Senior High School Entrepreneurship Quarter 2 – Module 3: Preparing, Analyzing, and Forecasting Financial Statements Writer: ARIEL G. GUTIERREZ T-II Diosdado Mcapagal Memorial HS Floridablanca Editors: JANE P. VALENCIA, EdD – Math/ABM Supervisor CHAIRMAN ` What I Need to Know This module was designed and written with you in mind. It is here to help you to explore forecasting financial statement for Entrepreneurship as a career. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. 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. After going through this module, you are expected to: 1. Forecast the revenues of the business. What I Know Hey there! Welcome to our lesson, how are you? I hope you’re doing good and enjoyed the previous lesson we had. Just like the previous lesson, let’s have a pre-test to check your prior knowledge about the topic. If you got a perfect score, you can skip this lesson and proceed to the next module, but if you didn’t get a perfect score, you don’t have to worry because this module will help and guide you to understand the topic Are you ready? Let’s start. I. Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. 1. It is a separate legal personality created by law. a. Partnership b. Company c. Corporation d. Store 2. It summarizes what is going to happen to the business if plans are carried out well. a. Financial Statements b. Income Statement c. Financial Forecast d. Outcome Source 3. Which the corporation would have to pay back in terms of principal payments and in terms of interest expenses. a. Goods b. Products c. Assets d. Loans 4. The one that will concoct an account called depreciation. a. Manager b. Accountant c. Contractor d. None of the above 1 5. They are the finished goods when sold. a. Cash flow b. Contingency plans c. Cost of goods sold d. Products sold 6. These are the selling, general, and administrative expenses. a. Period Costs b. Annual income c. Source of funds d. Cost of goods sold 7. These are the funds going from one container or one circle to another container or another circle comprise the funds flow except for the account called depreciation. a. Benchmarking b. Funds flow c. Scenario planning d. Participatory planning 8. It is a situation when cash inflows are greater than the cash outflow. a. Assets b. Net cash outflow c. Cash inflow d. Container of funds 9. It is the basis for the entire construction of the financial statement. a. Double entry accounting b. Credits c. Depreciated value d. None of the above 10. These are the stockholder’s equity, short-term debt, long term debt, suppliers credit, and accrued expenses. a. Liabilities b. Credits c. Assets d. Cash Flow 11. These are the accounts for cash, accounts receivable, inventory, fixed assets, and other assets. a. Income b. Cash outflow c. Container of funds d. Cash inflow 12. It is the source of funds. a. Cash b. Liabilities c. Salary d. None of the above 13. It is the uses of funds a. Paid liabilities b. Purchased assets c. Container flow d. None of the above 2 14. These are abstractions of all the business transactions going on in an enterprise. a. Flow of assets b. Income Statement c. Financial Statement d. None of the above 15. It is also called the profit and loss statement. a. Debt b. Income flow c. Financial statement d. Income Statement Lesson 3 Forecasting Financial Statements Hi! We are now in our module 4, how are you today? I hope you enjoyed the discussion and activities in our module 3. Before we talk about the forecasting financial statements for Entrepreneurship as a career, let’s have a simple activity first. What’s In Web Diagram 1. Complete the Web Diagram below. Think of terms that can be associated with the word at the center. Write as many terms as possible. Cash Flow 3 Now that you already know the relevance of “cash flow” in our lives and its importance in an entrepreneur, let’s have another question that you can answer to foresee the lesson. 2. How do you determine your own wealth? And, how would you know if an item is an asset, liability, or both? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ __________________________________________________________________ Notes to the Teacher This module is designed for the students to fully acquire the expected learning competencies. It includes series of activities which are suggested to be accomplished for better understanding and mastery of the lesson. The teacher should give proper assistance when necessary. What’s New Case Study Read and understand the case carefully and answer the given questions below. Ricardo Cortez and Josie Hernandez were partners in a apparel factory in Pampanga. They had 150 workers in the 2000s, who helped them manufacture different designs of clothes, shoes, slippers, etc. which they displayed and sold by the thousands in their store at the Clark Expo. They were considered very successful at that time. Their apparel business slowed down when either of them doesn’t know the problem regarding on their financial information on how badly their company is performing in terms of income management. Ricardo and Josie often quarreled about it and to their different management styles. Ricardo had more entrepreneurial characteristics: creative/innovative, flexible, updated on new trends, and was willing to take risks. Josie belonged to the “old school” of businessmen who could not understand Ricardo’s propositions regarding the rehabilitation of their business: 4 getting business loans, introducing unique clothes designs, opening “tiangge” stalls, online selling, etc. She was contented with the small profits they were making. Since their business is a partnership, Ricardo cannot carry out his plans without Josie’s consent. Josie’s pessimism, for him, is unacceptable and he foresees the closure of their business in a few more years if Josie will go on with her way of thinking. Who has the problem? What is their problem? 1. 2. 3. 1. What do you think will happen to their business’ market condition in the future? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ _________________________________________________________ What is It Congratulations! You were able to know your career path as early as now. Today, we will discuss the forecasting financial statements for Entrepreneurship as a career. This will help you to know more of the Entrepreneurship (negosyo) curriculum exit. Let us start now with the lesson. Forecasting Financial Statements Income Statement Forecasting There is usually a very close relationship between Sales and Cost of Sales (or Cost of Goods Sold). Many Companies, in determining their selling prices, conveniently add a specific percentage mark-up or margin to the Cost of Sales, thus establishing a predictable ratio between the two items. If an enterprise decides to slap a hundred percent mark-up on its Cost of Sales, the Sales figure will double the Cost of Sales. As a percentage, Cost of Sales will, therefore, be fifty percent of Sales. Table 1: Forecasting Sales and Cost of Sales for XYZ (Php in Thousands) Year Sale Forecast Past Sales (Php 100) Sales Forecast (Php 000) Past Cost of Sales (Php) Cost of Sales Forecast In Percentage Terms In Peso Value (Php 000) 2011 % 2012 % 2013 % 1,000.0 100.0 1,100.0 100.0 1,200.0 100.0 2014 % 100.0 1,331.00 700.0 70.0 781.0 71.0 835.0 2015 100.0 1,464.00 69.0 70.0 932.0 5 % 70.0 1025.0 -The Sales Figures are converted to 100.0% over those three years to get a common size picture. Next, the Cost of Sales is divided by the Sales figure to get a percentage or ratio of Cost of Sales to Sales. After deriving the percentage or ratios, one can make a fearless forecast of what the Cost of Sales percentage will be in the coming years. The Sales Forecast for the next two years can be set to approximate the growth trend of the last three years. Since Sales grew by 10% from 2011 to 2012 and by 10% from 2012 to 2013, the financial forecaster can reasonably assume a sales growth of 10% per annum in the next two years. The sales forecast for the year 2014 is, thus, Php 1,331.00 and for the year 2015, the forecast can be set at Php 1,464.00 -The forecast for the Cost of Sales percentage is 70% of sales for the years 2014 and 2015 as given in table 1. This percentage is merely an average of the percentages for the last three years (2011 to 2013). One can conceivably use the latest Cost of Sales percentage (2013) to reflect the most current scenario. The next step is to apply the 70.0% percentage to the Sales Forecast for the years 2014 and 2015 to get the Cost of Sales peso value forecast for those two years. Balance Sheet Forecasting Forecasting what the Balance Sheet of an enterprise will look like in the future depends a lot on the future Sales. The Current Assets of the balance Sheet include Cash, Marketable Securities, Accounts Receivables, Inventories (Raw Materials, Work-in-Process, and Finished Goods), and other current Assets. Assets in the Balance Sheet must always equal liabilities and owners’ equity. However, in financial forecasting, most probably, the respective totals of Assets and Liabilities plus Owners’ Equity will not be the same in the initial attempt to construct a forecasted or Pro Forma Balance Sheet. Table 2. Pro-Forma Balance Sheet As of Year Ending December 31, 2012 and December 31, 2013 (In Thousand Pesos) Audited Forecasted Balance Sheet Balance Sheet as as of Dec. 31, of Dec. 31, 2013 2012 ASSETS Current Assets Cash Accounts Receiveable Inventories Total Current Assets Gross Fixed Assets Accumulated Depreciation Php 10,000 30,000 15,000 55,000 100,000 60,000 5,000 Php 120,000 Accrued Expenses 5,000 Short Term Loans 10,000 Total Current Liabilities 30,000 Long Term Loans 50,000 Stockholder's Equity Paid in Capital Retained Earnings Total Stockholder's Equity Total Liabilities and Stockholders' Equity Php 10,000 Minimum cash balance 45,000 30 days of Sales (latest month) 22,500 15 days of Sales (ltest month) 77,500 119,000 Additional deptreciation computed at Php 19,000 50,000 Additional deptreciation computed at Php 10,000 69,000 5,000 Assume same level as last year 151,000 40,000 Net Fixed Assets Other Assets Total Assets LIABILITIES Current Liabilities Accounts Payable 15,000 30,000 10,000 40,000 Php 120,000 Assumption Used 22,500 Enterprise experience where the level of Accounts Payable is roughly the same as the inventories level 7,000 Same but additional Taxes Payable included. 7,000 Balancing Figure to make Liabilities equal to Assets 36,500 69,000 Increased by Php 19,000 due to additional Fixed Asset acquisition of Php 19,000 30,000 Same level as last year. 16,000 Additional Net profit after Taxes 46,000 Php 151,500 6 -Table 2 provides an example of a Pro-Forma Balance Sheet with explanatory notes on the side to indicate the assumptions used by the forecaster. -Since there would be additional long-term loan to finance the additional Fixed Assets, interest expenses would go up. This means that the forecaster would have to adjust the Pro-Forma Income Statement previously made as shown in Table 3. Since the Net Income After Taxes would go down from Php 6,000 to Php 5,400, there would be a need to increase loans by Php 600 in order to balance the Balance Sheet. Table 3. Pro-Forma Income Statement and Adjusted Pro-Forma Income Statement for year 2013. Income Forma Income Comments Statement Statement Sales Php 540,000 Php 540,000 Cost of Good Sold 340,000 340,000 Gross Profit 200,000 200,000 Operating Expenses 186,000 186,000 Less Interest Expenses 6,000 6,800 Additional Expenses of Php 800 Equals Net Profit before Taxes 8,000 7,200 Less Taxes 2,000 1,800 Taxes Decrease by Php 200 Equals Net Profit after Taxes Php 6,000 Php 5,400 Net effect of Php 600 Funds Flow Forecasting To forecast the Funds Flow, the financial forecaster should compute for the increase or decrease in the different items found in the Assets and Liabilities columns, when comparing the actual or previous year’s Balance Sheet and the Pro Forma Balance Sheet. Decreases in Assets and increases in Liabilities are sources of funds, while increases in Assets and Decreases in Liabilities are uses of funds. Table 4. Cash Position Forecast using Sources and Uses of Funds Beginning Cash balance (as of last Balance Sheet) Php 1,000 Add Source of Funds Increases in Liabilities Accounts Decreases in Assets Accounts Equals Cash Avalaible Subtract Uses of Funds: Decreases in Liabilities Accounts Increases in Assets Accounts Equals Net Cash Position 300 600 Php 1,900 500 200 1,200 -The Funds Forecast is also called the Cash Position Forecast as can be seen in Table 4. Starting from the beginning cash balance, the forecaster adds the Sources Funds to obtain Cash Available. From there, the Uses of Funds are subtracted in order to obtain the Net Cash Position (Ending cash Position) Table 5. Adjusted cash Position Forecast Beginning Cash Balance (as of last Balance Sheet) Php 1,000 Add Source of Funds: Increses in Liabilities Accounts 300 Decreases in Assets Accounts 600 Equals cash Available Php 2,100 Subtract Uses of Funds: Decreases in Liabilities Accounts 500 Increases in Assets Accounts 200 Equals Net Cash Position Php 1,200 7 add 200 add 200 -The Forecaster should adjust the reduction in the Net Fixed Assets account caused by the increase in additional Accumulated Depreciation form the previous year to the forecasted year. -if one assumes that the Additional Accumulated Depreciation is Php 200, then this means that the Depreciation Expenses for the year is also Php 200. Table 5. Reflects these adjustments. Other adjustments have to be made because of the accrual method used. Cash Flow Forecasting The entrepreneur or finance manager is concerned about the enterprise’s survival on a day-to-day basis as well as its long-term sustainability. Cash is a precious commodity that will make the enterprise live on and on. It is crucial, therefore, to monitor and budget the enterprise’s cash position on a daily, weekly, monthly, and yearly basis. Table 6. ACME Enterprises Actual and Projected Income Statements (In Pesos) Actual January to December 2012 Sales* 450,000 Cost of Sales Materials 130,000 Labor 68,000 Manufacturing Overhead 36,000 Depreciation 36,000 Total Cost of Sales 270,000 Gross Profit Selling General and Administrative Expenses** Operating Profit Interest Expenses*** Net Profit Before Taxes Taxes*** Net Profit After Taxes Jan 50,000 Feb 55,000 Projected for 2013 Mar Apr May 60,000 60,000 55,000 Jun 55,000 Jul 50,000 15,000 6,000 16,500 6,000 18,000 6,000 18,000 6,000 16,500 6,000 16,500 6,000 15,000 6,000 3,000 3,000 27,000 3,000 3,000 28,500 3,000 3,000 30,000 3,000 3,000 30,000 3,000 3,000 26,500 3,000 3,000 26,500 3,000 3,000 23,000 180,000 23,000 26,500 30,000 30,000 26,500 26,500 23,000 100,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 80,000 72,000 8,000 2,000 6,000 11,000 6,000 5,000 1,250 3,750 14,500 6,000 8,500 2,125 6,375 18,000 6,000 12,000 3,000 9,000 18,000 6,000 12,000 3,000 9,000 14,500 6,000 8,500 2,125 6,375 14,500 6,000 8,500 2,125 6,375 11,000 6,000 5,000 1,375 3,625 -Take the example of ACME Enterprises in Table 6. It has a policy and actually experiences a 30-day sales collection period. It purchases the raw materials and pays for the labor costs and outlays for overhead expenses in cash one month before they recognized as Cost of sales. In other words, ACME’s products must be produced one month bfore they get sold. Most (80%) of the Selling, General, and Administrative (SGA) Expenses are paid in cash during the operating month. However, 20% is paid one month later. -Interest expenses on long term debt are paid on June 30 and December 31. The amortization of principal payments is also paid on the same dates. Half of the taxes for the previous year’s income is paid on April 30 while the other half is paid on July 31. -Income Taxes are pegged at 25% of Net Income before Taxes. Beginning Cash Balance as January 1, 2012 is Php 25,000. Using Financial Forecast to Evalute Business Investment Decisions The Income and Cash payback period was introduced as a method to evaluate business investments. The construction and forecasting of Financial Statements would help the entrepreneur get a firmer grip on the viability of his or her enterprise. 8 What’s More Did you learn a lesson in this module? To better understand it, let’s have another activity. Enjoy! Activity 1: 1. Give the four financial statements. Give a brief a statement on how can we construct them. a. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ b. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ c. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ d. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ 2. How can planning through Financial Statement be useful for the entrepreneur? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _______________________________________________________________Activity 2. Use the following scenario to fill out the Monthly Cash Flow Statement Worksheet. You pay a $150 You re ce i ve your You pay re nt of You pay your Car payme nt monthly gross $450 pe r month me di cal i nsurance salary of $2,000 of $75 a month You pay your You pay your car You pay for Your monthly re nte r's i nsurance i nsurance of $150 monthly groce ri e s uti li ti e s are due . $200 You owe $125. of $20 Your monthly bi ll It's your mothe r's taxe s come out for gasoli ne bi rthday. You of your payche ck you go to a movi e come s i n and you purchase a $50 Fe de ral Tax $150 wi th a fri nd that must pay $75 pre se nt State tax $50 cost $10 Soci al se curi ty $200 You put $100 i nto You hi t a pothole You go out to You fi nd the savi ngs for a and have a flat di nne r wi th pe rfe ct outfi t for vacati on at the ti re . You must pay fri e nds. Your bi ll i s your date thi s be ach $75 for a ne w $25. we e ke nd. You pay Complete this one worksheet $100scenario. for the oufi t with the information from the above 9 Income Gross Salary Total Income Expenditures Fixed Expenses Rent Renter's Insurance Automobile loan payment Automobile insurance Medical Insurance Revolving Savings fund Federal Income tax State income tax Social Security tax Total fixed expenses Variable Expenses Food Utilities Gasoline and maintenace Clothing and personal upkeep Gifts Miscellaneous Total Variable Expenses Total Expenses SURPLUS (DEFICIT) Cash Flow Statement Worksheet Rubric The student did not follow directions. (minus 2) The student created a cash flow statement that was complete. The cash flow staement provided detail of income and expenses (plus 10) the student attempted to craete a cash flow statement but they were not thorough. (plus 5) The student did not attempt. (0 point) the student craeted a balance sheet that was complete. Detailed infromation was provided for assets and liabilities. (plus 10) the student did not attempt. (0 point) the assignment was late. (loss of one point per day) Total 10 What I Have Learned How’s the activity? Did you enjoy it? I hope so. This part is the generalization which contains the summary of what you learned. I want you to fil in the blanks to complete the sentence below. 1. 2. 3. 4. 5. In forecasting, it is important to examine the critical values that affect the industry and business that one is in and assess how these variables will behave so that ____________________________________________________________. In the deciphering the past financial condition of an enterprise, we have to quantify the relationships of the many items found in the different financial statements because _______________________________________________________. Market prices tend to be relatively low in a very competitive business for the reason that _______________________________________________________________. It is important to realize that if one expects inflation to affect major items in the Cost of Sales and in the selling prices of the company, then there is a need to ________________________________________________________________________. The forecaster can use either short or long term loans to fund any shortfall in the financing assets for the reason that ____________________________________. What I Can Do Now it’s your time to shine! It’s time to apply all the inputs that you learned from this module. It’s application time! 1. Observe your own financial expenses or monitor your wealth on this week. Identify one problem that you think you have in managing your expenses. Solve your identified problem by going through simple steps in managing your expenses. (Note: Minimum of 5 steps) My Own Financial Literacy PROBLEM: Step 1 Step 2 Step 3 Step 4 11 Step 5 Step 6 Step 7 Step 8 2. What have you learned in giving steps in managing your own financial expenses? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ____________________________________________________________________________ Assessment Before the presentation of the mini-lesson, you had your pre-test right? Now, this will serve as your post-test. This will test you if you were able to understand the lesson well. Good Luck! Please answer on a separate sheet of paper. CORRECT THE SENTENCES: Identify the word that makes the sentence incorrect and write down the correct one. 1. Market prices tend to be relatively high in a very competitive business. 2. After forecasting Sales and Cost of Sales, the Gross profit figures can be derived by adding the Cost of Sales from Sales. 3. The financial forecaster can go through each Operating Expense item and determine how it will behave in the future as Sales rise. 4. Once all the Operating Expenses are computed, they should be summed up. The total is then added from the Gross Profit forecasted in order to derive Operating Profit. 5. Once Current Liabilities must be individually looked up. Prepaid insurance, for example, can be determined by examining how much premium will be required to insure the company’s properties for the coming year. COMPLETE THE SENTENCES: Choose the correct word or phrase from the box to complete each sentence. ENTERPRISE GOODWILL FIXED ASSETS ENTREPRENEUR CASH BALANCE ORGANIZATIONAL EXPENSES 12 PATENTS DEPRECIATION EXPENSES BALANCE SHEET MARKETABLE SECURITIES 1. Whenever we talk about the __________________________, assets must always equal liabilities and owner’s equity. 2. ______________________________ comprise feasibility studies, enterprise promotion activities, pre-operating expenses, and other set-up costs. 3. ____________________ is the premium paid by the enterprise for an asset or share of stock whose book value is lower than the purchase or qcquisition price. 4. ____________________ are payments to holders of an invention or technology 5. Forecasting _________________________ requires an assessment of the enterprise’s future requirements for land, building, machinery, equipment, furniture, fixtures, and other long lasting assets. 6. If the Cash goes below the minimum balance, the forecaster can cover the cash shortfall by obtaining more loans or by liquidating _________________________ into cash. 7. Marketable Securities can be the repository of excess cash. It can be drawn down or reduced if the _______________________________ falls below the minimum required. 8. The ___________________________ may also decide to collect all of the Advances and not give any more of such Advances to employees, in which case the advances to Employees becomes zero for the next year. 9. The construction and forecasting of Financial Statements would help the _____________________ get a firmer grip on the viability of his or her enterprise. 10. To determine the _________________________, the forecaster has to refer to the depreciation schedules calculated by the enterprise’s accountants for each fixed asset. Additional Activities Now that you know the different forecasting of financial statements in Entrepreneurship. Answer the following questions or situations based on what you’ve learned from the lesson. 1. Name some challenges in making financial statement, other than those mentioned in this lesson that may occur in future scenarios. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 2. Which among the four financial statements will most likely you will use in forecasting your own business? Explain your answer. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 3. What do you think will the government impose in preventing financial crisis in our Country amidst this pandemic situation? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 13 14 Presents ideas in Ideas are too a consistent general manner Organized Some beg/mid/end organization; attempt at a beg/mid/end Understanding Writing shows Writing shows a Writing shows strong clear adequate understanding understanding understanding Word Choice Sophisticated use Nouns and verbs Needs more of nouns and make essay nouns and verbs verbs make the informative essay very informative Sentence Sentence Sentence Sentence Structure structure structure is structure is enhances evident; limited; meaning; flows sentences mostly sentences need throughout the flow to flow piece Mechanics Few (if any) errors Few errors Several errors 3 2 Numerous errors No sense of sentence structure or flow Writing shows little understanding Little or no use of nouns and verbs No organization; lack beg/mid/end Ideas are vague or unclear 1 Income Gross Salary Areas of 4 Assessment Ideas Presents ideas in an original manner Organization Strong and organized beg/mid/end Criteria for Activities $ 2,000 Total Income $ 2,000 Expenditures Fixed Expenses Rent $ 450 Renter's Insurance $ 20 Automobile loan payment $ 150 Automobile insurance $ 50 Medical Insurance $ 75 Revolving Savings fund $ 100 Federal Income tax $ 150 State income tax $ 50 Social Security tax $ 150 Total fixed expenses $ 1, 195 What I Know 1. c. Corporation 2. a. Financial Statements 3. D. Loans 4. B. Accountant 5. C. Cost of goods sold 6. A. Period Costs 7. b. Funds Flow 8. b. Net cash outflow 9. a. Double entry accounting 10. a. Liabilities 11. c. Container of funds 13. a. Cash 14. c. Financial Statements 15. d. Income Statement Variable Expenses Food $ 200 + $ 25 = $ 225 Utilities $ 125 Gasoline and maintenace $ 75 + $ 75 = $ 150 Clothing and personal upkeep $ 100 Gifts $ 50 Miscellaneous $ 10 Total Variable Expenses $ 660 Total Expenses $ 1, 855 Assessment CORRECT THE SENTENCES 1. Low – High 2. Subtracting – Adding 3. Forecaster – Accountant 4. Subtracted – Added 5. Assets – Liabilities COMPLETE THE SENTENCES 1.Balance Sheet 2. Organizational Expenses 3.Goodwill 4. Patents 5. Fixed Assets 6. Marketable Securities 7. Cash Balance 8. Enterprise 9. Entrepreneur 10. Depreciation Expenses Answer Key SURPLUS (DEFICIT) $ 145 Development Team of the Module Writer: Editor: Reviewer: ARIEL G. GUTIERREZ – T-II Diosdado Macapagal Memorial High School JANE P. VALENCIA, EdD – EPS – Mathematics JANE P. VALENCIA, EdD – EPS – Mathematics Illustrator: Layout Artist: Language Reviewer: Management Team ZENIA G. MOSTOLES, EdD, CESO V, Schools Division Superintendent LEONARDO C. CANLAS, EdD, CESE. Asst. Schools Division Superintendent ROWENA T. QUIAMBAO, CESE, Asst. Schools Division Superintendent CELIA R. LACNALALE, PhD, CID Chief JANE P. VALENCIA, EdD, Education Program Supervisor, Mathematics JUNE E. CUNANAN, Education Program Supervisor/ Language Editor RUBY M. JIMENEZ, PhD., Education Program Supervisor, LRMDS 15