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CH 13] Calculating Business 13-7

is an additional comparison for both in that it is easily recognized that the standard discount
(Example A) benefits the buyer more than a series discount (Example B). The student needs
to remember that both are valid methods of establishing discounts. The series discount is
common in business, and everybody knows about it and uses it.

Discount thinking only in terms of percentages
As it relates to discounts and discounting, begin thinking of any list price or the total
amount of an invoice as being 100%. As an example, the total value of an invoice for a sale
registers the total value to be $7,560. This would be the List Price for all items in the
transaction. This price, as it is for all items, can be considered simply as a percentage,
100%, of the value of the transaction. Simply stated, the invoice value of $7,560 as a
percentage of the transaction is 100%; the list-price percent is 100%, with a dollar value of
$7,560. Remember that 100% = 1.0 as a decimal value.
From this total, 100%, rates in any series of discounts may be subtracted as have been
discussed. The remainder, after all appropriate subtractions have been made, is the net
price percent. This is the percent that would be applied to the list price to calculate the net
price. Deducting the net price percent from 100% yields the single equivalent discount rate.
The algorithm for calculating the single equivalent discount rate from 100% has two
elements to it:

1. Calculate the net-price percent by subtracting the discount rates in series from 100%.
2. Calculate the equivalent discount rate by subtracting the net-price percent from 100%.
Example: Calculate the equivalent discount rate that is equal to the series of 10%, 10%,
and 5%.
Solution algorithm:
Step 1. 100.0% list price percent
- 10.0% first discount (10% of 100%) 13
Remainder of List Price 90.0%
- 9.0% second discount (10% of 90%)
Remainder of List Price 81.0%
- 5.0% third discount (5% of 81%)
Remainder of List Price 76.95% net price percent

Step 2. 100.00% list price percent
- 76.95% net price percent
23.05% single equivalent discount rate

With your hand held calculator and using the % key:

Cl/C 100 M+ − 10 % − 10 % − 5 %

M- MR —> 23.05 , means 23.05%

Another method of calculating the single equivalent discount rate is to add together the
equivalent rates that were subtracted in Step 1 of the previous example. Notice in the
example that the sum of 10%, 9%, and 5% equals 23.05% in Step 2 of the previous
example, which is the single equivalent discount rate.
Another method is recommended when a calculator is being used. This method utilizes
the complements of the discount rates. The solution to the example above using this method
is given below. Of course, list price equals 100% and as a decimal it is 1, the sum of the net
price percent and the single equivalent discount rate must equal 100%
Series Discount (10%, 10%, 5%)
As a percentage 1 − [100% x (100% - 10%) x (100% - 10%) x (100% - 5%)] =
As a percentage 1 − [100% x 90% x (90%) x 95% ] =

Converted to decimal values 1 − [ 1 x (0.90) x (0.9) x (0.95) ] =
1 − [ 0.7695 ] = 23.05 single equivalent discount rate

Series Discount
Net Price Equivalent Rate (NPER)
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