QMT 3301 BUSINESS MATHEMATICS REV 00 CHAPTER 4 MATHEMATICS OF BUYING QMT 3301 BUSINESS MATHEMATICS

4.1 Invoices and Trade Discounts 4.1.1 Invoice REV 00 Invoice – a printed record of a purchase or sale Sales invoice – records a sale Purchase invoice – records a purchase Extension total – the number of items purchased times the price per unit, any discounts, the shipping and insurance charges. Invoice total – the sum of all the extension totals. Total invoice amount – same as invoice total excluding shipping and insurance. QMT 3301 BUSINESS MATHEMATICS

Seller pays shipping and insurance Buyer pays shipping and insurance REV 00 Common shipping terms: Free on Board (FOB) shipping point or destination – seller pays for shipping to this destination. Beyond this point, the purchaser pays for shipping. FOB shipping point Seller pays shipping and insurance Buyer pays shipping and insurance QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Invoice terms: Trade discount: offered to businesses who buy an item that is to be sold. List price: suggested price at which the item is to be sold to the public. Net price: the amount to be paid by the buyer. Net price = List price – Trade discount QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example of an invoice: REV 00 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example of an invoice: REV 00 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 4.1.2 Trade Discount REV 00 Trade discount is a reduction from the list price offered by wholesalers to retailers so that they can re-sell the merchandise at a profit. The amount of discount that retailers receive from wholesalers is known as trade discount amount. Trade discount = List price – Net price Formula: NP = L (1 – r) Where: NP = Net price L = List price r = trade discount QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 1: REV 00 The list price of a personal desktop is RM 2599. A trade discount of 15% is offered. What is the net price of the personal desktop? Solution: List price = RM 2599 Trade Discount = 15% x RM 2599 = RM 389.85 NP = List price – Trade discount = RM 2599 – RM 389.85 = RM 2209.15 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 2: REV 00 USPD offers a discount of 10% on all the model of cars it sells. What is the net price of a Proton Savvy that is listed at RM 56490? Solution: NP = RM 56490 (1 – 0.1) = RM 56490 (0.9) = RM 50841 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Example 3: A bill of RM 3500 including a prepaid handling charge of RM 250 is offered a trade discount of 17%. What is the net price? Solution: List price = RM 3500 – RM 250 = RM 3250 NP = RM 3250 (1 – 0.17) = RM 3250 (0.83) = RM 2697.50 *(It should be noted that the discount is based on the cost of goods, excluding any other cost) QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 4.3 Chain Discount REV 00 A trade discount in a series of two or more successive discounts. Wholesaler lists the chain discount as a group, for example 15%, 10%, 5%. These discounts might also be given in circumstances such as when a large quantity is ordered. Formula: NP = L(1 - r1) (1 – r2) (1 – r3) Where: NP = Net price L = List price QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example: REV 00 A jeans is advertised for RM 280 less 10% and 5%. Find, a) The net price, b) The total discount. Solution: a) NP = L(1 - r1) (1 – r2) = RM 280 (1 – 0.1) (1 – 0.05) = RM 280 (0.9) (0.95) = RM 239.40 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 b) Total discount = RM 280 – RM 239.40 = RM 40.60 *(It should be noted that the chain discount of 10% and 5% is not the same as 15%) QMT 3301 BUSINESS MATHEMATICS

4.4 Single Discount Equivalent REV 00 A single discount equivalent is a single discount which is equivalent to a chain discount. The single discount equivalent, r for a chain discount of r1, r2 and r3 is given by: r = 1 – (1 - r1) (1 – r2) (1 – r3) QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example: REV 00 A pair of shoes is advertised at RM 229 less 15%, 10% and 5%. Find, a) The single discount equivalent, b) The net price. Solution: a) r = 1 – (1 - r1) (1 – r2) (1 – r3) = 1 – (1 – 0.15) (1 – 0.1) (1 – 0.05) = 1 – (0.85) (0.9) (0.95) = 1 – 0.72675 = 0.27325 = 27.325% QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 b) NP = L (1 – r) = RM 229 (1 – 0.27325) = RM 229 (0.72675) = RM 166.43 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 4.5 Cash Discount REV 00 Cash discounts are often stated under the heading of invoice as, for example 3/10, 2/20, n/30. This means, if the buyer pays the invoice within 10 days of the invoice date, the buyer is entitled to receive a 3% discount or, if payment is made within 20 days from the invoice date, the buyer will receive a 2% discount. N/30 (sometimes written net 30) means the credit period is 30 days. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example: REV 00 An invoice dated 15 November 2007 for RM 2800 was offered cash discount 2/10, 1/15, n/30. If the invoice was paid on 27 November 2007, what was the payment? Solution: 15 Nov – 27 Nov = 12 days, so entitle for a 1% cash discount Net Payment = NP – Cash Discount = RM 2800 – (0.01 x RM 2800) = RM 2800 – RM 28 = RM 2772 QMT 3301 BUSINESS MATHEMATICS

4.6 Partial Payment of Invoice REV 00 4.6 Partial Payment of Invoice If a buyer pays only part of the invoice within the discount period, he receives a proportionate fraction of the cash discount that is offered. He will only receive the full amount of the cash discount if he settles all the payment. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Example: An invoice amounting to RM 4500 and dated 27 October 2007 offered cash discount terms of 10/15, n/30. Find the amount outstanding if the buyer paid RM 2000 on 5 November 2007. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Solution: Amount paid = (Credit given) x (1 – Discount rate) RM 2000 = (Credit given) x (1 – 0.1) Credit given = RM 2000 0.9 = RM 2222.22 Outstanding amount = RM 4500 – RM 2222.22 = RM 2277.78 QMT 3301 BUSINESS MATHEMATICS