated using Formula 7.10:
[asciimath]"MoS Rate"=M/Sxx100%[/asciimath]
[asciimath]"MoS Rate" =26/156xx100%[/asciimath]
[asciimath]~~16.67%[/asciimath]
e) [asciimath]E=?[/asciimath]
[asciimath]E=10%*C[/asciimath]
[asciimath]=10%(130)[/asciimath]
[asciimath]=$13[/asciimath]
f) [asciimath]P=?[/asciimath]
To find the profit, we can rearrange Formula 7.7 for P:
[asciimath]M=E+P[/asciimath]
[asciimath]-> P=M-E[/asciimath]
[asciimath]P=26-13[/asciimath]
[asciimath]=$13[/asciimath]
Try an Example
A store purchases a set of cookware for $60. The overhead expenses for each set amount to 15% of its selling price, and the store aims for a profit of 10% of the selling price on each set. a) What should the selling price of the cookware be? b) How much profit does the store make per set of cookware? c) What are the overhead expenses for each set of cookware? d) What is the amount of markup on each set?
Show/Hide Solution
- The cost of each cookware is $60, so [asciimath]C=60[/asciimath]
- The operating expenses are 15% of the selling price, so [asciimath]E=15%*S[/asciimath]
- The operating profit is 10% of the selling price, so [asciimath]P=10%*S[/asciimath]
a) [asciimath]S=?[/asciimath]
Since we know the percentages for expenses and profit relative to the selling price for each set of cookware, but not their exact amounts, we can apply Formula 7.8 to calculate the selling price. However, as the actual values of expenses and profit are not provided, we need to express them in terms of the unknown selling price. By substituting these expressions for expenses and profit into the formula, we can solve for the selling price algebraically.
[asciimath]S=C+E+P[/asciimath]
[asciimath]1S=60+0.15S+0.10S[/asciimath]
[asciimath]1S-0.15S-0.10S=60[/asciimath]
[asciimath](1-0.15-0.10)S=60[/asciimath]
[asciimath]0.75S=60[/asciimath]
[asciimath]S=60/0.75[/asciimath]
[asciimath]=$80[/asciimath]
b) [asciimath]P=?[/asciimath]
Now that the selling price is known, we can calculate the profit and expenses.
[asciimath]P=10%S[/asciimath]
[asciimath]=10%(80)[/asciimath]
[asciimath]=$8[/asciimath]
c) [asciimath]E=?[/asciimath]
[asciimath]E=15%S[/asciimath]
[asciimath]=15%(80)[/asciimath]
[asciimath]=$12[/asciimath]
d) [asciimath]M=?[/asciimath]
The amount of markup can be calculated using Formula 7.7:
[asciimath]M=E+P[/asciimath]
[asciimath]=12+8[/asciimath]
[asciimath]=$20[/asciimath]
Try an Example
D. Break-even Selling Price
The break-even selling price is the price point where a product’s selling price covers exactly its cost (C) and overhead expenses (E), without generating any profit ([asciimath]P=0[/asciimath]). This means at the break-even price, a business neither makes a profit nor incurs a loss. The formula for calculating the break-even selling price is
[asciimath]S_(BE)=C+E[/asciimath] Formula 7.11
where [asciimath]S_(BE)[/asciimath] represents the break-even selling price. Note that Formula 7.11 is derived by setting the profit to zero in Formula 7.8.
Furry Friends Boutique purchased a cat tree for $80. The overhead expenses are 25% of the cost, and the desired profit is 15% of the cost. a) What is the regular selling price of the cat tree? b) During a clearance event, the cat tree was sold at the break-even price. What is the break-even selling price?
Show/Hide Solution
- Cost: [asciimath]C=80[/asciimath]
- The operating expenses are 25% of the cost, so [asciimath]E=25%*C[/asciimath]
- The profit is 15% of the cost, so [asciimath]P=15%*C[/asciimath]
a) [asciimath]S=?[/asciimath]
[asciimath]S=C+E+P[/asciimath]
[asciimath]S=80+25%(80)+15%(80)[/asciimath]
[asciimath]=80+20+12[/asciimath]
[asciimath]=$112[/asciimath]
b) [asciimath]S_(BE)=?[/asciimath]
The break-even selling price is given by Formula 7.11:
[asciimath]S_(BE)=C+E[/asciimath]
[asciimath]=80+20[/asciimath]
[asciimath]=$100[/asciimath]
At a selling price of $100, the business covers just its costs and expenses, resulting in neither a profit nor a loss.
Try an Example
Section 7.3 Exercises
- A retailer purchases cameras for $210 each and wants to sell them each for a profit of $210. The overhead expenses on each camera are $25. a) Calculate the amount of markup. b) Determine the selling price.
Show/Hide Answer
a) M = $235
b) S = $445
- A store pays $225 for a set of cookware. Overhead expense on each cookware is 13% of the selling price and the profit is 18% of the selling price. a) What is the selling price? b) What is the amount of markup? c) What is the rate of markup on cost? d) What is the rate of markup on the selling price?
Show/Hide Answer
a) S = $326.09
b) M = $101.09
c) MoC Rate = 44.93%
d) MoS Rate = 31%
- A store purchased an item for $130 and planned to sell it for $234.00 so that their profit would be 40% of their cost. If they were unable to sell it for this amount, what minimum selling price would allow them to break even?
Show/Hide Answer
S = $182
- A Retailer purchased headphones for $150 per unit. The overhead expenses are 25% of the cost, and the desired profit is 15% of the cost. a) What is the regular selling price of each headphone? b) During a clearance event, the headphone was sold at the break-even price. What is the break-even selling price?
Show/Hide Answer
a) S = $210
b) S = $187.50
