Buying and Selling. Francis Joseph H. Campena, Ph.D. Mathematics Department De La Salle University Manila. October 24, 2016

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1 Buying and Selling Francis Joseph H. Campena, Ph.D. Mathematics Department De La Salle University Manila October 24, 2016 Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

2 Outline 1 Mark-On, Mark-Up, Mark-Down, Gross Margin 2 Single Trade Discount and Discount Series 3 Profit Loss and Break Even 4 Commission Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

3 Mark-On, Mark-Up, Mark-Down, Gross Margin M o : Mark-on Price-The original price of the product M u : Mark-up Percentage-The amount of increase in the original price of the product M d : Mark-down Percentage-The amount of degrease in the original price of the product r: Mark-up rate- r = M u M o r: Mark-down rate- r = M d M o S: Selling Price S = M o + M u or S = M o M d M g : Gross margin-it is another way of looking at how a selling price of an item is affected by and add-on amount. M g = S M o r: Gross Margin rate- r = M g S Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

4 Single Trade Discount and Discount Series Definition Single Trade Discount: A single trade discount is a discount that is given to a customer (usually a wholesaler) when the customer buys a product. The discount is expressed simply as a single discount of a given percentage. D = r M o ; S = M o D Discount Series or Chain Discounts : A chain of discounts is usually offered by retail stores to give an illusion of a larger discount that they really are. This is just a sequence of discounts applied to a product being purchased. S = M o (1 r 1 )(1 r 2 ) (1 r k ), D = M o S where, D : Discount; M o : Mark-on Price; r, r 1,..., r k : Discount rates; S : Selling Price Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

5 Single Trade Discount and Discount Series A refrigerator with a Php12,990 mark-on price is on sale at 20% off. If you buy it now, how much will you save? ANS. D = (0.2)(Php12, 990) = Php2, 598 A stereo unit has list price of $1000. It goes on sale at a discount of 30%. However, too few buyers are interested and so the manager gives an additional 20% off. What is the final price of the stereo? ANS. S = $1000(1 0.3)(1 0.2) = $560. Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

6 EXERCISES 1. An evening gown lists for Php15,000 and is offered at a discount rate for 30%. Since it does not sell for quite some time, the store manager offers a second discount for 40% off the discounted price. However, it does not work also and does not sell. In desperation, the store offers another 50% off on top of the the previous discounts. What was the final price of the gown? 2. A branded shirt cost Php1,500 and is marked 20% off. How much was the discount? What is the selling price of the shirt? 3. A rice cooker was sold for Php450 during a holiday sale. It was marked at 70% off. How much was the mark-on price of the rice cooker? 4. The organizer of a conference ordered 250 pieces of bags for the conference kit priced at Php150 per bag. However, since the order was in bulk, they were given a 35%-20%-10% discount series. How much was the bill of the organizer for the said purchase? Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

7 Single Trade Discount and Discount Series Suppose a series of discounts r 1, r 2, r 3,..., r k were given, the equivalent single discount rate r is computed as r = (1 r 1 )(1 r 2 ) (1 r k ) The organizer of a conference ordered 250 pieces of bags for the conference kit priced at Php150 per bag. However, since the order was in bulk, they were given a 35%-20%-10% discount series. What single discount rate is equivalent to the given series of discounts? Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

8 Profit Loss and Break Even Fixed Cost: Expenses necessary to keep the business open. This cost is not dependent sales volume. Usually includes salaries of emplyes, rent basic utilities and other necessary expenses. Variable Cost: includes expenses in producing each product or item. Total Cost or Total Expenses: the sum of fixed cost and variable cost. Revenue: the income that the business has from its normal business activities. In a simple business activity of selling one product the revenue is the price per item times the quantity of products sold. Profit : the amount remaining from the revenue after all expenses have been deducted. Loss : if expenses are greater than the revenue the difference of these amount is called a loss. Break Even Point: the point where neither profit nor a loss is made. Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

9 Profit Loss and Break Even Total Cost Function TC(x) = vx + FC(x) where FC(x) represents the fixed cost, v represents the variable cost per unit and x represents the number of units produced. Total Revenue Function TR(x) = px where p is the price per unit of product or item and x is the number of units sold. Profit Funtion P(x) = TR(x) TC(x). Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

10 Example Assume that the fixed cost necessary to run a coffee shop on a monthly basis is Php30,000. In addition, a cup of coffee which is for sale at Php40 cost the shop Php10 for bulk coffee, filter and water expenses. 1 What is the break-even quantity? 2 How much profit is obtained when 3,000 cups of coffee are sold?when 4,500 cups are sold? 3 How many cups must be sold to earn a profit of Php12,000? Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

11 Exercises 1 A manufacturer of a certain commodity sells his product at Php10 per unit, selling all he produces. The fixed cost is Php5,000 and the variable cost is Php5 per unit. At what level of production will the manufacturer have a profit of Php1,000? at what level of production will he have a break-even? Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

12 Example A retailer purchased a printer for Php3,500. Operating expenses incurred were 5% based on cost. If the retailer wanted a 10% net profit based on cost, determine the following: selling price net profit break-even price Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

13 Example The unit price of a certain commodity is given by p = 24 4x for x units sold and the cost in producing the commodity consists of a fixed vost of Php16 and a variable cost of Php4 per unit. Price, cost and quantity are expressed in thousands. What are the total revenue, total cost and profit functions? What sales volume will the manufacturer have a break even? What is the highest possible revenue for this commodity? Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

14 EXERCISES In each item, TR(x) represents the total revenue and TC(x) represents the total cost function. If x is the number of unit produced and also the number of units sold, determine the break-even quantity/quantities. 1. TR(x) = 10x ; TC(x) = 2x TR(x) = 156x ; TC(x) = 86x + 10, TR(x) = 2x ; TC(x) = 0.01x x Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

15 Salaries and Wages content... Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

16 Commission Francis Joseph H. Campena, Ph.D. (DLSU) Buying and Selling October 24, / 15

Chapter 10: The Mathematics of Money

Chapter 10: The Mathematics of Money Percent Increases and Decreases If a shirt is marked down 20% and it now costs $32, how much was it originally? Simple Interest If you invest a principle of $5000 and