Business Math Chapter 8 Trade and Cash Discounts

Business Math Chapter 8: Trade and Cash Discounts 1

8. 1 Trade Discount and Net Price n Find the trade discount using a single trade discount rate; find the net price using the trade discount. n Find the net price using the complement of the single trade discount rate. 2 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key Terms n Suggested retail price, catalog price, list price: three common terms for the price which the manufacturer suggests an item be sold to the consumer. n 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 3 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key Terms n Net price: the price the manufacturer or retailer pays or the list price minus the trade discount. n Discount rate: a percent of the list price. 4 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Product flow Manufacturer Wholesaler Retailer Consumer 5 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Price flow Consumer List Price Retailer Wholesaler Net Price Manufacturer Cost $80 $56 $20 30% off list $40 50% off list 6 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

How to find the trade discount n Using a single trade discount rate: 1. Identify the single discount rate and the list price. 2. Multiply the list price by the single discount rate. n Trade discount = rate x list price 7 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at this example. n 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%. n 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. n n n 8 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples. n Find the trade discount for a porcelain vase that lists for $90 and has a trade discount of 70%. n n $63 Find the trade discount for styling gel that lists for $13 and has a trade discount of 40%. n $5. 20 9 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the net price n Using the trade discount: 1. Identify the list price and the trade discount. 2. Subtract the trade discount from the list price. Trade discount = Rate x List Price Net Price = List Price – Trade discount 10 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at this example. n Find the net price of a software program that lists for $220 and has a trade discount of 35%. n Trade discount = 0. 35 x $220 = $77 n Net price = List price – Trade discount n Net price = $220 - $77 = $143 11 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples. n Find the net price of a camera that lists for $300 and has a trade discount of 42%. n n $174 Find the net price of a down jacket that lists for $150 and has a trade discount of 20%. n $120 12 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the net price n Using the complement of the single trade discount rate. n Complement of percent: the difference between 100% and the given percent. n Examples: ¨ The complement of 30% is 70%. ¨ The complement of 55% is 45% ¨ The complement of 5% is 95%. 13 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

How to find the net price 1. Find the complement: subtract the single trade discount from 100%. 2. 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 14 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples. n Find the net price of a set of golf clubs that lists for $1, 500 and has a trade discount of 15%. n n $1275 Find the net price of a bicycle that lists for $102 and has a trade discount of 30%. n $71. 40 15 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 2 Net price and trade discount series n Find the net price, applying a trade discount and using the net decimal equivalent. n Find the trade discount, applying a trade discount series and using the single discount equivalent. 16 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Trade discount series n Trade discount series or chain discount: additional discounts that are deducted one after another from the list price. n Reasons to use discount series include: ¨ To encourage volume purchases ¨ To promote special or seasonal items ¨ To entice a new client 17 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Trade discount series step by step n An item lists for $400 and has a discount of 20%. $400 x 0. 2 = $80 $320 n An additional discount of 10% is taken on the previous price. $320 x 0. 1 = $32 $288 n An additional discount of 5% is taken on the previous price. $288 x 0. 05 = $14. 40 $273. 60 n $273. 60 is the final price. 18 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Can you add the discounts together and apply it as one? n If the item has three discounts of 20%, 10% and 5%, can you add them together and apply a 35% discount? n 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 ≠ $273. 60 19 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

The net decimal equivalent n To find the net decimal equivalent of a trade discount series: 1. Find the net decimal equivalent: multiply the decimal form of the complement of each trade discount rate in a series. 2. Multiply the list price by the net decimal equivalent. 20 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at this example. n Find the net price of an order with a list price of $600 and a trade discount series of 15/10/5. n Find the complement of each of the trade discount rates. n They are 0. 85, 0. 90 and 0. 95. Multiply them together. n The net decimal equivalent is 0. 72675 n Apply the net decimal equivalent to the list price. n NP = 0. 72675 x $600 = $436. 05 21 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples. n A tire lists for $85 and has a trade discount series of 10/10/5. Find the net price. n n $65. 41 A silk tie lists for $125 and has a trade discount series of 20/10/5. Find the net price. n $85. 50 22 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 2. 2 Find the trade discount By applying a trade discount series and using the single discount equivalent 1. Find the single discount equivalent by subtracting the net decimal equivalent from “ 1. ” 2. Multiply the list price by the single discount equivalent. TD = single discount equivalent x list price 23 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key Terms n 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. n Total amount of a series of discounts = single discount equivalent x list price n Net amount you pay = net decimal equivalent x list price 24 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at this example n Use the single discount equivalent to calculate the trade discount on a $1, 500 fax machine with a discount series of 30/20/10. n Find the net decimal equivalent by multiplying the complements of each discount rate. 0. 70 x 0. 80 x 0. 90 = 0. 504 n To find the single discount equivalent, subtract the net decimal equivalent from “ 1. ” 25 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at this example (continued) n Subtract the net decimal equivalent (0. 504) from “ 1” to find the single discount equivalent. n The result is 0. 496 (or 49. 6%). n The single discount equivalent is 0. 496; apply it to the price of $1, 500. n TD = $1, 500 x 0. 496 = $744 n The trade discount on the fax machine is $744. [That is the amount that you do not pay. ] 26 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 3 Net amount and the cash discount n Find the cash discount and the net amount using ordinary dating terms n Interpret and apply EOM terms n Interpret and apply ROG terms n Find the amount credited and the outstanding balance from partial payments n Interpret freight terms 27 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 3. 1 Find the cash discount and the net amount n Bills are often due within thirty days from the date of the invoice. n To encourage prompt payment, companies offer an incentive of a cash discount if the invoice is paid within a specified period. n “ 2/10 n/30” means “take a 2% cash discount if paid within 10 days; pay the net price if covered within 30 days. ” 28 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at this example n Find the cash discount for an invoice dated December 1 for $750 with terms of 2/10 n/30. n If the invoice is paid on December 9 th, for example, the payment would include the discount and the amount would be $735. n If the invoice is paid on or after December 11 th, the amount to pay would be $750. 29 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples n Annie’s Plants has received an invoice for $450. 00 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? n n $427. 50 What if the bill is paid on November 30? n They would not be able to take the discount and would have to pay the full amount of $450. 30 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

“Thirty days has September…” n 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. n There are two tips in the text to help you. 31 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Use the complement to find the net amount of an invoice n 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. n To calculate the net amount directly, use the complement of the discount (in this case, 0. 98) and multiply it by the total amount. n $500 x 0. 98 = $490 = net amount to be paid 32 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try this example n 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. n September 12 (2% discount) = $1, 223. 04 n September 15 (1% discount) = $1, 235. 52 n October 1 (no discount) = $1, 248. 00 n October 3 (5% penalty) = $1, 310. 40 33 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 3. 2 Interpret and apply EOM (end-of-month) terms n Another type of sales term are EOM terms. n 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. n If the invoice is dated November 19, then the 2% discount is allowed up to and including December 10. 34 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at these examples n An invoice dated March 4 with terms of 3/15 EOM would mean that a 3% discount would be applicable until April 15. n An invoice dated August 25 with terms of 5/10 EOM would mean that a 5% discount would be applicable until September 10. n An invoice dated December 2 with terms of 2/20 EOM would mean that a 2% discount would be applicable until January 20. 35 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

An EOM exception! n An exception occurs when the invoice is dated on or after the 26 of the month. n The discount would be applicable until the specified day of the month following the month of the invoice. n 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. 36 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 3. 3 Apply ROG (receipt of goods) terms n 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. n Multiply the invoice amount times the complement of the discount rate. n 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. 37 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try this example n 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? n $533. 50 38 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 3. 4 Find the amount credited and the outstanding balance n Partial payment: a payment that does not equal the full amount of the invoice less any cash discount. n Partial discount: a cash discount applied only to the amount of the partial payment. n Amount credited: the sum of the partial payment and the partial discount. n Outstanding balance: the invoice amount minus the amount credited. 39 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Applying the percentage formula n 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. n B = P/R n 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. 40 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at this example n 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? n B (amount credited) = P (partial payment) divided by R (complement of the discount rate) n B = 500/0. 97= $515. 46 = amount credited n The balance would be the difference. n $875 - $515. 46 = $359. 54 = balance 41 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 3. 5 Interpret freight terms n 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. n FOB shipping point: “free on board” buyer pays for shipping when shipment is received. n Freight collect: The buyer pays the shipping when the shipping is received. 42 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

More key terms n FOB destination: “free on board” at the destination point. The seller pays the shipping when the merchandise is shipped. n Freight paid: The seller pays the shipping when the merchandise is shipped. n 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. 43 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Remember that cash discounts do not apply to shipping costs n 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. n Subtract the shipping charges: $800– 125 = $675 n Apply the discount: $675 x 0. 97 = $654. 75 n Add the shipping charges back in: $654. 75 + 125 = $779. 75= amount to be paid 44 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved