BUS.MATH-11-Q1-Module-8-final-W3.pdf
- 1. Business Mathematics Quarter 1 – Module 8: Break-even Analysis and Problem Solving Involving Buying and Selling Products 11
- 2. Business Mathematics – Grade 11 Self-Learning Module (SLM) Quarter 1 – Module 8: Break-Even Analysis and Problem Solving Involving Buying and Selling Products First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Development Team of the Module Writers: Marjohn C. Mantawil, Sherwin P. Uy, Marjonel B. Vargas Editors: Adam Julian L. Che, Joecel S. Rubinos, Chery Lou F. Bacongco Reviewers: Floramae A. Dullano, Zaida N. Abiera Illustrators: Marjohn C. Mantawil, Sherwin P. Uy, Marjonel B. Vargas Layout Artist: Sherwin P. Uy Cover Art Designer: Ian Caesar E. Frondoza Management Team: Allan G. Farnazo, CESO IV – Regional Director Fiel Y. Almendra, CESO V – Assistant Regional Director Romelito G. Flores, CESO V – Schools Division Superintendent Mario M. Bermudez, CESO VI – Assist. Schools Division Superintendent Gilbert B. Barrera – Chief, CLMD Arturo D. Tingson Jr. – REPS, LRMS Peter Van C. Ang-ug – REPS, ADM Jade T. Palomar – REPS, Mathematics Juliet F. Lastimosa – CID Chief Sally A. Palomo – Division EPS In- Charge of LRMS Gregorio O. Ruales – Division ADM Coordinator Zaida N. Abiera – Division EPS, Mathematics Printed in the Philippines by Department of Education – SOCCSKSARGEN Region Office Address: Regional Center, Brgy. Carpenter Hill, City of Koronadal Telefax: (083) 2288825/ (083) 2281893 E-mail Address: region12@deped.gov.ph
- 3. 11 Business Mathematics Quarter 1 – Module 8: Break-even Analysis and Problem Solving Involving Buying and Selling Products
- 5. 2 Introductory Message For the facilitator: Welcome to the Business Mathematics for Grade 11 Self-Learning Module (SLM) on Break-even Analysis and Problem Solving Involving Buying and Selling Products! This module was collaboratively designed, developed and reviewed by educators both from public and private institutions to assist you, the teacher or facilitator in helping the learners meet the standards set by the K to 12 Curriculum while overcoming their personal, social, and economic constraints in schooling. This learning resource hopes to engage the learners into guided and independent learning activities at their own pace and time. Furthermore, this also aims to help learners acquire the needed 21st century skills while taking into consideration their needs and circumstances. In addition to the material in the main text, you will also see this box in the body of the module: As a facilitator you are expected to orient the learners on how to use this module. You also need to keep track of the learners' progress while allowing them to manage their own learning. Furthermore, you are expected to encourage and assist the learners as they do the tasks included in the module. For the learner: Notes to the Teacher This contains helpful tips or strategies that will help you in guiding the learners.
- 6. 3 Welcome to the Business Mathematics – Grade 11 Self-Learning Module (SLM) on Break-even Analysis and Problem Solving Involving Buying and Selling Products! The hand is one of the most symbolized part of the human body. It is often used to depict skill, action and purpose. Through our hands we may learn, create and accomplish. Hence, the hand in this learning resource signifies that you as a learner is capable and empowered to successfully achieve the relevant competencies and skills at your own pace and time. Your academic success lies in your own hands! This module was designed to provide you with fun and meaningful opportunities for guided and independent learning at your own pace and time. You will be enabled to process the contents of the learning resource while being an active learner. This module has the following parts and corresponding icons: What I Need to Know This will give you an idea of the skills or competencies you are expected to learn in the module. What I Know This part includes an activity that aims to check what you already know about the lesson to take. If you get all the answers correct (100%), you may decide to skip this module. What’s In This is a brief drill or review to help you link the current lesson with the previous one. What’s New In this portion, the new lesson will be introduced to you in various ways such as a story, a song, a poem, a problem opener, an activity or a situation. What is It This section provides a brief discussion of the lesson. This aims to help you discover and understand new concepts and skills. What’s More This comprises activities for independent practice to solidify your understanding and skills of the topic. You may check the answers to the exercises using the Answer Key at the end of the module. What I Have Learned This includes questions or blank sentence/paragraph to be filled in to process what you learned from the lesson. What I Can Do This section provides an activity which will help you transfer your new knowledge or skill into real life situations or concerns. Assessment This is a task which aims to evaluate your level of mastery in achieving the learning competency. Additional Activities In this portion, another activity will be given to you to enrich your knowledge or skill of the lesson learned. This also tends retention of learned concepts.
- 7. 4 Answer Key This contains answers to all activities in the module. At the end of this module you will also find: References This is a list of all sources used in developing this module. The following are some reminders in using this module: 1. Use the module with care. Do not put unnecessary mark/s on any part of the module. Use a separate sheet of paper in answering the exercises. 2. Don’t forget to answer What I Know before moving on to the other activities included in the module. 3. Read the instruction carefully before doing each task. 4. Observe honesty and integrity in doing the tasks and checking your answers. 5. Finish the task at hand before proceeding to the next. 6. Return this module to your teacher/facilitator once you are through with it. If you encounter any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator. Always bear in mind that you are not alone. We hope that through this material, you will experience meaningful learning and gain deep understanding of the relevant competencies. You can do it! What I Need to Know This module was designed to help you master the topic on break-even analysis and problem solving involving buying and selling products. The scope of this module permits it to be used in many different learning real-life situations. The language used recognizes the diversity of your vocabulary level. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using. In this module, you will be able to: • determine the break-even point; and
- 8. 5 • solve problems involving buying and selling products. ABM_BM11BS-Ij-9 Specifically, you are expected to: 1. illustrate the break-even point; 2. compute for the break-even point; and 3. solve problems involving buying and selling products.
- 9. 6 What I Know Before we begin this lesson, let us check first your prior knowledge on this module. After taking and checking this short test, take note of the items that you are not able to answer correctly and look for the right answer as you go through this module. Direction: Encircle the letter of the correct answer. 1. What type of cost includes product ingredients and materials? a. fixed b. revenue c. total d. variable 2. What type of cost includes the rental of space? a. fixed b. revenue c. total d. variable 3. What type of cost is the product of the price and the quantity sold? a. fixed b. revenue c. total d. variable 4. What concept is being described when the business will neither earn a profit nor suffer a loss? a. break-even b. loss c. profit d. summit 5. What type of analysis shows equal revenue and total cost? a. break-even b. cost of variable c. profit-loss d. volume of sales
- 10. 7 Read the selection for questions 6-10. Junedyl is planning to run a coffee shop where he plans to sell each cup of coffee at ₱50.00. The fixed cost that is amounting to ₱40,000.00 includes all his expenses for the rent, wages, basic needs and others. So even if Junedyl will not be able to sell, he is still obliged to pay this amount. If it costs Junedyl an average of ₱10.00 for every cup of coffee which is allotted for the bulk of coffee beans, purified water and coffee filters, then: 6. What equation represents the variable cost (VC) when x is the number of cups of coffee? a. 𝑉𝐶 = 5𝑥 b. 𝑉𝐶 = 10𝑥 c. 𝑉𝐶 = 5 𝑥 d. 𝑉𝐶 = 𝑥 5 7. What is the break-even quantity? a. 50 cups of coffee b. 100 cups of coffee c. 500 cups of coffee d. 1,000 cups of coffee 8. Which of the following ordered pairs determine a break-even point? a. (500, 1000) b. (1000, 50000) c. (1500, 50000) d. (5000, 1000) 9. How much profit will he earn if he sells 500 cups? a. ₱20,000.00 b. ₱40,000.00 c. incur loss of ₱20,000.00 d. cannot be determined 10. How many cups of coffee must be sold to earn a profit of ₱50,000.00? a. 1,250 b. 1,500 c. 2,250 d. 2,500
- 11. 8 Read the selection for questions 11-15. Mike owns a gadget store. He purchases his stocks from a supplier in Luzon. Each unit of earphone is listed at ₱300.00. If he buys a dozen, he gets a 5 % trade discount. He plans to sell each unit of earphone at a price with 20% mark-up based on cost. 11. How much will Mike pay for a dozen of earphone if he will avail of the trade discount? a. ₱3,000.00 b. ₱3,240.00 c. ₱3,420.00 d. ₱3,600.00 12. How much will be Mike’s net sales if he will be able to sell a dozen of earphones? a. ₱3,140.00 b. ₱3,215.00 c. ₱4,104.00 d. ₱4,405.00 13. How much profit will Mike gain for this transaction? a. ₱160.00 b. ₱365.00 c. ₱500.00 d. ₱684.00 14. If a new model will come out in the market and Mike decides to markdown the price of the earphone by 10%, how much will be the amount of markdown? a. ₱30.00 b. ₱31.50 c. ₱34.20 d. ₱35.00 15. What is the new markdown price of each unit of earphone? a. ₱270.00 b. ₱283.50 c. ₱307.80 d. ₱315.00
- 12. 9 Lesson 8 Break-even Analysis and Problem Solving Involving Buying and Selling Products Recalling your previous lessons, you have learned that entrepreneurs do experience profit or loss situations. However, in some circumstances, they also reach a point where they don’t experience both. This is when they experience a break-even situation wherein their businesses neither gain a profit nor experience a loss. What’s In In the previous module, you have learned how to obtain profit and avoid loss in a given transaction. Now, let us have a review. Activity 1: Watch My Profit and Loss Direction: Solve the following problems below. 1. The annual earnings (in million pesos) of a calculator manufacturer is given by 𝑃(𝑥) = 50𝑥 − 10, how much is the profit when 5 calculators are sold? Answer: 2. Breggy bought a computer desktop for ₱22,000.00 and ₱5,000.00 for its spares. He later sold it for ₱25,000.00. How much is Breggy’s loss? Answer: 3. Ben bought two digital cameras at ₱15,490.00 each. He sold one of the cameras to his friend at ₱13,500.00 while the other one was sold to his neighbor at ₱16,200.00. How much is Ben’s profit or loss? Answer:
- 13. 10 Alright! You are now ready to discover deeper the concepts of profit and loss. Let’s explore the next activity. What’s New How far have you gone? Have you recalled the formulas and solutions in obtaining a profit or realizing how to avoid loss? So now, a new topic will be served. Worry not because you will be guided. Activity 2: Did I Gain Profit or Loss? Direction: Choose from the selection the terms described in each guide question. Also, answer each question to determine whether a profit is gained or a loss is obtained in the given real-life problem. Problem: Andy sells chiffon cakes at her cake house. She pays ₱2,000.00 monthly for the rental of space and she spends ₱50.00 to make each chiffon cake which she sells for ₱150.00. Compute for the profit or loss if she was able to sell 20 chiffon cakes for this month. Variable Cost Fixed Cost Break-even Point Selling Price Neither Profit/loss Total Cost Guide Questions: Important Terms Answers
- 14. 11 1. How much does she pay for the rental of space each month? 2. How much does she spend for each chiffon cake? 3. How much does she sell each chiffon cake? 4. How much is the total amount of total expenses incurred for this month? 5. How much is the profit for this month? 6. Did she gain a profit? What is It You have learned in the previous activity that you could either gain a profit or obtain a loss depending on the number of sales that you sell. And, there is a specific number of sales that you should be able to sell in order for you to cover all the costs. That is now the focus of this module, the break-even point. So, let us discuss what break-even analysis and break-even point are! But before that, let us define the following terms for you to better understand this module. Important Terms to Remember: 1. Fixed cost (FC) – This is the cost of expenses that does not vary over time on a certain relevant range, the number of products sold, and production of goods to be sold. This may also include payment for lease and rental, salaries of workers, insurance, and interests. 2. Variable Cost (VC) – This may refer to the amount of money spent for raw materials used in the production of the goods including the labor, utility expenses, and commissions. This means that this cost varies depending on the number of units of goods produced. 3. Total Cost (TC) – This is the sum of the fixed cost and variable cost.
- 15. 12 4. Selling Price (SP) – This is the price of the product being sold. Why Use Break-Even Analysis? Break-even analysis is the process used to determine the number of units of products to sell in order to cover the costs. It is necessary for business owners to determine the quantity of products to sell for them to avoid loss. What is the Breakeven Point (BEP)? Break-even point is the number of units of goods or products needed to be sold in order to cover the all the costs. The Break-Even Point can be solved using the given formula below. Fixed Cost Break-even Point = Selling Price per unit - Variable Cost per unit 𝑭𝑪 In symbols, 𝑩𝑬𝑷 = 𝑺𝑷 − 𝑽𝑪 How to Solve for the Break-Even Point? To solve for the break-even point, the steps are as follows: 1.Identify and/or compute for the total fixed cost. 2.Identify and/or compute for the variable cost per unit. 3.Identify the selling price per unit. 4.Substitute the values in Steps 1 to 3 to the given formula and solve for the break-even point. 5.Check your answer. 6.Make your conclusion. Let’s Have an Example! Problem: Regine sells apples at the local market. She pays ₱100.00 daily for the rental of space and spends ₱20.00 to buy each apple which she sells for ₱30.00. Solve for the break-even point. Solution: 1. Identify and/or compute for the total fixed cost. Fixed Cost (FC) = ₱100.00 (daily rental)
- 16. 13 2. Identify and/or compute for the variable cost per unit. Variable Cost (VC) per unit = ₱20.00 3. Identify the selling price per unit. Selling Price (SP) = ₱30.00 4. Substitute the values in Steps 1 to 3 to the given formula and solve for the break-even point. ₱100.00 BEP = ₱30.00 - ₱20.00 ₱100.00 BEP = ₱10.00 BEP = 10 units 5. Check your answer. If Andy will be able to sell 20 units, Net Sales: (BEP × SP) ₱300.00 Less: Variable Cost (BEP × VC ) ₱200.00 Contribution Margin: ₱100.00 Less: Fixed Cost ₱100.00 Profit/Loss: ₱0 6. Make your conclusion. Since the profit or loss is 0, hence, the breakeven point is 10 units. Therefore, Regine has to sell 10 apples for her to break-even.
- 17. 14 What’s More We have already discussed the steps on how to solve for the break-even point. So now, be ready for our next activity. Let’s find out how you have developed your skills in problem solving. You can do this! Activity 3: Break It Even! Direction: Solve the problem involving buying and selling of products. Show all your solutions. Problem: Marco Juan is a business owner. He sells bananas in his store at the local market. He pays ₱2,500.00 monthly for the rental of the space. He buys bananas from a supplier for ₱25.00 per kilo and sells it to his customers for ₱50.00 per kilo. Solve for the break-even point. Solution: 1. Identify and/or compute for the total fixed cost. 2. Identify and/or compute for the variable cost per unit. 3. Identify the selling price per unit. 4. Substitute the values in Steps 1 to 3 to the given formula and solve for the break-even point. 5. Check your answer. 6. Make your conclusion.
- 18. 15 What I Have Learned Now, let us check what you have learned. Let us do this activity! Activity 4: Fill Me! Direction: Fill each blank with a word or phrase to make each statement correct. 1. Profit happens in business when the revenue generated from net sales is ____________________ than the total cost incurred in the business. 2. Loss happens in business when the revenue generated from net sales is ____________________ than the total cost incurred in the business. 3. Break-even point in business happens when the revenue generated from net sales is ___________________ to the total cost incurred in the business. 4. The quantity of products sold should be ___________________ than the breakeven point to avoid loss. 5. Loss is likely to happen when quantity of products sold is ____________________ than the break-even point. What I Can Do In this section, you will be applying your knowledge given a real-life situation. Activity 5: Cookies 4 Your Heart! Direction: Solve the problem involving buying and selling of products. Show all your solutions. Problem: Lisa is passionate in baking. She plans to bake cookies at home and to post it online for orders. She plans to sell it by 10 pieces in a pack. She estimates that the materials and ingredients needed for 50 packs of cookies will cost her ₱2,500.00. She plans to sell each pack of cookies at 50% mark- up based on cost. Since her business will be home-based, she promised to give her mom ₱ 3,000.00 as her share in water, electricity and internet bills every month. Determine the break-even point. Solution:
- 19. 16 1. Identify and/or compute for the total fixed cost. 2. Identify and/or compute for the variable cost per unit. 3. Identify the selling price per unit. 4. Substitute the values in Steps 1 to 3 to the given formula and solve for the break-even point. 5. Check your answer. 6. Make your conclusion.
- 20. 17 Assessment Congratulations! You have done a good job. At this point, let us test what you have learned from the very start of our lesson. Direction: Read carefully and answer the questions below. Encircle the letter of the correct answer. 1. Which of the following is an example of a variable cost? a. interest b. ingredients c. insurance d. lease 2. What type of cost varies depending on the quantity of products being produced? a. fixed b. net sales c. total d. variable 3. Which among the following concepts is usually seen on the top item in an income statement from which all costs and expenses is subtracted to arrive at net income? a. fixed cost b. net sales c. total cost d. variable cost 4. When do we obtain the break-even point? a. When the fixed cost is equal to the total cost b. When the total cost is equal to the variable cost c. When the variable cost is equal to the fixed cost d. When the number of units of goods sold covers the all the costs 5. Which of the following is NOT true? a. The fixed cost does not vary over time. b. The total cost is the sum of the fixed cost and the variable cost. c. The total cost is the difference between the fixed cost and the variable cost.
- 21. 18 d. It is necessary for business owners to determine the quantity of the products to sell in order for them not to obtain loss. Read the selection for questions 6-10. Mark rents a stall in the public market for ₱5,000.00 a month. He has a helper who helps in his business and he pays him salary of ₱8,000 a month. He orders fresh chicken from a supplier that cost him ₱140.00 per kilo. He sells the chicken to his customers at ₱160.00 per kilo. 6. How you will illustrate the variable cost (VC) when x be the number kilos of chicken sold? a. 𝑉𝐶 = 140𝑥 b. 𝑉𝐶 = 160𝑥 c. 𝑉𝐶 = 5000𝑥 d. 𝑉𝐶 = 8000𝑥 7. How many kilos of chicken does Mark need to sell to break-even? a. 200 b. 450 c. 650 d. 800 8. Which of the following ordered pairs determines a break-even point? a. (500, 32000) b. (650, 104000) c. (700, 32000) d. (750, 104000) 9. How much profit will he earn if he sells 700 kilos of chicken? a. ₱1,000.00 b. ₱2,000.00 c. ₱3,000.00 d. ₱4,000.00 10. How many kilos of chicken must be sold to earn a profit of ₱192,000.00? a. 10,050 b. 10,150 c. 10,250 d. 10,300 Read the selection for questions 11-15.
- 22. 19 A reseller bought 50 handbags that cost ₱40,000.00. The reseller availed 10 % trade discount for this transaction. She plans to sell each handbag at a markup based on cost of 40%. 11. What is the original price of each handbag? a. ₱200.00 b. ₱400.00 c. ₱600.00 d. ₱800.00 12. How much is the trade discount availed for this transaction? a. ₱2,000.00 b. ₱4,000.00 c. ₱6,000.00 d. ₱8,000.00 13. How much is the cost of each handbag after the trade discount is availed? a. ₱1800.00 b. ₱360.00 c. ₱540.00 d. ₱720.00 14. What is the mark-up rate based on the selling price? a. 28.57% b. 36.00% c. 40.00% d. 45.00% 15. If a new model will come out in the market, and the reseller decides to markdown the price of the handbag by 10%, what is the amount of the markdown? a. ₱80.00 b. ₱91.50 c. ₱100.08 d. ₱110.08 Good Job! You did well on this module. Keep going!
- 23. 20 Additional Activities Activity 6: Buying & Selling 3-2-1 Chart Direction: In this activity, you will be asked to complete the 3-2-1 chart regarding break-even analysis and problem solving involving buying and selling products that you have discovered. My 3-2-1 Chart Three things I found out: Two interesting things: One question I still have: : Here’s your 3 stars for a job well done. You are now ready to answer the next module on Buying and Selling. 1. 2. 3 1. 2. 1.
- 24. 21 References Business Mathematics Textbook, pp. 96-101 Teaching Guide for Senior High School Business Mathematics, pp. 66-84
- 25. DISCLAIMER This Self-learning Module (SLM) was developed by DepEd SOCCSKSARGEN with the primary objective of preparing for and addressing the new normal. Contents of this module were based on DepEd’s Most Essential Learning Competencies (MELC). This is a supplementary material to be used by all learners of Region XII in all public schools beginning SY 2020-2021. The process of LR development was observed in the production of this module. This is version 1.0. We highly encourage feedback, comments, and recommendations. For inquiries or feedback, please write or call: Department of Education – SOCCSKSARGEN Learning Resource Management System (LRMS) Regional Center, Brgy. Carpenter Hill, City of Koronadal Telefax No.: (083) 2288825/ (083) 2281893 Email Address: region12@deped.gov.ph 22