Cost-Volume-Profit Relationships
Cost Behavior Analysis
1. Cost behavior analysis is the study of how specific costs respond to changes in the level
of activity within a company.
2. The starting point in cost behavior analysis is measuring the key activities in the
company’s business.
3. Activity levels may be expressed in terms of
 sales dollars (retail company),
 miles driven (trucking company),
 Room occupancy (hotel).
4. For an activity level to be useful in cost behavior analysis there should be correlation
between changes in the level or volume of activity and changes in the costs
Distinguish between variable and fixed costs.
Variable Costs
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Variable costs are costs that vary in total directly and proportionately with
changes in the activity level.
A variable cost may also be defined as a cost that remains the same per unit at
every level of activity.
Damon Company manufactures radios that contain a $10 digital clock. The
activity level is the number of radios produced. As each radio is manufactured,
the total cost of the clocks increases by $10.
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Fixed Costs
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Fixed costs are costs that remain the same in total regardless of changes in the
activity level.
Since fixed costs remain constant in total as activity changes, fixed costs per unit
vary inversely with activity. As volume increases, unit cost declines and vice
versa.
Damon Company leases all of its productive facilities at a cost of $10,000 per
month. Total fixed costs of the facilities will remain constant at every level of
activity.
Relevant range.
Nonlinear Behavior of Variable and Fixed Costs
In the previous two slides, the assumption was made that total variable costs and total
fixed costs were linear, and straight lines were used to represent both types of costs. A
straight-line relationship does not usually exist for variable costs throughout the entire
range of activity.
In the real world, the relationship between variable cost behavior and changes in the
activity level is often curvilinear, as shown in part (a) on the right. The behavior of total
fixed costs through all levels of activity is shown in part (b).
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Linear Behavior within Relevant Range
Operating at zero or at 100% capacity is the exception for most companies. Companies
usually operate over a narrower range – such as 40-80% of capacity. The relevant range
of the activity level is the range over which a company expects to operate during a year.
Within this range, as shown in both diagrams to the right, a straight-line relationship
normally exists for both fixed and variable costs.
Mixed Cost
Mixed costs contain both a variable cost element and a fixed cost element.
Sometimes called semi variable costs, mixed costs change in total but not proportionately with
changes in the activity level.
Behavior of a Mixed Cost
The rental of a truck is a good example of a mixed cost. Local rental terms for a truck are $50 per
day plus $.50 per mile. The per diem charge is a fixed cost with respect to miles driven, while
the mileage charge is a variable cost. The graphic presentation of the rental cost for a one-day
rental is shown on the right.
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Mixed Cost Classification for CVP Analysis
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In CVP analysis, it is assumed that mixed costs must be classified into their fixed and
variable elements.
The high-low method is a mathematical method that uses the total costs incurred at the
high and low levels of activity. The High-Low Method
The steps in calculating fixed and variable costs under this method are as follows:
1- Determine variable cost per unit from the following formula:
Change in Total Costs  High minus Low Activity Level = Variable Cost per Unit (b)
2- Determine the fixed cost by subtracting the total variable cost at either the high or the
low activity level from the total cost at that activity level(a=y – bx)
To illustrate, assume that Metro Transit Company has the following maintenance
costs and mileage data for its fleet of busses over a 4-month period
Month
January
February
march
April
Miles Driven (X)
20,000
40,000
35,000
50,000
Total Cost (Y)
$30,000
48,000
49,000
63,000
The high and low levels of activity are 50,000 miles in April and 20,000 miles in January. The
difference in maintenance costs at these levels is $33,000 ($63,000-$30,000) and the difference
in miles is 30,000 (50,000 - 20,000). Therefore, for Metro Transit, variable cost per unit is $1.10,
computed as follows:
Maintenance costs are therefore $8,000 per month plus $1.10 per mile. For example at 45,000
miles, estimated maintenance costs would be $49,500 variable (45,000 x $1.10), and $8,000
fixed.
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The high-low method generally produces a reasonable estimate for analysis. However, it does
not produce a precise measurement of the fixed and variable elements in a mixed cost because
other activity levels are ignored in the computation
Exercise:
Sara company accumulates the following data concerning a mixed cost,using units
produced as the activity level.
march
April
May
June
July
Unite produced
9,800
8,500
7,000
7,600
8,100
Total cost
$14,740
13,250
11,100
12,000
12,460
(a) Compute the variable and fixed cost element using the high-low method.
(b) Estimate the total cost if the company produced 6,000 units.
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Cost-Volume Profit Analysis
Cost-volume-profit (CVP) analysis is the study of the effects of changes of costs and
volume on a company’s profits.
CVP analysis involves a consideration of the interrelationships among the following
components :( five component of cost –volume-profit analysis)
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Volume or activity level (sales)
Unit selling price
Variable cost per unit
Total fixed costs
Sales mix
In CVP analysis applications, the term cost includes manufacturing costs plus selling and
administrative expenses. We will use Vargo Video Company as an example. Relevant
data for the VCRs made by this company are as follows:
Unit selling price
Unit variable costs
Total monthly fixed costs
$500
$300
$200,000
Meaning of contribution margin and the ways it may be expressed.One of
the key relationships in CVP analysis is contribution margin (CM). Contribution margin is
the amount of revenue remaining after deducting variable costs. The CM is then
available to cover fixed costs and to contribute income for the company.
1-Contribution margin per unit
Unit Selling price - unit Variable Costs = contribution margin per unit
$500 - $300 = $200
CM per unit indicates that for every (DVD player) VCR sold, Vargo Video will have $200
to cover fixed costs and contribute to income.
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2-Contribution margin
For example, assume that Vargo Video sells 1,000 VCRs in one month, sales are
$500,000 (1,000 x $500) and variable costs are $300,000 (1,000 x $300). Thus,
contribution margin is $200,000, computed as follows:
Sales - Variable Costs = contribution margin
$500,000 - $300,000 = $200,000
3-Contribution Margin Ratio
Others prefer to use a contribution margin ratio.
At Vargo Video, the contribution margin ratio is 40%.
Contribution Margin per Unit  Unit Selling Price= Contribution Margin Ratio
$200  $500=40%
The CM ratio means that 40 cents of each sales dollar ($1 x 40%) is available to apply to
fixed costs and to contribute to income
Break-Even Analysis:

The second key relationship in CVP analysis is the break-even point

Level of activity where total revenues equal total costs (both fixed and
variable).
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Since no income is involved when the break-even point is the objective, the
analysis is often referred to as break-even analysis.
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The break-even point can be:
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–
Computed from a mathematical equation.
–
Computed by using contribution margin.
–
Derived from a CVP graph.
The break-even point can be expressed in either sales dollars or sales units.
1- Mathematical Equation for unit:
The equation for break-even: (Break-even point net income is zero; break-even occurs
where total sales equal variable cost plus fixed cost.)
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Sales = Variable costs + Fixed costs
Computation of break-even point:
Where Q=Sales volume in unit, $500=selling price, $3000=variable cost per unit
$200,000=total fixed cost :
$500 Q = $300 Q +200,000
$200Q= $200,000
Q=1,000 unit
Vargo Video must sell 1,000 units to break even.
To find break even sales dollars (1,000*500=$500,000)
The accuracy of the previous computations can be proved as follows
2-CM Technique for Units:
Because we know that CM equals total revenues less variable costs, it follows that at the
break-even point, contribution margin must equal total fixed costs.
When the CM per unit is used, the formula to compute break-even point in units is
shown below: Once again, the CM per unit for Vargo Video is $200
Break-even point in unit:
When the CM ratio is used, the formula to compute break-even point in dollars is shown
below: Again, the CM ratio for Vargo Video is 40%.
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Break-even point in dollars:
Or
Break-even point in dollars = Break-even point in unit *selling price
1000
*
500
=$500,000
Margin of Safety:
The margin of safety is another relationship that may be calculated in CVP analysis.
Margin of safety is the difference between actual or expected sales and sales at the
break-even point.
The margin of safety may be expressed in dollars or as a ratio.
Assuming that actual (expected) sales for Vargo Video are $750,000, the
computations are:
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Target Net Income:
Determining sales required to earn target net income
Management usually sets an income objective for individual product lines. This
objective, called target net income, is extremely useful to management because
it indicates the sales necessary to achieve a specified level of income.
The amount of sales necessary to achieve target net income can be determined
from each of the approaches used in determining break-even sales.
1-Mathematical Equation
We know that at the break-even point no profit or loss results for the company.
By adding a factor for target net income to the break-even equation, we obtain
the formula shown below for determining required sales.
Required Sales
= Variable Costs + Fixed Costs + Target Net Income
Required sales may be expressed in either sales dollars or sales units.
Example:
Where Q=Sales volume in unit, $500=selling price, $3000=variable cost per unit
$200,000=total fixed cost .Assuming the target net income is $120,000 for Vargo Video,
the computation of required sales in unit is as follows:
Required Sales = Variable Costs +Fixed Costs +Target Net Income
$500Q = $300Q
+ $200,000 + $120,000
$200Q = $320,000
Q=1,600 unit
Required sales in dollars to achieve the target net income = 1,600*$500= $800,000
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2- CM Technique
As in the case of break-even sales, the sales required to meet a target net income can be
computed in either dollars or units.
Required Sales in unit = Fixed Costs +Target Net Income  contribution margin per unit
=
($200,000+$120,000)
 $200
= 1,600 units
This computation tells Vargo that to achieve its desired target net income of $120,000
it must sell 1,600 unit (or DvD players)
To compute Required Sales in dollars:
Required Sales in unit* selling price
1,600 units *500= $800,000
Or
Required Sales in dollars = Fixed Costs +Target Net Income  contribution margin Ratio
=
($200,000+$120,000)
 %40
= $800,000
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