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A company needs to sell 10,000 units of its only product in order to break even. Fixed costs are \(\$ 110,000,\) and the per unit selling price and variable costs are \(\$ 20\) and \(\$ 9,\) respectively. If total sales are \(\$ 220,000,\) the company's margin of safety will be equal to: a. \(\$ 0\) b. \(\$ 20,000\) c. \(\$ 110,000\) d. \(\$ 200,000\)

Short Answer

Expert verified
The company's margin of safety is \(\$ 20,000\). The correct answer is (b).

Step by step solution

01

Calculate Breakeven Sales

To calculate the breakeven sales, we can use the formula: Breakeven Sales = Fixed Costs ÷ (Selling Price per Unit - Variable Costs per Unit) We're given that fixed costs are \(110,000, the selling price per unit is \)20, and the variable cost per unit is $9. Plug these values into the formula: Breakeven Sales = \(110,000 ÷ (\)20 - $9)
02

Calculate the Breakeven Sales

Now we simplify the expression and find the Breakeven Sales: Breakeven Sales = \(110,000 ÷ \)11 Breakeven Sales = 10,000 units The company needs to sell 10,000 units to break even.
03

Calculate Total Sales in Dollars

Given that the total sales are $220,000, we can determine the number of units sold using the selling price per unit: Total Sales = Number of Units Sold × Selling Price per Unit \(220,000 = Number of Units Sold × \)20 Number of Units Sold = \(220,000 ÷ \)20 Number of Units Sold = 11,000 units
04

Calculate Margin of Safety

Now, we can calculate the Margin of Safety: Margin of Safety = (Actual Sales - Breakeven Sales) × Selling Price per Unit Margin of Safety = (11,000 units - 10,000 units) × $20 Margin of Safety = 1,000 units × $20 Margin of Safety = \(\$ 20,000\) The company's margin of safety is \(\$ 20,000.\) The correct answer is (b).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Breakeven Analysis
Breakeven analysis is a financial calculation used to determine the number of products or services a company must sell to cover its costs. Put simply, it's the point at which total revenues equal total costs, and the company neither makes a profit nor experiences a loss. This analysis is vital for any business as it helps in setting sales targets and understanding the impact of different cost structures.

To perform a breakeven analysis, you should first differentiate between fixed and variable costs. Fixed costs are expenses that remain constant regardless of production volume, such as rent or salaries. In contrast, variable costs are those that fluctuate with production output, such as raw materials. Knowing both these costs is essential to find the breakeven point.

Once you are clear about your costs, you evaluate your sale price per unit, which, when multiplied by the number of units sold, will represent your total revenue. By comparing this to your accumulated costs (fixed plus variable), you find the magic number of units that must be sold to hit the breakeven point.
Fixed and Variable Costs
Understanding fixed and variable costs is crucial for any financial analysis, especially when calculating a company's breakeven point. Fixed costs, as mentioned, do not change with the level of production or sales. They are the 'constant' costs of doing business, such as rent, salaries, and insurance. Even if a company makes no sales, these costs still need to be paid.

Variable costs, on the other hand, are directly tied to the business's production level. These include costs like raw materials, direct labor, and utilities associated with manufacturing a product. These costs vary with the volume of production - the more products made, the higher the variable costs. Mixed costs, which have both fixed and variable components, can also exist but typically need to be dissected into their components for accurate analysis.

When you're running a business, keeping both types of costs optimized is important to maximize profits. The lower you can keep your breakeven point through careful management of these costs, the better the opportunity you have to turn a profit sooner rather than later.
Breakeven Sales Calculation
To calculate the breakeven sales in units, one simple formula is used: \[\text{Breakeven Sales in Units} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Costs per Unit}}\]In the context of our given exercise, the fixed costs were established at \(110,000, the selling price per unit at \)20, and the variable cost per unit at $9. With these figures at hand, we calculate a breakeven point of 10,000 units using the described formula:

\[\text{Breakeven Sales} = \frac{\$110,000}{\$20 - \$9}\]
\[\text{Breakeven Sales} = \frac{\$110,000}{\$11}\]
\[\text{Breakeven Sales} = 10,000 \text{ units}\]

It's fundamental to get the breakeven sales calculation right, as it paints a clear picture of what the minimum sales target should be to ensure the business does not lose money. The better you understand your fixed and variable costs, the more accurate your breakeven analysis will be, and the more strategically you can operate your business.

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Most popular questions from this chapter

Marketing Docs prepares marketing plans for growing businesses. For 2017, budgeted revenues are \ 1,500,000$ based on 500 marketing plans at an average rate per plan of 3,000 . The company would like to achieve a margin of safety percentage of at least 45 \% The company's current fixed costs are 400,000 and variable costs average 2,000 per marketing plan. (Consider each of the following separately. 1\. Calculate Marketing Docs' breakeven point and margin of safety in units. 2\. Which of the following changes would help Marketing Docs achieve its desired margin of safety? a. The average revenue per customer increases to 4,000 b. The planned number of marketing plans prepared increases by 5 \% c. Marketing Docs purchases new software that results in a 5 \% increase to fixed costs but reduces variable costs by 10 \% per marketing plan.

Genesee Music Society is a not-for-profit organization that brings guest artists to the community's greater metropolitan area. The music society just bought a small concert hall in the center of town to house its performances. The lease payments on the concert hall are expected to be \(\$ 4,000\) per month. The organization pays its guest performers \(\$ 1,800\) per concert and anticipates corresponding ticket sales to be \(\$ 4,500\) per concert. The music society also incurs costs of approximately \(\$ 1,000\) per concert for marketing and advertising. The organization pays its artistic director \(\$ 33,000\) per year and expects to receive \(\$ 30,000\) in donations in addition to its ticket sales. 1\. If the Genesee Music Society just breaks even, how many concerts does it hold? 2\. In addition to the organization's artistic director, the music society would like to hire a marketing director for \(\$ 25,500\) per year. What is the breakeven point? The music society anticipates that the addition of a marketing director would allow the organization to increase the number of concerts to 41 per year. What is the music society's operating income/(lloss) if it hires the new marketing director? 3\. The music society expects to receive a grant that would provide the organization with an additional \(\$ 17,000\) toward the payment of the marketing director's salary. What is the breakeven pointif the music society hires the marketing director and receives the grant?

Megaphone Corporation produces a molded plastic casing, M\&M101, for many cell phones currently on the market. Summary data from its 2017 income statement are as follows: Joshua Kirby, Megaphone's president, is very concerned about Megaphone Corporation's poor profitabil ity. He asks Leroy Gibbs, production manager, and Tony DiNunzo, controller, to see i i there are ways to reduce costs After 2 weeks, Leroy returns with a proposal to reduce variable costs to 55\% of revenues by reducing the costs Megaphone currently incurs for safe disposal of wasted plastic. Tony is concerned that this would expose the company to potential environmental liabilitities. He tells Leroy, "We would need to estimate some of these potential environmental costs and include them in our analysis." "You can't do that," Leroy replies. "We are not violating any laws. There is some possibility that we may have to incur environmental costs in the future, but if we bring it up now, this proposal will not go through because our senior managementt danger of shutting down the company and costing all of us our jobs. The only reason our competitors are making money is because they are doing exactly what lam proposing. 1\. Calculate Megaphone Corporation's breakeven revenues for 2017 2\. Calculate Megaphone Corporation's breakeven revenues if variable costs are 55\% of revenues. 3\. Calculate Megaphone Corporation's operating income for 20171 it variable costs had been 55\% of revenues. 4\. Given Leroy Gibbs's comments, what should Tony DiNunzo do?

During the current year, XYZ Company increased its variable SG\&A expenses while keeping fixed SG\&A expenses the same. As a result, XYZ's: a. Contribution margin and gross margin will be lower. b. Contribution margin will be higher, while its gross margin will remain the same. c. Operating income will be the same under both the financial accounting income statement and contribution income statement. d. Inventory amounts booked under the financial accounting income statement will be lower than under the contribution income statement.

Classical Glasses operates a kiosk at the local mall, selling sunglasses for \(\$ 30\) each. Classical Glasses currently pays \(\$ 1,000\) a month to rent the space and pays two full-time employees to each work 160 hours a month at \(\$ 10\) per hour. The store shares a manager with a neighboring kiosk and pays \(50 \%\) of the manager's annual salary of \(\$ 60,000\) and benefits of \(\$ 12,000\). The wholesale cost of the sunglasses to the company is \(\$ 10\) a pair. 1\. How many sunglasses does Classical Glasses need to sell each month to break even? 2\. If Classical Glasses wants to earn an operating income of \(\$ 5,300\) per month, how many sunglasses does the store need to sell? 3\. If the store's hourly employees agreed to a \(15 \%\) sales-commission-only pay structure, instead of their hourly pay, how many sunglasses would Classical Glasses need to sell to earn an operating income of \(\$ 5,300 ?\) 4\. Assume Classical Glasses pays its employees hourly under the original pay structure, but is able to pay the mall \(10 \%\) of its monthly revenue instead of monthly rent. At what sales levels would Classical Glasses prefer to pay a fixed amount of monthly rent, and at what sales levels would it prefer to pay \(10 \%\) of its monthly revenue as rent?

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