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Lesson 3.7
Profit or Loss
A businessman opens a business to earn profit. Thus, he should know how to prepare a profit and loss statement to find out if his business is making profit or losing at any given period of time.The profit or loss of a business is the amount left after deducting all costs and expenses from the sales/revenues.The Income Statementis a financial report that tells how much a business earned or lost for a given period of time, such as one month, three months (one quarter) or one year. The income and expenses of the business are summarized in this statement. This statement shows the amount of revenues (sales), the costs and expenses (operating expenses) incurred, and the net income (profit) for a given period of time.The income statement contains five basic sections:a. revenues or sales, b. cost of goods sold, c. gross profit from sales, d. operating expenses, and e. net income profit.The basic formulas/equations of the income statement are: Net sales = Gross Sales – Sales Returns Gross Profit = Net sales – Costs of Goods Sold Net Income = Gross Profit – Operating ExpensesTerms on Income StatementThe Gross Sales or Total Revenues represents the total sales made by the business, whether in cash or in credit. Sales discounts are discounts (reductions) in price given by the business to customers as a gesture for early or prompt payment of accounts. Sales Returns represent the goods that are returned to suppliers due to product defects, low quality of materials used, noncompliance with the contract specifications and the like. Sales Allowances are the damaged goods that are paid by the buyer at a reduced price. The Net Sales is the difference between the gross sales and the sales returns, discounts and allowances.The Cost of Goods Sold represents the total cost spent by the business in acquiring the goods that are sold to customers. This section shows the beginning inventory, purchases made (including purchase discounts, sales returns and allowances, if any), and ending inventory.The process of counting the remaining goods and obtaining the price based on the purchase price of the goods is called inventory. Merchandise inventory accounts for the cost of inventory or the goods available at hand at any given accounts for the cost of inventory or the goods available at hand at any given specific date. The Beginning Inventory shows the cost of goods before the period, while the Ending Inventory presents the costs of goods at the said period.The Gross Profit or Gross Profit on Sales are represented by the net sales minus the cost of goods sold.The Operating or Overhead Expenses are the expenses incurred in operating the business. Examples of expenses incurred in operating a business include salaries, benefits and allowances paid to employees, insurance, taxes, utilities, delivery expenses, depreciation of building, cars and equipment, cost of selling and advertising, office supplies and miscellaneous expenses.The Net income or Net Profit shows the amount earned by the business for the period specified in the financial statement. It is the difference between the gross profit and the operating expenses.Preparing an Income StatementTo prepare an income statement, the following steps and procedures are suggested:1. Write on top of the report the name of the business, the type of financial statement and the time or period covered.2. Enter gross sales or revenue. Enter and subtract sales return, discounts and allowances to find net sales.3. Enter beginning inventory and add purchases to find goods available for sale. Subtract ending inventory from goods available for sale to obtain the cost of goods sold.4. Subtract the cost of goods sold from the net sales to find the gross profit on sales.5. Enter and add all operating expenses to get the total operating expenses.6. Subtract the total operating expenses from the gross profit on sales to find the net income or profit.Example 1:CBA Store reported the following information for its first quarter operation, ending March 20XX: Net sales, P185, 000.00 Cost of goods sold, P95, 000.00; and Operating expenses, P27, 750.00. Find the net income/profit for the first quarter that ended 31 March 20XX.CBA StoreIncome StatementFor the First Quarter Ended 31 March 20XXNet Sales P185, 000.00Less: Cost of Goods Sold  P95, 000.00Gross Profit from Sales P90, 000.00Less: Operating Expenses  P27, 750.00Net Income (Profit) P62, 250.00Example 2:Prepare an income statement and find the net income of DCB Supermarket for its April 20XX operations based on the following information: Gross Sales, P1,820,400.00; Sales Returns and Discounts, P21,700.00; Cost of Goods Sold, P1, 092,000.00; and Operating Expenses, P373,000.00.Solution:DCB SupermarketIncome StatementFor the Month of April 20XXGross Sales P1,820,400.00Less: Sales Returns and discounts  P21,700.00Net Sales P1,798,700.00Less: Cost of Goods Sold  P1,092,000.00Gross Profit P706,700.00Less: Operating Expenses  P373,000.00Net income (Profit) P333,700.00In the preceding two (2) examples, we assume that the amounts for the cost of goods sold were determined after considering the amounts of their remaining or available stocks/merchandise and the purchases made during the period under consideration.In the following example, we will prepare an income statement considering the inventories taken before and at the end, and the purchases made during the statement period.The formula to calculate the cost of goods sold considering the above items is:Cost of Goods Sold = Beginning Inventory + Purchases – Ending InventoryExample 3:Prepare the 2nd quarter, 20XX Income Statement for EC Department Store which reported the following information. Find its gross profit and net income for the quarter. Gross Sales P3, 175, 000 Sales Returns and Discounts P20, 000 Beginning Inventory P2, 120, 000 Purchases P1, 874, 000 Ending Inventory P1, 785, 000 Expenses Salaries P258, 750 Rent P195, 000 Utilities P27, 200 Advertising 4, 000 Insurance 1, 500 Depreciation 45, 000 Supplies 5, 300 Taxes 5, 100 Miscellaneous 1, 900Solution:EDC Department StoreFor 2nd Quarter Ending 30 June 20XXRevenue Gross Sales P3,175,000 Less: Sales Returns and Discounts 20,000 Net Sales P3,155,000Cost of Goods Sold Merchandise Inventory (01 April) 2,120,000 Add: Purchases 1,874,000 Goods Available for Sale 3,994,000 Less: Merchandise Inventory (30 June) 1,785,000 Cost of Goods Sold P2,209,000Gross Profit on Sales P946,000Operating Expenses Salaries P258,750 Rent 195,000 Utilities 27,200 Advertising 4,000 Insurance 1,500 Depreciation 45,000 Supplies 5,300 Taxes 5,100 Miscellaneous 1,900 Total Operating Expenses P543,750Net Income/Profit P402,250Therefore, EDC Department Store had a gross profit in sales of P946,000 and a net income or net profit of P402,250 for the 2nd quarter ending 30 June 20XX.If the sales/revenues are greater than the cost of goods sold and the operating expenses, the business registers a profit that sis represented by a positive number. However, if the sales/ revenues are less than the cost of goods and the operating expenses, the business registers a loss that is represented by a number, enclosed in parentheses.Analyzing Comparative Income StatementsWhile it is important for a business owner to know that his business venture is profitable, it is also equally important to find out whether the business is growing or not, and if so, by how much.One way to find this is to compare quantitatively the results of the business operation of one period against the result of another period. The comparison of the result may be between the results covering the same periods of the past 2 years or the past 2 succeeding periods, (e.g. quarters) in the same year or other comparative periods, depending on the objectives and requirements of the business.It is true that the appreciation of the profitability of a business varies by the type or kind of business it is in, and by other factors such as location, capitalization and the like. Different types of business have different standards for growth. A new business or some businesses may incur losses throughout their entire first year of operations although they are well managed. For instance, a company that needs a lot of capitol to begin its business is not expected to make a profit right away, such as a firm that is putting up a dormitory or developing a tourist resort. A business providing services like a beauty parlor or store selling rice and food products could most often make profit in its first year of operation. Therefore, the performance of a business should be measured not only by comparing its operations using short periods but considering various factors such as those previously mentioned.There are two (2) ways to analyze an income statement – the horizontal analysis and vertical analysis. The horizontal analysis involves finding the percent change (increase or decrease) between the latter time period and the earlier time period. The result of this comparison could indicate significant changes in important items in the income statement such as decline in sales or increase in operating expenses. The vertical analysis involves using the net sales as a percent of each of the items on the income statement.Comparing Income Statements by Horizontal AnalysisTo conduct a horizontal analysis of items in income statements covering comparative periods of business operations, we shall use the following formulas: = x 100% = x 100%Note that the percent (%) increase or decrease of an item between periods is calculated by subtracting the smaller figure from the bigger figure, whichever periods they represent and the result divided by the earlier period’s figure. The quotient then obtained is multiplied by 100%. Negative percentages are placed inside parentheses.To illustrate the calculations for profitability of the operations of a business, let us analyze the following condensed financial income statements of EFG Enterprises for the years that ended 31 December 20XX (earlier year) and 31 December 20XY (latter year).EFG Enterprises Condensed Income Statements For the Years Ended 31 December 20XX and 31 December 20XYRevenues (Sales) 20XX (Earlier Year) 20XY (Latter Year)Gross Sales P3,402,000 P3,710,000Net Sales P3,384,000 P3,621,000Cost of Goods Sold P1,788,000 P2,102,400Gross Profit on Sales P1,596,000 P1,518,600Operating Expenses P1,087,000 P963,000Net Income P509,000 P555,600Determine the:1. Percent (%) Change in Net Sales Solution:Amount of Increase in Net Sales = 20XY Net Sales – 20XX Net Sales = P3,621,000 – P3,384,000 = P237,000 = x 100% = x 100% = 7.00% (rounded to hundredths place)2. Percent (%) Change in Gross Profit on SalesSolution: = – = P1,596,000 – P1,518,600 = P77,400 = x 100% = x 100% = (4.85%) rounded to the hundredths place3. Percent (%) Change in operating Expenses = 20XX Operating Expenses – 20XY Operating Expenses = P1,087,000 – P963,000 = P124,000 = x 100% = x 100% = (11.41%) rounded to the hundredths place4. Percent (%) Change in Net Income = 20XY Net Income – 20XX Net Income = P555,600 – P509,000 = P46,600 = x 100% = x 100% = 9.16% (rounded to the hundredths place)3.7.1.5 Comparing Income Statements by Vertical AnalysisThe financial performance of a business through its income statement report can also be analyzed by determining some ratios commonly used in the business sector. The ratio of two numbers is the relationship of the first number to the second number.Many successful business managers and owners use ratios to study the significant relationships between the various items found in their income statements. These ratios are good indicators in determining the overall picture of the financial condition, growth, strengths, and weaknesses of the business. For instance, if a business has an operating expenses ration of 50% on the relationship of its operating expenses to its net sales, a business is definitely alarmed and has to immediately implement strategies to lower the ratio. This 50% ratio is alarming because it indicates how much of the net sales is spent by the business for its operating expenses. Note that his 50% ratio means that the operating expenses of the business is 0.5 times its net sales. In other words, the business spends 50 centavos in operating the business for every peso of its net sales.The 50% operating expenses ratio can also be expressed mathematically as 0.5 : 1. In a ratio, the base (second number) is always pegged at 1.To find the ratio of the items in the income statement, we shall use the vertical analysis. As stated earlier, the net sales is used as a percent of each of the items on the income statement.The most commonly used ratios using the income statement, expressed in percent, are the following:Percent (%) of Net Income/Profit = x 100%Percent (%) of Cost of Goods Sold = x 100%Percent (%) of Gross Profit on Sales = x 100%Percent (%) of Operating Expenses = x 100%The above ratios can also be written using the dots (:) symbol. For example the ratio of net income profit to net sales may be written: Ratio = Net income/Profit : Net SalesThe net income or net profit ratio indicates how much of the net sales goes to profit. Thus, ratio is important in figuring out how to calculate the retail price of a merchandise starting with it cost then adding a margin to cover the operating expenses and net profit. A high net profit ratio registered by a business is an indication of a good performance.The cost of goods sold ratio is important in determining the value of inventory of merchandise. A higher figure for cost of goods sold in the income statement results in a high net profit.The gross profit ratio reveals the relationship between the gross profit on sales and the net sales. Therefore, a higher gross profit ratio is an indication of a better performance for the business.As earlier stated, the ratio on operating expenses shows how much of the sales is spent by the business owner in running the operations of the business. Hence, the lower the ratio on operating expenses, the higher the efficiency of the business.For illustration, using vertical analysis, let us calculate the ratios of net income/profit, cost of goods sold, gross profit on sales and operating expenses using the condensed income statement report of EFG Enterprises for the years that ended 31 December 20XX (earlier year) and 31 December 20XY (latter year).We shall find the ratios of EFG Enterprises, as follows:1. Net Income/Profit on Sales Ratio 20XX (Earlier Year) 20XY (Latter Year)Net Income/Profit P509,000 P555,600 = x 100% = x 100% = 15.04% = 15.34%A comparative analysis of the net income/profit on sales ratios for the two income statement reports revealed an increase of 0.30% from 15.04% in net sales in 20XX to 15.34% of net sales in 20XY.2. Cost of Goods Sold Ratio 20XX (Earlier Year) 20XY (Latter Year)Cost of Goods Sold P1,788,000 P2,102,400 = x 100% = x 100% = 52.84% = 58.06%There was an increase of 5.22% in the cost of Goods sold from 52.84% of net sales in 20XX to 58.06% of net sales in 20XY.3. Gross Profit on Sales Ratio 20XX (Earlier Year) 20XY (Latter Year)Gross Profit on Sales P1,596,000 P1,518,600 = x 100% = x 100% = 47.16% = 41.94%The gross profit on sales ratio resulted in decrease by 5.22% from 47.16% of net sales in 20XX to 41.94% of net sales in 20XY.4. Operating Expenses Ratio 20XX (Earlier Year) 20XY (Latter Year)Operating Expenses P1,087,000 P963,600 = x 100% = x 100% = 32.12% = 26.59%A decrease of 5.53% in the operating expenses ratio is noted from 32.12% of net sales in 20XX to 26.59% of net sales in 20XY. This is a good indication of good performance by the business considering that there was an increase in net sales by 7.00% from P3,384,000 in 20XX to P3,621,000 in 20XY.
Lesson 3.8
BreakEven Analysis
Is a business method of using mathematics for finding the monetary value needed for a business operation to breakeven.This is done to calculate the level of activity and performance of a business when its operation neither makes profit nor incurs loss. It is concerned about having a specific amount of revenues or sales before a profit is achieved or below which is a loss is incurred. BreakEven Point Is the point in which the business neither makes a profit nor incurs a loss. This means that at breakeven point, business’ sales/revenues are equal to the total costs. To determine the breakeven point, we shall make use of the following business concepts: Gross Profit = Sales/Revenues – Variable Costs and Gross Profit – Fixed Costs = 0 (BreakEven Point) Sales/Revenues = Variable Costs + Fixed Costs To determine the number of units to be sold to breakdown, we shall make use of the following formulas: Px = Vx + FcWhere P – the unit price of item for sale x – the number of units V – the variable price of each unit FC – the total fixed costsThus, the breakeven point or the number of units to be sold by a business to breakdown is designated bySales or Revenues are the amounts (money) received from the sale of all products over a certain period of time. Variable Costs are the costs or expenses that may increase or decrease depending on the volume or quantity of sales. The variable costs include the cost of goods sold. Gross Profit is the difference between the sales/revenues and the variable costs. Thus, the gross profit minus the fixed costs equals the breakeven point or O. Fixed Costs are the expenses of the business that remain constant regardless of the volume or quantity of sales. Examples: 1. If the sales/revenues of company MNO are ₱1,200,000; variable expenses are ₱840,000 and fixed costs are ₱360,000 for a certain period, the company will have a breakeven operation. Thus, the breakeven sales operation or breakeven point for Company MNO is ₱1,200,000, where there will be a 0 profit and 0 loss. Solutions: 2.Determine the breakeven point in quantity or volume and the corresponding amount of sales of ORS Enterprises based on its reported business transactions for a certain month in 20XY. Unit Price ₱55.75 Variable Cost Per Unit 25.50 Total Fixed Cost ₱45,375 Solutions:The breakeven point in the amount of sales per unit price of ₱55.75 isBreakeven Point in Amount of Sales Sold (BEPAmount) = Unit Price x Breakeven Point in Number of Units Sold (BEPnumber) = P x x BEPnumber = ₱55.75 x 1,500 BEPAmount = ₱83,625 Hence, the breakeven point in the number of units sold is 1,500 units and in the amount of sales is ₱83,625. 3.QRS Distributors, Inc. sells certain rods at ₱280 each. Production and variable costs per unit amount to 70% of the unit selling price. Total fixed costs are ₱218,400. What is the breakeven point in the number of units to be sold and the amount of sales? Solutions: Unit Price = ₱280 Production and Variable Cost Per Unit = 70% of ₱280 = ₱280 x 0.70 = ₱196 Total Fixed Cost = ₱218,400 Thus, the breakeven point in number of production units is 2,600 units and in the amount of sales is ₱728,000.
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Mathstig
What is Mathstig?Mathstig is an educational application that gives lessons, activities and excercises in Mathematics.Who can use this application?ABM Grade 11 student of Don Honorio Ventura Technological State University.What are the lessons under Mathstig?Business MathematicsHow do I set up a new user account?Use your gmail account or phone number in creating an account. Please use your given name in putting your name.If you don't have gmail account create one here gmail.comDo I need to validate my account?Yes to secure your account.
Lesson 3.6
Cash Discounts
Cash discount is calculated separately from trade discounts. It is an amount or a percentage of the net price that is deducted from the net price if the bill is paid on or before a specified time period called the discount period. Based on regular dating, the discount period begins with the receipt of goods (R.O.G.) by the buyers.Suppliers indicate the discount period and the payment terms on the invoice. The discount period may not necessarily be the date when the invoice was sent to the buyer. For instance, the invoice could be dated June 5, but the discount period starts June 12.There are times when the discount period is extended. If the invoice is dated June 10 and marked 15 E.O.M. under payment terms, the discount period extends until the 15th of the next month, lasting until July 15. If the invoice is dated late in the month such as 26th to 31th, and marked 15 E.O.M., the discount period extends to the 15th of the second upcoming calendar month. For example, an invoice dated June 26th and marked 15 E.O.M. has a discount period up to August 15.If the invoice is marked C.O.D. or cash on delivery, the buyer would have to pay at the time of the delivery of the goods.Some examples of payment terms that are commonly found on sales invoices are the following:1. 1/10, n/30. A 2% cash discount is deducted from the total amount of the merchandise if payment is made during the 10day discount period. The n/30 indicates that the total amount must be paid within 30 days. A late payment charge of approximately 1% is usually added to the bill if not paid on due date.2. 5/10, 2/10, n/30. This means that 5% may be deducted from the bill if paid within 10 days of the discount period; 2% if paid from the 11th to the 20th day; or if not, full payment of the goods is due from 21th to the 30th day of the date of the invoice.3. 3/7 E.O.M. The buyer will receive a 3% cash discount if the bill is paid within 7 days of the next month.4. 3/7 E.O.M., n/30. This means that the buyer will receive a 3% discount if the bill is paid within 7 days of the next month; or if not, the bill would have to be paid in full from the 8th to the 30th day of the next month.5. R.O.G. This means that the discount period begins upon the receipt of the goods by the buyer.6. C.O.D. or cash on delivery. Payment would have to be made upon delivery of the goods.Examples:1. State the payment due dates of the following invoices:Solutions:a. The payment for the invoice dated January 5 is due on February 10.b. The August 1 payment invoice is due on August 31.c. For the March 2 invoice, 5% discount will be granted on or before March 12; and if not paid, full payment is due on April 1.d. The invoice dated October 27 is late of the month. Hence, the payment due date would be the 15th of the second upcoming month which is December 15.e. For the April 12 invoice, payment due date is upon delivery of the merchandise.f. An 8% discount will be granted on the March 10 invoice if paid on or before April 10; no discount is granted if paid from April 11 to the 60th day from the date of the invoice.g. For the January 5 invoice, the payment due date is February 14 which is 40 days (10 + 30x means 10 days plus an extension of 30 days) after the date of the invoice.h. For the May 7 invoice, the payment due dates is 10 days after the receipt of the goods. If the merchandise is received on May 15, then the payment due date is May 25.2. The total bill of an invoice dated March 12, 20XX is P15, 225.00. If the bill has terms of 5/15, n/30 and is paid on March 24, find the amount of cash discount and the amount due.Solutions:March 24, 20XX is within 15 days from March 12, 20XX, then 5% discount is deducted from P15, 225.00Cash Discount = Total Amount of Invoice x Cash Discount Rate = P15, 225.00 x 0.05 = P761.25Amount of Payment = Total Amount of Invoice – Cash Discount = P15, 225.00 – P761.25 = P14, 463.753. Find the amounts of cash discounts and amount of payment due for the following invoices:Solutions:a. The 2/30 payment term applies since August 25 is 20 days from August 5. Hence, we have: Cash Discount = Total Amount of Invoice x Cash Discount Rate = P25, 700.00 x 0.02 = P514.00 Amount of Payment = Total Amount of Invoice – Cash Discount = P25, 700.00 – P514.00 = P25, 186.00b. The 3/10 E.O.M. applies to the invoice since October 7 is within the first 10 days from September 30 (e.o.m.). Therefore, Cash Discount = Total Amount of Invoice x Cash Discount Rate = P18, 650.00 x 0.03 = P559.50 Amount of Payment = Total Amount of Invoice – Cash Discount = P18, 650.00 – P559.50 = P18, 090.50a. The 3/10 + 30x means 40 days from January 6, which is February 15. February 27 from January 6 is 52 days. The n/60 payment term applies to the transaction, which is up to March 7. Hence, there will be no cash discount and the total amount to be paid on February 27 is P35, 400.00.Exercise:1. State the payment due dates of the following invoices:2. On May 8, Abegon bought merchandise worth ₱15,000.00 with terms 2/10, n/30. How much would be needed to pay for the merchandise on May 15 of the same year?3. By taking a cash discount of 3% on a bill of goods, a retailer saved ₱1,500.00. what was the invoice price of the goods?4. Find the amounts of cash discounts and payments for the following invoices:
Lesson 3.5
Trade Discounts
is a reduction in price of a merchandise granted by a manufacturer or a wholesaler to the retailer. The discount can be in the form of TD (Amount of Trade Discount) or TDR (Trade Discount Rate in Percent).is most often applied by the manufacturer in its list price. This discount is subtracted from the list price to obtain the net price.The net price is the price the retailer actually pays for the merchandise.In most cases, manufacturers recommend to the retailers the price that should be charged to the customers. This recommended price by the manufacturer is called the list price (LP) or suggested retail price (SRP).A trade discount is offered by manufacturer or wholesalers for various reasons. Some of these reasons are:a) adjust list prices to prevailing market prices, b) secure the trade of desirable customers, and c) attract retailers to buy in large quantities.To calculate the single trade discount or simply trade discount and the net price, we shall use the following formulas:Trade Discount (TD) = List Price (LP) x Trade Discount Rate (TDR) or TD = LP x TDRNet Price (NP) = List Price (LP) – Trade Discount (TD) or NP = LP x (100%  TDR)The trade discount rate (TDR) which is the quotient of the trade discount (TD) as the percentage and the list price as the base, is calculated as follows:Trade Discount Rate (TDR) = x 100% TDR = x 100%Examples:1. If a business man buys a box of can goods listed at P680.00 with a trade discount of 25%, how much will be the net price?Solution 1: TD = LP x TDR = P680.00 x 0.25 TD = P170.00 NP = LP – TD = P680.00 – P170.00 NP = P510.00Hence, the net price is P510.00.Solution 2:Using the alternative formula, we shall have: NP = LP x NPR = P680.00 x (100%  25% or 1 – 0.25) = P680.00 x 0.75 NP = P510.002. XYZ suppliers gives a trade discount of 18% on a certain appliance item for a minimum purchase of 1 dozen at a list price of P2500.00 per piece. If a retailer buys a dozen of the appliance, how much will he pay per piece? For a dozen?Given: TDR = 18% LP per piece = P2500.00Solution 1: TD (per piece) = LP x TDR = P2,500.00 x 0.18 = P450.00 NP (per piece) = LP – TD = P2,500.00 – P450.00 = P2050.00 NP (per dozen) = NP (per piece) x 12 (one dozen) = P2,050.00 x 12 = P24, 600.00Solution 2: NP (per piece) = LP x NPR = P2,500.00 x (100%  18% or 1 – 0.18) = P2,500.00 x 0.82 = P2,050.00 NP (per dozen) = P2,050.00 (per piece) x 12 (one dozen) = P24,600.003. The list price of a box of bar soap is P1,250.00. If the retailer buys the box at P937.50, calculate the a) trade discount, and b) trade discount rate.Solution:a. TD = LP – NP = P1,250.00 – P937.50 TD = P312.50b. TDR = x 100% = x 100%TDR = 25%Trade Discounts SeriesOn account of decline of market prices or to encourage further purchases for more merchandise in large quantities or to receive frequent orders, manufacturers and wholesalers offer trade discounts series to retailers. Giving trade discount series is a method of granting two or more trade discounts to the retailers. This method is also known as successive trade discounts, chain or multiple discounts.In trade discount series, the first discount is based on the list price; the second, on the remainder after deducting the first discount; the third, on the remainder after deducting the first two discounts; and so on.To find the net price (NP) resulting from trade discount series, we have:NP (for k successivediscount rates) = LP (1 – TDR1) (1 – TDR2), …, (1 – TDRk)Examples:1. If a DVD player has a list price of P3,400.00 and trade discounts of 20% and 10%, how much is the a) net price, and b) trade discount?Solution:a. NP = LP (1 – TDR1) (1 – TDR2) = P3,400.00 (1 – 0.20) (1 – 0.10) = P3,400.00 (0.80) (0.90) = P2,448.00b. TD = LP – NP = P3,400.00 – P2,448.00 = P952.00Hence, the net price is P2, 448.00 and the trade discount is P952.002. Ms. C. Navarro bought a flat television set with a listed price of P14, 600.00 subject to 15%, 10% and 5% trade discounts. How much did she pay?Solution: NP = LP (1 – TDR1) (1 – TDR2) (1TDR3) = P14, 600.00 (1 – 0.15) (1 – 0.10) (1 – 0.05) = P14, 600.00 (0.85) (0.90) (0.95) NP = P10, 610.55Hence, Ms. C. Navarro paid P10, 610.55 for the flat television set.Single Equivalent Trade Discount Rate (SETDR) An easy way of dealing with successive trade discount rates is to combine the rates into a single equivalent trade discount rate (SETDR). This can be done by subtracting each trade discount rate from 100%; then multiplying the results together to obtain the overall net price rate (NPR). If this overall net price rate is subtracted from 100% or 1, the result is the overall trade discount rate, known as the single equivalent trade discount rate (SETDR).In symbols, we shall have: SETDR = [1 – (1 – TDR1) (1 TDR2), …, (1 – TDRk)] x 100%Examples:1. A certain item is subject to 20% and 10% trade discounts. Find the single equivalent trade discount rate.Given: TDR1 = 20% TDR2 = 10%Solution: SETDR = [1 (1 – 0.20) (1 – 0.10)] x 100% = [1 – (0.80) (0.90) x 100% = (1 – 0.72) x 100% SETDR = 28%2. A calculator has a list price of P845.00 subject to 20%, 10% and 5% trade discounts. Find the:a. Single equivalent trade discount rateb. Net pricec. Trade discountGiven: LP = P845.00 TDR1 = 20% TDR2 = 10% TDR3 = 5%Solutions:a. SETDR = [1  (1 – TDR1) (1 – TDR2) (1TDR3)] x 100% = [1  (1 – 0.20) (1 – 0.10) (10.05)] x 100% = [1  (0.80) (0.90) (0.95)] x 100% = (1 – 0.684) x 100%SETDR = 31.6%b. NP = LP (1 – SETDR) = P845.00 (1 – 0.316) = P845.00 (0.684) NP = P577.98c. TD = LP – NP = P845.00 – P577.98 TD = P267.02Therefore, the single equivalent trade discount rate is 31.6%, the net price is (P577.98 and the amount of trade discount is P267.02).3. The list price of an electric fan is P894.00 subject to 20% trade discount. What additional trade discount rate should be given to bring down the price to P607.92?Given: LP = P894.00 TDR1 = 20% NP = P607.92Solution: NP = LP (1 – TDR1) (1 – TDR2) P607.92 = P894.00 (1 – 0.20) (1 – TDR2) P607.92 = P894.00 (0.80) (1 – TDR2) P607.92 = P715.20 (1 – TDR2) = 1 – TDR2 0.85 = 1 – TDR2 TDR2 = 1 – 0.85 = 0.15 x 100% TDR2 = 15%Hence, the additional trade discount rate is 15%.Example 3 above can also be calculated by using the following derived formula: TDR2 = x 100% = x 100% = x 100% = (1 – 0.85) x 100% TDR2 = 15%Using a scientific calculator, we can solve the above, as follows: TDR2 = 1 – ((607.92 ÷ (894 x (1 – 0.20))) = x 100% = 15% Exercise:Exercise:1. A retail dealer purchases a washing machine listed in the manufacturer’s catalog at ₱18,500.00 less 30% discount. Find the invoice price and the amount of trade discount for the washing machine?2. An electric range listed in AMP Company’s catalog at ₱23,000.00 is billed to the retailer at ₱20,100.00. Determine the:a. amount of trade discountb. trade discount rate3. The invoice price of a vehicle’s tire is ₱12,600.00 after deducting a trade discount of ₱2,268.00 from the list price. Find the:a. list price of the tireb. trade discount rate4. RMZ Sales offers a trade discount of 24% on a microwave oven for a minimum purchase of 1 dozen at a list price of ₱3,450.00 per microwave oven. If a retailer buys 1 dozen microwave ovens, how much will he pay per oven? For a dozen?
Lesson 3.2
Markon and Markup
Markon is the difference between the initial or first selling price and the cost of the item. Hence, the markon is the initial or first amount added to the cost of an item to cover the operating expenses, net profit and ± final adjustment. This markon may be expressed as an amount added to or as a percent of the cost. Sometimes, even after setting up the selling price of our item based on cost and the markon, the retailer may find it necessary to adjust this selling price. For instance, if there is an extremely strong demand or unexplained scarcity for a product, increase in operating expenses, etc., the retailer may have to increase such selling price. Now, the amount increase from the previous selling price (cost + markon) to the new selling price is called markup. In other words, the markup is the difference between the new selling price and the initial or previous selling price. The markup, similar to markon, may be expressed also as the amount added to or as a percent of the initial, previous or first selling price. For purposes of all discussions in this chapter, we shall prefer to the selling price, whether the initial, previous or first selling price and the new selling price as decided selling price since the ± final adjustment is a matter decided only by the retailer. In symbols, we have: Selling Price (SP) = Cost ( C ) + Markon (MO) And New Selling Price (NSP) = Selling price (SP) + Markup (MU) Where: Markon (MO) or Markup (MU) = operating expenses + Net Profit ± Final Adjustment Markon Based on Cost When based on cost, the markon is added to the cost of the item to determine the selling price as follows: Selling price (SP) = Cost ( C ) + Markon (MO) Markon (amount) = Cost ( C ) x MO Rate (MOR) Markon rate (MOR) = [Markon (amount) / Cost ( C )] x 100% Cost ( C ) = Selling price (SP) / 1+Markon Rate (MOR) on Cost ( C ) EXAMPLE: 1.If an item was purchased at P35.00 and the markon rate of 40% based on cost was added, find the amount of markon and the selling price. SOLUTION: A) Markon (amount) = Cost ( C ) x Markon Rate (MOR) = P35.00 x 40% = P35.00 x 0.40 = P14.00 B) Selling Price (SP) = Cost ( C ) + Markon (MO) = P35.00 + P14.00 = P49.00 Thus, the amount of markon is P14.00 and the selling price is P49.00. 2.A retailer buys a dozen calculator at P3,000.00. If his markon rate based on cost is 25%, how much is the selling price of each calculator? SOLUTIONS: Cost of one calculator = P3,000.00 / 12 = P250.00 Solution 1: Makon (MO) of one Calculator = Cost (C) x Markon Rate (MOR) = P250.00 x 25% = P250.00 x 0.25 = P62.50 Selling Price (SP) of 1 calculator = Cost (C ) + Markon (MO) = P250.00 + P62.50 = P312.50 Solution 2: Selling price of on Calculator = Cost ( C ) x (1+MOR) = P250.00 x 1.25 = P312.00 Therefore, the selling price of each calculator is P312.50. 3. A retailer buys ball pens at P750.00 per box of 50 pieces. He suggested selling price for each ball pen is P19.50.Find the suggested markon rate based on cost for each ball pen. SOLUTION: Cost of one ball pen = P750.00 / 50 = P15.00 Markon (MO) = Suggested Selling Price (SP)  Cost ( C ) = P19.50  P15.00 = P4.50 Markon Rate (MOR) Based on Cost = [Markon (MO) / Cost ( C )] x 100% = (P4.50 / P15.00) x 100% = 30% Hence, the suggested markon rate for each ball pen based on cost is 30%. 4.A store sold a box of rubber band at P48.60. If the store added a markon rate of 35% based on cost, how much did it purchase the box of rubber band? SOLUTION: Cost ( C ) = Selling Price (SP) / 1+Markon Rate (MOR) on Cost ( C ) = P48.60 / 1+35% = P48.60 / 1.35 = P36.00 Markon Based on Cost When based on cost, the markon is added to the cost of the item to determine the selling price as follows: Selling price (SP) = Cost ( C ) + Markon (MO) Markon (amount) = Cost ( C ) x MO Rate (MOR) Markon rate (MOR) = [Markon (amount) / Cost ( C )] x 100% Cost ( C ) = Selling price (SP) / 1+Markon Rate (MOR) on Cost ( C ) EXAMPLE: 1. If an item was purchased at P35.00 and the markon rate of 40% based on cost was added, find the amount of markon and the selling price. SOLUTION: A) Markon (amount) = Cost ( C ) x Markon Rate (MOR) = P35.00 x 40% = P35.00 x 0.40 = P14.00 B) Selling Price (SP) = Cost ( C ) + Markon (MO) = P35.00 + P14.00 = P49.00Thus, the amount of markon is P14.00 and the selling price is P49.00. 2.A retailer buys a dozen calculator at P3,000.00. If his markon rate based on cost is 25%, how much is the selling price of each calculator? SOLUTIONS: Cost of one calculator = P3,000.00 / 12 = P250.00 Solution 1: Makon (MO) of one Calculator = Cost ( C ) x Markon Rate (MOR) = P250.00 x 25% = P250.00 x 0.25 = P62.50 Selling Price (SP) of 1 calculator = Cost (C ) + Markon (MO) = P250.00 + P62.50 = P312.50 Solution 2: Selling price of on Calculator = Cost ( C ) x (1+MOR) = P250.00 x 1.25 = P312.00 Therefore, the selling price of each calculator is P312.50. 3.A retailer buys ball pens at P750.00 per box of 50 pieces. He suggested selling price for each ball pen is P19.50.Find the suggested markon rate based on cost for each ball pen. SOLUTION: Cost of one ball pen = P750.00 / 50 = P15.00 Markon (MO) = Suggested Selling Price (SP)  Cost ( C ) = P19.50  P15.00 = P4.50 Markon Rate (MOR) Based on Cost = [Markon (MO) / Cost ( C )] x 100% = (P4.50 / P15.00) x 100% = 30% Hence, the suggested markon rate for each ball pen based on cost is 30%. 4.A store sold a box of rubber band at P48.60. If the store added a markon rate of 35% based on cost, how much did it purchase the box of rubber band? SOLUTION: Cost ( C ) = Selling Price (SP) / 1+Markon Rate (MOR) on Cost ( C ) = P48.60 / 1+35% = P48.60 / 1.35 = P36.00 Thus, the cost or purchase price of the rubber band was P36.00. 3.2.2 Markon (MO) based on Selling Price When a retailer has to purchase to replenish a merchandise whose selling price is already given the problem is to determine the cost he shall pay for the merchandise and still have the desired rate of gross profit on the selling price. This can be done by calculating the markon based on the selling price, as follows: Markon (MO) Amount = Selling Price (SP) x Markon Rate (MOR) Based on Selling Price (SP) Thus, Markon rate (MOR) based on Selling Price (SP) = Markon (MO) / Selling Price (SP) EXAMPLES: 1.A businessman wishes to have a selling price of P50.40 for a stapler which he bought for P37.80. Find the a) markon and b) rate of markon based on selling price. SOLUTION: Markon (MO) = Selling Price (SP)  Cost ( C ) = P50.40  P37.80 = P12.60 Markon Rate (MOR) based on Selling Price (SP) = [Markon (MO) / Selling Price (SP)] x 100% = (P12.60 / P50.40) x 100% = 25% Thus, the amount of markon is P12.60 and the markon rate for the stapler based on SP is 25% 2.A merchant bought a dozen shirts for P2,100.00 and sold each shirt for P250.00. Based on the selling price, find a) markon and b) markon rate. SOLUTION: Cost of one shirt = P2,100.00/ 12 = P175.00 Markon (MO) per shirt = Selling Price (SP)  Cost ( C ) = P250.00  P175.00 = P75.00 Markon Rate (MOR) Based on Selling Price (SP) = [Markon (MO) / Selling Price (SP)] x 100% = (P75.00 / P250.00) x 100% = 30% Thus, the amount of markon per shirt is P75.00 and the markon rate based on SP is 30%. 3.A dealer of appliances purchased 18 DVD players at P2,100.00 per unit. If he sold each unit at 30% markon based on selling price, how much was the selling price per unit? SOLUTION: Selling Price (SP) = Cost ( C ) / 1  Markon (MO) based on selling price (SP) = P2,100.00 / 10.30 = P2,100.00 / 0.70 = P3,000.00 Hence, the selling price of each unit was P3,000.00 based on a markon rate of 30% of SP. 4.A grocery store plans to buy 12 dozens of canned goods at P5,616.00 and get a 25% markon based on selling price. How much will be the selling price per canned good? SOLUTION: Cost of 1 canned good = Cost ( C ) / 144 pieces = P5,616.00 / 144 = P39.00 Selling Price (SP) = Cost ( C ) / 1  MOR based on SP = P39.00 / 10.25 = P39.00 / 0.75 =P52.00 Thus, the selling price per canned good is P52.00 on a 25% markon based on selling price. MarkUp For various reasons such as scarcity or great demand for a product, inflation increased operating expenses, influenced of market forces, i,e. oil, etc., the original selling price of items has to be increased. This amount of increase in price from the old or original previous selling price is called markup. Thus, New Selling Price (NSP) = Cost + Markon(MO) + Markup (MU) Or NSP = Old Selling Price (OSP) + Markup (MU) Markup amount (MU) = Old Selling Price (OSP) x Markup Rate (MUR) Markup Rate (MUR) = [Markup (MU) / Old Selling Price (OSP)] x 100% Original Selling Price (OSP) = New Selling Price (NSP) / 1+Markup Rate (MUR) on OSP EXAMPLES: 1.If a markup rate of 15% is added to the original selling price of an item at P120.00, how much will be the new selling price? SOLUTION 1: MU = OSP x MUR = P120.00 x 0.15 =P18.00 NSP = OSP + MU = P120.00 + P18.00 = P138.00 SOLUTION 2: NSP = OSP x (1+MUR) = P120.00 x (1+0.15) = P120.00 x 1.15 = P138.00 Thus, the new selling price of the item is P138.00. 2.A businessman is selling a radio at P1,200.00. Due to the increase in his operating expenses, he decides to add a markup of P200. Find the new selling price and the rate of markup added to the original selling price. SOLUTION: NSP = OSP + MU = P1,200.00 + P200.00 = P1,400.00 MUR = (MU / OSP) x 100% = (P200 / P1,200) x 100% = 16.67% (rounded to 2 decimal places) Hence, the new selling price is P1,400 and the markup rate added to the original selling price is 16.67%. Note that for various reasons, there is no limitation to the number of succeeding markups that may be added to the price of a merchandise. Thus the formula when successive markups are to be imposed on the selling price of an item is: NSPn = SPn1 x (1+MURn+1) EXAMPLE 1.The new selling price (NSP1) of an item is P160.80. If another markup of 8% will be added to the NSP1, how much will be the new selling price (NSP2)? SOLUTION: NSPn = NSPn1 x (1+MURn+1) NSP2 = NSP21 x (1+MUR2) = P160.80x (1+0.08) = P160.80 x 1.08 = P173.66 (rounded to nearest centavo) Thus, the NSP2 is P173.66.Exercise:1. A retailer purchased 12 boxes of ball pens at ₱4,800.00. each box contained 50 pieces of ball pens. If he added 35% markon based on cost, determine the:a. Markon per ball penb. Selling price per ball pen2. R. Torres pays ₱900.00 per dozen for plastic containers. If his costbased markon is 30%, what is the selling price of each container?3. The manufacturer suggests a selling price of ₱210.00 each for plastic chairs that costs ₱1,800.00 per dozen. What markon based on cost is the manufacturer suggesting?4. A merchant decided to sell a travelling bag for ₱1,125.00 from which he made a 25% markon rate based on cost. How much did he pay for the bag?