Another method of calculating trade discounts, and one applicable to a series of any number of discounts, is to treat the discount off as equivalent to one-minus-the-discount on. Thus a discount of 15% is equivalent to 85% of the list. An additional discount of 10% is equivalent to 90% of the new base, or 90% of 85% of the original list, or 76.5%. Thus a continued multiplication of the “percentages on” gives the single sale price multiplier to be applied to the list price. If the single discount rate is desired, it is secured by subtracting the multiplier from 1, or 100%. Take the series 60, 20, 10, and 10 off. This is equivalent to 40, 80, 90, and 90 on, or 25.92% on
(.40 × .80 × .90 ×. 90 = .2592).
The single discount rate equivalent to the series is, therefore, 74.08% (100%-25.92% = 74.08%).
The order in which the discounts of a series are used is immaterial, as the order of the factors does not affect the product.
The method just illustrated develops the reason for the first special rule given above for a series of two discounts. Let the discounts be “a”% and “b”%. The “percentages on” are, therefore, (1 -a)% and (1-b)% whose product, algebraically, is 1- [(a + b)-ab], which is the single “percentage on”; from which it is readily seen that the single rate discount is a + b-ab, i.e., the sum of the two rates minus their product. Similar rules can be developed for longer series, but they are too complicated for easy application.
There is now available a “discolog” table, an ingenious reference table, which is operated somewhat like a logarithmic table. It gives quickly and easily the single discount rate equivalent to any series of discounts.
The chief value of the single rate equivalent to the discount series is in its use for comparative purposes, as it indicates which of two discount series is the more favorable. When a large number of selling prices must be computed, all having the same discount series, the single rate method of calculation also has a great advantage over the long method, which makes use of the series. This is true especially when the work is done with the use of a calculating machine.
The Nature of Cash Discount—Its Basic Elements.—Where goods are sold on credit with a cash discount offering, four main factors of cost, not incurred when goods are sold for cash, must be provided for. These are:
- 1. Credit investigation and collection expense.
- 2. Bookkeeping and billing expense.
- 3. Loss from uncollectible accounts.
- 4. Interest for the use of the money—credit.
The cash discount is offered to free the vendor especially from costs (3) and (4), which are the heaviest of the four.