How to Calculate Single Equivalent Discount Rate

Single Equivalent Discount Rate Calculator

Discount Series (%)

function calculateEquivalentRate() { // Get inputs var priceInput = document.getElementById('listPrice').value; var d1Input = document.getElementById('discount1').value; var d2Input = document.getElementById('discount2').value; var d3Input = document.getElementById('discount3').value; // Clean inputs (handle empty strings) var price = parseFloat(priceInput); var d1 = parseFloat(d1Input); var d2 = parseFloat(d2Input); var d3 = parseFloat(d3Input); // Defaults for discounts if empty if (isNaN(d1)) d1 = 0; if (isNaN(d2)) d2 = 0; if (isNaN(d3)) d3 = 0; // Validate inputs if (d1 < 0 || d2 < 0 || d3 0) { var netPrice = price * npf; var discountAmount = price – netPrice; document.getElementById('origPriceResult').innerHTML = "$" + price.toFixed(2); document.getElementById('netPriceResult').innerHTML = "$" + netPrice.toFixed(2); document.getElementById('totalDiscountResult').innerHTML = "$" + discountAmount.toFixed(2); priceDiv.style.display = 'block'; } else { priceDiv.style.display = 'none'; } }

How to Calculate Single Equivalent Discount Rate

In business, retail, and supply chain management, products are often subject to "trade discounts" or "chain discounts." This occurs when a supplier offers multiple successive discounts on a list price. For example, a wholesaler might offer a 20% discount for a seasonal promotion, followed by an additional 10% discount for bulk purchasing.

A common mistake is to simply add these percentages together (20% + 10% = 30%). This is incorrect. Because the second discount is applied to the already reduced price, the total effective discount is actually less than the sum of the parts. The Single Equivalent Discount Rate (SEDR) is the single percentage that, if applied to the original list price, would result in the same net price as the series of successive discounts.

The Single Equivalent Discount Rate Formula

To calculate the single equivalent discount rate, you must first calculate the Net Price Factor (NPF). The logic works by looking at what percentage of the price remains after each discount is applied.

Step 1: Calculate Net Price Factor (NPF)
NPF = (1 – d₁) × (1 – d₂) × (1 – d₃)…
Where d₁, d₂, etc., are the discount rates expressed as decimals.

Step 2: Calculate Equivalent Rate
SEDR = 1 – NPF

Step-by-Step Calculation Example

Let's look at a real-world scenario. A manufacturer lists an item for $1,000. They offer a trade discount series of 20%, 10%, and 5%.

1. Convert percentages to decimals:
20% = 0.20
10% = 0.10
5% = 0.05

2. Calculate the "complement" of each discount (what you pay):
1 – 0.20 = 0.80
1 – 0.10 = 0.90
1 – 0.05 = 0.95

3. Multiply these complements to get the Net Price Factor:
0.80 × 0.90 × 0.95 = 0.684
(This means the customer pays 68.4% of the original price).

4. Subtract from 1 to get the SEDR:
1 – 0.684 = 0.316

5. Convert back to percentage:
0.316 × 100 = 31.6%

Notice that if you had simply added the discounts (20 + 10 + 5), you would have expected a 35% discount. However, the true mathematical equivalent is only 31.6%. This difference is crucial for calculating profit margins accurately.

Why is this important?

• Accurate Accounting: Ensuring that invoices and ledger entries reflect the true cost of goods sold.
• Competitive Pricing: Understanding exactly how much margin you have to play with when setting your own retail prices.
• Vendor Comparison: Comparing Vendor A (who offers 25% flat) vs Vendor B (who offers 15% and 10%). Vendor A is actually cheaper (25% discount) than Vendor B (15% then 10% results in a 23.5% SEDR).

Frequently Asked Questions

Does the order of discounts matter?

Mathematically, no. Because multiplication is commutative, applying a 20% discount followed by a 10% discount results in the exact same net price as applying a 10% discount followed by a 20% discount. However, on invoices, they are usually listed in a specific order for clarity.

What is the Net Price Factor?

The Net Price Factor is the decimal representing the percentage of the list price that the buyer actually pays. If the NPF is 0.75, the buyer pays 75% of the list price.

Can I calculate this for more than 3 discounts?

Yes. The formula simply extends. You continue multiplying (1 – d) for as many discounts as are in the chain.