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Mathematical Models with Applications Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Teacher Notes, Student Activities, and Transparencies 81 Unit III: Finance Section 1: Assumptions Teacher Notes Section 1: Assumptions Teacher Notes Context Overview: Making assumptions is an important part of the entrepreneurial experience. In this section, students will learn how to create an assumption statement based on the assumptions needed to make projections for a business. The teacher will discuss various kinds of financial statements. Each student will complete an assumption statement for Grape Expectations using realistic or justifiable numbers as estimates. TEKS Addressed: Mathematical Models with Applications: The student is expected to 1A - compare and analyze various methods for solving a real–life problem; 1B - use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; 2A - interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, and scatterplots to draw conclusions from the data; 2B - analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences; 3A-formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions. Goal: The goal of this section is to give students an overview of the financial statements necessary to start and maintain a business and to provide more information on Grape Expectations, the entrepreneurial case that will be used to demonstrate concepts. Materials: Grape Expectations Case (1 per student) Assumption Statement: Grape Expectations (1 per student) Procedures: Show the transparency of the financial statements for a business, discuss the various statements and introduce the following terms to the class. Gross Profit: The gross profit is the net sales minus the cost of sales. Income Statement: The income statement presents your venture’s performance over a specified period of time in terms of sales, costs, and profits or losses. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 82 Unit III: Finance Section 1: Assumptions Teacher Notes Balance Sheet: A balance sheet is a statement of the financial position of a venture at a specific point in time. Cash Flow Statement: The cash flow statement keeps a record of the amount of cash that goes in and out of the business. These are some of the financial aspects of Grape Expectations that students will investigate before developing their own business ideas. Student Activity—Assumption Statements Ask the students to read the student activity case study, Grape Expectations: An Entrepreneur is Born. They received some of this information in Unit II, but the case tells the entire story. Then give students the Assumption Statement for Grape Expectations. Have the students answer the questions in Part I of Student Activity: Assumption Statements. Possible answers to the questions follow below. Questions and Possible Answers: 1. What does it cost to make each CD (including the cover), and what must be purchased in order to produce each CD? It costs $2.00 to duplicate the CD; $.50 for the plastic case; $.50 for the 4-color jacket. The total cost per CD is $3.00. 2. Throughout the year, what are the main activities that Chuck believes will aid his sales? He believed he would sell 175 at a school concert in January and 125 at the St. Valentine’s Day Dance in February. He figured he wouldn’t make any sales in March, April, and May because he would be busy with spring break and exams. He planned to sell around 25 CDs at the End–of-School-Year BBQ in June. He would be working on the farm over the summer, so there would be no sales in July or August. In September, he figured he’d sell 175 CDs at the Back-to-School Dance, when Grape Expectations would appear again. He believed he could sell 100 units in October, when the band would perform at a pre-game concert and dance. In November, he guessed he’d sell 150 because of the Thanksgiving Dance. And finally, he figured many people would want to give copies of the CD as gifts during the holidays, so he estimated he’d sell 300 units during that time. 2. As a guide, lead the students as they complete Part II (entering the information into the statement). They should use the answers to Question #1 in order to complete the table. On the next page is a copy of the completed table. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 83 Unit III: Finance Section 1: Assumptions Teacher Notes Assumption Statement for Grape Expectations Costs – PER UNIT Cost to duplicate one CD Cost for one plastic case Cost for each 4-color CD jacket Other costs (per unit) Total Cost for one CD, ready to sell Expenses Royalties rate to be paid to artists Cost of goods percentage Other expenses Monthly Activities to Sell CDs School concert $2.00 .50 .50 $3.00 10% As agreed upon by Chuck Dickens with artists 20% Price, divided by total cost of goods Expenses not on list, but should be Month January Valentine’s Day dance February No sales – exams March No sales – back-to-school pressures April No sales – Final Exams prep May End-of-School-Year BBQ June No sales – no school July No sales – no school August Back-to-School Dance September Pre-Game Concert & Dance October Thanksgiving Dance November Holiday Dance December Other sales Total CD Units Sold for the Year # of CDs Sold 175 125 0 0 0 25 0 0 175 100 150 300 1,050 Monthly @ $15.00 each $2,625.00 $1,875.00 $375.00 $2,625.00 $1,500.00 $2,250.00 $4,500.00 $15,750.00 Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 84 Unit III: Finance Section 1: Assumptions Case Study Case Study Grape Expectations: An Entrepreneur Is Born It had been an awesome night! Everyone was at last night’s school dance. And everyone believed that they had witnessed the launch of the newest, and perhaps greatest, rock and roll band since the Beatles. The name of the band was Grape Expectations. One of the students, Chuck Dickens, was in charge of media, and his job was to record the performance for the school’s local cable channel. He did his job very well, and it was not long before everyone at school wanted a CD copy of Grape Expectations’ performance. At first, being the good guy that he is, Chuck gave a few friends a free copy of the CD, thinking that would satisfy everyone’s hunger for more of this new group. But instead, putting a few free CD copies into circulation only fueled the fire, and the number of students begging for a copy became a burden. Chuck decided he’d like to try to make money from the CDs. So he began to explore the possibility of starting up a new company that would be called Grape Expectations. The first thing he did was talk to his parents to get their advice and support. He also talked to his school counselor, his math teacher, and a few other adults at the school who had either been in business themselves or knew something about it. His parents were very enthusiastic and offered to help as long as Chuck’s grades did not slip. A deal is struck! Chuck had enjoyed a long-term friendship with the band members, and they unanimously agreed that they would love to get the added exposure for their music. They were hopeful that it really would launch their music careers. So Chuck and the band members drew up a short legal agreement (Chuck’s mom is a lawyer and wrote up a legal agreement for no charge). Chuck would record the band’s music, market and sell it (probably on a CD), and pay the band members 10 percent of everything he sold (gross sales). Since there were five members in the band, 10 percent would divide evenly among the band members, with each receiving 2 perent of the sales. It was agreed that Chuck would call his company Grape Expectations, and that was just great with the band. The Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 85 Unit III: Finance Section 1: Assumptions Case Study copyright notice on the CD would read: © Grape Expectations, 20011. All rights reserved. Chuck recorded seven or eight of the band’s most popular songs onto a master CD, which he could then copy and sell to anyone and everyone he could. All of the music was original and had been written by the band members together, so there was no dispute about who would receive the bulk of the royalties. Since they recorded and sold only their own music, it wasn’t necessary to pay royalties to other artists or other companies. It would be easy to make lots of copies of the CD. Chuck could either take them to the local copy shop and get them duplicated at a cost of $2.00 each, or he could purchase a CD burner and copy them himself. Chuck decided to take the easier route and just have the copies made by the local copy shop, as he needed them. The copy shop would require a copy of his legal agreement with the band, but after the first set of copies were made it would be easier to make other copies as needed. Costs. Chuck estimated his costs to be as follows: $2.00 to copy each CD, with the name and copyright notice on the CD .50 for the plastic case to put the CD into .50 for each 4-color jacket that is displayed in the plastic CD case with the band logo, and the words to the songs $3.00 total cost for one CD, ready to sell Chuck figured that he could sell the CDs at $15.00 each. With a cost of only $3.00, that would mean that his cost of goods percentage would be reasonable, at 20 percent. (Cost of goods percentage = total cost of goods divided by price = $3.00 / $15.00 = one-fifth = 20 percent). Chuck figured that over the year he could sell a total of 1,050 CDs. He believed he would sell 175 at a school concert in January and 125 at the St. Valentine’s Day Dance in February. He figured he wouldn’t make any sales in March, April, and May because he would be busy with spring break and exams. He planned to sell around 25 CDs at the End-of-School-Year A copyright notice has three elements: The copyright symbol (©), the name of the person or company claiming copyright ownership, and the year. The words “All rights reserved.” Mean that any and all rights of ownership pertaining to the copyrighted material belong to the copyright holder. Effectively, the band turned over their ownership rights to Grape Expectations, in exchange for 10% royalties. 1 Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 86 Unit III: Finance Section 1: Assumptions Case Study BBQ in June. He would be working on the farm over the summer, so there would be no sales in July or August. In September, he figured he’d sell 175 CDs at the Back-to-School Dance, when Grape Expectations would appear again. He believed he could sell 100 units in October, when the band would perform at a pre-game concert and dance. In November, he guessed he’d sell 150 because of the Thanksgiving Dance. And finally, he figured many people would want to give copies of the CD as gifts during the holidays, so he estimated he’d sell 300 units during that time. Even though there were only about 2,000 families in the schools, he figure his estimates were conservative since others outside of the school (families, friends, other fans, etc.) would buy, too, especially since the school had agreed to run the Grape Expectation’s performance on the local cable channel from time to time at no charge to Chuck. Since he would run the business out of his house, his expenses would be minimal. He figured that he would pay himself 5 percent of sales and be okay. Of course, he would also have to give 10 percent of his pay to Uncle Sam for taxes. He had agreed to pay his artists (also called Grape Expectations) 10 percent of gross sales (all sales). He also had asked a graphic arts student at school to design the jacket for the CD, and Chuck agreed to pay him $50, one time, for the art work. Chuck felt that he could successfully market the CDs by having about 2,000 flyers printed up and circulated at school and school activities. He had the flyers printed up in January for $60. The thought of preparing financial statements for his business was a bit frightening, so his father (an accountant) provided him with some easy-touse, fill-in-the-blank forms he could use to prepare the following financial statements. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 87 Unit III: Finance Section 1: Assumptions Assumption Statement Revenues (forecasted) Income Statement Cash Flow Statement Balance Sheet Case Study To detail his costs, expenses, and the activities necessary to produce his monthly unit sales To predict the revenues (sales) he would make, he needed to predict the number of CD units he would sell and multiply that by the price he would charge for the CD To predict whether his business would make a profit or lose money To be sure that he would not run out of cash and would have enough money to pay all of his bills To see whether he was “building” a company. If his net equity (net worth) went up, he would be making money and creating value. If not, he should consider doing something else because the business probably would not stand the test of time. Chuck was pleased to realize that he could probably make about $15,750 in sales by selling 1,050 CDs at $15.00 per CD. Not bad for a part-time business. The Future. Now Chuck could see the potential for even more sales if he were successful. He could try other recording artists. He could market the CDs outside of the school. He could try to get his CDs into other stores in other towns, and he was really excited about the possibility of putting information about the CD onto a website he would develop. If he did that, he could take orders over the web and possibly deliver the music over the web, too. Of course, these ideas presented more questions and other issues. But Chuck was excited about the potential of his new business. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 88 Unit III: Finance Section 1: Assumptions Student Activity Student Activity Assumption Statements Part I. Refer to the Grape Expectations case in order to answer the following questions. 1. What does it cost to make each CD (including the cover), and what must be purchased in order to produce each CD? 2. Throughout the year, what are the main activities that Chuck believes will aid his sales? Part II. Using the answers to questions 1 and 2, complete the assumptions statement below. Assumption Statement: Grape Expectations Costs – PER UNIT Cost to duplicate one CD Cost for one plastic case Cost for each 4-color CD jacket Other costs (per unit) Total cost for one CD, ready to sell Expenses Royalties rate to be paid to artists Cost of goods percentage 10% 20% Other expenses Monthly Activities to Sell CDs Month As agreed to by Chuck Dickens and artists Price, divided by total cost of goods Expenses that are not on the list # of CDs Sold Monthly Sales January February March April May June July August September October November December Total Sales for the year Other sales Total CD Units Sold for the Year Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 89 Unit III: Finance Section 2: Projections Assumptions Statement Prices Units Sold Transparen Income Statement Income - Expenses =Net Profit (Loss) Balance Sheet Assets - Liabilities = Net Worth (Not included in this unit) Note: These are your “assumptions” about price, sales, etc. Note: These are the two basic financial statements: 1) Income Statement 2) Balance Sheet Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Transparency Section 2: Projections Section 2: Projections Teacher Notes Context Overview: In the first activity, students read about revenues (sales), and they complete a revenue table for Grape Expectations. In the next activities, students will read more information about the company Grape Expectations, and they will use this information to complete a one-month projected income statement and a one-year projected income statement for Grape Expectations. Goal: This section should provide students with an understanding of the income flow of a business. TEKS Addressed: Mathematical Models with Applications: The student is expected to 1A - compare and analyze various methods for solving a real–life problem; 1B - use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; 2A - interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, and scatterplots to draw conclusions from the data; 2B - analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences; 3A-formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions; Materials:Projected Revenue Worksheet (1 per student) Sales Projection Table (1 per student) Assumptions Statement for Grape Expectations (completed in section 1) One-Month Projected Income Statement (Worksheet (1 per student) One-Year Projected Income Statement (1 per student) Procedures: Activity 1: Projected Revenue for Grape Expectations 1. Ask the students to read the information on the Projected Revenue Worksheet. 2. Help the students fill in the Projected Revenue Worksheet for Grape Expectations. A transparency for the first three months may be used for this purpose. The completed Projected Revenue Worksheet is on the next page. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 91 Unit III: Finance Section 2: Projections Revenues # of Units Sold x Price of CD Gross Sales from CDs Transparen Projected Revenue Worksheet for Grape Expectations Mar Apr May June July Aug Sept Jan Feb 175 125 0 0 0 25 0 0 175 100 $15 $15 $15 $15 $15 $15 $15 $15 $15 $15 0 0 0 $375 0 0 $2,625 $1,875 Oct $2,625 $1,500 Student Activity 2: One-Month Projected Income Statement 1. Hand out the One-Month Projected Income Statement for Grape Expectations worksheet to each studen 2. Ask the students to read the information on the income statement (there is new information regarding so Expectations). 3. Help the students complete the Projected Income Statement for Grape Expectations for January. Some o to complete the income statement was given in the case. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Section 2: Projections Transparen One-Month Projected Income Statement for Grape Expectations January 2001 Gross Sales (# of Units Sold x Price) ____175_______ x _____$15______ = ____$2,625____ Cost of Sales (Cost per Unit x # of Units Sold) ____$3.00_____ x _____175______ = ____$525______ Gross Profits (Gross Sales – Cost of Sales) ____$2,625____ - ____$525______ = ____$2,100____ Expenses Salaries Payroll Tax Royalties Paid to Band Members Jacket Design Advertising Flyer Bank Fees Supplies Cell Phone Car Expense 5% of Gross Sales = $131.25 10% of Salaries = $13.13 10% of Gross Sales = $262.50 One-time Fee = $50 One-time Fee = $60 ____$5________ ____$15_______ ____$20_______ ____$10_______ Total Expenses ____$566.88___ Net Profit (Gross Profit – Total Expenses) ____$2,100____ - ___$566.88____ = ___$1,533.12__ Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Section 2: Projections Teacher Notes Student Activity 3: One-Year Projected Income Statement for Grape Expectations 1. Explain that a one-year income statement shows all 12 one-month income statements on one single statement. 2. Hand out a copy of the One-Year Projected Income Statement for Grape Expectations to each student. 3. Ask the students to complete the One-Year Projected Income Statement for Grape Expectations. Use the transparency of the first two months to guide the discussion. A completed copy of the statement appears on the next page. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 94 Unit III: Finance Section 2: Projections Teacher Notes One-Year Projected Income Statement for Grape Expectations Jan Feb Mar Apr May June July Aug Sept Gross Sales Cost of Sales Gross Profit $2,625 $525 $2,100 $1,875 $375 $1,500 0 0 0 0 0 0 0 0 0 $375 $75 $300 0 0 0 0 0 0 $2,625 $525 $2,100 Expenses Salaries and Wages 10% Payroll Tax 10% Royalties Paid to Artists Jacket Design Advertising Flyer Bank Fees Supplies Cell Phone Car Expense Total Expenses $131.25 $13.13 $262.50 $50 $60 $5 $15 $20 $10 $566.88 $93.75 $9.38 $187.5 0 0 $5 $15 $20 $10 $340.63 0 0 0 0 0 $5 $15 $20 $10 $50 0 0 0 0 0 $5 $15 $20 $10 $50 0 0 0 0 0 $5 $15 $20 $10 $50 $18.75 $1.88 $37.50 0 0 $5 $15 $20 $10 $108.13 0 0 0 0 0 $5 $15 $20 $10 $50 0 0 0 0 0 $5 $15 $20 $10 $50 $131.25 $13.13 $262.50 0 0 $5 $15 $20 $10 $456.88 ($50) ($50) ($50) $191.87 ($50) ($50) $1,643.12 Net Profit (Loss) $1,533.12 $1,159.37 Gross sales equals the number of units sold times the price. The price is $15.00, and the number of units sol follows: January – 175, February – 125, March – 0, April – 0, May – 0, June – 25, July – 0, August – 0, Se 100, November – 150, December – 300. The cost of sales equals the cost per unit times the number of units sold. The cost per unit is $3.00. The gross profit equals the gross sales minus the cost of sales. Total expenses are the sum of all the expenses. Net profit is the gross profit minus the total expenses. A loss parentheses. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Section 2: Projections Student Activity Student Activity 1 Projected Revenue Estimating or projecting sales is pretty much a guessing game if a business is just getting started or has no history of selling its product. One of the biggest mistakes most entrepreneurs make is to overestimate sales. They either put too high a price on their product, or they overestimate the number of customers they think will buy the product. Sometimes it takes longer than anticipated for customers to become aware of a product and to feel confident enough to buy it. Many times, the entrepreneur will simply “want” sales of a certain number, and he or she thinks that by simply plugging in the number on the spreadsheet, the sales will magically happen. This can be very hazardous, especially if the entrepreneur agrees to pay employees or agrees to other expenses before he or she actually generates the sales needed to pay for those expenses. But it is possible to make a realistic projection of sales by researching and considering carefully the product’s price and desirability in the marketplace. Price One of the best ways to set a realistic price for a product is to take a survey to see what potential customers would actually pay for the product. Another way is to try to sell the product at several different prices to see which price best suits the customers and their needs. For example, a high price might be okay when selling directly to students who are excited about the product and who want it right then and there. A slightly lower price might be appropriate after a product has been on the market for a while, and an “on sale, limited time offer” might re-ignite interest in the product. Units Sold The product’s price and desirability certainly impact sales—specifically, the number of units sold. The more units you sell, the higher the sales become. Sales (Revenue) You can project what your sales, or revenue, will be by guessing the number of units you think you can sell based on your customer survey and market research and multiplying that number by the price. The result is Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 96 Unit III: Finance Section 2: Projections Student Activity your “projected sales.” The word “projected” implies that you are estimating, or that this is your goal. Since no one knows what the future may hold, you are saying, “I think I can sell this many units of my product . . . during this month . . . at this price . . . or over this period of time.” (Formula: # of units x price = projected sales). Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 97 Unit III: Finance Section 2: Projections Student Activity Projected Revenue Worksheet for Grape Expectation Fill in the revenue table below for Grape Expectations. Refer to the Assumption Stat Expectations in order to determine the number of units sold each month and the pric Projected Revenue Worksheet for Grape Expectations Revenue # of units sold x price of CD = gross sales from CDs Jan Feb Mar Apr May June July Aug Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Sept Oct Unit III: Finance Section 2: Projections Student Activity Student Activity 2 One-Month Projected Income Statement for Grape Expectations The Income Statement The income statement covers a period of time, such as a month or a year. If you are looking at a one-month income statement, you will see the sales, expenses, and net profit for that entire month. The formula for net profit is sales minus expenses. If expenses exceed sales, the result will be a net loss. Chuck opened an account for Grape Expectations at the local bank. He chose an account that charged a $5 monthly fee, but it required no minimum balance. He also decided to get a cell phone for $20 a month, and he estimated that his car expenses would be $10 a month. Because he planned to make the CDs only when an order was placed, he did not need an office or inventory. However, he decided he might need some supplies, such as order forms and a receipt book as well as other general office supplies. He figured these supplies would cost him about $15 per month. Chuck was then ready to put his business on paper! Complete the One-Month Projected Income Statement for Grape Expectations for the month of January. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 99 Unit III: Finance Section 2: Projections Student Activity One-Month Projected Income Statement for Grape Expectations January 2001 Gross Sales (# Units Sold x Price) ______________ x ______________ = ______________ Cost of Sales (Cost per Unit x # of Units Sold) ______________ x ______________ = ______________ Gross Profits (Gross Sales – Cost of Sales) ______________ - ______________ = ______________ Expenses Salaries Payroll Tax Royalties Paid to Band Members Jacket Design Advertising Flyer Bank Fees Supplies Cell Phone Car Expense ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ Total Expenses ______________ Net Profit (Gross Profit – Total Expenses) ______________ - ______________ = ______________ Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 100 Unit III: Finance Section 2: Projections Student Activity 3 One-Year Projected Income Statement for Grape Expecta Complete the One-Year Projected Income Statement for Grape Expectations. Refer to the One-M as well as the Assumption Statement. Projected Income Statement Jan Feb Mar Apr May June July Aug Sept Gross Sales Cost of Sales Gross Profit Expenses Salaries and Wages 10% Payroll Tax 10% Royalties Paid to Artists Jacket Design Advertising Flyer Bank Fees Supplies Cell Phone Car Expense Total Expenses Net Profit (Loss) The gross sales are the number of units sold times the price. The cost of sales is the cost per unit times the number of units sold. The gross profit is the gross sales minus the cost of sales. Total expenses are the sum of all the expenses. Net profit is the gross profit minus the total expenses. A loss is denoted with parentheses. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Section 2: Projections Projected Revenue Revenues Jan Feb # of Units Sold x Price of CD Gross Sales from CDs Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Section 2: Projections Projected Income Statement Jan Gross Sales Cost of Sales Gross Profit Expenses Salaries and Wages 10% Payroll Tax 10% Royalties Paid to Artists Jacket Design Advertising Flyer Bank Fees Supplies Cell Phone Car Expense Total Expenses Net Profit (Loss) Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Feb Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Teacher Notes Section 3: The Cash Flow Statement and the Balance Sheet Teacher Notes Context Overview: In this section, students will learn about the importance of a cash flow statement. They will then work though an example using Grape Expectations. They will read about the purpose of a balance sheet and complete an example for Grape Expectations. Goal: To gain an understanding of a cash flow statement and a balance sheet, and to recognize that monitoring cash is very important. TEKS Addressed: Mathematical Models with Applications: The student is expected to 1A - compare and analyze various methods for solving a real–life problem; 1B - use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; 2A - interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, and scatterplots to draw conclusions from the data; 2B - analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences; 3A-formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions; Materials: Cash Flow Pre-reading (1 per student) Cash Flow Statement (1 per student) One-Year Projected Income Statement for Grape Expectations (completed in previous section) Balance Sheet for Grape Expectations (1 per student) Procedures: Student Activity 1: Cash Flow Statement for Grape Expectations 1. Hand out the Cash Flow Statement for Grape Expectations to each student and ask them to read the first section, which describes what a cash flow statement is. Ask the students, “Why is a Cash Flow Statement important?” Possible answer: If you run out of cash, you are in danger of going “out ofbBusiness! Point out to students that running out of cash is a problem that many entrepreneurs experience. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 104 Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Teacher Notes 2. Help the students complete the Cash Flow Statement for Grape Expectations by filling the columns on the transparency. A completed statement follows on the next page. Student Activity 2: Balance Sheet for Grape Expectations 1. Ask students to use Grape Expectation’s Cash Flow Statement and oOne-Year Income Statements to complete the Balance Sheet for Grape Expectations. A transparency of the first few months is provided. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 105 Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Teacher Notes Cash Flow Statement for Grape Expectations Cash Flow Statement Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec $2,625 $1,875 0 0 0 $375 0 0 $2,625 $1,500 $2,250 $4,500 0 0 0 0 0 0 0 0 0 0 0 0 $2,625 $1,875 0 0 0 $375 0 0 $2,625 $1,500 $2,250 $4,500 $947.50 $612.50 $50 $50 $50 $162.50 $50 $50 $837.50 $500 $725 $1,400 $103.13 0 0 0 $20.63 0 0 $144.38 $82.50 $123.75 $247.50 $715.63 $50 $50 $50 $183.13 $50 $50 $981.88 $582.50 $848.75 $1,647.50 $1,159.37 ($50) ($50) ($50) $191.87 ($50) ($50) $1,643.12 $917.50 $1,401.25 $2,852.50 $1,533.12 $2,692.49 $2,642.49 $2,592.49 $2,542.49 $2,734.36 $2,684.36 $2,634.36 $4,277.48 $5,194.98 $6,596.23 $2,692.49 $2,642.49 $2,592.49 $2,542.49 $2,734.36 $2,684.36 $2,634.36 $4,277.48 $5,194.98 $6,596.23 $9,448.73 CASH INFLOWS Cash Sales - Collected Other Sales Total Cash Inflows TOTAL CASH OUTFLOWS New Accounts Payable Salaries, Wages & Taxes $144.38 Total Cash Outflows $1,091.88 CASH INFLOWS MINUS $1,533.12 OUTFLOW Previous Cash Balance 0 Ending Net Cash Flow $1,533.12 Cash Sales are the same as monthly sales which are determined by multiplying the number of units sold times the price. Other Sales are the sales made to customers on a credit basis. For Grape Expectations this is always zero. New Accounts Payable are all costs, fees, and royalties associated with the product or service. This amount will vary according to the amount of product or service sold. Salaries, Wages & Taxes are all salaries, commissions, wages and taxes paid to employees during the month. Previous Cash Balance is the amount of Cash owned by the company at the end of the previous month. Ending Net Cash Flow is the amount of Cash the company owns at the end of each month. Example: January : Cash Sales = 175 sold x $15 each = $2625; New Accounts Payable = cost of CDs + 10% of sales to band members + Jacket + Advertising Flyer + Bank Fee + Supplies + Cell Phone + Car Expenses = $525 + $262.50 + $50 + $60 + $5 + $15 + $20 + $10 = $947.50; Salaries, Wages & Taxes = Sally’s commission + Taxes = $131.25 + $13.13 = $144.38; Total Cash Outflows = $947.50 + $144.38 = $1,091.88; Cash Inflows minus Outflows = $2,625 $1,091.88 = $1,533.13; Previous Cash Balance = 0; Ending Net Cash Flow = $1,533.13 – 0 = $1,533.1 Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 106 Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Teacher Notes Balance Sheet for Grape Expectations Balance Sheet Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Year Current Assets Cash $1,533.13 $2,692.50 $2,642.50 $2,592.50 $2,542.50 $2,734.37 $2,684.37 $2,634.37 $4,277.49 $5,194.99 $6,596.24 $9,448.74 $9,448.74 Other Assets Total Assets $1,533.13 $2,692.50 $2,642.50 $2,592.50 $2,542.50 $2,734.37 $2,684.37 $2,634.37 $4,277.49 $5,194.99 $6,596.24 $9,448.74 $9,448.74 Current Liabilities Accounts Payable 0 0 0 0 0 0 0 0 0 0 0 0 0 Other Liabilities 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Liabilities 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Equity Contributed Capital 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Retained Earnings 1,533.13 2,692.50 2,642.50 2,592.50 2,542.50 2,734.37 2,684.37 2,634.37 4,277.49 5,194.99 6,596.24 9,448.74 9,448.74 Total Shareholders' Equity 1,533.13 2,692.50 2,642.50 2,592.50 2,542.50 2,734.37 2,684.37 2,634.37 4,277.49 5,194.99 6,596.24 9,448.74 9,448.74 Total Liabilities & Equity 1,533.13 2,692.50 2,642.50 2,592.50 2,542.50 2,734.37 2,684.37 2,634.37 4,277.49 5,194.99 6,596.24 9,448.74 9,448.74 YES YES YES YES YES YES YES YES YES YES YES Does the Balance Sheet balance? Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics YES YES 107 Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Student Activity 1 Cash Flow Statement for Grape Expectations The cash flow statement keeps track of one thing only: cash. When running a business, you n “cash position” very carefully. Without enough cash, you might not be able to pay your bills, inventory, or pay your expenses. If you run out of cash, you are in danger of going “out of Bu Basically, you determine the total amount of cash taken into your business as a result of sales amount of cash spent to run your business. (Formula: Cash In – Cash Out = Net Cash) Cash is not the same as sales. For example, you may have sold some of your product “on cre pays you late, or not at all, this could get you into trouble since you are continuing to spend m create your product, but you haven’t been paid yet for the products you have sold. This probl demise of many businesses that eventually must declare bankruptcy due to “insufficient cash What a dilemma. You can sell your product, but you don’t have enough cash because you are much or not being paid at all. For Grape Expectations, we are assuming that all sales are made on a “cash basis,” meaning collection of cash occurs within the month. Otherwise, the balance would have to include “ac receivable”—another way of saying, “money that is owed as a result of sales, but has not bee Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Use Grape Expectation’s One-Year Income Statement to complete the following Cash Flow State Cash Flow Statement for Grape Expectations Cash Flow Statement Jan Feb Mar Apr May June July Aug Sept CASH INFLOWS Cash Sales - Collected Other Sales Total Cash Inflows TOTAL CASH OUTFLOWS New Accounts Payable Salaries, Wages & Taxes Total Cash Outflows CASH INFLOWS MINUS OUTFLOW Previous Cash Balance Ending Net Cash Flow Cash Sales are the same as monthly sales, which are determined by multiplying the number of un Other Sales are the sales made to customers on a credit basis. For Grape Expectations this is alw New Accounts Payable are all costs, fees, and royalties associated with the product or service. Th according to the amount of product or service sold. Salaries, Wages & Taxes are all salaries, commissions, wages, and taxes paid to employees duri Previous Cash Balance is the amount of Cash owned by the company at the end of the previous m Ending Net Cash Flow is the amount of Cash the company owns at the end of each month. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Student Activity 2 Balance Sheet for Grape Expectations Use Grape Expectations Cash Flow and one-year Income Statement in order to c Sheet. See the notes on the next page describing each row in the table Balance Sheet Jan Feb Mar Apr May June July Current Assets Cash Other Assets Total Assets Current Liabilities Accounts Payable Other Liabilities Total Liabilities Total Equity Contributed Capital Retained Earnings Total Shareholders' Equity Total Liabilities & Equity Does the Balance Sheet balance? Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Aug Sept Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Cash Flow Statement for Grape Expectations Cash Flow Statement Jan CASH INFLOWS Cash Sales - Collected Other Sales Total Cash Inflows TOTAL CASH OUTFLOWS New Accounts Payable Salaries, Wages & Taxes Total Cash Outflows CASH INFLOWS MINUS OUTFLOW Previous Cash Balance Ending Net Cash Flow Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Feb Unit III: Finance Section 3: The Cash Flow Statement and the Balance Sheet Balance Sheet for Grape Expectations Balance Sheet Jan Current Assets Cash Other Assets Total Assets Current Liabilities Accounts Payable Other Liabilities Total Liabilities Total Equity Contributed Capital Retained Earnings Total Shareholders' Equity Total Liabilities & Equity Does the Balance Sheet balance? Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics Feb Unit III: Finance Section 4: Mathematical Models and Projections Teacher Notes Section 4: Mathematical Models and Projections Teacher Notes Context Overview: Students will write a mathematical function to model the expense of producing CDs. They will also write a function to model Grape Expectations’ gross sales. They will notice that the price and the number of units sold play a big role in determining the total profit. The students will then perform a break-even analysis for Grape Expectations based on these models. Goal: To use a mathematical model to examine the break-even point for Grape Expectations. TEKS Addressed: 1) The student uses a variety of strategies and approaches to solve both routine and non-routine problems: The student is expected to 1B - use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; 1C - select a method to solve a problem, defend the method, and justify the reasonableness of the results. Materials: “A Mathematical Model for Grape Expectations” activity (1 copy per student) Assumption Statement for Grape Expectations (Completed in Section 1) Procedures: Student Activity: A Mathematical Model for Grape Expectations Hand out the “A Mathematical Model for Grape Expectations” activity to each student. Lead the students through the worksheet. Questions and possible answers follow below. Questions and possible answers: 1. A. What price is Grape Expectations charging per CD? $15.00 B. Write a function that models revenues, y, as a function of the number of CDs sold, x. y = $15x 2. A. For Grape Expectations, how much does it cost to make one CD? $3.00 – $2.00 to duplicate one CD; $.50 for one plastic case; $.50 for one 4-color CD jacket. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 113 Unit III: Finance Section 4: Mathematical Models and Projections Teacher Notes B. Write a mathematical function that models the expenses of duplicating CDs (y) as a function of the number of CDs sold (x) y = $3x 3. A. For Grape Expectations, what are the other expenses of producing the CDs for one year? Salary and wages (5% of revenue), payroll tax (10% of wages), royalties (10% of revenues), jacket design and advertising flyer = $110; all other fees (bank, supplies, etc.) = $50 per month = $710 per year B. Write a mathematical function that models the expenses paid in royalties to the band (y) as a function of the number of CDs sold (x) Royalty expenses = 10% of revenues; y = .1(15x) = 1.5x C. Write a mathematical function that models the expense of Chuck’s salary (y) as a function of the number of CDs sold (x). Chuck’s salary = 5% of revenues; y = .05(15x) = .75x D. Write a mathematical function that models the payroll tax expenses on Chuck’s salary (y) as a function of the number of CDs sold (x). Payroll tax = 10% of Chuck’s salary; y = .1(.05(15x)) = .075x 4. Write a mathematical function that models all the expenses of producing CDs (y) as a function of the number of CDs sold (x). y = 1.5x + .75x + .075x + 3x + 710; y = 5.325x + 710 5. Based on our model, how much profit would Chuck make if he sold: A. 200 CDs in 1 year? Expense = 5.325x + 710 = $1775; Sales = 15x = $3000; Profit = $3000 - $1775 = $1225 B. 20 CDs in 1 year? Expense = 5.325x + 710 = $816.50; Sales = 15x = $300; Profit = $300 - $816.50 = $516.50 • What does a negative number mean for Grape Expectations? It means the company is losing money. 6. Based on a price of $15.00 per CD, how many CDs will Chuck have to sell in order to break even (meaning that he does not make or lose money) for the month? This is a break-even analysis. Students may solve by graphing y = 15x and y = 5.325x + 710 to find the intersection of the two lines. They may solve using a table on the graphing calculator, or they may solve the system of equations for x (the number of CDs). 15x = 5.325x + 710; x = 73.38 . . . (approximately 74 CDs). • What is the expense of producing 74 CDs? $1104.05 Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 114 Unit III: Finance Section 4: Mathematical Models and Projections • • • • • • Teacher Notes How much revenue does Chuck make by selling 74 CDs? $1110.00 How much profit does Chuck make by selling 74 CDs? $5.95 What is the expense of producing 73 CDs? $1098.73 How much revenue does Chuck make by selling 73 CDs? $1095.00 How much profit does Chuck make by selling 73 CDs? -$3.73 Why does Chuck earn a negative profit by selling 73 CDs? It costs more to produce the CDs than he made. Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 115 Unit III: Finance Section 4: Mathematical Models and Projections Student Activity Student Activity A Mathematical Model for Grape Expectations Answer the following questions in order to help you make a mathematical model of sales and expenses for Grape Expectations. 1. A. What price is Grape Expectations charging per CD? B. Write a function that models revenues (y) as a function of the number of CDs sold (x). 2. A. For Grape Expectations, how much does it cost to make one CD? B. Write a mathematical function that models the expenses of duplicating CDs (y) as a function of the number of CDs sold (x). 3. A. For Grape Expectations, what are the other expenses of producing the CDs for one year? B. Write a mathematical function that models the expenses paid in royalties to the band (y) as a function of the number of CDs sold (x). C. Write a mathematical function that models the expense of Chuck’s salary, y, as a function of the number of CDs sold, x. D. Write a mathematical function that models the payroll tax expenses on Chuck’s salary (y) as a function of the number of CDs sold (x). Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 116 Unit III: Finance Section 4: Mathematical Models and Projections Student Activity 4. Write a mathematical function that models all the expenses of producing CDs (y) as a function of the number of CDs sold (x). 5. Based on our model, how much profit would Chuck make if he sold: A. 200 CDs in 1 year? B. 20 CDs in 1 year? 6. Based on a price of $15.00 per CD, how many CDs will Chuck have to sell in order to break even (meaning that he does not make or lose money) for the month? Mathematical Models with Applications / Entrepreneurship: Keeping Score with Mathematics 117