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**Break-even point Definition**

The break-even point is a point of sales at which there is no gain no loss. In simple words it the level of sales at which sales are exactly equal to its expenses. Break-even analysis assumes that there are two types of costs; fixed and variable. Breakeven sales cover only variable costs and fixed costs. Sales less variable cost is called “contribution margin” that covers the fixed costs and of course profit. But at the break-even point the contribution covers only fixed cost. The following statement is explaining a state of break-even.

Sales – Variable cost = Fixed cost or

Contribution margin = Fixed cost

**Break-even point Formula**

Since break-even point is a level of sales so it can be in units as well as in dollar amount. However formulas for both are slightly different.

**Break-even point Example**

Mr. Bake runs a bakery by selling breads for $5 each and it costs him $2 to bake each bread. The only fixed cost of the bakery is rent of the shop that is $2,100 a month. Now the break-even point will decide that how many breads should Mr. Bake sell to cover all his costs.

Here are some basic calculations that are required by formula:

Contribution margin per unit= CM = SP – VC = $5 - $2 = $3 per bread

Contribution margin ratio = CM/ SP = $3/$5 = 60%

There is another way to find out the breakeven sales if you already know the number of units required to break-even.

Break-even point in Sales dollars = Break-even units x SP = 700 x $5 = $3,500

**Proof**

To understand the break-even point concept in more detail here is the proof that by selling 700 breads there will be no gain and no loss to the bakery.

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1. If the variable cost per unit goes up, Contribution margin Break-even point a. Increases increases. b. Increases decreases. c. Decreases decreases. d. Decreases increases. e. Decreases remains unchanged. 2. The amount of revenue required to earn a targeted profit is equal to a. Fixed cost divided by contribution margin. b. Fixed cost divided by contribution margin ratio. c. Fixed cost plus targeted profit divided by contribution margin ratio. d. Targeted profit divided by contribution margin ratio. e. Targeted profit divided by variable cost ratio. 3. Break-even revenue for the multiple-product firm can a. Be calculated by dividing total fixed cost by the overall contribution margin ratio. b. Be calculated by dividing segment fixed cost by the overall contribution margin ratio. c. Be calculated by dividing total fixed cost by the package contribution margin. d. Be calculated by multiplying total fixed cost by the contribution margin ratio. e. Not be calculated; break-even revenue can only be computed for a single-product firm. 4. In the cost-volume-profit graph, a. The break-even point is found where the total revenue curve crosses the x-axis. b. The area of profit is to the left of the break-even point. c. The area of loss cannot be determined. d. Both the total revenue curve and the total cost curve appear. e. Neither the total revenue curve nor the total cost curve appear. 5. An important assumption of cost-volume-profit analysis is that a. Both costs and revenues are linear functions. b. All cost and revenue relationships are analyzed within the relevant range. c. There is no change in inventories. d. Sales mix remains constant. e. All of the above are assumptions of cost-volume-profit analysis. 6. The use of fixed costs to extract higher percentage changes in profits as sales activity changes involves a. Margin of safety. b. Operating leverage. c. Degree of operating leverage. d. Sensitivity analysis. e. Variable cost reduction. 7. If the margin of safety is 0, then a. The company is operating at a loss. b. The company is precisely breaking even. c. The company is earning a small profit. d. The margin of safety cannot be less than or equal to 0; it must be positive. e. None of the above is true. 8. The contribution margin is the a. Amount by which sales exceed fixed costs. b. Difference between sales and total expenses. c. Difference between sales and operating income. d. Difference between sales and total variable expense. e. Difference between variable expense and fixed expense. Use the following information for 4-9 and 4-10. Corleone Company produces a single product with a price of $15, variable costs per unit of $12, and fixed costs of $9,000. 9. Corleone’s break-even point in units a. Is 600. b. Is 750. c. Is 9,000. d. Is 3,000. e. cannot be determined from the information given. 10. The variable cost ratio and the contribution margin ratio for Corleone are Variable cost ratio Contribution margin ratio a. 80% 80%. b. 20% 80%. c. 20% 20%. d. 80% 20%. e. The contribution margin ratio cannot be determined from the information given. 11. If a company’s fixed costs rise by $10,000, which of the following will be true? a. The break-even point will decrease. b. The variable cost ratio will increase. c. The break-even point will be unchanged. d. The variable cost ratio will decrease. e. The contribution margin ratio will be unchanged. 12. Solemon Company has fixed costs of $15,000, variable cost per unit of $5, and a price of $8. If Solemon wants to earn a targeted profit of $3,600, how many units must be sold? a. 6,200 b. 5,000 c. 1,200 d. 3,720 e. 1,875

Salamanca produces and sells refrigerator magnets to be sold as novelty items by resorts. Last year, Salamanca sold 198,400 units. The income statement for Salamanca, Inc., for last year is as follows: Sales ............ $992,000 Less: Variable expenses .... 545,600 Contribution margin .... $446,400 Less: Fixed expenses .... 180,000 Operating income .... $266,400 Required: 1. Compute the break-even point in units and in revenues. Compute the margin of safety in sales revenue for last year. 2. Suppose that the selling price decreases by 8 percent. Will the break-even point increase or decrease? Recompute the break-even point in units. 3. Suppose that the variable cost per unit decreases by $0.20. Will the break-even point increase or decrease? Recompute the break-even point in units. 4. Can you predict whether the break-even point increases or decreases if both the selling price and the unit variable cost decrease? Recompute the break-even point in units incorporating both of the changes in Requirements 2 and 3. 5. Assume that total fixed costs increase by $50,000. (Assume no other changes from the original data.) Will the break-even point increase or decrease? Recompute it.

Multiple Choice Questions 1. If a company has a $25,000 reduction in sales and an increase of $7,000 in fixed costs with a contribution margin ratio of 34 percent, by how much will net income change? a. Decrease $1,500 b. Decrease $32,000 c. Increase $1,500 d. Decrease $15,500 2. Which of the following statements is correct as it relates to a company that sells multiple products? a. CVP analysis cannot be used. b. Contribution margin is based on sales mix. c. CVP analysis is much easier to use. d. The break-even point remains the same even if sales mix changes. 3. Hoagland Company has the following product information: Sales price ....... $6.00 per unit Variable costs ..... $2.00 per unit Fixed costs ...... $12,000 Units sold ....... 20,000 What is the break-even point in sales dollars? a. $12,000 b. $15,000 c. $18,000 d. $21,000 4. Greer Corp. has the following product information: Sales price ............ $6.00 per unit Contribution margin ratio ...... 35% Fixed costs ............$42,000 What is the break-even point in units? a. 7,000 b. 2,471 c. 20,000 d. 18,850 5. Greer Corp. has the following product information: Sales price ............ $6.00 per unit Contribution margin ratio....... 35% Fixed costs ............. $42,000 How many units must Greer Corp sell in order to reach a target before-tax profit of $50,000? a. 43,810 b. 44,000 c. 44,545 d. 45,105 6. Scuffy Company has the following product information: Sales price .......... $7.25 per unit Variable costs ......... $2.25 per unit Fixed costs .......... $10,000 What is the break-even point in units? a. 1,380 b. 2,000 c. 4,445 d. 5,000 7. Which of the following is a correct form of the break-even equation when using activity-based costing? a. Break-even ($) = (Fixed costs + Batch-level costs) ÷÷ Contribution margin per unit b. Break-even (units) = (Fixed costs + Facility-level costs) ÷ Contribution margin per unit c. Break-even ($) = (Fixed costs + Batch-level costs + Product-level costs) ÷ Contribution margin per unit d. Break-even (units) = (Fixed costs + Batch-level costs + Product-level costs) ÷ Contribution margin per unit 8. John Abner Enterprises has a contribution margin ratio of 80 percent and fixed costs of $20,000. What would sales have to be for an after-tax net income of $60,000? The company is in the 40 percent tax bracket. a. $80,000 b. $100,000 c. $120,000 d. $150,000 9. Which of the following is not an assumption of cost-volume-profit analysis? a. Selling prices change only at the end of the month. b. Costs can be thought of as fitting a linear function within the relevant range. c. Sales mix is constant. d. Inventory levels do not change.

Reconsider the Special Products Company problem presented in Section 1.2. Although the company is well qualified to do most of the work in producing the iWatch, it currently lacks much expertise in one key area, namely, developing and producing a miniature camera to be embedded into the iWatch. Therefore, management now is considering contracting out this part of the job to another company that has this expertise. If this were done, the Special Products Company would reduce its research-and-development cost to $5 million, as well as reduce its marginal production cost to $750. However, the Special Products Company also would pay this other company $500 for each miniature camera and so would incur a total marginal cost of $1,250 (including its payment to the other company) while still obtaining revenue of $2,000 for each watch produced and sold. However, if the company does all the production itself, all the data presented in Section 1.2 still apply. After obtaining an analysis of the sales potential, management believes that 30,000 watches can be sold. Management now wants to determine whether the make option (do all the development and production internally) or the buy option (contract out the development and production of the miniature cameras) is better. a. Use a spreadsheet to display and analyze the buy option. Show the relevant data and financial output, including the total profit that would be obtained by producing and selling 30,000 watches. b. Figure 1.3 shows the analysis for the make option. Compare these results with those from part a to determine which option (make or buy) appears to be better. FIGURE 1.3 An expansion of the spreadsheet in Figure 1.1 that uses the solution for the mathematical model to calculate the break-even point. c. Another way to compare these two options is to find a break-even point for the production and sales volume, below which the buy option is better and above which the make option is better. Begin this process by developing an expression for the difference in profit between the make and buy options in terms of the number of grandfather clocks to produce for sale. Thus, this expression should give the incremental profit from choosing the make option rather than the buy option, where this incremental profit is 0 if 0 watches are produced but otherwise is negative below the break-even point and positive above the break-even point. Using this expression as the objective function, state the overall mathematical model (including constraints) for the problem of determining whether to choose the make option and, if so, how many units of the LCD display (one per watch) to produce. d. Use a graphical procedure to find the break-even point described in part c. e. Use an algebraic procedure to find the break-even point described in part c. f. Use a spreadsheet model to find the break-even point described in part c. What is the conclusion about what the company should do?

You have recently been engaged by Dominic’s Italian Cafe to evaluate the financial impact of adding gourmet pizza items to the menu. A survey of the clientele indicates that demand for the product exists at an average selling price of $18 per pizza. Fixed costs related to new equipment would be $12,000 per month. Variable costs for ingredients, labor, and electricity for the oven would average $6 per pizza. You decide that a good starting point is to conduct an initial break-even analysis on the new project. Knowing that many commercial Internet companies provide free downloads or online demos of their products for your evaluation and testing pleasure, you decide to conduct the break-even analysis using break-even calculators that have been located at several Web sites. Required: a. Calculate the break-even point in pizzas per month and print your results using the online break-even analysis tools at each of the following Web sites: 1. www.entrepreneur.com/calculators/breakeven.html 2. www.steinermarketing.com/calc_break_even.htm 3. www.anz.com/aus/Small-Business/Tools-Forms-And-Guides/Benchmark- Your-Business/Breakeven-Analyser/default.asp b. Calculate the break-even point in pizzas per month and print your results using the break-even chart analysis spreadsheet available at the following Web site: 1. Go to www.jaxworks.com, the Small Business Spreadsheet Factory. 2. Click on the “Downloads” link to access the list of free spreadsheets and other files. 3. Scroll down the file list and open the file “Breakeven Simple Chart Analysis” for Excel. c. Write a comparative analysis of each of the four tools that you used to calculate the break-even point. You might discuss strengths, weaknesses, usefulness, and user interaction for each tool. d. Dominic’s now is interested in the amount of operating income available from the gourmet pizza operation if sales are initially expected to be 2,000 pizzas each month. Calculate the operating income and print your results using the Excel file “Contribution Income Analysis” available at www.jaxworks.com. e. Dominic’s now would like to understand the effect on operating income if certain changes in costs or volume occur. Use the “Contribution Income Analysis” Excel spreadsheet to evaluate each of the following independent cases assuming sales are initially expected to be 2,000 pizzas each month: 1. Selling price is decreased by 10%, and pizza sales are expected to increase by 5%. 2. Selling price is increased to $20, and pizza sales are expected to decrease by 20%. 3. Higher-quality ingredients are used at a cost increase of $2 to $8 per pizza, and pizza sales are expected to increase to 2,200 pizzas per month. 4. A more efficient pizza oven is available that would reduce the electricity used in baking each pizza. Variable costs would be reduced to $5 per pizza. The more efficient oven would increase the fixed costs to $15,000 per month. f. Write a memo to Dominic’s explaining the results of your analysis.

Smithen Company, a wholesale distributor, has been operating for only a few months. The company sells three products—sinks, mirrors, and vanities. Budgeted sales by product and in total for the coming month are shown below based on planned unit sales as follows: Break-even point in sales dollars = Fixed expenses = $223,600 = $430,000 Overall CM ratio 0.52 Break-even point in unit sales: Total Fixed expenses = $223,600 = 1,720 units Weighted-average CM per unit $130* *($168 × 0.50) + ($40 × 0.25) + ($144 × 0.25) As shown by these data, operating income is budgeted at $36,400 for the month, break-even sales dollars at $430,000, and break-even unit sales at 1,720. Assume that actual sales for the month total $504,000 (2,100 units), with the CM ratio and per unit amounts the same as budgeted. Actual fixed expenses are the same as budgeted, $223,600. Actual sales by product are as follows: sinks, $126,000 (525 units); mirrors, $210,000 (1,050 units); and vanities, $168,000 (525 units). Required: 1. Prepare a contribution format income statement for the month based on actual sales data. Present the income statement in the format shown above. 2. Compute the break-even point in sales dollars for the month, based on the actual data. 3. Calculate the break-even point in unit sales for the month, based on the actual data. 4. Considering the fact that the company exceeded its $500,000 sales budget for the month, the president is shocked at the results shown on your income statement in (1) above. Prepare a brief memo for the president explaining why both the operating results and the break-even point in sales dollars are different from what was budgeted.

Jasmine Richards met her boss, Rick McNeil, at the pop machine in the lobby. McNeil is the vice-president of marketing at Down East Lures Corporation. Richards was puzzled by some calculations she had been doing, so she initiated this conversation: Richards: Rick, I’m not sure how to go about answering the questions that came up at the meeting with the president yesterday. McNeil: What’s the problem? Richards: The president wanted to know the break-even point for each of the company’s products, but I’m having trouble figuring them out. McNeil: I’m sure you can handle it, Jasmine. And, by the way, I need your analysis on my desk tomorrow morning at 8:00 A.M. sharp so I can look at it before the follow-up meeting at 9:00. Down East Lures makes three fishing lures in its manufacturing facility in Prince Edward Island. Data concerning these products appear below: Total fixed expenses for the entire company are $282,000 per year. All three products are sold in highly competitive markets, so the company is unable to raise its prices without losing unacceptable numbers of customers. The company has no work in process or finished goods inventories due to an extremely effective lean manufacturing system. Required: 1. What is the company’s overall break-even point in total sales dollars? 2. Of the total fixed costs of $282,000, $18,000 relate directly to the Frog lure product, $96,000 relate directly to the Minnow lure product, and $60,000 relate directly to the Worm lure product. The remaining fixed expenses of $108,000 consist of common fixed costs such as administrative salaries, rent on the factory building, and advertising expenses for the company as a whole. These common fixed expenses are not directly related to any particular product but must be incurred as part of operating the business. a. What is the break-even point in units for each product? Note: Management insists that Richards separately calculate the break-even point for each product using its CM per unit and only the fixed expenses that relate directly to that product. b. If the company sells exactly the break-even quantity of each product calculated in (a), calculate the overall profit of the company. Explain this result to management. c. Calculate the company’s overall break-even point in units using the weighted average CM approach. How many units of each product must be sold at the break-even level? Comment on any significant differences you see between these results and those of ( a ) above.

Plata produces and sells plastic storage containers. Last year, Plata sold 125,000 units. The income statement for Plata, Inc., for last year is as follows: Sales ...........$625,000 Less: Variable expenses ....343,750 Contribution margin ........$281,250 Less: Fixed expenses .....180,000 Operating income ......$101,250 Required: 1. Compute the break-even point in units and in revenues. Compute the margin of safety for last year. 2. Suppose that the selling price increases by 10 percent. Will the break-even point increase or decrease? Recompute it. 3. Suppose that the variable cost per unit increases by $0.35. Will the break-even point increase or decrease? Recompute it. 4. Can you predict whether the break-even point increases or decreases if both the selling price and the unit variable cost increase? Recompute the break-even point incorporating both of the changes in Requirements 1 and 2. 5. Assume that total fixed costs increase by $50,000. (Assume no other changes from the original data.) Will the break-even point increase or decrease? Recompute it.

Rajiv and Laurie Amin are recent college graduates looking to purchase a new home. They are purchasing a $200,000 home by paying $20,000 down and borrowing the other $180,000 with a 30-year loan secured by the home. The Amins have the option of (1) paying no discount points on the loan and paying interest at 8 percent or (2) paying one discount point on the loan and paying interest of 7.5 percent. Both loans require the Amins to make interest-only payments for the first five years. Unless otherwise stated, the Amins itemize deductions irrespective of the amount of interest expense. The Amins are in the 25 percent marginal ordinary income tax bracket. a. Assuming the Amins do not itemize deductions, what is the break-even point for paying the point to get a lower interest rate? b. Assuming the Amins do itemize deductions, what is the break-even point for paying the point to get a lower interest rate? c. Assume the original facts except that the amount of the loan is $300,000. What is the break-even point for the Amins for paying the point to get a lower interest rate? d. Assume the original facts except that the $180,000 loan is a refinance instead of an original loan. What is the break-even point for paying the point to get a lower interest rate? e. Assume the original facts except that the amount of the loan is $300,000 and the loan is a refinance and not an original loan. What is the break-even point for paying the point to get a lower interest rate?

Whittier Company plans to sell 1,000 mowers at $400 each in the coming year. Product costs include: Direct materials per mower $180 direct labor per mower $100 Variable factory overhead per mower $25 Total fixed factory overhead $15,000 Variable selling expense is a commission of $20 per mower; fixed selling and administrative expense totals $30,000. a. Prepare a contribution margin income statement. b. Calculate the contribution margin ratio. c. Calculate the break-even point in sales dollars. d. Calculate the margin of safety, in terms of sales revenue. Scenario 2 The executive team at Whittier Company has requested that you perform some analysis. In some cases, you will need to rearrange the equations used above in question parts b, c or d to perform the requested analysis. Respond to question parts e - k in this CengageNOW problem regarding the analysis. e. The executive team has set a contribution margin ratio goal of 20%. Will a 1% increase in the unit selling price achieve this goal? Additionally the executive team has asked you to determine the unit selling price that will achieve the contribution margin ratio goal of 20%. What is the unit selling price that you will report to the executive team? $ f. The sales manager is opposed to increasing the unit selling price. She believes that the number of units sold will drop if the unit selling price is increased. You have been asked to analyze the impact of decreasing variable expenses, rather than increasing unit selling price. In your spreadsheet, create a formula to determine the amount of unit variable expense at which the unit selling price is $400 and the contribution margin ratio is 20%. What is the unit variable expense that you report to the executive team (round to 2 decimal places)? $ g. The production manager then argues that a decrease in variable expenses can only be achieved by using lesser quality direct materials. This would have a negative impact on the product quality. The manager feels that the focus should be on reduction of fixed cost. Can a change in fixed costs impact the contribution margin ratio? h. The executive team is also focusing on the break-even point in sales dollars. The team believes this break-even point needs to be decreased. Recalling your discussions with the sales manager and the production manager regarding unit selling price and variable expenses, you know that unit sales will drop if unit selling price is increased. Also a reduction in variable expenses would have a negative impact on quality. Therefore, in order to reduce the break-even point in sales dollars, you turn your attention to reducing. i. Keeping unit selling price at $400 and unit variable cost at $325, at what fixed cost amount will the break-even point in sales dollars be decreased to $224,000 (round to 2 decimal places)? j. Additionally the executive team would like to know how a reduction of fixed expenses would impact the margin of safety. the impact on the margin of safety. What impact would a reduction of fixed expenses have on Whittier's risk of earning a loss rather than a profit? k. What is the margin of safety when fixed costs are reduced to achieve the break-even point in sales dollars of $224,000? (take your answer for the amount of fixed costs from question part i, change the fixed costs amount on the contribution margin income statement spreadsheet above in question part a, if formulas are done correctly this will recalculate the margin of safety) (round to 2 decimal places). $

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