# Significance of the Relevant Range to CVP Relationships

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• 0:03 Cost-Volume-Profit Analysis
• 0:54 Variable and Fixed Costs
• 2:30 Mixed Costs and Assumptions
• 3:31 Relevant Range and Its…
• 5:40 Lesson Summary
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Lesson Transcript
Instructor: Deborah Schell

Deborah teaches college Accounting and has a master's degree in Educational Technology.

Management must understand the cost of producing each item at different volumes of production. In this lesson, you'll learn how the relevant range impacts cost, volume and profit.

## Cost-Volume-Profit (CVP) Analysis

Mr. Spoke owns the Rider Bicycle Company, which produces children's bikes. He is thinking about expanding his operation but is unsure if such a move would result in greater profit. Let's examine Rider's cost structure to evaluate if this would be a good idea.

Mr. Spoke's business incurs many different costs as it produces bicycles. In order to understand how these costs impact profitability, businesses must determine the relationship that exists between its costs, its production volume, and its profit. This relationship is known as cost-volume-profit (CVP) analysis and assists management in setting targets for profitability given its cost structure and the volume of products it produces. Costs incurred to manufacture a product can be classified as variable, fixed, or mixed.

## Variable Costs & Fixed Costs

Variable costs are those costs that change with the amount of activity. For example, the total amount of steel used by Rider Bicycle will vary depending on how many bicycles are produced, but the variable cost per unit will remain the same.

For example, let's assume that total variable costs of steel in May were \$50,000 when 500 bicycles were produced and \$75,000 in June when 750 bicycles were produced. To calculate the variable cost we just divide the total variable costs by the amount of bicycles produced each month. We can see that the variable costs were \$100 per bicycle in both May and June.

Fixed costs are those costs that do not change with the volume of production. For example, Mr. Spoke will have to pay the same amount of rent on his building whether he produces one bicycle or 1,000 bicycles. Although the total fixed cost remains unchanged, the fixed cost per bicycle will change depending on the volume of bicycles produced.

Let's assume that Rider Bicycle's total fixed costs are \$150,000 per month and 500 bicycles were made in May and 750 bicycles were manufactured in June. To determine our fixed cost per bicycle, we divide the total fixed costs by the number of bicycles produced in that month.

As you can see, even though the total fixed costs remain unchanged at \$150,000, the fixed cost per unit will change depending on how many bicycles are produced. In May, the fixed costs per bicycle were \$300, while in June, that number was \$200.

## Mixed Costs & Assumptions

Mixed costs are those costs that have elements of both fixed and variable costs. For example, Rider Bicycle's utility costs would be a mixed cost as part of the cost depends on the amount of electricity used (which is a variable cost). The business also has a constant cost for delivery of the hydro regardless of usage (which is a fixed cost). When examining a company's cost structure, mixed costs must be separated into their variable and fixed components.

In order to determine the proper volume of bicycles to produce, Mr. Spoke would use cost-volume-profit (CVP) analysis. A number of assumptions are used in CVP analysis, specifically:

• It is assumed that all costs behave in the same manner in the relevant range
• Costs can be determined and categorized as either fixed or variable
• The only factor that impacts the cost of producing an item is a change in the volume
• The business sells all the items that it produces
• The sales mix will not change

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