QMT 3301 BUSINESS MATHEMATICS REV 00 CHAPTER 6 MATHEMATICS OF SELLING QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 6.1 Markup REV 00 In order to gain profit from selling, the company must sell their product at a higher price than the product cost. The difference between a product’s cost and selling price is refer to as markup. It can be either in money value or percentage. The rate of mark-up is known as markup percentage. Formula: Markup = Selling Price – Cost Price QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 6.2 Markup Percent REV 00 Markup is usually expressed as a percent. It can be expressed as: a) Markup percent based on retail price % Mr = M x 100% R b) Markup percent based on cost price % Mc = M x 100% C QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 1: REV 00 The cost price of a piano is RM 4500. What is the retail price if the seller wants a 15% mark-up based on a) Cost price, and b) Retail price. Solution: a) R = C + M R = RM 4500 + (RM 4500 x 15%) R = RM 4500 + RM 675 R = RM 5175 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 b) Let the retail price be X. Then R = C + M X = RM 4500 + 0.15X X – 0.15X = RM 4500 0.85X = RM 4500 X = RM 4500 0.85 X = RM 5294.12 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 2: REV 00 ABC boutique purchases 100 dresses at a cost of RM 18 each. The boutique expects that 20% of the dresses will be sold at a reduced price of RM 12 each. If the boutique is to maintain a 65% mark-up on cost on the entire purchase, find the regular price of the dresses. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Solution: Cost of 100 dresses = RM 18 x 100 = RM 1800 Mark-up 65% Sale of 100 dresses = RM 1800 x 0.65(RM 1800) = RM 2970 Sale of 20 dresses = RM 12 x 20 = RM 240 Sale of remaining 80 dresses = RM 2970 – RM 240 = RM 2730 Regular selling price = RM 2730 = RM 34.13 per 80 dress QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 3: REV 00 A retailer purchased 150 kg of tomato at RM 1.20 per kg. A 8% spoilage is expected. If he plans to make a 55% mark-up based on overall cost, what is the selling price of the tomato? Solution: Overall cost = RM 1.20 x 150 kg = RM 180 Amount left after deducting spoilage = 150 kg – 0.08(150) = 138 kg QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Mark-up 55% R = C + M = RM 180 + 0.55(RM 180) = RM 279 (retail price for 138 kg) Selling price per kg = RM 279 138 = RM 2.02 QMT 3301 BUSINESS MATHEMATICS

6.3 Conversion of Markup Percent REV 00 Markup percent based on retail price: Since R = C + M 1 + % Mc = 100% + % Mc Hence : QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Markup percent based on cost price: Since R = C + M 100% = 1 - % MR + % MR Hence : QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Example : a) The mark-up percent on cost price of an item is 20%. What is its mark-up percent based on retail price? b) The mark-up percent based on retail price of an item is 15%. What is its mark-up percent based on cost price? QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Solution: a) % Mr = % Mc 1 + % Mc = 0.2 1 + 0.2 = 0.1667 = 16.67% b) % Mc = % MR 1 - % MR = 0.15 1 - 0.15 = 0.1765 = 17.65% QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 6.4 Markdown REV 00 Sometimes retailer may reduce the marked price due to special promotions, festive seasons or the items being obsolete. Markdown is the reduction from the selling price or marked price, normally in terms of percentage. Formula: Markdown Amount = Old Selling Price – New Selling Price Markdown percent based on old price, % MD = MD x 100% OP QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 1: REV 00 The markdown percent on a handphone is 15%. If the new retail price is RM 850, find the old retail price. Solution: Let the old price be RM K % MD = MD x 100% OP 0.85 K = 850 0.15 = (K – 850) K = 850 K 0.85 0.15K = K – 850 = RM 1000 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 2: REV 00 During the year end sales, a department store marked down a pair of shoes by 25%, making the selling price RM 270. At this selling price, the department store made a 18% mark-up on the selling price. Find a) The regular price of the shoes. b) The cost of the shoes. c) The mark-up percent of the shoes at the regular price. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Solution: a) NP = L (1 – r) 270 = L (1 – 0.25) L = 270 0.75 = RM 360 b) R = C + M 270 = X + 0.18(270) X = 270 – 48.6 = RM 221.40 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 c) Mark-up percent at regular price, % Mr = M x 100% R = (Regular price – Cost) x 100% Regular price = (360 – 221.40) x 100% 360 = 38.5% QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 6.5 Profit and Loss REV 00 Business does not always generate income or profit. If the business is not managed properly, it may increase operating expense and indirectly increase cost of the product. The actual cost of the product is the purchase price plus operating expenses. In accounting, operating expenses include cost of goods sold, official rental, advertising, salary, commission and so on. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 In general, there are three possibilities in business: a) M = OE : Break-even b) M > OE : Profit c) M < OE : Loss Where: M = Markup OE = Operating Expenses QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Formula: Break-even Price, BEP = Cost Price + OE Retail Price = Cost + Net Profit + OE Net Profit / (Loss) = Retail Price – BEP Gross Profit = NP + OE QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example : REV 00 A retailer bought a radio for RM 200. Buying expenses amounted to RM 20. Operating expenses incurred were 20% of the cost price. If the retailer made a 25% net profit based on cost, find a) The retail price, b) The gross profit , c) The net profit, d) The breakeven price, and e) The maximum markdown that could be offered so that there is no profit or loss. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Solution: a) Retail price = 220 + 0.25(220) + 0.2(220) = RM 319 b) Gross profit = NP + OE = 0.25(220) + 0.2(220) = RM 99 c) Net profit = Gross profit – OE = 99 – 44 = RM 55 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 d) Breakeven price = C + OE = 220 + 44 = RM 264 e) Maximum reduction in price = R – BEP = 319 – 264 = RM 55 QMT 3301 BUSINESS MATHEMATICS