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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