8 1 Single Trade Discounts n Find the

8. 1 Single Trade Discounts 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Product flow Manufacturer Wholesaler Retailer Consumer Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Price flow Consumer List Price $80 Retailer Wholesaler Net Price $56 30% off list Business Math, Eighth Edition Cleaves/Hobbs $40 Manufacturer Cost $20 50% off list © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 cd player that retails at $120 and has a trade discount rate of 35%. n Trade discount = 0. 35 x $120 Trade discount = $42 What does the $42 mean? That the wholesaler or retailer will not pay $42 of the $120 list price. n n n Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples n Find the trade discount for a rug that lists for $290 and has a trade discount of 30%. n n $87 Find the trade discount for styling gel that lists for $18 and has a trade discount of 15%. n Business Math, Eighth Edition Cleaves/Hobbs $2. 70 © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at this example n Find the net price of a desk that lists for $320 and has a trade discount of 30%. n Trade discount = 0. 30 x $320 = $96 n Net price = List price – Trade discount n Net price = $320 - $96 = $224 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 $240 and has a trade discount of 45%. n n $132 Find the net price of a patio table that lists for $460 and has a trade discount of 20%. n Business Math, Eighth Edition Cleaves/Hobbs $368 © 2009 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%. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs $71. 40 © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 2 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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; $400 - $80 = $320 n An additional discount of 10% is taken on the previous price. $320 x 0. 1 = $32; $320 - $32 = $288 n An additional discount of 5% is taken on the previous price. $288 x 0. 05 = $14. 40; $288 - $14. 40 = $273. 60 n $273. 60 is the final price Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 $800 and a trade discount series of 20/10/5. n Find the complement of each of the trade discount rates. n They are 0. 80, 0. 90 and 0. 95. Multiply them together. n The net decimal equivalent is 0. 684 n Apply the net decimal equivalent to the list price. n NP = 0. 684 x $800 = $547. 20 Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples n A tool set lists for $325 and has a trade discount series of 20/10/10. Find the net price. $210. 60 n n A dress shirt lists for $125 and has a trade discount series of 15/10/7. 5. Find the net price. n Business Math, Eighth Edition Cleaves/Hobbs $88. 45 © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 2. 2 Find the Trade Discount To 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 $3, 200 lawn tractor 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. ” Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 $3, 200. n TD = $3, 200 x 0. 496 = $1, 587. 20 n The trade discount on the tractor is $1, 587. 20. That is the amount that you do not pay. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 3 Cash Discount and Sales Terms 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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. ” Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 $1, 500 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 $1, 470. n If the invoice is paid on or after December 11 th, the amount to pay would be $1, 500. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples 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 n 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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; using a chart is usually the most reliable. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 month or up until 10 days of the month after the month on 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 th 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8. 3. 3 Apply Receipt of Goods (ROG) 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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. Business Math, Eighth Edition Cleaves/Hobbs © 2009 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 Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved