Chain Discounts, Chapter 7

If a company offers us a 9/21/15 chain discount, we might ask, "What am I actually saving, compared with a single trade discount, like 45%?"

To find the answer, we first find what rate we're paying with the chain discount.
This rate is called the net price equivalent rate or NPER.

Take the complement of each chain discount rate (subtract from 100%), write each complement as a decimal, and multiply the decimal numbers together.

Once we get the NPER, which is the rate we Pay, we subtract that rate from one (1.0000000) to find the rate we Save, which is the single equivalent discount rate, or SEDR.

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Example 1: Find NPER and SEDRfor a 9/21/15 chain discount.

100% - 9% = 91% = 0.91

100% - 21% = 79% = 0.79

100% - 15% = 85% = 0.85

(0.91)(0.79)(0.85) = 0.611065 = NPER

1.000000 - 0.611065 = 0.388935= SEDR

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Example 2: An item lists for $600 with a 9/21/15 chain discount (same discount as Example 1).

Find the net price and the trade discount amount.

Net price = NPER * List Price = (0.611065)($600) = $366.64 rounded to nearest cent

TD Amt. = SEDR * List Price = (0.388935)($600) = $233.36 rounded to nearest cent

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An alternate solution for the examples above is to perform the chain discount directly:

$600 List Price – 9% – 21% – 15% = $366.639 Net Price

Is this Net Price a lot to pay, or not? Compared to what?

We find that the Net Price, $366.639, compared to (divided by) the List Price, $600, is
366.639 / 600 = 0.611065, which is the net price equivalent rate, or NPER.

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Net Price + Trade Discount = List Price

Net Price / Trade Discount / List Price
$ 366.64 = Portion 1 / $ 233.36 = Portion 2 / $ 600.00 = Base Amount
61% = Rate 1 (rounded) / 39% = Rate 2 (rounded) / 100% = Base Rate
0.611065 = NPER / 0.388935 = SEDR / 1.000000 = NPER + SEDR

Notice that a chain discount is the same regardless of the order of the percentages:

9/21/15 , 21/9/15 , and 15/9/21 chain discounts all give the same result:

(0.91)(0.79)(0.85) = (0.79)(0.91)(0.85) = (0.85)(0.91)(0.79) = 0.611065