Grades 35, 68
Concepts
Students participate in a group activity in which they are assigned a business. They use breakeven analysis to calculate the number of units that must be sold or at what price each unit needs to sell in order to recover the variable and fixed costs and eventually realize a profit. They incorporate math skills in using the breakeven analysis formula to analyze different options for investing in capital resources (physical capital) to determine which option would allow a business to most quickly reach the breakeven point.
Time Required
70 minutes
Will Be Able To
 Identify and explain the difference between variable costs and fixed costs.
 Define total cost and total revenue.
 Analyze business costs and revenues to determine the number of units that must be sold to cover all operating costs.
Materials

Lesson interactive: BreakEven Analysis.

BreakEven Analysis presentation PowerPoint  pdf File

Activity 1, one copy per student

Activity 2, one copy cut apart

Activity 3, one copy per group

Activity 4, one copy cut apart

4050 index cards

1 large poster paper for each business group

Tape

12 markers for each group

1 calculator for each group

1 computer for each group
 Prizes for winning group (optional)
Assessment Activity
Multiple Choice

Timmy wants to start a lemonade stand. He has decided to use his savings to purchase the newest and fastest blender called the BlendAll which costs $400, and in addition he buys lemons, water, sugar, and ice at a cost of $.15 per cup of lemonade. If Timmy decides to sell his lemonade at $1.25 per cup, how many cups of lemonade will he have to sell to break even?

[364]

320

275

90

[364]

Why is it important for a new business owner to calculate his or her breakeven point?

It is the point at which the company is making a loss and may need to consider restructuring or closing.

It is a way the business owner can predict the amount that he or she needs to spend to keep the business functioning.

It allows the company owner to predict what his or her sales will be.

[It is a way for the company owner to see the point at which he or she will cover all costs and begin making a profit.]

It is the point at which the company is making a loss and may need to consider restructuring or closing.

Profit =________ ___ ________

Costs+ Materials

[Total Revenue –Total Costs]

Revenue + Costs
 Total Costs – Fixed Costs

Costs+ Materials
Constructed Response:
 Using the information below, determine whether Twin Star Inc. is breaking even with the number of units sold.
[BEQ=200/402.15=5.28. Twin Star is doing well because to break even they have to sell six units, so at seven units they are actually making a profit.]
Total Fixed Costs for the week 
$200.00 
Cost to produce one product per week 
$2.15 
Products sold during week 
7 
Selling price of product 
$40.00 
 Write a paragraph explaining what breakeven analysis is and the important role it plays for a business. [Students should have key points in their response such as the sales dollars (i.e., total revenue) equaling or exceeding the total costs, calculating the number of units that must be sold to break even, or profit being realized once the sales dollars are above the costs.]
Conclusion

Review the important content in the lesson by asking the following:

Identify and explain the difference between variable costs and fixed costs. [Fixed costs are costs that do not change if the number of units produced changes. Examples of fixed costs include rent and interest payments. Variable costs are those that change based on the number of units produced. Examples include raw materials.]

What is profit? [Income earned by entrepreneurs. The amount of revenue that remains after a business pays the costs of producing a good or service.]

What is an entrepreneur? [Someone who takes the risk in order to develop new products or start new businesses.]

What are total costs? [The sum of fixed and variable costs.]

What is total revenue? [The product of price per unit multiplied by the number of units sold.]

What is breakeven analysis? [A calculation that an entrepreneur uses to determine the quantity of a good or service a company needs to sell to recover its total costs and start earning a profit.]
 How does an entrepreneur determine the breakeven point? [Breakeven point = fixed costs/average price per unit – average variable cost per unit.]

Identify and explain the difference between variable costs and fixed costs. [Fixed costs are costs that do not change if the number of units produced changes. Examples of fixed costs include rent and interest payments. Variable costs are those that change based on the number of units produced. Examples include raw materials.]
Overview
Running a business is an expensive venture that requires hard work and careful planning. The goal for any business is to earn profit, but before that happens businesses must cover the costs of running the business and these costs include the purchase of new equipment, rent, wages, salaries, and other resources used in the production process.
Good business executives carefully calculate all of their costs, and the amount of product and/or services that are produced. By carefully looking at this data, business people are able to better determine how much they should spend on new physical capital. Physical capital includes any buildings, tools, equipment, and machinery used in the production of goods and services. New capital usually provides a company with higher levels of output, efficiency, and eventually more profit.
Assessment

Divide the students into groups of about four. Distribute about 10 index cards to each group. Tell the students that they will have 60 seconds to list as many ways as possible that math is used in the process of creating and/or running a business. Using the index cards that were handed to each group, have the students write one response on each card. Keep time with a stop watch.

Once the 60 seconds are up, have the groups add up how many index cards they filled. Ask each group how many index cards they filled and have the group with the most share its responses with the class by taping its index cards to the board. If desired, you may give a small prize to the winning group, such as candy. Ask the other groups to share their responses that are different from those taped on the board.
[Answers will vary. Some of the responses may be calculating production costs, determining price, measuring profits, calculating wages, calculating payroll taxes, salaries of workers, graphing sales and costs, or predicting profits.]

Ask the students to share what math skills are needed to complete the tasks that they identified in the previous activity. [Answers will vary. The student’s responses may include addition, subtraction, multiplication, statistics, and division.]

For the following procedures students can remain in groups or return to their original seats. Explain that entrepreneurs are people who are willing and able to take a risk in starting a new business with the aim of making a profit. Discuss the following:

Give examples of entrepreneurs and also encourage the students to share if any of their family members are entrepreneurs:
 Bill Gates: Microsoft
 Mark Zuckerberg: Facebook

Elon Musk: PayPal and Tesla Motors

Point out that not all entrepreneurs are famous. An entrepreneur wants to start a business as a handyman. Ask students to name some of the materials that he or she will need to purchase. (Truck, saw, hammer, nails, drill, drywall, plunger, etc.)

Give examples of entrepreneurs and also encourage the students to share if any of their family members are entrepreneurs:

Explain that the materials that they identified are known as inputs – the things needed to produce an output – which is a good or service. In this case the inputs are needed to produce a service. Many of these inputs are known as capital resources or physical capital. Capital resources are goods produced by people and used in the production of other goods and services.

Show Slide 1 and review the terms that define the different types of costs that any business has.

Ask the students the following questions to check for prior knowledge and expand understanding of business vocabulary and concepts:

What are some examples of fixed costs for a business? [Rent for any resource(s) not owned, insurance.]

What are some examples of variable costs for a business? [Wages, operating costs such as power, water, and fuel].

What is total revenue? [Total revenue is all the money a business receives from selling a good or service. It is computed as the price of the product multiplied by the quantity of the product sold.] Clarify for students that total revenue is the amount that companies receive prior to deducting variable and fixed costs.

How is profit calculated? [Answers will vary. Some students may know that Profit = Total Revenue – Total Costs.]

What are some examples of fixed costs for a business? [Rent for any resource(s) not owned, insurance.]

Explain that profit is the money that remains after an entrepreneur/business owner pays all costs of production. Note that this lesson does not cover economic profit. Economic profit is a firm's total revenue minus all explicit and implicit costs of production, including opportunity costs.

Tell the students that the activities that follow will focus on calculating the fixed costs, variable costs, and using these costs to calculate the breakeven point also known as breakeven analysis.

Explain that the breakeven analysis is used to determine the quantity of a good or service a company needs to sell to recover its costs and start earning profit.

Hand out Activity 1, one copy for each student. Tell students that they are going to practice how to calculate the breakeven point.

Show Slide 2 and discuss the steps in the calculation with the students as follows: when calculating the breakeven point, first total the fixed costs. For example, if rent is $400 and insurance is $300, the fixed costs total $700. Then you take the selling price or price per unit and subtract the variable cost of producing each unit. For example, if the selling price per unit is $8.00 and the variable costs to produce one unit is $3.00, the calculation would be $8$3=5. When setting up the formula: $700/$5=140. This means that in order to breakeven this business would have to sell about 140 units of output. Give students a few moments to read over question 1 of Activity 1. Allow students time to work through the equation. Walk around as students are working on the problem and check for comprehension.

Review the problem with the students by having a student show his/her work on the board. [1100+40/12010=10.36 or 11 auto break jobs.] Give students several moments to read question 2 on Activity 1. Allow students time to work through the equation. Walk around as students are working on the problem and check for comprehension.

Review the problem with the students by having a student show his/her work on the board. [1300+250+60/3010.25=81.5 or 82 units.]

Divide the students into eight small groups (preferably no more than three to a group). Explain that each startup business will calculate its breakeven point. They should take into account the fixed and variable costs to calculate the breakeven point. Tell students that once they have calculated their breakeven point they will create a breakeven graph using an online graphing source.

Distribute a business information card from Activity 2, a name tent from Activity 3, a large postersized paper, markers, tape and a calculator to each group.

Explain to the students that those in a group are part of startup businesses and that today they are having a business meeting about acquiring new equipment. They have to decide which piece of equipment to buy in order to earn the most profit. Students should set up their groups close to a wall where they can hang their poster paper. Groups should have two cards. One is for them to write their company name on, the other provides costs and pricing and information about the two options that they have for buying new equipment.

Tell students that as a group they need to come up with a company name and write that name on the name tent. Have them fold the card so that the name tent is visible.

Tell the students that they will use the large poster paper to complete the calculations together and analyze their results so that they can decide which equipment they will purchase. Stress that the goal is to use the data and calculate which of the choices in equipment will allow the company to reach the breakeven point within the first month of business. All of the fixed costs that they will use are monthly costs.

Give students about 35 minutes to look over the data. Explain that they must show their work on the poster paper so that the entire group can see it. Once they have calculated their costs, they should raise their hand so that they have the opportunity to explain their calculations to you before moving on. Try to spend 12 minutes with each group as they work so that you can provide feedback and/or help if needed.

Allow 1520 minutes for students to complete their work. As the groups finish their calculations, distribute the appropriate group solution card from Activity 4.

Once the groups have finished their calculations, ask the students if every group has made a decision as to which new capital resource they will be purchasing. Have each group share its decisions by introducing its business, the choice in a new capital resource, and how the calculations brought them to this choice.

Ask if any of the groups decided on the more expensive equipment with the lower running costs and if so, why. [Answers will vary, and be sure to have the students show examples of their calculations to the class. For example, the Automotive Brake Changes business will breakeven more quickly with the more expensive car lift (option B) which costs $5,000 but for which the maintenance costs are only $40, compared to option A which costs $3,200 but has maintenance costs of $100.]

Show Slide 3, the breakeven graph. Explain to students that this graph is used to provide a graphical representation of the breakeven point. Line A represents the sales dollars (revenue) that are generated through sales of the good or service and line B represents the costs that are associated with production of the good or service. Point out that where both costs (line B) and sales dollars (line A) intersect is the breakeven point.

Explain to the students that they will now be taking their calculations and using a breakeven calculator and graph generator to create a breakeven graph for their business.

Assign one computer per group. Have the students use the costs from both of their choices in new equipment so that they can graphically see the changes in the breakeven point. Guide the students on how to access the interactive BreakEven Analysis.

Once the students have accessed the program, tell the students that there are different cells in which they will enter the amounts from their calculations. Project the program so that all of the students can see and model using an unassigned business example.

Tell students to begin working on their group’s calculation. As the students begin working, be sure to walk around and observe each group for a minute or so, to make sure that they are placing the right information in the cells. Allow students to work for 1520 minutes.

When the students have finished, discuss the following:

Instruct the students to increase their fixed costs by any amount on the program calculator. Then ask, "What does your graph show now? Does your breakeven point change?" [Answers will vary. In general students should observe that their breakeven point has changed and that as a result of increased costs, it will take more sales dollars and units to breakeven.]
 Instruct the students to decrease their revenue by any amount on the program calculator. Ask: What does your graph show now? Does your breakeven point change? [Answers will vary. In general students should observe that their breakeven point has changed and that as a result of decreased revenue, it will take more sales dollars and units to breakeven.]

Instruct the students to increase their fixed costs by any amount on the program calculator. Then ask, "What does your graph show now? Does your breakeven point change?" [Answers will vary. In general students should observe that their breakeven point has changed and that as a result of increased costs, it will take more sales dollars and units to breakeven.]
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