1Copyright © 2008 Cengage Learning South-Western.

Heitger/Mowen/Hansen

Cost-Volume-Profit Analysis: A Managerial Planning Tool

Chapter Three

Fundamental Cornerstones of Managerial Accounting

Fundamental Cornerstones of Managerial Accounting

2

Cost-Volume-Profit Analysis

A powerful tool for planning and decision making. It can be used to calculate:

The number of units that must be sold to

break-even

The impact of a given reduction in fixed

costs on the break-even point.

The impact of an increase in price on

profit.

3

Break-Even Point

Total Revenue

Or to put it another way:

– Total Cost

=

Total Revenue

Zero Profit

Total Cost

4

Contribution Margin

Sales - Variable Expense

Contribution Margin

=

Contribution Margin is then used to cover Fixed Costs

and Operating Income.

Using Operating Income inCost-Volume-Profit Analysis

5

Contribution Margin Income Statement

• Divides costs based on behavior

• Costs are divided into variable and fixed components

• Important subtotal is contribution margin

◦ Sales revenue minus variable expenses

6

Contribution Margin

Sales - Variable Expense

Contribution Margin

=

Break-even point is when Operating Income is zero.

Contribution Margin -

Fixed Costs =

Operating Income

7

Units to Be Sold to Achieve a Target Income

Two ways:

1.Using Operating Income equation2.Using the Basic Break-even equation

Cornerstone 4-5 will walk us through these computations

8

Number of units to earn target

income =

Fixed Cost + Target Income

$400 - $325

Price – Variable Cost per unit

$45,000 + $37,500 =

Units to Be Sold to Achieve a Target Income

Number of units to earn target

income

=Number of units to earn target

income1,100

9

Sales Revenue to Achieve a Target Income

Sales dollars to earn target

income =

Fixed Cost + Target Income

0.1875

Contribution margin ratio

$45,000 + $37,500

$440,000

Sales dollars to earn target

income =

Sales dollars to earn target

income =

10

Profit-Volume Graph

• Visually portrays the relationship between profits and units sold

• Operating Income is the dependent variable

• Units sold is the independent variable

11

Cost-Volume-Profit Graph

• Depicts the relationship among cost, volume, and profits

• To obtain the more detailed relationships, it is necessary to graph two separate lines:

◦ Total revenue

◦ Total cost

• The vertical axis is measured in dollars

• The horizontal axis is measured in units sold

12

Assumptions of Cost-Volume-Profit Analysis

• Revenue and cost functions are linear

• Price, total fixed costs, and unit variable costs can be identified and remain constant over relevant range

• All units produced are sold-there are no change in inventory levels

• Sales mix is constant

• Selling prices and costs are known with certainty

13

Linear Cost and Revenue Functions

Cost-Volume-Profit assumes that cost and revenue functions are linear. In other words they are straight lines.

14

Production Equal to Sales

• Cost-Volume-Profit assumes that what is produced is actually sold

• Inventory levels do not change over the period

• CVP focuses on current costs by excluding inventory costs of previous periods

15

Constant Sales Mix

Multiple product break-even analysis requires a constant sales mix.

Relative combination of products being sold by a firm

Sales mix is difficult to predict with certainty

16

Certainty of Prices and Costs

In actuality, firms seldom know prices, variable costs, and fixed costs with certainty. There are formal ways of

explicitly building uncertainty into the Cost-Volume-Profit model.

17

Multiple-Product Analysis

Cost-Volume-Profit analysis becomes more complex with multiple products.

We need to adapt the single-product formulas.

18

Direct Fixed Expenses

Those fixed costs that can be traced to each segment and would be avoided if the

segment did not exist.

19

Common Fixed Expenses

The fixed costs that are not traceable to the segments and would remain even if

one of the segments was eliminated.

20

Multiple-Product Analysis

Key is to identify the expected sales mix.

Sales mix is the relative combination of products being sold by a firm.

Break-even point in units

21

Sales Mix

• Measured in units sold

• Reduced to the smallest possible whole numbers

• Required in order to determine break even point in units

22

Changes in any of the above will affect the sales mix.

CVP Analysis: Risk and Uncertainty

• The break-even point can be affected by changes in:

◦ Price

◦ Unit contribution margin

◦ Fixed cost

23

Risk and Uncertainty Effects on Managers

• Management must realize the uncertain nature of future prices, costs, and quantities.

• Managers move from consideration of a break-even point to what might be called a “break-even band”.

• Managers may engage in sensitivity or what-if analysis.

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Margin of Safety

• The units sold or the revenue earned above the break-even volume.

• Can be viewed as a crude measure of risk.

◦ When there is a downturn in sales, the risk of suffering losses will be less if the firm’s margin of safety is large than if the margin of safety is small.

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Margin of Safety

Margin of Safety in units =

Sales in units

Break-even units-

Margin of Safety in units = 1,000 - 600

Margin of Safety in units = 400

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Margin of Safety

Margin of Safety in sales revenue = Sales

Break-even sales -

Margin of Safety in sales revenue = $400(1,000) - $400(600)

Margin of Safety in sales revenue = $160,000

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Operating Leverage

• The relative mix of fixed costs to variable costs in a company

• Higher proportions of fixed costs to the amount of variable costs create higher operating leverage

• The greater the degree of operating leverage, the larger the effect on operating income when sales change

Degree of Operating Leverage Operating Income

Contribution Margin=

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The degree of operating leverage (DOL) can be measured for a given level of sales.

Degree of operating leverage

= Contribution MarginOperating Income

Operating Leverage

($400 – $325)(1,000 units)

$30,000

Degree of operating leverage

=

Degree of operating leverage

= 2.5

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% change in operating leverage = DOL % change in sales

Percentage Change in Operating Leverage

2.5=

= 50%

x

20%x % change in operating

leverage

% change in operating leverage

30

Expected Operating Income

$30,000=

(% change x Orig. operating income)

+ (0.50 x $30,000)Expected Operating

Income

=Expected Operating

Income$45,000

Expected Operating

Income=

Original operating income

+