Mathematics of Merchandising
7.4 Markdown
Returning to the previous example, consider a retailer who purchases USB flash drives from a manufacturer at $5 each. The retailer’s operating expenses amount to $3 for each USB, aiming for a profit of $2 per unit, leading to an initial selling price of $10. However, suppose market demand decreases, prompting the retailer to lower the USBs’ selling price by $4. This adjustment results in a reduced selling price of $6. Retailers sometimes reduce their selling price to clear old or excess stock, make room for new inventory, respond to reduced demand, or compete with other retailers’ pricing strategies. This reduction in the original selling price of goods is referred to as Markdown (MD).
Figure 7.4.1: The relationship among selling price, markdown, and reduced selling price
[asciimath]"Markdown Amount" =[/asciimath] [asciimath]"Original Price" - "Reduced Price"[/asciimath]
[asciimath]MD=S-S_(Red)[/asciimath]Formula 7.12
where [asciimath]S_(Red)[/asciimath] represents the reduced selling price or sale price.
The markdown is often expressed as a percentage of the original price.
[asciimath]"Markdown (MD) Rate"=(MD)/Sxx100%[/asciimath]Formula 7.13
Reduced selling price can be directly obtained using the net price factor.
[asciimath]S_(Red)=S(1-"MD Rate)"[/asciimath]Formula 7.14
A boutique initially offers a dress for $120, but during a seasonal clearance event, the price is marked down to $72. Calculate the rate of markdown.
Show/Hide Solution
- Regular selling price: [asciimath]S=120[/asciimath]
- Reduced selling price: [asciimath]S_(Red)=72[/asciimath]
[asciimath]MD \ Rate=?[/asciimath]
We first need to find the amount of markdown using Formula 7.12.
[asciimath]MD=S-S_(Red)[/asciimath]
[asciimath]MD=120-72[/asciimath]
[asciimath]=$48[/asciimath]
The rate of markdown is then given by Formula 7.13.
[asciimath]MD\ Rate=(MD)/Sxx100%[/asciimath]
[asciimath]MD \ Rate=48/120xx100%[/asciimath]
[asciimath]=40%[/asciimath]
Try an Example
A retailer purchased a product for $110 and had operating expenses of 10% of the cost and operating profit of 40% of the cost of each product. During a seasonal sale, the product was marked down by 25%. a) What was the regular selling price? b) What was the amount of markdown? c) What was the reduced selling price during the seasonal sale? d) What was the profit or loss at the sale price?
Show/Hide Solution
- Cost: [asciimath]C=110[/asciimath]
- Expense: [asciimath]E=10%*C[/asciimath]
- Profit: [asciimath]P=40%*C[/asciimath]
- Markdown rate is 25% of the regular selling price: [asciimath]"MD Rate"=25%[/asciimath]
a) [asciimath]S=?[/asciimath]
Applying Formula 7.8 gives
[asciimath]S=C+E+P[/asciimath]
[asciimath]S=110+10%(110)+40%(110)[/asciimath]
[asciimath]=110+11+44[/asciimath]
[asciimath]=$165[/asciimath]
b) [asciimath]MD=?[/asciimath]
[asciimath]MD=25%*S[/asciimath]
[asciimath]=25%(165)[/asciimath]
[asciimath]=$41.25[/asciimath]
c) [asciimath]S_(red)=?[/asciimath]
The reduced selling price is the difference between the regular selling price and the amount of markdown:
[asciimath]S_(red)=S-MD[/asciimath]
[asciimath]S_(red)=165-41.25[/asciimath]
[asciimath]=$123.75[/asciimath]
Alternatively, you can calculate the reduced selling price directly from the markdown rate using Formula 7.14:
[asciimath]S_(red)=S(1-"MD Rate)"[/asciimath]
[asciimath]S_(red)=165(1-25%)[/asciimath]
[asciimath]=165(0.75)[/asciimath]
[asciimath]=$123.75[/asciimath]
d) [asciimath]P_(Red)=?[/asciimath]
Since the cost of the product and overhead expenses are fixed, reducing the selling price will also decrease the operating profit. Consequently, we can use Formula 7.8 with the reduced selling price to calculate the profit during the sale period.
[asciimath]S_(Red)=C+E+P_(Red)[/asciimath]
[asciimath]P_(Red)=S_(Red)-C-E[/asciimath]
[asciimath]=123.75-110-11[/asciimath]
[asciimath]=$2.75[/asciimath]
Since the profit during the sale is a positive value, the retailer made a profit of $2.75.
Try an Example
Section 7.4 Exercises
- A boutique initially offers a dress for $119, but during a seasonal clearance event, the price is marked down to $97.58. Calculate the rate of markdown.
Show/Hide Answer
MD Rate = 18%
- A retailer purchased a product for $65 and had operating expenses of 35% of the cost and operating profit of 50% of the cost of each product. During a seasonal sale, the product was marked down by 35%. a) What was the regular selling price? b) What was the sale price? c) What was the profit or loss at the sale price?
Show/Hide Answer
a) S = $120.25
b) S = $78.16
c) Loss of $9.59
- A retailer applied a markup of 48% on selling price on a product that cost $145 per unit. During a sale, the store marked the items down by 35%. a) Calculate the regular selling price of the product. b) Calculate the reduced selling price of the product.
Show/Hide Answer
a) S = $278.85
b) S = $181.25
