Download Fixed Costs

CHAPTER
19
Cost-Volume-Profit Analysis
Financial and
Managerial
Accounting
10e
Needles
Powers
Crosson
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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).
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Variable Costs
(slide 2 of 3)
 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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Variable Costs
(slide 3 of 3)
– 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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Fixed Costs
(slide 2 of 2)
 Fixed costs change when activity exceeds the
relevant range.
– These costs are called step costs or step-variable, stepfixed, 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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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).
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.