Chapter 5Cost Behavior and Cost-Volume-Profit Analysis
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Conceptual Learning ObjectivesC1: Describe different types of
cost behavior in relation to production and sales volume.C2:
Identify assumptions in cost-volume profit analysis and explain
their impact.C3: Describe several applications of
cost-volume-profit analysis.
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Analytical Learning ObjectivesA1: Compare the scatter diagram,
high-low, and regression methods of estimating costs.A2: Compute
contribution margin and describe what it reveals about a companys
cost structure.A3: Analyze changes in sales using the degree of
operating leverage.
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Procedural Learning ObjectivesP1: Determine cost estimates using
three different methods. P2: Compute the break-even point for a
single product company. P3: Graph costs and sales for a single
product company.P4: Compute break-even point for a multiproduct
company.
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Questions Addressed byCost-Volume-Profit Analysis CVP analysis
is used to answer questions such as:What sales volume is needed to
earn a target income?What is the change in income if selling prices
decline and sales volume increases?How much does income increase if
we install a new machine to reduce labor costs?What is the income
effect if we change the sales mix of our products or
services?C2
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Total Fixed CostNumber of Local CallsMonthly Basic Telephone
BillTotal fixed costs remain unchanged when activity changes.Your
monthly basic telephone bill probably does not change when you make
more local calls.C1
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Fixed Cost Per UnitFixed costs per unit decline as activity
increases.Number of Local Calls Monthly Basic Telephone Bill per
Local CallYour average cost per local call decreases as more local
calls are made.C1
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Total Variable CostMinutes TalkedTotal Long Distance Telephone
BillTotal variable costs change when activity changes.Your total
long distance telephone bill is based on how many minutes you
talk.C1
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Variable Cost Per Unit Variable costs per unit do not change as
activity increases. Minutes TalkedPer Minute Telephone ChargeThe
cost per long distance minute talked is constant. For example, 7
cents per minute.C1
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Cost Behavior SummaryC1
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Mixed Costs Mixed costs contain a fixed portion that is incurred
even when the facility is unused, and a variable portion that
increases with usage. Example: monthly electric utility chargeFixed
service feeVariable charge per kilowatt hour used C1
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Step-Wise CostsActivityCostTotal cost remains constant within a
narrow range of activity.C1
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Identifying and MeasuringCost Behavior P1
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Vertical distance is the change in cost.Horizontal distance is
the change in activity.P1Scatter Diagram
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The High-Low MethodThe following relationships between units
produced and costs are observed:
Using these two levels of activity, compute: the variable cost
per unit. the total fixed cost. P1
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P1The High-Low Method
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Least-Squares RegressionThe objective of the cost analysis
remains the same: determination of total fixed cost and the
variable unit cost.Least-squares regression is usually covered in
advanced cost accounting courses. It is commonly used with
spreadsheet programs or calculators.P1
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Computing Break-Even PointThe break-even point (expressed in
units of product or dollars of sales) is the sales level at which a
company earns neither a profit nor incurs a loss. P2
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Computing Break-Even PointContribution margin is amount by which
revenue exceeds the variable costs of producing the revenue.P2
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How much contribution margin must this company have to cover its
fixed costs (break even)?
Answer: $24,000
P2Computing Break-Even Point
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How many units must this company sell to cover its fixed costs
(break even)?
Answer: $24,000 $30 per unit = 800 unitsP2Computing Break-Even
Point
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Computing Break-Even PointWe have just seen one of the basic CVP
relationships the break-even computation.Unit sales price less unit
variable cost ($30 in previous example)P2
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The break-even formula may also be expressed in sales dollars.
Unit contribution margin Unit sales priceP2Computing Break-Even
Point
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Preparing a CVP ChartVolume in UnitsCosts and Revenue in
DollarsTotal fixed costs Plot total fixed costs on the vertical
axis.P3
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Preparing a CVP ChartSalesVolume in UnitsCosts and Revenue in
Dollars Starting at the origin, draw the sales line with a slope
equal to the unit sales price.Break-even PointTotal costsTotal
fixed costsP3
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Assumptions of CVP Analysis A limited range of activity called
the relevant range, where CVP relationships are linear. Unit
selling price remains constant.Unit variable costs remain
constant.Total fixed costs remain constant. Production = sales (no
inventory changes). C2
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Computing Income from Expected SalesIncome (pretax) = Sales
Variable costs Fixed costsC3
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Computing Sales for a Target Income Break-even formulas may be
adjusted to show the sales volume needed to earn any amount of
income. Unit sales = Fixed costs + Target incomeContribution margin
per unit Dollar sales = Fixed costs + Target incomeContribution
margin ratioC3
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Computing Sales (Dollars) for aTarget Net IncomeTarget net
income is income after income tax. But we can use target income
before tax in our calculations.Dollar sales = Fixed Target income
costs before tax Contribution margin ratio+C3
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Computing Sales (Dollars) for aTarget Net IncomeTo convert
target net income to before-tax income, use the following
formula:Before-tax income = Target net income1 - tax rateC3
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Computing the Margin of Safety Margin of safety is the amount by
which sales can drop before the company incurs a loss. Margin of
safety may be expressed as a percentage of expected sales.C3
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Sensitivity Analysis The basic CVP relationships may be used to
analyze a number of situations such as changing sales price,
changing variable cost, or changing fixed cost.
C3
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Computing MultiproductBreak-Even Point The CVP formulas may be
modified for use when a company sells more than one product. The
unit contribution margin is replaced with the contribution margin
for a composite unit.A composite unit is composed of specific
numbers of each product in proportion to the product sales
mix.Sales mix is the ratio of the volumes of the various
products.P4
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Computing MultiproductBreak-Even PointThe resulting break-even
formula for composite unit sales is:Break-even point in composite
unitsFixed costs Contribution margin per composite unit=P4
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Operating LeverageA measure of the extent to which fixed costs
are being used in an organization.A measure of how a percentage
change in sales will affect profits.A3
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End of Chapter 5
In presentations for each chapter in this text, we will provide
you with sound to go along with the material on your screen. There
will be sound on every slide you view. Please make sure your
computer speakers are setup properly when viewing the material.
Good luck and we hope you enjoy this new format.
This chapter shows how information on both costs and sales
behavior is useful to managers in performing cost-volume-profit
analysis. This analysis is an important part of successful
management and sound business decisions.
In this chapter, you will learn the following conceptual
objectives:C1: Describe different types of cost behavior in
relation to production and sales volume.C2: Identify assumptions in
cost-volume profit analysis and explain their impact.C3: Describe
several applications of cost-volume-profit analysis.
In this chapter, you will learn the following analytical
objectives:A1: Compare the scatter diagram, high-low, and
regression methods of estimating costs.A2: Compute contribution
margin and describe what it reveals about a companys cost
structure.A3: Analyze changes in sales using the degree of
operating leverage.
In this chapter, you will learn the following procedural
objectives:P1: Determine cost estimates using three different
methods.P2: Compute the break-even point for a single product
company. P3: Graph costs and sales for a single product company.P4:
Compute break-even point for a multiproduct company.
Cost-volume-profit analysis will allow us to answer many
questions and make important decisions involving the relationships
between the volume of activity and costs and revenues. Before we
can answer these questions using cost-volume-profit analysis, we
must first study cost behavior. We begin our study of cost behavior
with fixed costs. Your basic land-line telephone has a monthly
connect charge that remains constant regardless of the number of
local calls that you might make. The monthly charge that is
independent of call activity is a fixed cost..
Fixed costs per unit decline as activity increases. Dividing
your monthly connect fee by more local calls reduces the cost per
call by spreading the fixed amount over a higher number of calls.
For example, if your monthly connect charge is twenty dollars and
you make forty local calls in a month, your cost per local call is
fifty cents. If you make one hundred local calls in a month, your
cost per local call is twenty cents. Total variable costs increase
as activity increases. For most people, the total land-line long
distance telephone bill is based on the number of minutes talked.
So theres a direct relationship between the number of minutes
talked and your total bill. You can see a graph of that
relationship in the lower left-hand part of your screen.
The cost per land-line long distance minute talked is normally
constant. For example, for your service, it may be seven cents per
minute. Talking more or less minutes will not change the per minute
charge. So, on a per unit basis, variable costs remain unchanged.
You can see the graph of that in the lower right-hand side of your
screen.
We know that some of the language we use to differentiate fixed
and variable costs in total and per unit can be very confusing when
you first see it. So weve prepared this chart to help you identify
how those costs behave.
Many costs are mixed in nature. That is, they have both a fixed
and variable component. Think about your utility bill. You have a
fixed monthly charge for the hook-up, and the variable portion of
your bill depends upon the number of kilowatt hours you consume.
The more the kilowatt hours you use, the higher your total utility
bill will be. Another type of cost is referred to as a step cost.
Step costs remain constant in total within a relatively narrow
range of activity.When presented with a mixed cost, we will
separate the variable portion of the cost from the fixed portion of
the cost. There are number of ways to do this. We will use a
scatter diagram and the high-low method. A more sophisticated
method, the least squares regression model, is also available, but
we will not use it here. A scatter diagram is a plot of cost data
points on a graph. It is almost always helpful to plot cost data to
be able to observe a visual picture of the relationship between
cost and activity. We begin by plotting the data points on our
graph. The vertical axis is cost and the horizontal axis is
activity. Next, we draw a straight line through the data points
with about an equal number of observations above and below the
line. We continue the line past the observed points until it
intersects with the vertical axis. The intercept in this case is
our fixed cost, which is estimated to be ten thousand dollars.Next,
we determine the slope of the line. The slope of the line is the
change in cost divided by the change in activity. The slope, the
amount of change in cost for a one unit change in activity, is the
variable cost per unit of activity.
Now lets look at the high-low method. In our example, were going
to look at a companys relationship between cost and sales activity.
During the year, the company reports sales and costs on a monthly
basis. The month with the high level of sales shows sales of sixty
seven thousand five hundred dollars and a corresponding cost of
$29,000, and the month with the low level of sales show sales of
$17,500 with a corresponding cost of $20,500. We will use this
information to compute the variable cost per dollar of sales and
the total fixed cost.To determine the variable costs per unit of
activity, we divide the change in cost by the change in activity,
sales dollars in this example. In our case, the change in cost is
$8,500 and the change in sales dollars is $50,000. The result is a
variable cost rate of $0.17 per dollar of sales.Next, we calculate
the fixed cost by subtracting the total variable cost from the
total cost. Since total cost and total variable cost are different
amounts at different sales levels, we must choose either the high
level or the low level for our computations.Lets choose the high
level of activity, sixty seven thousand five hundred dollars in
sales. Our first step is to calculate the total variable cost. At
sixty seven thousand, five hundred dollars of sales, the total
variable cost is point one seven per dollar of sales times sixty
seven thousand, five hundred dollars, resulting in a total variable
cost of eleven thousand, four hundred seventy five dollars. Next,
we subtract eleven thousand, four hundred seventy-five dollars from
the total cost at the high sales activity, to get the fixed cost,
seventeen thousand, five hundred twenty-five dollars. You will
obtain the same result if you select the low level of activity to
compute fixed cost. Why dont you compute fixed cost using the low
level of sales activity before advancing to the next screen. You
should wind up with the exact same result.
If we have a large number of observations, well probably want to
use computer software that can do regression analysis to determine
cost volume relationships. Excel is a wonderful tool to carry out
this computation. You can review the chapters appendix if this of
interest to you.Now that we have improved our knowledge of cost
behavior, we are ready to apply the concepts to break-even
analysis. The break-even point is the level of sales where a
companys income is exactly equal to zero. At breakeven, total costs
equal total revenues.Were going to concentrate exclusively on the
contribution format income statement for our break-even analysis.
Contribution margin is the amount remaining after we deduct all our
variable expenses from sales revenue. Contribution margin can be
expressed as a total amount, sixty thousand dollars in this
example, or as an amount per unit, thirty dollars in this example.
Each unit sold contributes twenty dollars toward covering fixed
costs and providing for profits. Part IContribution margin goes to
cover our fixed costs. If all our fixed costs are covered, the
company will operate in the profit area. If we fail to cover our
fixed expenses, we will operate in the loss area. How much
contribution must this company have to cover its fixed costs?Part
IIFixed costs are twenty-four thousand dollars, so this company
must generate twenty-four thousand dollars in contribution margin
to cover its fixed costs. When contribution margin is exactly
twenty-four thousand dollars, the companys sales are at breakeven
as its income will be zero.
Part IThis company is earning thirty-six thousand dollars income
by selling two thousand units. The breakeven point will obviously
occur at a sales volume less than two thousand units. If each unit
contributes thirty dollars to covering fixed costs, can you compute
the number of units that must be sold to cover the twenty four
thousand dollars in fixed costs and allow the company to
breakeven?
Part IIWe compute the break-even sales volume in units by
dividing fixed costs by the unit contribution margin. The results
of the previous question can be expressed in equation form as seen
on your screen. The break-even point in units is equal to fixed
costs divided by the unit contribution margin.The break-even point
in sales dollars is equal to fixed costs divided by the
contribution margin ratio. The contribution margin ratio is equal
to the the unit contribution divided by the unit sales price. In
the earlier example, the contribution margin ratio is thirty
percent, resulting from dividing the thirty dollars unit
contribution margin by the one hundred dollars unit sales price.
You might want to refer back to the example to verify these
numbers. The contribution margin ratio tells us that thirty cents
of each sales dollar contributes to covering fixed costs and
providing for income.The relationships between cost, volume and
profit can also be shown in a graph. In this graph, we have plotted
costs and revenues on the vertical axis and volume in units on the
horizontal axis. The total cost line has a slope equal to the
variable cost per unit and intercepts the vertical cost axis at the
fixed cost.
When we add the sales line to our graph, we see the break even
point where the sales line crosses the total cost line. The sales
line begins at the origin and has a slope equal to the unit sales
price. The sales line is steeper, that is increases at a faster
rate than the total cost line, because because the unit sales price
is greater than the unit variable cost.
There are some basic assumptions related to cost volume profit
analysis that we are studying in this chapter. Some of these
assumptions may be very restrictive. First, costs and revenues are
assumed to be linear in nature, meaning that the selling price is
assumed to be constant, the unit variable cost is assumed to be
constant, and total fixed costs are assumed to be constant. Also,
for manufacturing companies, inventories dont increase or decrease
during the period. All units produced, are sold.
We have seen what it takes for a company to breakeven, but we
are not in business just to breakeven. Hopefully our business will
earn an income. The break-even relationships that we have studied
can be slightly altered to include income. We can adjust the
break-even formulas that we used earlier to incorporate income.
Recall that we calculated breakeven by dividing fixed costs by
contribution. When we incorporate income, contribution must cover
the fixed cost as well as provide for income. To adapt the
break-even formulas for income, we add the desired amount of income
to the numerator.
Our previous formulas allowed us to solve for sales necessary to
earn a target income used pretax income. Pretax income which has
two components, net income (after tax) and the income taxes paid on
the pretax income are shown on your screen. If our target income is
stated as after-tax net income, we can covert to pretax income by
dividing the target after-tax net income by one minus the tax rate.
The margin of safety is the excess of expected sales (or actual
sales) over the breakeven sales. Its the amount by which expected
sales can drop before the company begins to incur losses. We can
also express the margin of safety as a percent of sales. The margin
of safety percentage is equal to the margin of safety in dollars
divided by the expected sales in dollars.Our basic assumptions
related to cost volume profit analysis such as the selling price is
assumed to be constant, the unit variable cost is assumed to be
constant, and total fixed costs are assumed to be constant, can be
restrictive. To this point, weve assumed that a company sells a
single product. We can extend the cost-volume-profit relationships
to cover multiproduct companies. Instead of unit contribution
margin for one unit, we will have a composite unit contribution for
all units. The composite unit contribution margin is dependent on
the sales mix of the products sold.
.
Note that the break-even formula looks the same for a
multiproduct company. The only difference is the denominator. The
unit contribution margin for one unit is replaced by a composite
unit contribution for all units. A composite unit is composed of
specific numbers of each product in proportion to the product sales
mix. Operating leverage is an important concept for managers to
understand. Its a measure of how sensitive operating income is to
changes in sales. When operating leverage is high, a small
percentage increase in sales can result in a much larger percentage
increase in operating income. The degree of operating leverage is
equal to contribution margin divided by net income. These cost,
volume, profit analyses are some of the basic concepts and
principles of managerial accounting. They are important ones for
you to understand.
