1. Chapter 8: Trade and Cash Discounts
Business Math
Chapter 8: Trade and Cash Discounts

2. 8.1 Trade Discount and Net Price
Find the trade discount using a single trade discount rate; find the net price using the trade discount.
Find the net price using the complement of the single trade discount rate.

3. Key Terms
Suggested retail price, catalog price, list price: three common terms for the price which the manufacturer suggests an item be sold to the consumer.
Trade discount: the amount of discount that the wholesaler or retailer receives off the list price or the difference between the list price and the net price

4. Key Terms
Net price: the price the manufacturer or retailer pays or the list price minus the trade discount.
Discount rate: a percent of the list price.

5. Product flow
Manufacturer Wholesaler Retailer Consumer

6. Price flow Consumer Retailer Wholesaler Manufacturer
List Price Net Price Net Price Cost
$ $56 $ $20
30% 50%
off list off list

7. How to find the trade discount
Using a single trade discount rate:
Identify the single discount rate and the list price.
Multiply the list price by the single discount rate.
Trade discount = rate x list price

8. Look at this example. Trade discount = rate x list price
Find the trade discount for a lamp that retails at $140 and has a trade discount rate of 45%.
Trade discount = 0.45 x $140
Trade discount = $63
What does the $63 mean?
That the wholesaler or retailer will not pay $63 of the $140 list price.

9. Try these examples.
Find the trade discount for a porcelain vase that lists for $90 and has a trade discount of 70%.
$63
Find the trade discount for styling gel that lists for $13 and has a trade discount of 40%.
$5.20

10. Find the net price Using the trade discount:
Identify the list price and the trade discount.
Subtract the trade discount from the list price.
Trade discount = Rate x List Price
Net Price = List Price – Trade discount

11. Look at this example.
Find the net price of a software program that lists for $220 and has a trade discount of 35%.
Trade discount = 0.35 x $220 = $77
Net price = List price – Trade discount
Net price = $220 - $77 = $143

12. Try these examples.
Find the net price of a camera that lists for $300 and has a trade discount of 42%.
$174
Find the net price of a down jacket that lists for $150 and has a trade discount of 20%.
$120

13. Find the net price
Using the complement of the single trade discount rate.
Complement of percent: the difference between 100% and the given percent.
Examples:
The complement of 30% is 70%.
The complement of 55% is 45%
The complement of 5% is 95%.

14. How to find the net price
Find the complement: subtract the single trade discount from 100%.
Multiply the list price by the complement of the single trade discount.
Example:
Find the net price of a coffee maker that lists for $20 and has a trade discount rate of 20%.
80% is the complement of 20%
NP = $20 x 0.80 = $16

15. Try these examples.
Find the net price of a set of golf clubs that lists for $1,500 and has a trade discount of 15%.
$1275
Find the net price of a bicycle that lists for $102 and has a trade discount of 30%.
$71.40

16. 8.2 Net price and trade discount series
Find the net price, applying a trade discount and using the net decimal equivalent.
Find the trade discount, applying a trade discount series and using the single discount equivalent.

17. Trade discount series
Trade discount series or chain discount: additional discounts that are deducted one after another from the list price.
Reasons to use discount series include:
To encourage volume purchases
To promote special or seasonal items
To entice a new client

18. Trade discount series step by step
An item lists for $400 and has a discount of 20%. $400 x 0.2 = $80 $320
An additional discount of 10% is taken on the previous price. $320 x 0.1 = $32 $288
An additional discount of 5% is taken on the previous price. $288 x 0.05 = $ $273.60
$ is the final price.

19. Can you add the discounts together and apply it as one?
If the item has three discounts of 20%, 10% and 5%, can you add them together and apply a 35% discount?
No, because each time you apply the additional discount, the base becomes smaller. Directly applying a 35% discount would result in a final price of $260.
$260 ≠ $273.60

20. The net decimal equivalent
To find the net decimal equivalent of a trade discount series:
Find the net decimal equivalent: multiply the decimal form of the complement of each trade discount rate in a series.
Multiply the list price by the net decimal equivalent.

21. Look at this example.
Find the net price of an order with a list price of $600 and a trade discount series of 15/10/5.
Find the complement of each of the trade discount rates.
They are 0.85, 0.90 and Multiply them together.
The net decimal equivalent is
Apply the net decimal equivalent to the list price.
NP = x $600 = $436.05

22. Try these examples.
A tire lists for $85 and has a trade discount series of 10/10/5. Find the net price.
$65.41
A silk tie lists for $125 and has a trade discount series of 20/10/5. Find the net price.
$85.50

23. 8.2.2 Find the trade discount
By applying a trade discount series and using the single discount equivalent
Find the single discount equivalent by subtracting the net decimal equivalent from “1.”
Multiply the list price by the single discount equivalent.
TD = single discount equivalent x list price

24. Key Terms
Single discount equivalent: the complement of the net decimal equivalent. It is the decimal equivalent of a single discount rate that is equal to the series of discount rates.
Total amount of a series of discounts = single discount equivalent x list price
Net amount you pay = net decimal equivalent x list price

25. Look at this example
Use the single discount equivalent to calculate the trade discount on a $1,500 fax machine with a discount series of 30/20/10.
Find the net decimal equivalent by multiplying the complements of each discount rate x 0.80 x 0.90 = 0.504
To find the single discount equivalent, subtract the net decimal equivalent from “1.”

26. Look at this example (continued)
Subtract the net decimal equivalent (0.504) from “1” to find the single discount equivalent.
The result is (or 49.6%).
The single discount equivalent is 0.496; apply it to the price of $1,500.
TD = $1,500 x = $744
The trade discount on the fax machine is $744. [That is the amount that you do not pay.]

27. 8.3 Net amount and the cash discount
Find the cash discount and the net amount using ordinary dating terms
Interpret and apply EOM terms
Interpret and apply ROG terms
Find the amount credited and the outstanding balance from partial payments
Interpret freight terms

28. 8.3.1 Find the cash discount and the net amount
Bills are often due within thirty days from the date of the invoice.
To encourage prompt payment, companies offer an incentive of a cash discount if the invoice is paid within a specified period.
“2/10 n/30” means “take a 2% cash discount if paid within 10 days; pay the net price if covered within 30 days.”

29. Look at this example
Find the cash discount for an invoice dated December 1 for $750 with terms of 2/10 n/30.
If the invoice is paid on December 9th, for example, the payment would include the discount and the amount would be $735.
If the invoice is paid on or after December 11th, the amount to pay would be $750.

30. Try these examples
Annie’s Plants has received an invoice for $ for potting soil dated November 3 with terms of 5/10 N/30. If the invoice is paid on November 12, how much would Annie’s pay?
$427.50
What if the bill is paid on November 30?
They would not be able to take the discount and would have to pay the full amount of $450.

31. “Thirty days has September…”
To calculate the exact number of days for a cash discount, you must know how many days are in each month, so if you are not sure…learn them.
There are two tips in the text to help you.

32. Use the complement to find the net amount of an invoice
An invoice of $500 which reads 2/10 N/30 tells you that a discount of 2% is available if the payment is made within 10 days.
To calculate the net amount directly, use the complement of the discount (in this case, 0.98) and multiply it by the total amount.
$500 x 0.98 = $490 = net amount to be paid

33. Try this example
Sycamore Enterprises received a $1,248 bill for computer supplies dated September 2 with sales terms of 2/10, 1/15 n/30. A 5% penalty is charged after 30 days. Find the amount due for the following dates: September 12, September 15, October 1, October 3.
September 12 (2% discount) = $1,223.04
September 15 (1% discount) = $1,235.52
October 1 (no discount) = $1,248.00
October 3 (5% penalty) = $1,310.40

34. 8.3.2 Interpret and apply EOM (end-of-month) terms
Another type of sales term are EOM terms.
For example, an invoice might be 2/10 EOM, meaning that a 2% discount is allowed if the bill is paid during the first 10 days of the month after the month in the date of the invoice.
If the invoice is dated November 19, then the 2% discount is allowed up to and including December 10.

35. Look at these examples
An invoice dated March 4 with terms of 3/15 EOM would mean that a 3% discount would be applicable until April 15.
An invoice dated August 25 with terms of 5/10 EOM would mean that a 5% discount would be applicable until September 10.
An invoice dated December 2 with terms of 2/20 EOM would mean that a 2% discount would be applicable until January 20.

36. An EOM exception!
An exception occurs when the invoice is dated on or after the 26 of the month.
The discount would be applicable until the specified day of the month following the month of the invoice.
Example: An invoice dated April 27 with terms of 3/10 EOM would be eligible for the discount if the bill is paid on or before June 10.

37. 8.3.3 Apply ROG (receipt of goods) terms
A cash discount is allowed when the bill is paid within the specified number of days from the receipt of goods, not from the date of the invoice.
Multiply the invoice amount times the complement of the discount rate.
Sales terms stating 1/10 ROG mean that a 1% discount is applicable 10 days after the goods are received; not when the invoice is dated.

38. Try this example
Judy’s Fine Jewelry received an invoice for 50 silver charm bracelets for a total of $550. The invoice is dated April 1. She received the bracelets on April 6. If the terms are 3/10 ROG and the invoice is paid on April 11, how much will she pay?
$533.50

39. 8.3.4 Find the amount credited and the outstanding balance
Partial payment: a payment that does not equal the full amount of the invoice less any cash discount.
Partial discount: a cash discount applied only to the amount of the partial payment.
Amount credited: the sum of the partial payment and the partial discount.
Outstanding balance: the invoice amount minus the amount credited.

40. Applying the percentage formula
In applying the percentage formula to find the amount credited, the rate is the complement of the discount rate; the percentage is the partial payment; and the amount credited is the base.
B = P/R
Sometimes a customer cannot pay the entire amount of an invoice, but takes advantage of a discount period to apply that discount to a part of the total due.

41. Look at this example
If the Semmes Corporation received a $875 invoice with terms of 3/10 n/30 and could not pay the full amount within 10 days, but chose to send in a $500 partial payment on Day 5, what amount was credited to their account?
B (amount credited) = P (partial payment) divided by R (complement of the discount rate)
B = 500/0.97= $ = amount credited
The balance would be the difference.
$875 - $ = $ = balance

42. 8.3.5 Interpret freight terms
Bill of lading: shipping document that includes a description of the merchandise, the number of pieces, weight, name of the consignee (sender), destination, and method of payment of freight charges.
FOB shipping point: “free on board” buyer pays for shipping when shipment is received.
Freight collect: The buyer pays the shipping when the shipping is received.

43. More key terms
FOB destination: “free on board” at the destination point. The seller pays the shipping when the merchandise is shipped.
Freight paid: The seller pays the shipping when the merchandise is shipped.
Prepay and add: The seller pays the shipping when the merchandise is shipped; but, the shipping costs are added to the invoice for the buyer to pay.

44. Remember that cash discounts do not apply to shipping costs
Example: The Home Doctor received a shipment of hand tools with an invoice total of $800 (including shipping) and sales terms of 3/10 n/30. The invoice is dated June 2 and the shipping costs are $125. Calculate the payment of the invoice if it is paid on June 10.
Subtract the shipping charges: $800–125 = $675
Apply the discount: $675 x 0.97 = $654.75
Add the shipping charges back in:
$ = $779.75= amount to be paid