Cornerstones of cost management 3rd edition hansen mowen chapter 16

THE BREAK EVEN POINT AND TARGET PROFIT IN UNITS AND SALES REVENUE • Two frequently used approaches to finding the break-even point • Operating income approach • Contribution margin appr

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COST-VOLUME-PROFIT

ANALYSIS

COST-VOLUME-PROFIT

CHAPTER 16

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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

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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

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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

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• 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 Income

Operating income = Sales revenues – Variable

expenses – Fixed expenses

Operating 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 zero

Break-even units = (Total fixed cost + 0)/Price -

Variable cost per unit

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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

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Sales-Revenue Approach

Operating income = Sales – Variable costs – Total

fixed costs

Operating income = Sales – (Variable cost ratio ×

Sales) – Total fixed costs

Operating income = Sales (1- Variable cost ratio) –

Total fixed costs

Operating income = Sales × Contribution margin

ratio – Total fixed costs

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Sales-Revenue Approach

Sales = (Total fixed costs + Operating income)/

Contribution margin ratio

At break even, operating income equals zero

Break-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

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

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multiple-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

known with certainty

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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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ALTERNATIVE 2

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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

changes in profits as sales activity changes

more that changes in sales activity will affect profits

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

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