Cost-Volume-Profit (CVP) Analysis ( critical Thinking )

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Chapter 6

Cost-Volume-Profit Analysis

Cost Behavior (slide 1 of 2)

Cost Behavior (slide 2 of 2)

Variable Costs

Variable costs are costs that vary in proportion to changes in the activity base.

When the activity base is units produced, direct materials and direct labor costs are normally classified as variable costs.

Variable Costs and Their Activity Bases

Type of Business	Cost	Activity Base
University	Instructor salaries	Number of classes
Passenger airline	Fuel	Number of miles flown
Manufacturing	Direct materials	Number of units produced
Hospital	Nurse wages	Number of patients
Hotel	Housekeeping wages	Number of guests
Bank	Teller wages	Number of banking transactions

Fixed Costs

Fixed costs are costs that remain the same in total dollar amount as the activity base changes.

When the activity base is units produced, many factory overhead costs such as straight-line depreciation are classified as fixed costs.

Fixed costs have the following characteristics:

Cost per unit decreases as the activity level increases and increases as the activity level decreases.

Total cost remains the same regardless of changes in the activity base.

Fixed Costs and Their Activity Bases

Type of Business	Fixed Cost	Activity Base
University	Building (straight-line) depreciation	Number of students
Passenger airline	Airplane (straight-line) depreciation	Number of miles flown
Manufacturing	Plant manager salary	Number of units produced
Hospital	Property insurance	Number of patients
Hotel	Property taxes	Number of guests
Bank	Branch manager salary	Number of customer accounts

Mixed Costs

Variable and Fixed Cost Behavior

Effect of Changing Activity Level

Cost	Total Amount	Per-Unit Amount
Variable	Increases and decreases proportionately with activity level.	Remains the same regardless of activity level.
Fixed	Remains the same regardless of activity level.	Increases and decreases Inversely with activity level.

Variable, Fixed, and Mixed Costs

Variable Costs	Fixed Costs	Mixed Costs
Direct materials	Straight-line depreciation	Quality Control Department salaries
Direct labor	Property taxes	Purchasing Department salaries
Electricity expense	Production supervisor salaries	Maintenance expenses
Supplies	Insurance expense	Warehouse expenses

Cost-Volume-Profit Relationships

Cost-volume-profit analysis is the examination of the relationships among selling prices, sales and production volume, costs, expenses, and profits.

Contribution Margin

Contribution margin is the excess of sales over variable costs, computed as follows:

Contribution margin covers fixed costs. Once the fixed costs are covered, any additional contribution margin increases operating income.

Contribution Margin Ratio (slide 1 of 2)

The contribution margin ratio, sometimes called the profit-volume ratio, indicates the percentage of each sales dollar available to cover fixed costs and to provide operating income.

The contribution margin ratio is computed as follows:

The contribution margin for Lambert Inc. is computed as follows:

Contribution Margin Ratio (slide 2 of 2)

The contribution margin ratio is most useful when the increase or decrease in sales volume is measured in sales dollars. In this case, the change in sales dollars multiplied by the contribution margin ratio equals the change in operating income, computed as follows:

For example, if Lambert adds $80,000 in sales from the sale of an additional 4,000 units, its operating income will increase by $32,000, computed as follows:

Unit Contribution Margin (slide 1 of 2)

The unit contribution margin is useful for analyzing the profit potential of proposed decisions.

The unit contribution margin is computed as:

If Lambert Inc.’s unit selling price is $20 and its variable cost per unit is $12, the unit contribution margin is computed as follows:

Unit Contribution Margin (slide 2 of 2)

The unit contribution margin is most useful when the increase or decrease in sales volume is measured in sales units (quantities). In this case, the change in sales volume (units) multiplied by the unit contribution margin equals the change in operating income, computed as follows:

Assume that Lambert’s sales could be increased by 15,000 units, from 50,000 units to 65,000 units. The increase in Lambert’s operating income is computed as follows:

Break-Even Point (slide 1 of 3)

The break-even point is the level of operations at which a company’s revenues and expenses are equal.

At break-even, a company reports neither an operating income nor an operating loss.

The break-even point in sales units is computed as follows:

Break-Even Point (slide 2 of 3)

Break-Even Point (slide 3 of 3)

The break-even point in sales dollars can be determined directly as follows:

The contribution margin ratio can be computed using the unit contribution margin and unit selling price as follows:

Effect of Changes in Fixed Costs

Fixed costs do not change in total with changes in the level of activity. However, fixed costs may change because of other factors such as advertising campaigns, changes in property tax rates, or changes in factory supervisors’ salaries.

Changes in fixed costs affect the break-even point as follows:

Increases in fixed costs increase the break-even point.

Decreases in fixed costs decrease the break-even point.

Effect of Change in Fixed Costs on Break-Even Point

Effect of Changes in Unit Variable Costs

Unit variable costs do not change with changes in the level of activity. However, unit variable costs may be affected by other factors such as changes in the cost per unit of direct materials, changes in the wage rate for direct labor, or changes in the sales commission paid to salespeople.

Changes in unit variable costs affect the break-even point as follows:

Increases in unit variable costs increase the break-even point.

Decreases in unit variable costs decrease the break-even point.

Effect of Change in Unit Variable Cost on Break-Even Point

Effect of Changes in Unit Selling Price

Changes in the unit selling price affect the break-even point as follows:

Increases in the unit selling price decrease the break-even point.

Decreases in the unit selling price increase the break-even point.

Effect of Change in Unit Selling Price on Break-Even Point

Effects of Changes in Selling Price and Costs on Break-Even Point

Target Profit

The sales required to earn a target or desired amount of profit is determined by modifying the break-even equation as follows:

Cost-Volume-Profit (Break-Even) Chart (slide 1 of 2)

Cost-Volume-Profit (Break-Even) Chart (slide 2 of 2)

The cost-volume-profit chart is constructed using the following steps:

Step 1: Volume in units of sales is indicated along the horizontal axis. The range of volume shown is the relevant range in which the company expects to operate. Dollar amounts of total sales and total costs are indicated along the vertical axis.

Step 2: A total sales line is plotted by connecting the point at zero on the left corner of the graph to a second point on the chart. The second point is determined by multiplying the maximum number of units in the relevant range, which is found on the far right of the horizontal axis, by the unit sales price. A line is then drawn through both of these points. This is the total sales line.

Step 3: A total cost line is plotted by beginning with total fixed costs on the vertical axis. A second point is determined by multiplying the maximum number of units in the relevant range, which is found on the far right of the horizontal axis by the unit variable costs and adding the total fixed costs. A line is then drawn through both of these points. This is the total cost line.

Step 4: The break-even point is the intersection point of the total sales and total cost lines. A vertical dotted line drawn downward at the intersection point indicates the units of sales at the break-even point. A horizontal dotted line drawn to the left at the intersection point indicates the sales dollars and costs at the break-even point.

Profit-Volume Chart (slide 1 of 2)

Another graphic approach to cost-volume-profit analysis is the profit-volume chart, which plots only the difference between total sales and total costs (or profits).

In this way, the profit-volume chart allows managers to determine the operating profit (or loss) for various levels of units sold.

Profit-Volume Chart (slide 2 of 2)

The profit-volume chart is constructed using the following steps:

Step 1: Volume in units of sales is indicated along the horizontal axis. The range of volume shown is the relevant range in which the company expects to operate. Dollar amounts indicating operating profits and losses are shown along the vertical axis.

Step 2: A point representing the maximum operating loss is plotted on the vertical axis at the left. This loss is equal to the total fixed costs at the zero level of sales.

Step 3: A point representing the maximum operating profit within the relevant range is plotted on the right.

Step 4: A diagonal profit line is drawn connecting the maximum operating loss point with the maximum operating profit point.

Step 5: The profit line intersects the horizontal zero operating profit line at the break-even point in units of sales. The area indicating an operating profit is identified to the right of the intersection, and the area indicating an operating loss is identified to the left of the intersection.

Assumptions of Cost-Volume-Profit Analysis

Cost-volume-profit analysis depends on several assumptions. The primary assumptions are as follows:

Total sales and total costs can be represented by straight lines.

Within the relevant range of operating activity, the efficiency of operations does not change.

Costs can be divided into fixed and variable components.

The sales mix is constant.

There is no change in the inventory quantities during the period.

Sales Mix Considerations (slide 1 of 2)

Many companies sell more than one product at different selling prices. In addition, the products normally have different unit variable costs and, thus, different unit contribution margins.

In such cases, break-even analysis can still be performed by considering the sales mix.

The sales mix is the relative distribution of sales among the products sold by a company.

Sales Mix Considerations (slide 2 of 2)

For break-even analysis, it is useful to think of the individual products as components of one overall enterprise product.

The unit selling price of the overall enterprise product equals the sum of the unit selling prices of each product multiplied by its sales mix percentage.

Likewise, the unit variable cost and unit contribution margin of the overall enterprise product equal the sum of the unit variable costs and unit contribution margins of each product multiplied by its sales mix percentage.

Operating Leverage (slide 1 of 3)

A company’s operating leverage is computed as follows:

Operating Leverage (slide 2 of 3)

Operating Leverage (slide 3 of 3)

Operating leverage can be used to measure the impact of changes in sales on operating income.

Using operating leverage, the effect of changes in sales on operating income is computed as follows:

Effect of Operating Leverage on operating income

Operating Leverage	Percentage Impact on Operating Income from a Change in Sales
High	Large
Low	Small

Margin of Safety (slide 1 of 2)

The margin of safety indicates the possible decrease in sales that may occur before an operating loss results.

Thus, if the margin of safety is low, even a small decline in sales revenue may result in an operating loss.

Margin of Safety (slide 2 of 2)

The margin of safety may be expressed in the following ways:

Dollars of sales

Units of sales

Percent of current sales

The margin of safety expressed as a percent of current sales is computed as follows:

Cost-Volume-Profit Analysis for Service Companies

Cost-volume-profit relationships in a service company are measured with respect to customers and activities, rather than units of product.

Break-even analysis for a service company involves identifying the correct unit of analysis and the correct measure of activity for that unit.

At other units of analysis, the measure of activity may change.

The unit of analysis can influence whether costs are defined as fixed or variable.

Contribution margin

Contribution margin ratio

Sales

$400,000

Contribution margin ratio= = 40%

$1,000,000

Change in operating income = Change in s

ales dollars × Contribution margin ratio

Change in operating income = Change in s

ales dollars × Contribution margin ratio

Change in operating income =$80,000 × 40

% =$32,000

–

Unit contribution margin Sales price pe

r unit Variable cost per unit

–

Unit contribution margin Sales price pe

r unit Variable cost per unit

Unit contribution margin = $20 $12 = $8

Change in operating income = Change in s

ales units × Unit contribution margin

Change in operating income = Change in s

ales units × Unit contribution margin

Change in operating income =15,000 units

× $8 =$120,000

Fixed costs

Break-even sales (units) =

Unit contribution margin

Fixed costs

Break-even sales (dollars) =

Contribution margin ratio

Unit contribution margin

Contribution Margin Ratio =

Unit selling price

Fixed costs + Target profit

Sales (units) =

Unit contribution margin

Contribution margin

Operating leverage =

Operating income

Percent change in operating income = Per

cent change Operating

in sales

leverage

Sales Sales at break-even point

Margin of safety =

Sales