Chain discounts, sometimes referred to as series discounts, or multiple discounts are a series of trade discounts applied to the list or catalog price of a product.

A business offers trade discounts to avoid having to produce multiple price lists. From a single price list it can offer customers trade discounts for a number of reasons such as making additional purchases, buying in volume or at a particular time of the year, or for purchasing a specific product. For example, a customer might be offered 15% off the list price of a particular product and then a further 5% for purchasing in volume. This chain discount would be written as 15/5.

## Calculating Chain Discounts Example

Because the discounts occur one after the other (in series), each one has to be calculated in its correct order and not simply added together. For example, if there are two discounts (discount 1 and discount 2), then discount 1 is applied to the original list price, and then discount 2 is applied to the list price less discount 1.

Suppose by way of example, a business is looking to clear a product and offers an initial 20% discount to encourage sales of the product together with a further 5% discount for purchasing the product in bulk quantities. The chain discount would be written as 20/5.

Assume the list (original) price of the products purchased is 600, and that this is sufficient quantity to qualify for the volume discount of 5%.

The first step is to calculate the net price after the first discount of 20%. (The net price of a product is the amount the customer actually pays after deducting the chain discounts).

List price = 600 Discount % = 20% Discount = List price x 20% Discount = 600 x 20% = 120 Net price = 600 - 120 = 480

The net price after deducting the first chain discount of 20% is 480. The second discount of 5% is now applied to this net price as follows:

Net price = 480 Discount % = 5% Discount = Net price x 5% Discount = 480 x 5% = 24 Net price = 480 - 24 = 456

So the total discount is 144 (120 + 24), and the final net price is 456 (600 – 144).

While it is possible to calculate chain discounts in this manner, a much simpler approach is to calculate the final net price and then deduct this from the original list price.

## Net Price and the Chain Discount Formula

Since the chain discounts are applied in series, the net price can be calculated using the chain discount formula. For a business offering two discounts, the formula can be stated as follows:

In order to understand how this works, lets look at the example used above again. In the example, the list price was 600 and the chain discounts were 20% and 5%. Applying the chain discount formula we get.

List = 600 Discounts = 20/5 Net price = List price x (1-Discount 1) x (1-Discount 2) Net price = 600 x ( 1 - 20%) x (1 - 5%) Net price = 456

Using the formula the net price is 456 the same as before. The chain discounts are them simply calculated as follows:

List = 600 Net price = 456 Chain discounts = List price - Net price Chain discounts = 600 - 456 Chain discounts = 144

While the application of the chain discount formula might not seem to save a great deal of time when applied to two chain discounts, it comes into its own when there are additional discounts given.

Suppose a business offers four levels of chain discounts 25/10/5/2. Using the chain discount formula the net price is calculated simply as follows:

List = 600 Discounts = 25/10/5/2 Net price = List price x (1-Discount 1) x (1-Discount 2) x (1-Discount 3) x (1-Discount 4) Net price = 600 x (1 - 25%) x (1 - 10%) x (1 - 5%) x (1 - 2%) Net price = 377

And the chain discount is calculated as

Chain discounts = List price - Net price Chain discounts = 600 - 377 Chain discounts = 223

## Single Equivalent Discount

In order to be able to compare the total discount received from applying a series of chain discounts, a single equivalent discount or SED can be calculated.

In the above example, the total chain discounts were 223 on a list price of 600. Using this information we can calculate a single equivalent discount as follows:

Single equivalent discount = Chain Discounts / List Price Single equivalent discount = 223 / 600 Single equivalent discount = 37.2%

What this means is that chain discounts quoted as 25/10/5/2 are equivalent to a single discount rate of 37.2%.

In general the single equivalent rate can be calculated using the SED formula which can be stated as follows:

For example the business above offers 25/10/5/2 chain discounts on a product with a list price of 600, and the SED is calculated using the formula as follows:

SED = (List price - Net price) / List price SED = (600 - 600 x (1-25%) x (1-10%) x (1-5%) x (1-2%)) / 600 SED = 37.2%

Notice that the single equivalent rate is actually independent of the list price and in the above example could be simply calculated using the chain discounts as follows:

SED = 1 - (1-25%) x (1-10%) x (1-5%) x (1-2%) SED = 37.2%

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.