Cost-Volume-Profit Analysis

Chapter 22

Objective 1Identify how changes in volume affect

costs.

Variable

Fixed

Mixed

Types of Costs

Minutes Talked

To

tal L

on

g D

ista

nce

Tel

eph

on

e B

illTotal variable costs change

when activity changes.

Your total long distancetelephone bill is basedon how many minutes

you talk.

Total Variable Cost

Minutes Talked

Per

Min

ute

Tel

eph

on

e C

har

ge

Variable Cost Per Unit

Variable costs per unit do not changeas activity increases.

The cost per long distance

minute talked is constant.

For example, 10cents per minute.

Variable Costs ExampleConsider Grand Canyon Railway.Assume that breakfast costs Grand Canyon

Railway $3 per person.If the railroad carries 2,000 passengers, it

will spend $6,000 for breakfast services.

Variable Costs Example

0 1 2 3 4 5

$24 –

$18 –

$12 –

$6 –

– – ––

Volume(Thousands of passengers)

Tot

al V

aria

ble

C

osts

(th

ousa

nd

s)

Number of Local Calls

Mo

nth

ly B

asic

T

elep

ho

ne

Bill

Total fixed costs remain unchangedwhen activity changes.

Your monthly basic

telephone bill probably

does not change when

you make more local calls.

Total Fixed Cost

Mixed CostsContain fixed portion that is incurred even

when facility is unused & variable portion that increases with usage.

Example: monthly electric utility chargeFixed service feeVariable charge per kilowatt hour used

Total mixed cost

Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

st

Fixed Monthly

Utility Charge

Mixed Costs

Relevant Range...…is a band of volume in which a specific

relationship exists between cost and volume.

Outside the relevant range, the cost either increases or decreases.

A fixed cost is fixed only within a given relevant range and a given time span.

Relevant Range

Fix

ed

Cos

ts

Volume in Units

$160,000 –

$120,000 –

$80,000 –

$40,000

0 5,000 10,000 15,000 20,000 25,000

– – –

Relevant Range

Objective 2Use CVP analysis to compute breakeven

point.

Assumptions of CVP AnalysisExpenses can be classified as either

variable or fixed.CVP relationships are linear over a wide

range of production and sales.Sales prices, unit variable cost, and total

fixed expenses will not vary within the relevant range.

Assumptions of CVP AnalysisVolume is the only cost driver.The relevant range of volume is specified.Inventory levels will be unchanged.The sales mix remains unchanged during

the period.

Contribution Margin Income Statement

Sales- Variable Costs

Contribution Margin- Fixed Costs

Operating Income

Contribution Margin ExampleLuis and Tom manufacture a device that

allows users to take a closer look at icebergs from a ship.

The usual price for the device is $100.Variable costs are $70 per unit.They receive a proposal from a company in

Newfoundland to sell 20,000 units at a price of $85.

Contribution Margin ExampleThere is sufficient capacity to produce the

order.How do we analyze this situation?$85 – $70 = $15 contribution margin.$15 × 20,000 units = $300,000 (total

increase in contribution margin)

Contribution Margin Income StatementSales (20,000 x $85)

$1,700,000Variable costs (20,000 x $70)

(1,400,000)Contribution margin

$300,000

Computing Break-Even Point

The unique sales level at which a company earns neither a profit nor incurs a loss.

Sales – Variable Costs – Fixed Costs = 0

Breakeven Point Example

Let’s look back at Luis and Tom’s manufacturing, assuming that the fixed

cost are $90,000.

Objective 3Use CVP analysis for profit planning and

graph the cost-volume-profit relations

Volume in Units

Co

sts

and

Rev

enu

ein

Do

llar

s Total fixed costs

Plot total fixed costs on the vertical axis.

Preparing a CVP Chart

Total costs

Draw the total cost line with a slopeequal to the unit variable cost.

Volume in Units

Co

sts

and

Rev

enu

ein

Do

llar

s Total fixed costs

Preparing a CVP Chart

Total costs

SalesStarting at the origin, draw the sales line with a slope equal to the unit sales price.

Break-even Point

Various Sales Levels Example

What operating income is expected when sales are _____ units?

Target Operating Income ExampleSuppose that our business would be

content with operating income of _________________.

How many units must be sold?

Objective 4Use CVP method to perform sensitivity

analysis.

Change in Sales Price ExampleSuppose that the sales price per device is

_____ rather than ____What is the revised breakeven sales in

units?

Change in Variable Costs ExampleSuppose that variable expenses per device

are ____ instead of ____Other factors remain unchanged.

Change in Fixed Costs ExampleSuppose that fixed costs increased by

$30,000.What are the new fixed costs?What is the new breakeven point?

Margin of Safety ExampleExcess of expected sales over breakeven

sales.

E22-7

Atlanta Braves

$-$1,000$2,000$3,000$4,000$5,000$6,000$7,000

- 50 100 150 200 250

(in thousands)

(in

th

ou

sa

nd

s)

Revenues

Total Expense

Fixed expenseBreak even point

Profit

Loss

Break even in units = 1,200,000Break even in $ = 1,200,000 x 24 = $28,800,000

Effect of sales mix on CVP analysis.

Computing MultiproductBreak-Even PointUnit contribution margin is replaced with

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.

Computing MultiproductBreak-Even Point

The resulting break-even formulafor composite unit sales is:

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Windows Doors

Selling Price $200 $500 Variable Cost 125 350 Unit Contribution 75$ 150$ Sales Mix Ratio 4 1

Computing MultiproductBreak-Even Point A company sells windows and doors.

They sell 4 windows for every door.

Step 1: Compute contribution margin per composite unit.

Computing MultiproductBreak-Even Point

Windows Doors Selling Price $200 $500 Variable Cost 125 350 Unit Contribution 75$ 150$ Sales Mix Ratio Composite C/M

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Step 2: Compute break-even point in composite units.

Computing MultiproductBreak-Even Point

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Break-even pointin composite units

$900,000

$450 per composite unit

=

Step 2: Compute break-even point in composite units.

Computing MultiproductBreak-Even Point

Break-even pointin composite units

= 2,000 composite units

Sales CompositeProduct Mix Units UnitsWindow 4 × 2,000 = 8,000

Door 1 × 2,000 = 2,000

Step 3: Determine the number of windows and doors that must be sold to break even.

Computing MultiproductBreak-Even Point

Windows Doors Combined

Selling Price $200 $500 Variable Cost 125.00 350.00 Unit Contribution 75.00$ 150.00$ Sales Volume × 8,000 × 2,000 Total Contribution 600,000$ 300,000$ 900,000$

Fixed Costs 900,000 Income $ 0

Step 4: Verify the results.

Multiproduct Break-EvenIncome Statement