cost-volume-profit analysis cost-volume-profit analysis

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COST-VOLUME-PROFIT ANALYSIS

COST-VOLUME-PROFIT ANALYSIS

CHAPTER 16


CHAPTER 16 OBJECTIVES

1. Determine the number of units and amount of sales revenue needed to break even and to earn a target profit

2. Determine the number of units and sales revenue needed to earn an after-tax target profit

3. Apply cost-volume-profit analysis in a multiple-product setting


CHAPTER 16 OBJECTIVES

4. Prepare a profit-volume graph and a cost-volume-profit graph, and explain the meaning of each

5. Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis

6. Discuss the impact of non-unit cost drivers on cost-volume-profit analysis


THE BREAK EVEN POINT AND TARGET PROFIT IN UNITS AND SALES REVENUE

Cost-Volume-Profit (CVP) Analysis•Powerful tool for planning and decision making• As it emphasizes the interrelationships of costs,

quantity sold, and price, it brings together all of the financial information of the firm

LO-1



• Two frequently used approaches to finding the break-even point• Operating income approach• Contribution margin approach

• Break-even point: the point of zero profit

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• First step in implementing a units-sold approach to CVP analysis is to determine just what a unit is • Second step is to separate costs into fixed

and variable components• CVP focuses on the firm as a whole• All costs of the company—manufacturing,

marketing, and administrative—are taken into account

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Basic Concepts for CVP Analysis •A useful tool for organizing the firm’s costs into fixed and variable categories is the contribution-margin-based income statement • Operating income: income before income taxes

(includes only revenues and expenses from the firm’s normal operations)

• Net income: operating income minus income taxes

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The Equation Method for Break-Even and Target IncomeOperating income = Sales revenues – Variable expenses – Fixed expensesOperating income = (Price × Number of units) – (Variable cost per unit × Number of units) – Total fixed costs

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The Equation Method for Break-Even and Target Income•Equation for a target profit put in terms of units

Units for a target profit = (Total fixed cost + Target income)/(Price - Variable cost per unit)

•Break-even equation when target income is zeroBreak-even units = (Total fixed cost + 0)/Price -

Variable cost per unitLO-1



Contribution Margin Approach•Contribution margin is sales revenue minus total variable costs•By substituting the unit contribution margin for price minus unit variable cost in the operating income equation, the following break-even expression is obtained • Number of units = Fixed costs/Unit contribution

margin

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EXHIBIT 16.1—DIVISION OF REVENUE INTO VARIABLE COST AND CONTRIBUTION MARGIN

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Break-Even Point and Target Income in Sales Revenue•A units sold measure can be converted to a sales-revenue measure by multiplying the unit sales price by the units sold•To calculate the break-even point in sales revenue, variable costs are defined as a percentage of sales rather than as an amount per unit sold•The contribution margin ratio is the proportion of each sales dollar available to cover fixed costs and provide for profit LO-

1



Sales-Revenue ApproachOperating income = Sales – Variable costs – Total fixed costsOperating income = Sales – (Variable cost ratio × Sales) – Total fixed costsOperating income = Sales (1- Variable cost ratio) – Total fixed costsOperating income = Sales × Contribution margin ratio – Total fixed costs

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Sales-Revenue ApproachSales = (Total fixed costs + Operating income)/ Contribution margin ratio

At break even, operating income equals zeroBreak-even sales = Total fixed costs/Contribution margin ratio

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AFTER TAX PROFIT TARGETS

• When calculating the break-even point, income taxes play no role because the taxes paid on zero income are zero• The after-tax profit, or net income, is

computed by subtracting income taxes from the operating income (or before-tax profit)Operating Income = Net income /(1-tax rate)

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MULTIPLE PRODUCT ANALYSIS

• Direct fixed expenses: fixed costs that can be traced to each segment and would be avoided if the segment did not exist

• Common fixed expenses: fixed costs that are not traceable to the segments and that would remain even if one of the segments was eliminated

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MULTIPLE PRODUCT ANALYSIS

Break-Even Point in Units for the Multiple-Product Setting

Break-even sales = Fixed costs/Contribution margin ratio

•Sales mix is the relative combination of products being sold by a firm• Defining a particular sales mix

allows us to convert a multiple-product problem to a single-product CVP format LO-

3


GRAPHICAL REPRESENTATIONS OF CVP RELATIONSHIPS

The Profit-Volume Graph•Portrays the relationship between profits and sales volume•The graph of the operating income equation [Operating income = (Price × Units) – (Unit variable cost × Units) – Fixed Costs]•Operating income is the dependent variable and number of units is the independent variable

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EXHIBIT 16.2—PROFIT VOLUME GRAPHS

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GRAPHICAL REPRESENTATIONS OF CVP RELATIONSHIPS

The Cost-Volume-Profit Graph•Depicts relationships among cost, volume, and profits•To obtain the more detailed relationships, it is necessary to graph two separate lines• The total revenue line; revenue = price × units• The total cost line; (unit variable cost × units) +

Fixed costs•Vertical axis is measured in dollars and horizontal axis is measured in units sold

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EXHIBIT 16.3—COST-VOLUME-PROFIT GRAPH

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ASSUMPTIONS OF COST-VOLUME-PROFIT ANALYSIS

Assumptions of Cost-Volume-Profit Analysis•A linear revenue function and a linear cost function•Price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range•What is produced is sold•For multiple-product analysis, the sales mix is assumed to be known•The selling price and costs are assumed to be known with certainty LO-

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EXHIBIT 16.4—COST AND REVENUE RELATIONSHIPS

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EXHIBIT 16.5—SUMMARY OF EFFECTS OF ALTERNATIVE 1

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EXHIBIT 16.6—SUMMARY OF EFFECTS OFALTERNATIVE 2

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EXHIBIT 16.7—SUMMARY OF EFFECTS OF ALTERNATIVE 3

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CHANGES IN THE CVP VARIABLES

Margin of Safety•Units sold or expected to be sold or the revenue earned or expected to be earned above the break-even volume•If a firm’s margin of safety is large given the expected sales for the coming year, the risk of suffering losses should sales take a downward turn is less than if the margin of safety is small

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Operating Leverage•Use of fixed costs to extract higher percentage changes in profits as sales activity changes•The greater the degree of operating leverage, the more that changes in sales activity will affect profits•The mix of costs than an organization chooses can have a considerable influence on its operating risk and profit level

Degree of operating leverage = Total contribution margin/Profit

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Sensitivity Analysis and CVP•A what-if technique that examines the impact of changes in underlying assumptions on an answer•It is relatively simple to input data on prices, variable costs, fixed costs, and sales mix and set up formulas to calculate break-even points and expected profits•Then, the data can be varied as desired to see what impact changes have on the expected profit

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EXHIBIT 16.8—DIFFERENCES BETWEEN MANUAL AND AUTOMATED SYSTEMS

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CVP ANALYSIS AND NON-UNIT COST DRIVERS

• Conventional CVP analysis assumes that all costs can be divided into variable and fixed costs• Costs are assumed to be a linear function of

sales volume

• An activity-based costing (ABC) system divides costs into unit and non unit based categories

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Total cost = Fixed costs + (Unit variable cost × Number of units) + (Setup cost × Number of setups) + (Engineering cost X Number of engineering hours)

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Operating income = Total revenue – [Fixed costs + (Unit variable cost × Number of units) + (Setup cost × Number of setups) + (Engineering cost × Number of engineering hours)]

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Break-even units = [Fixed costs + (Setup cost × Number of setups) + (Engineering cost × Number of engineering hours)]/Price – Unit variable cost)

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Differences Between ABC Break-Even Point and Conventional Break-Even Point•The fixed costs differ•The numerator of the ABC break-even equation has two non unit-variable cost terms

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END OF CHAPTER 16

cost-volume-profit analysis cost-volume-profit analysis

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