University:
California State University, Northridge
Course:
ACCT 230 | Introduction to Managerial Accounting
Academic year:

2024
Views:

253

Pages:

21
Author:

u1cen279b

Chapter 5 Cost-Volume-Profit Relationships Part 2 Study Objective 4 State the five components of costvolume-profit analysis. Cost-Volume Profit Analysis  Cost-volume-profit (CVP) analysis is the study of the effects of changes of costs and volume on a company’s profits.  CVP analysis involves a consideration of the interrelationships among the following components: – Volume or activity level – Unit selling price – Variable cost per unit – Total fixed costs – Sales mix CVP Assumptions The following assumptions underlie each CVP application: When these assumptions are not valid, the results of CVP analysis may be inaccurate. 1 The behavior of both costs and revenues is linear throughout the relevant range of the activity index. 2 All costs can be classified as either variable or fixed with reasonable accuracy. 3 Changes in activity are the only factors that affect costs. 4 All units produced are sold. 5 When more than one type of product is sold, total sales will be in a constant sales mix. CVP Analysis In CVP analysis applications, the term cost includes manufacturing costs plus selling and administrative expenses.  We will use Vargo Video Company as an example. Relevant data for the VCRs made by this company are as follows: Unit selling price Unit variable costs Total monthly fixed costs $500 $300 $200,000 Illustration 5-10 Study Objective 5 Indicate the meaning of contribution margin and the ways it may be expressed. Contribution Margin One of the key relationships in CVP analysis is contribution margin (CM). Contribution margin is the amount of revenue remaining after deducting variable costs. The CM is then available to cover fixed costs and to contribute income for the company.  For example, assume that Vargo Video sells 1,000 VCRs in one month, sales are $500,000 (1,000 x $500) and variable costs are $300,000 (1,000 x $300). Thus, contribution margin is $200,000, computed as follows: Sales $500,000 Illustration 5-11 - Variable Costs = Contribution Margin - $300,000 = $200,000 Unit Contribution Margin Views differ as to the best way to express contribution margin (CM). Some favor a per unit basis.  At Vargo Video, the contribution margin per unit is $200. Illustration 5-12 Unit Selling Price $500 - Unit Variable Cost = Contribution Margin per Unit - $300 = $200  CM per unit indicates that for every VCR sold, Vargo Video will have $200 to cover fixed costs and contribute to income. Contribution Margin Ratio Others prefer to use a contribution margin ratio.  At Vargo Video, the contribution margin ratio is 40%. Contribution Margin per Unit $200 Illustration 5-13 ÷ Unit Selling Price = Contribution Margin Ratio ÷ $500 = 40%  The CM ratio means that 40 cents of each sales dollar ($1 x 40%) is available to apply to fixed costs and to contribute to income. Study Objective 6 Identify the three ways that the breakeven point may be determined. Break-Even Analysis  The second key relationship in CVP analysis is the break-even point, which is the level of activity where total revenues equals total costs, both fixed and variable.  Since no income is involved when the breakeven point is the objective, the analysis is often referred to as break-even analysis. Break-Even Analysis  The break-even point can be: – Computed from a mathematical equation. – Computed by using contribution margin. – Derived from a CVP graph.  The break-even point can be expressed in either sales dollars or sales units. Break-Even Analysis: Mathematical Equation In its simplest form, the equation for breakeven sales is: Break-even Sales = Variable Costs + Fixed Costs Illustration 5-14 Break-Even Analysis: Mathematical Equation for Dollars The break-even point in dollars is found by expressing variable costs as a percentage of unit selling price.  For Vargo Video, the percentage is 60% ($300 ÷ $500). Sales must be $500,000 for Vargo Video to break even. The computation to determine sales dollars at the break-even point is: where: X = .60X + $200,000 .40X = $200,000 X = $500,000 X = sales dollars at the break-even point .60 = variable costs as a percentage of unit selling price $200,000 = total fixed costs Illustration 5-15 Break-Even Analysis: Mathematical Equation for Units The break-even point in units can be computed directly from the mathematical equation by using unit selling prices and unit variable costs. Vargo must sell 1,000 units to break even. The computation is: where: $500X = $300X + $200,000 $200X = $200,000 X = 1,000 units X = sales volume $500 = unit selling price $300 = variable cost per unit $200,000 = total fixed costs Illustration 5-16 Break-Even Analysis: Mathematical Equation Proof The accuracy of the previous computations can be proved as follows: Sales (1,000 x $500) Total costs: Variable (1,000 x $300) Fixed Net Income $500,000 $300,000 200,000 500,000 $ -0- Illustration 5-16 Break-Even Analysis: CM Technique for Units Because we know that CM equals total revenues less variable costs, it follows that at the break-even point, contribution margin must equal total fixed costs. When the CM per unit is used, the formula to compute break-even point in units is shown below:  Once again, the CM per unit for Vargo Video is $200. Fixed Costs $200,000 ÷ Contribution Margin per Unit = Break-even Point in Units ÷ $200 = 1,000 Break-Even Analysis: CM Technique for Dollars When the CM ratio is used, the formula to compute break-even point in dollars is shown below:  Again, the CM ratio for Vargo Video is 40%. Fixed Costs $200,000 ÷ Contribution Margin Ratio = Break-even Point in Dollars ÷ 40% = $500,000 Break-Even Analysis: Graphic Presentation  An effective way to derive the break-even point is to prepare a break-even graph.  The graph is referred to as a cost-volumeprofit (CVP) graph since it shows costs, volume, and profits. Break-Even Analysis: Graphic Presentation The construction of the graph, using the Vargo Video Company data, is as follows: 1 Plot the total revenue line starting at the zero activity level. 2 Plot the total fixed cost by a horizontal line. 3 Plot the total cost line starting at the fixed cost line at zero activity and increasing the amount by the variable cost at each level of activity. 4 Determine the break-even point from the intersection of the total cost line and the total revenue line. In addition to identifying the break-even point, the CVP graph shows both the net income and net loss areas. Thus, the amount of income or loss at each level of sales can be derived from the total sales and total cost lines. CVP Graph Sales Line $900 700 Dollars (000) In the graph to the right, sales volume is shown on the horizontal axis. This axis needs to extend to the maximum level of expected sales. Both total revenues (sales) and total costs (fixed plus variable) are recorded on the vertical axis. 600 Profit Area Break-even Point Total Cost Line 500 400 300 200 100 Fixed Cost Line Loss Area 200 400 600 800 1000 1200 1400 1600 1800 Units of Sales Illustration 5-20