needles powers crosson principles of accounting 12e cost-volume-profit analysis 21 c h a p t e r...

NeedlesPowersCrosson

Principles of Accounting

12e

Cost-Volume-Profit Analysis21C H A P T E R

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Concepts Underlying Cost Behavior

Cost behavior—the way costs respond to changes in volume or activity—is a factor in almost every decision managers make.– Some costs vary with volume or operating

activity (variable costs). – Others remain fixed as volume changes

(fixed costs). – Between those two extremes are costs that

exhibit characteristics of each type (mixed costs).

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Variable Costs(slide 1 of 3)

Total costs that change in direct proportion to changes in productive output (or any other measure of volume) are called variable costs.– They are referred to as unit-level activities,

since the cost is incurred each time a unit is produced or a service is delivered.

– Direct labor, direct materials, operating supplies, and gasoline are examples of variable costs.

– Total variable costs go up or down as volume increases or decreases, but the cost per unit remains unchanged.



Variable cost can be computed using the variable cost formula:

Total Variable Cost = Variable Rate X Units Produced

An activity base (or denominator activity or cost driver) is the activity for which relationships are established.- The general guide for selecting an activity base is to relate

costs to their most logical or causal factor, such as direct labor costs to number of units produced.

Because variable costs increase or decrease in direct proportion to volume or output, it is important to know an organization’s operating capacity. Operating capacity is the upper limit of an organization’s productive output capability, given its existing resources.



– There are three common measures, or types, of operating capacity: Theoretical capacity (or ideal capacity) is the maximum

productive output for a given period in which all machinery and equipment are operating at optimum speed, without interruption. No company actually operates at such a level.

Practical capacity (or engineering capacity) is theoretical capacity reduced by normal and expected work stoppages, such as machine breakdowns and employee breaks. It is used primarily as a planning goal of what could be produced if all went well, but no company actually operates at such a level.

Normal capacity is the average annual level of operating capacity needed to meet expected sales demand. It is the realistic measure of what an organization is likely to produce.


Fixed Costs(slide 1 of 2)

Fixed costs (referred to as facility-level activities) are total costs that remain constant within a relevant range of volume or activity.– Relevant range is the span of activity in which

a company expects to operate.– Fixed cost behavior is expressed mathematically

in the fixed cost formula as follows:

Total Fixed Cost = Fixed Cost in Relevant Range- On a per unit basis, fixed costs go down as

volume goes up, as long as a firm is operating within the relevant range of activity.


Fixed Costs(slide 2 of 2)

Fixed costs change when activity exceeds the relevant range.– These costs are called step costs or step-

variable, step-fixed, or semifixed costs.– A step cost remains constant in a relevant

range of activity and increases or decreases in a step-like manner when activity is outside the relevant range.


Mixed Costs(slide 1 of 2)

Mixed costs have both variable and fixed cost components.– Part of a mixed cost changes with volume

or usage, and part is fixed over a particular period.

– Electric, telephone, and heating costs are examples of mixed costs.


Mixed Costs(slide 2 of 2)

Mixed cost behavior is expressed mathematically in the mixed cost formula as follows:

Total Mixed Cost = (Variable Rate × Units Produced) + Fixed Cost

Many mixed costs vary with operating activity in a nonlinear fashion.–To simplify cost analysis procedures and make mixed costs easier to use, managers and accountants use linear approximation to convert nonlinear costs into linear ones.


Mixed Costs and the Contribution Margin Income Statement

For cost planning and control, mixed costs must be divided into their variable and fixed components. – The separate components are then grouped with

other variable and fixed costs for analysis.– Four methods are commonly used to separate mixed

cost components: Scatter diagram method High-low method Statistical methods Engineering method

– Managers usually use multiple approaches to find the best possible estimate for a mixed cost.


The Scatter Diagram Method

A scatter diagram is a chart of plotted points that helps determine whether a linear relationship exists between a cost item and its related activity measure. It is a form of linear approximation.


The High-Low Method(slide 1 of 2)

The high-low method is another approach to determining the variable and fixed components of a mixed cost, which is based on the premise that only two data points are necessary to define a linear cost-volume relationship. This method has three steps, as described below for electricity costs and machine hours.– Step 1: Find the variable rate.

Select the periods of highest and lowest activity within the accounting period.

Find the difference between the highest and lowest amounts for both the machine hours and their related electricity costs.

Compute the variable cost per machine hour by dividing the difference in cost by the difference in machine hours.


The High-Low Method(slide 2 of 2)

– Step 2: Find the total fixed costs. Compute total fixed costs for a month by putting

the known variable rate and the information from the month with the highest volume into the cost formula and solve for the total fixed costs.

You can check your answer by recalculating total fixed costs using the month with the lowest activity.

– Step 3: Express the cost formula to estimate the total costs within the relevant range.

Total Mixed Cost = (Variable Rate × Volume Level) + Fixed Costs

Remember that the cost formula will work only within the relevant range.


Statistical Methods

Statistical methods, such as regression analysis, mathematically describe the relationship between costs and activities and are used to separate mixed costs into variable and fixed components.– Because all data observations are used, the resulting

linear equation is more representative of cost behavior than either the high-low or scatter diagram methods.

– Regression analysis can be performed using one or more activities to predict costs.

For example, overhead costs can be predicted using only machine hours (a simple regression analysis) or using both machine hours and labor hours (a multiple regression analysis).


The Engineering Method

The engineering method separates costs by performing a step-by-step analysis (sometimes called a time and motion study) of the tasks, costs, and processes involved. – This method is expensive because it is so

detailed.– It is generally used to estimate the cost of

activities or new products.


Contribution Margin Income Statements

Once an organization’s costs are classified as either variable or fixed, the traditional income statement can be reorganized into a more useful format for internal operations.– A contribution margin income statement (or

variable costing income statement) emphasizes cost behavior rather than organizational function.

– Contribution margin (CM) is the amount that remains after all variable costs are subtracted from sales.


Cost-Volume-Profit Analysis

Cost-volume-profit (CVP) analysis is an examination of the relationships among cost, volume of output, and profit.– It usually applies to a single product, product

line, or division of a company.– In the context of CVP analysis, profit and

operating income mean the same thing.

– The CVP equation is expressed as:Sales Revenue − Variable Costs − Fixed Costs = Profit OR (Sales Price × Units Sold) − (Variable Rate × Units Sold) −

Fixed Costs = Profit


Breakeven Analysis

The breakeven point is the point at which total revenues equal total costs. It is thus the point at which an organization can begin to earn a profit.– The margin of safety is the number of sales units

or amount of sales dollars by which actual sales can fall below planned sales without resulting in a loss.

– The general equation for finding the breakeven point is expressed as:

Breakeven Point = Sales − Variable Costs − Fixed Costs

or as: (Sales Price × Units Sold) − (Variable Rate × Units Sold) − Fixed

Costs = Profit


Using an Equation to Determine the Breakeven Point

A simpler method of determining the breakeven point uses contribution margin in an equation.– Contribution margin is the amount that remains after all

variable costs are subtracted from sales:

Sales − Variable Costs = Contribution Margin - Profit is what remains after fixed costs are paid and

subtracted from the contribution margin:Contribution margin − Fixed Costs = Profit

- The breakeven point (BE) can be expressed as the point at which contribution margin minus total fixed costs equals zero.

In terms of units of product, the equation for the breakeven point looks like this:

(Contribution Margin per Unit × Breakeven Point Units) − Fixed Costs = $0


Breakeven in Sales Units

It can also be expressed like this:Breakeven Point Units = Fixed Costs_______

Contribution Margin per Unit

The breakeven point in total sales dollars may be determined as follows:

Breakeven Point Dollars = Selling Price × Breakeven Point Units An alternative way of determining the breakeven point in

total sales dollars is to divide the fixed costs by the contribution margin ratio. The contribution margin ratio is the contribution margin divided by the selling price:

Contribution Margin Ratio = Contribution Margin Selling Price

Breakeven Point Dollars = Fixed Costs______

Contribution Margin Ratio


The Breakeven Point for Multiple Products(slide 1 of 2)

Most companies sell a variety of products or services that often have different variable and fixed costs and different selling prices.

To calculate the breakeven point for each product, its unit contribution margin must be weighted by the sales mix.– The sales mix is the proportion of each product’s

unit sales relative to the company’s total unit sales. If a website company sells 500 units, of which 300 units

are standard and 200 are express, the sales mix would be 3:2.


The Breakeven Point for Multiple Products(slide 2 of 2)

To compute the breakeven point for multiple products, follow these steps:– Step 1: Compute the weighted-average contribution margin.

Multiply the contribution margin for each product by its percentage of the sales mix.

– Step 2: Calculate the weighted-average breakeven point. Divide total fixed costs by the weighted-average contribution

margin.

– Step 3: Calculate the breakeven point for each product. Multiply the weighted-average breakeven point by each

product’s percentage of the sales mix.

– Step 4: Verify the results. Determine the contribution margin of each product, total the

contribution margins, and then subtract the total fixed costs. The result should be zero.


Using CVP Analysis to Plan Future Sales, Costs, and Profits

For planning, managers can use CVP analysis to calculate net income when sales volume is known, or they can determine the level of sales needed to reach a targeted amount of net income.

CVP analysis is also a way of measuring how well an organization’s departments are performing.

Managers can also use CVP analysis to measure the effects of alternative courses of action, such as changing variable or fixed costs, expanding or contracting sales volume, and increasing or decreasing selling prices.


Assumptions Underlying CVP Analysis

CVP analysis is useful only when the following assumptions hold true:– The behavior of variable and fixed costs can be

measured accurately.– Costs and revenues have a close linear

approximation throughout the relevant range.– Efficiency and productivity hold steady within the

relevant range of activity.– Cost and price variables also hold steady.– The sales mix does not change during the period.– Production and sales volume are roughly equal.


Applying CVP to Target Profits

CVP analysis adjusted for targeted profit can be used to estimate the profitability of a venture.

This approach is excellent for “what-if” analysis, in which managers select several scenarios and compute the profit that may be anticipated from each.


Equation Approach

Using the equation approach, add the targeted profit to the numerator of the contribution margin breakeven equation and solve for targeted sales in units.


CVP and the Management Process

Besides using CVP analysis for planning and evaluating, it can be a useful tool in the performing and communicating stages of the management process: Plan Perform Evaluate Communicate


needles powers crosson principles of accounting 12e cost-volume-profit analysis 21 c h a p t e r...

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