CHAPTER 5 COST – VOLUME - PROFIT Study Objectives Distinguish between variable and fixed costs. Explain the significance of the relevant range. Explain

CHAPTER 5

COST – VOLUME - PROFIT

Study Objectives

Distinguish between variable and fixed costs.

Explain the significance of the relevant range.

Explain the concept of mixed costs.

List the five components of cost-volume-profit analysis.

Indicate what contribution margin is and how it can be expressed.

Study Objectives: Continued

Identify the three ways to determine the break-even point.

Give the formulas for determining sales required to earn target net income.

Define margin of safety, and give the formulas for computing it.

COST BEHAVIOR ANALYSIS

Definition: The study of how specific costs respond to changes in the level of business activity

Some costs change; others remain the same

Helps management plan operations and make decisions

Applies to all types of businesses and entities

COST BEHAVIOR ANALYSISContinued

Starting point is measuring key business activities

Activity levels may be expressed in terms of Sales dollars (in a retail company)

Miles driven (in a trucking company)

Room occupancy (in a hotel) Dance classes taught (by a dance studio)

COST BEHAVIOR ANALYSIS Continued

Many companies use more than one measurement base

For an activity level to be useful:

Changes in the level or volume of activity should be correlated with changes in cost

COST BEHAVIOR ANALYSISContinued

The activity level selected is called the activity (or volume) index

Identifies the activity that causes changes in the behavior of costs

Allows costs to be classified according to their response to changes in activity as:

Variable Costs

Fixed Costs

Mixed Costs

COST BEHAVIOR ANALYSISVARIABLE COSTS

Study Objective 1

Costs that vary in total directly and proportionately with changes in the activity level

If the activity level increases 10 percent, total variable costs increase 10 percent

If the activity level decreases by 25 percent, total

variable costs will decrease by 25 percent

COST BEHAVIOR ANALYSISVARIABLE COSTS - Continued

Variable costs also remain constant per unit at every level of activity

Examples of variable costs include Direct material and direct labor for a manufacturer Sales commissions for a merchandiser Gasoline in airlines and trucking companies

COST BEHAVIOR ANALYSISVARIABLE COSTS - Continued

Example

Damon Company manufactures radios that contain a $10 clock

Activity index is the number of radios produced

For each radio produced, the total cost of the clocks increases by $10

If 2,000 radios are made, the total cost of the clocks is $20,000 (2,000 X $10)

If 10,000 radios are made, the total cost of the clocks is $100,000 (10,000 X $10)

COST BEHAVIOR ANALYSIS VARIABLE COSTS - Continued

Example: Continued

COST BEHAVIOR ANALYSISFIXED COSTS

Costs that remain the same in total regardless of changes in the activity level.

Per unit cost varies inversely with activity:

As volume increases,

unit cost decline, and vice versa

Examples include Property taxes Insurance Rent Depreciation on buildings and equipment

COST BEHAVIOR ANALYSISFIXED COSTS - Continued

Example

Damon Company leases its productive facilities for $10,000 per month

Total fixed costs of the facilities remain constant at all levels of activity - $10,000 per month

On a per unit basis, the cost of rent decreases as activity increases and vice versa

At 2,000 radios, the unit cost is $5 ($10,000 ÷ 2,000 units)

At 10,000 radios, the unit cost is $1 ($10,000 ÷ 10,000 units)

COST BEHAVIOR ANALYSISFIXED COSTS - Continued

Example: Continued

COST BEHAVIOR ANALYSISRELEVANT RANGE

Study Objective 2

Throughout the range of possible levels of activity, a straight-line relationship usually does not exist for either variable costs or fixed costs

The relationship between variable costs and changes in activity level is often curvilinear

For fixed costs, the relationship is nonlinear – some fixed costs will not change over the entire range of activities, others may

COST BEHAVIOR ANALYSISRELEVANT RANGE - Continued

COST BEHAVIOR ANALYSISRELEVANT RANGE - Continued

Defined as the range of activity over which a company expects to operate during a year

Within this range, a straight-line relationship usually exists for both variable and fixed costs

COST BEHAVIOR ANALYSISMIXED COSTS

Study Objective 3

Costs that have both a variable cost element and a fixed cost element

Sometimes called semivariable cost

Change in total but not proportionately with changes inactivity level

COST BEHAVIOR ANALYSISMIXED COSTS – High-Low Method

Mixed costs must be classified into their fixed and variable elements

One approach to separate the costs is called the high-low method

Uses the total costs incurred at both the high and the low levels of activity to classify mixed costs

The difference in costs between the high and low levels represents variable costs, since only variable costs change as activity levels change

COST BEHAVIOR ANALYSISMIXED COSTS – High-Low Method - Continued

Steps in Method

STEP 1: Determine variable cost per unit using the following formula:

STEP 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 level

÷ =Change in Total Costs

High minus Low Activity Level

Variable Cost per Unit


ExampleData for Metro Transit Company

for the last 4-month period:

High Level of Activity: April $63,000 50,000 milesLow Level of Activity: January 30,000 20,000 miles

Difference $33,000 30,000 miles

Step 1: Using the formula, variable costs per unit are $33,000 30,000 = $1.10 variable cost per mile

MonthJanuaryFebruary

Miles Driven20,00040,000

Total Cost$30,000$48,000

MonthMarchApril

Miles Driven35,00050,000

Total Cost$49,000$63,000


Example: ContinuedStep 2: Subtract total variable costs at either the high or low

activity level from the total cost at that same level

Total CostLess: Variable costs (50,000 x $1.10) (20,000 x $1.10)Total fixed costs

High $63,000

55,000

$ 8,000

Low $30,000

22,000

$ 8,000

Activity Level


Example: Continued

Maintenance costs: $8,000 per month plus $1.10 per mile

To determine maintenance costs at a particular activity level:multiply the activity level times the variable cost per unitthen add that total to the fixed cost

EXAMPLE: If the activity level is 45,000 miles, the estimated maintenance costs would be $8,000 fixed and $49,500 variable ($1.10 X 45,000 miles) for a total of $57,500.

COST-VOLUME-PROFIT ANALYSIS

Study Objective 4

Study of the effects of changes of costs and volume on a company’s profits

A critical factor in management decisions Important in profit planning

COST-VOLUME-PROFIT ANALYSIS

Considers the interrelationships among the five components of CVP analysis:

ASSUMPTIONS UNDERLYINGCVP ANALYSIS

Behavior of both costs and revenues is linear throughout the relevant range of the activity index

All costs can be classified as either variable or fixed with reasonable accuracy

Changes in activity are the only factors that affect costs

All units produced are sold

When more than one type of product is sold, the sales mix will remain constant

CVP INCOME STATEMENTStudy Objective 5

A statement for internal use

Classifies costs and expenses as fixed or variable

Reports contribution margin in the body of the statement.

Contribution margin –amount of revenue

remaining afterdeducting variable costs

Reports the same netincome as a traditionalincome statement

CVP INCOME STATEMENTExample

Vargo Video Company produces DVD players. Relevant data for June 2005:

Unit selling price of DVD player $500Unit variable costs $300Total monthly fixed costs $200,000Units sold

1,600

CVP INCOME STATEMENT Contribution Margin Per Unit

Contribution margin is available to cover fixed costs and to contribute to income

Formula for contribution margin per unit:

Example: Computation for Vargo Video

– =Unit Selling Price Unit Variable Costs

Contribution Margin per Unit

– =Unit Selling Price $500

Unit Variable Costs $300


$200

CVP INCOME STATEMENT Contribution Margin Ratio

Shows the percentage of each sales dollar available to apply toward fixed costs and profits

Example: Computation for Vargo Video

÷ = Contribution Margin Ratio

Unit Selling PriceContribution Margin per Unit

÷ =Contribution Margin Ratio

40%

Unit Selling Price

$500


S200

CVP INCOME STATEMENT Contribution Margin Ratio - Example

Ratio helps to determine the effect of changes in sales on net income

BREAK-EVEN ANALYSISStudy Objective 6

Process of finding the break-even point

Break-even point

Level of activity at which total revenues equal total costs (both fixed and variable)

Can be computed or derived

• from a mathematical equation

• by using contribution margin

• from a cost-volume-profit (CVP) graph

Expressed either in sales units or in sales dollars

BREAK-EVEN ANALYSIS Mathematical Equation

Variable Costs

$300 Q

Fixed Costs

$200,000

Net Income

$0

Sales$500 Q = + +

Example using the Vargo Video data:

Where: Q = sales volume; $500 = selling price; $300 = variable cost per unit; $200,000 total fixed costs

To find sales dollars required to break-even:1000 units X $500 = $500,000 (break-even sales dollars)

$200 Q $200,000

Q 1000 units

=

=

BREAK-EVEN ANALYSIS Contribution Margin Technique

At the break-even point, contribution margin must equal total fixed costs (CM = total revenues – variable costs)

The break-even point can be computed using either contribution margin per unit or contribution margin ratio

When the break even point in units is desired, contribution margin per unit is used in the following formula

When the break even point in dollars is desired, contribution margin ratio is used in the following formula

÷ =Fixed CostsBreak-even Point

in UnitsContribution

Margin per Unit

÷ =Fixed CostsBreak-even Point

in DollarsContribution Margin Ratio

BREAK-EVEN ANALYSIS Contribution Margin Technique

Example using Vargo Video data:

÷ =Fixed Costs

$200,000

Break-even Point in Units

1,000 units


$200

÷ =Fixed Costs

$200,000

Break-even Point in Dollars

$500,000


40%

BREAK-EVEN ANALYSISGraphic Presentation

A cost-volume-profit (CVP) graph shows costs, volume, and profits

Used to visually find the break-even point To construct a CVP graph,

Plot the total revenue linestarting at the zero activity level

Plot the total fixed costby a horizontal line

Plot the total cost line. (Starts at the fixed cost line at zero activity)

Determine the break-even point from the intersection of the total cost line and the total revenue line

BREAK-EVEN ANALYSIS CVP Graph for Vargo Video

BREAK-EVEN ANALYSIS Target Net Income

Study Objective 7

Level of sales necessary to achieve a specified income

Can be determined from each of the approaches used to determine break-even sales/units

May be expressed either in sales dollars or sales units

BREAK-EVEN ANALYSIS Target Net Income - Example

Using the Contribution Margin Approachand the Vargo Video Data:

Formula for required sales in units:

Formula for required sales in dollars

÷ =Contribution Margin Ratio

40%

Fixed Costs + Target Net Income

$200,000 + $120,000

Required Sales in Dollars

$800,000

÷ =Contribution

Margin Per Unit

$200

Fixed Costs + Target Net Income

$200,000 + $120,000

Required Sales in Units

1,600 units

BREAK-EVEN ANALYSIS Margin of Safety

Difference between actual or expected sales and sales at the break-even point

May be expressed in dollars or as a ratio

Example -

To determine the margin of safety in dollars for Vargo Video assuming that actual (expected) sales are $750,000:

– =Margin of Safety

in Dollars

$250,000

Break-even Sales

$500,000

Actual (Expected) Sales

S750,000

BREAK-EVEN ANALYSIS Margin of Safety Ratio

Study Objective 8

Computed by dividing the margin of safety in dollars by the actual or expected sales (using Vargo Video data)

Results indicate that Vargo Video’s sales could fall by 33 percent before it would be operating at a loss.

The higher the dollars or the percentage, the greater the margin of safety.

÷ =Margin of Safety

Ratio

33%

Actual (Expected) Sales

$750,000

Margin of Safety in Dollars

$250,000

Documents

CHAPTER 5 COST – VOLUME - PROFIT Study Objectives Distinguish between variable and fixed costs. Explain the significance of the relevant range. Explain