The Marked Price (MP) formula, when considering the aim of achieving a specific profit margin after offering a discount, is designed to calculate the price at which an item should be labelled. It ensures that even after providing a discount to the customer, the desired profit on the Cost Price (CP) is still realized.
To understand the Marked Price formula for profit, it's essential to grasp the fundamental relationships between Cost Price, Selling Price, Profit, Discount, and Marked Price:
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Profit is the gain made when the Selling Price (SP) is greater than the Cost Price (CP).
Profit = Selling Price (SP) – Cost Price (CP)- This also means:
Selling Price (SP) = Cost Price (CP) + Profit
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Discount is the reduction offered on the Marked Price to arrive at the Selling Price.
Discount = Marked Price (MP) – Selling Price (SP)- This implies:
Selling Price (SP) = Marked Price (MP) – Discount
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Discount Percentage is calculated on the Marked Price:
Discount Percentage (%) = (Discount / Marked Price) × 100- From this,
Selling Price (SP) = Marked Price (MP) × (1 - Discount Percentage / 100)
The Core Marked Price Formula for Profit
By combining these relationships, we can derive the Marked Price formula that incorporates both profit and discount:
The most common way to express the Marked Price (MP) when aiming for a specific profit percentage (P%) on the Cost Price (CP) and offering a discount percentage (D%) on the Marked Price is:
Marked Price (MP) = Cost Price (CP) × [(100 + Profit % on CP) / (100 - Discount % on MP)]
Where:
- CP: Cost Price (the price at which the item was bought or produced).
- Profit % on CP: The desired profit percentage calculated on the Cost Price.
- Discount % on MP: The percentage of discount intended to be offered on the Marked Price.
This formula allows businesses to set a Marked Price that is high enough to absorb a planned discount while still achieving their target profit margin on the initial cost.
Alternative Expressions of Marked Price for Profit
While the above is the most comprehensive, Marked Price can also be expressed in relation to profit if we first determine the Selling Price:
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If you know the desired Selling Price (SP) and the Discount Percentage (D%):
Marked Price (MP) = Selling Price (SP) / (1 - Discount Percentage / 100)- Insight: This version highlights that the Selling Price is a certain percentage of the Marked Price after the discount. If a 10% discount is given, SP is 90% of MP (MP = SP / 0.90).
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Using Absolute Profit and Discount Values (less common for formula, but conceptually important):
Marked Price (MP) = Cost Price (CP) + Profit + Discount- Insight: This is the simplest conceptual understanding: the Marked Price must cover your cost, the profit you want to make, and the amount you plan to reduce the price by (discount).
Practical Application and Examples
Let's illustrate with an example:
Scenario: A shopkeeper buys an item for $800 (Cost Price). They want to make a 20% profit on the Cost Price and also plan to offer a 10% discount to customers on the Marked Price.
Steps to find the Marked Price:
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Identify the variables:
- CP = $800
- Desired Profit % on CP = 20%
- Desired Discount % on MP = 10%
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Apply the formula:
MP = CP × [(100 + Profit % on CP) / (100 - Discount % on MP)]
MP = 800 × [(100 + 20) / (100 - 10)]
MP = 800 × [120 / 90]
MP = 800 × [4 / 3]
MP = 3200 / 3
MP ≈ $1066.67 -
Verify the outcome:
- Marked Price (MP) = $1066.67
- Discount (10% of MP) = 0.10 × 1066.67 = $106.67
- Selling Price (SP) = MP - Discount = 1066.67 - 106.67 = $960
- Profit = SP - CP = 960 - 800 = $160
- Profit Percentage on CP = (Profit / CP) × 100 = (160 / 800) × 100 = 20%
As confirmed, by marking the item at approximately $1066.67, the shopkeeper can offer a 10% discount and still achieve a 20% profit on their cost.
Key Formulas Summary
Understanding these formulas is crucial for pricing strategies in retail and business.
| Concept | Formula |
|---|---|
| Profit | Profit = Selling Price (SP) – Cost Price (CP) |
| Selling Price | SP = CP + Profit |
| Discount | Discount = Marked Price (MP) – Selling Price (SP) |
| Selling Price (from MP & Discount) | SP = MP × (1 - Discount Percentage / 100) |
| Marked Price (for Profit & Discount) | MP = CP × [(100 + Profit % on CP) / (100 - Discount % on MP)] |
| Marked Price (from SP & Discount) | MP = SP / (1 - Discount Percentage / 100) |
