Optimizing Pricing Strategies: Mark-up Percentages for Profitable Sales

In the field of retail, accurately determining the mark-up percentage is crucial for maximizing profits. This article explores the relationship between cost price, marked price, and discount, providing a detailed breakdown of how much more than the cost price a shopkeeper should mark their goods to achieve desired profit margins after allowing for discounts.

Understanding the Elements: Cost Price, Marked Price, and Sale Price

Let's start by defining the terms:

Cost Price (CP): The original purchase price of the goods. Marked Price (MP): The price at which goods are initially listed or marked in the store. Sale Price (SP): The price at which goods are finally sold to the customers, after any discounts have been applied.

Calculating Mark-up Percentages Based on Profit and Discount

In each case, we'll follow a step-by-step approach to determine the mark-up percentage needed for the shopkeeper to achieve a desired profit margin after offering a discount on the marked price.

Scenario 1: 36% Profit with a 20% Discount

Profit Margin: The shopkeeper aims for a 36% profit, so the selling price (SP) will be 136% of the cost price (CP):
CP : SP ~ 100 : 136 Discount Offered: A 20% discount on the marked price (MP) reduces it to 80% of the original marked price:
SP : MP ~ 80 : 100 Relating SP and CP: To find the relationship between SP and CP, we use the proportions from the two statements above:
136 : 100 × 136 / 80 ~ 136 : 169 Marked Price Calculation: Using the derived relationship, the marked price should be set to make the selling price 169% of the cost price:
CP : SP : MP ~ 100 : 136 : 169 Mark-up Percentage: The marked price is 69% more than the cost price:
MP - CP 69%

Scenario 2: 20% Profit with a 26% Discount

Profit Margin: The shopkeeper aims for a 20% profit, so the selling price (SP) will be 120% of the cost price (CP):
CP : SP ~ 100 : 120 Discount Offered: A 26% discount on the marked price (MP) reduces it to 74% of the original marked price:
SP : MP ~ 74 : 100 Relating SP and CP: To find the relationship between SP and CP, we use the proportions from the two statements above:
120 : 100 × 120 / 74 ~ 120 : 162.1 Marked Price Calculation: Using the derived relationship, the marked price should be set to make the selling price 162.1% of the cost price:
CP : SP : MP ~ 100 : 120 : 162.1 Mark-up Percentage: The marked price is 62.1% more than the cost price:
MP - CP 62.1%

Scenario 3: 26% Profit with a 10% Discount

Profit Margin: The shopkeeper aims for a 26% profit, so the selling price (SP) will be 126% of the cost price (CP):
CP : SP ~ 100 : 126 Discount Offered: A 10% discount on the marked price (MP) reduces it to 90% of the original marked price:
SP : MP ~ 90 : 100 Relating SP and CP: To find the relationship between SP and CP, we use the proportions from the two statements above:
126 : 100 × 126 / 90 ~ 126 : 140 Marked Price Calculation: Using the derived relationship, the marked price should be set to make the selling price 140% of the cost price:
CP : SP : MP ~ 100 : 126 : 140 Mark-up Percentage: The marked price is 40% more than the cost price:
MP - CP 40%

General Formula for Profit Percentage after Discount

To generalize the formula, let's consider a fixed cost price (CP), marked price (MP), and a discount percentage (D) to find the required mark-up percentage (M) to achieve a desired profit percentage (P).

Mark-up Relationship: The relationship between SP, MP, and CP after a discount is given by the formula:
SP MP - (MP × D / 100) Determining MP: To achieve a desired profit ( P%), the selling price should be
SP CP (CP × P / 100) Combining Equations: By equating the two expressions for SP, we can solve for M (Marked Price) in terms of CP and D:
MP CP (MP × (D / 100 P / 100)) Mark-up Percentage Calculation: Rearrange the equation to find the required mark-up percentage (M - CP) in percentage terms:
M - CP (CP × (D / 100 P / 100)) / (1 - D / 100)

Conclusion

Understanding the interplay between cost price, marked price, and discounts is crucial for achieving desired profit margins in retail. By applying the appropriate mark-up percentage, shopkeepers can ensure that they still achieve their profit goals even after offering discounts to customers. The general formula provided here can be a valuable tool for retail businesses looking to streamline their pricing strategies and increase profitability.