cost behavior, operating leverage, & profitability analysis

Cost Behavior, Operating Leverage, & Profitability Analysis

Cost Behavior

• Manner in which a cost changes as a related activity changes.

• Classifications of Cost Behavior– Variable Costs– Fixed Costs– Mixed Costs

Cost Behavior

• Behavior is relative to the context it is presented in

• The term fixed or variable is based on the total cost.

Summer Vacation

• Let’s say you and 2 friends are going to Cabo for 4 nights.

• You are going to fly down there and stay in a hotel.

• The hotel charges $100 per night regardless of how many people stay in the room.

• TOTAL Expected Lodging Cost = $400

• Two days before you leave one more friend decides to come along.

• How does this affect your hotel bill?

• No change – total lodging is still $400

• This is a fixed cost – The total cost does not change.

• The day before you leave one friend gets sick and can’t go.

• What happens to your hotel bill now?

• No Change

• This is a fixed cost – The total cost does not change

How does all this affect you?

• Total Hotel Bill = $400• How much do you have to

pay?

Fixed Cost Behavior

# of People (a) 2 people 3 people 4 people

Total Lodging (b) $400 $400 $400

Lodging per person (b / a)

$200 $133 $100

What about the airfare?

• You were able to get plane tickets

for $200 roundtrip per person.

Variable Cost Behavior

# of tickets (a) 2 3 4

Total Airfare (a * b) $400 $600 $800

Cost per ticket (b) $200 $200 $200

• Under a variable cost structure the cost per unit stays the same and the total cost changes

• Using the Variable Cost Structure avoids Fixed Cost Risk

• Whether a cost is fixed or variable depends on the underlying circumstances.

• Let’s look back at our lodging for vacation.• What if we decide to stay 5 nights instead of 4?• What if we come home a day early?

# of Nights (a) 3 4 5

Total Lodging (a * b) $300 $400 $500

Cost per night (b) $100 $100 $100

• Here the lodging is a variable cost.

• The cost per night stays the same and the total cost changes.

# of Nights (a) 3 4 5

Total Lodging (a * b) $300 $400 $500

Cost per night (b) $100 $100 $100

Relevant Range

• What happens if three more friends decide to come along and you have a total of 6 people?

• You will more than likely have to rent 2 rooms each night.

• Now your total lodging is $200 per night.

• The structures work within a relevant range.

• Our range here is 1 to 4 people.

When the activity level increases, total fixed costs

1. Increases

2. Decreases

3. Remains constant

When the activity level increases, fixed cost per unit

1. Increases

2. Decreases

3. Remains constant

When the activity level increases, variable cost per unit

1. Increases

2. Decreases

3. Remains constant

When the activity level increases, total variable costs

1. Increases

2. Decreases

3. Remains constant

Mixed Cost

• Has characteristics of both a variable and a fixed cost.

• e.g. – Copy machine lease– Cost = $1,000 per month– Plus $1 for every copy over 2,000

Art on Tour, Inc. (AOTI)

• Art on Tour Inc. contracts with artists to exhibit their works to the public. AOTI has agreed to pay a well known artist a $20,000 commission for the right to exhibit his work for one month.

• We need to determine the total commission cost and the commission cost per person if 1,000 / 2,000 / 4,000 people attend the exhibition.

• Is this commission cost fixed or variable?

• Fixed – Total cost does not change

# of people (a) 1000 2000 4000

Total Commission (b)

$20,000 $20,000 $20,000

Commission per person (b / a)

$20 $10 $5

• AOTI provides patrons with books illustrating the artist’s work.

• The books cost AOTI $5 each.• We need to determine the total cost of books

and the cost per person if 1,000 / 2,000 / 4,000 people attend.

# of People (a) 1,000 2,000 4,000

Total Cost of Books (a * b)

$5,000 $10,000 $20,000

Cost per Book (b) $5 $5 $5

• AOTI expects 4,000 people to attend the exhibition and the tickets are $6 each.

• AOTI decided not to give the attendees a book.• Let’s prepare an income statement

Revenue ($6 / ticket) $ 24,000

Commission Cost (20,000)

Net Income $ 4,000

• What if actual attendance is 10% higher or lower than expected?

# of People 3600 4000 4400Revenue $21,600 $24,000 $26,400Commission (20,000) (20,000) (20,000)Net Income $ 1,600 $ 4,000 $ 6,400

*Alt. Measure – Base Measure = DifferenceDifference / Base Measure = % Change

10% 10%

60% 60%

Operating Leverage

• Magnifies small changes in revenue into dramatic changes in profitability

• The Lever = Fixed Cost

Risk vs. Reward

• Risk – refers to the possibility that sacrifices may exceed benefits

• What if no one comes to the exhibition?

What if we change the way we pay the commission?

• Now we pay $5 in commission per person attending the exhibition.

# of People 1 2000 4000

Revenue $6 $12,000 $24,000

Commission (5) (10,000) (20,000)

Net Income $1 $ 2,000 $ 4,000

Using Fixed Cost to Provide a Competitive Operating

Advantage• My Company and Your Company

provide rafting tours on Big Bear River. My Company pays tour guides fixed salaries. It budgets salaries expense at $160,000 per year. Your Company pays tour guides $40 per rafter served. Rafters are charged $50 per tour. Both companies expect to carry approx. 4,000 rafters during the year.

Let’s look at an Income Statement for each Company

My Co. Your Co.

Revenue ($50 * 4,000) $200,000 $200,000

Salary Exp. 160,000 160,000*

Net Income $ 40,000 $ 40,000

* $40 * 4,000

• In an effort to lure rafters away from Your Company, My Company lowers the price per rafter to $39.

• Now My Company serves 6,000 rafters who each pay $39 per tour.

• Your Company serves only 2,000 rafters who pay $50 per tour.

Income Statement

My Co. Your. Co.

Revenue($39*6000) $234,000 ($50*2000)$100,000

Salary Exp. ( 160,000) ($40*2000)( 80,000)

Net Income $ 74,000 $ 20,000

• Now let’s say Your Company lowered its price to $39 per rafter and lured 2,000 rafters from My Company that is still charging $50 per rafter.

Income Statement

My Co. Your Co.

Revenue ($50*2000) $100,000 ($39*6000)$234,000

Salary Exp. ( 160,000) ($40*6000)( 240,000)

Net Income ($ 60,000) ($ 6,000)

• What should My Company do?• My Company matches the $39 price set by

Your Company.• Now they each serve 4,000 customer

Income StatementMY CO. YOUR CO.

Revenue $156,000 $156,000Salary Exp. ( 160,000) ( 160,000)Net Income ($ 4,000) ($ 4,000)

I suppose fixed costs arebetter if volume is increasing,

but variable costs may be betterif business is declining.

Using Fixed Cost to Provide a Competitive Operating Advantage

Cost Behavior Summarized Your monthly basic telephone bill is

probably fixed and does not change when you make more local calls.

Number of Local Calls

Mon

thly

Basic

Tele

ph

on

e B

ill

Total Fixed Cost

Number of Local Calls

Mon

thly

Basic

Tele

ph

on

e B

ill p

er

Local C

all

The fixed cost per local call decreasesas more local calls are made.

Cost Behavior Summarized

Your total long distance telephone bill is based on how many minutes you talk.

Minutes Talked

Tota

l Lon

g

Dis

tan

ce

Tele

ph

on

e B

ill

Cost Behavior Summarized

Tota

l Var

iabl

e Cos

t

Minutes Talked

Per

Min

ute

Tele

ph

on

e C

harg

e

The cost per minute talked is constant.For example, 10 cents per minute.

Cost Behavior Summarized

Variable Cost Per Unit

Total Cost Cost Per Unit

Fixed CostsRemains Constant

Changes Inversely

Variable CostsChanges in

Direct ProportionRemains Constant

Cost Behavior SummarizedWhen activity level changes . . .

Contribution Margin

• CM = Revenue – Variable Costs

• CM represents the amount available to cover fixed expenses and thereafter provides profits.

• Sharon Virgil owns a delivery service company. She charges customers $10 per delivery. The company’s variable expenses average $2 per delivery and fixed costs are $600 per month. Sharon provided 100 deliveries during January.

Contribution MarginIncome Statement

Revenue $ 1,000

(Variable Costs) ( 200)

Contribution Margin $ 800

(Fixed Costs) ( 600)

Net Income $ 200

Measuring Operating LeverageUsing Contribution Margin

• Operating Leverage = Contribution Margin Net Income

• OL = $800 / $200 = 4• What does this 4 tell us?• If you take the OL and multiply it by the %

increase in sales it gives you the % increase in net income.

• Let’s say deliveries increase 10% for February.

• 4 * 10% = 40% in net income

Let’s test our theory!

• In February sales increased by 10%

• 100 deliveries * 110% = 110 deliveries

Revenue $1,100

(Variable Costs) ( 220)

Contribution Margin 880

(Fixed Costs) ( 600)

Net Income $ 280

• Sharon made 10 more deliveries in February.

• Sales rose from $1,000 to $1,100

• This is a 10% increase• Net income rose from $200

to $280• This is a 40% increase• % change = (280 – 200) = 80

80 / 200 = 40%

Estimating Fixed Estimating Fixed and Variable Costsand Variable Costs

High Low Method

• Used to estimate future costs

Step 1: Assemble Sales Volume and Cost History

Step 2: Find High and Low Points

Step 3: Determine the estimated variable cost per unit

Step 4: Determine the estimated total fixed costs

Units Sold Total Cost

Jan 12 195,000

Feb 10 150,000

March 11 175,000

April 18 210,000

May 30 375,000

June 35 450,000

July 25 325,000

August 20 250,000

September 15 360,000

October 11 180,000

November 10 145,000

December 12 190,000

HIGH HIGH

LOW LOW

Step 3

(High Cost – Low Cost) = VC per unit

(High Units – Low Units)

(450,000 – 145,000) = $12,200 / unit

(35 – 10)

Step 4

FC + VC = Total Cost

FC = TC – VC

FC = $450,000 – (35 * $12,200)

FC = $450,000 – 427,000

FC = $23,000