Chapter 11

Cost Behavior and Cost-Volume-Profit Analysis

Cost Behavior

• Refers to the manner in which a cost changes as a related activity changes.

• Can be variable, fixed, or mixed.

The Activity Base/Cost Driver

A measure of what causes the

incurrence of a variable cost

UnitsUnitsproducedproduced

Miles driven

Labor hours

Machine hours

Variable CostsVariable Costs

Total Variable Cost GraphTotal Variable Cost GraphTo

tal C

osts

$300,000$250,000$200,000$150,000$100,000 $50,000

10 20 300

Unit Variable Cost GraphUnit Variable Cost Graph$20$15$10 $5

0Cos

t per

Uni

t

10 20 30

5,000 $ 50,000 $10 10,000 100,000 10 15,000 150,000 10 20,000 200,000 10 25,000 250,000 10 30,000 300,000 10

Units Total CostProduced Cost per Unit

Units Produced (000)

Units Produced (000)

Fixed CostsFixed Costs

Total Fixed Cost GraphTotal Fixed Cost GraphTo

tal C

osts

0

Unit Fixed Cost GraphUnit Fixed Cost Graph

Cos

t per

Uni

t

50,000 $75,000 $1.500 100,000 75,000 .750 150,000 75,000 .500 200,000 75,000 .375 250,000 75,000 .300 300,000 75,000 .250

Units Total CostProduced Cost per Unit

$150,000$125,000$100,000$75,000$50,000

$25,000

100 200 300

$1.50$1.25$1.00$.75$.50

$.25

100 200 3000Units Produced (000) Units Produced (000)

ExamplesAdvertising and Research and Development

ExamplesDepreciation on Equipment and

Real Estate Taxes

Types of Fixed Costs

DiscretionaryMay be altered in the short-term by current managerial decisions

CommittedLong-term, cannot be significantly reduced

in the short term.

Quick Check

Which of the following statements about cost behavior are true?

1. Fixed costs per unit vary with the level of activity.2. Variable costs per unit are constant within the

relevant range.3. Total fixed costs are constant within the relevant

range.4. Total variable costs are constant within the

relevant range.

Problem: Fixed or Variable

Hamburger buns in McDonald’s restaurant

Advertising by a dental office

Apples processed and canned by Del Monte

Shipping apples from Del Monte plant to customers

Insurance on a Bausch and Lomb factory producing contact lenses

Problem: Continued

Insurance on IBM’s corporate headquarters

Salary of supervisor overseeing production of circuit boards at HP

Commissions paid to Encyclopedia Brit salespeople

Depreciation of factory lunchroom facilities at GE plant

Steering wheels installed in BMWs

Cost Behavior Patterns Example

Bicycles by the Sea incurs variable costs of $52 for each of its bicycles.

Bicycles by the Sea also incurs $94,500 infixed costs per year

Total Costs and Unit Costs Example

What is the unit cost when Bicycles assembles 1,000 bicycles in a year?

Use Unit Costs Cautiously

Assume that Bicycles management uses aunit cost of $146.50

Management is budgeting costs fordifferent levels of production.

What is their budgeted cost for anestimated production of 600 bicycles?

600 × $146.50 = $87,900?

Use Unit Costs Cautiously

What is their budgeted cost for an estimatedproduction of 3,500 bicycles?3,500 × $146.50 = $512,750?

Fixed Charge

Variable Cost per Mile

Activity (Miles Driven)

Tota

l Cos

t

X

Y

A mixed cost has both fixed and variablecomponents. Consider the example of renting a car.

Mixed Costs

Total mixed cost

Fixed Charge

Variable Cost per Mile

Activity (Miles Driven)

Tota

l Cos

t

X

Y

Mixed Costs

Total mixed cost

Mixed Costs ExampleIf your fixed daily rental charge is $40, your variable cost is $0.20 If your fixed daily rental charge is $40, your variable cost is $0.20

per mile, and your activity level is 100 miles, what is the amount of per mile, and your activity level is 100 miles, what is the amount of your rental cost?your rental cost?

Y = a + bXY = $40 + ($0.20 × 100)Y = $60

The High-Low MethodCost and Activity Data for Six Months

1. Estimate the fixed and variable components of the maintenance costs as a function of the maintenance hours using the high-low method.

2. Determine the cost formula.3. What would maintenance costs be if 600 maintenance hours are worked?

The Contribution Format

Used primarily forUsed primarily forexternal reporting.external reporting.

Used primarily byUsed primarily bymanagement.management.

Total Per Unit PercentSales (500 ovens) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%Less: fixed expenses 80,000 Operating Income 20,000$

Micro Wave Corporation

Contribution Format Income Statement for June

Pop Quiz Tasty Bagel is a snack shop in a strip mall. The

average selling price of a bagel is $1.49 and the average variable expense per bagel is $0.36. The average fixed expense per month is $1,300. 2,100 bagels are sold each month on average. What is the CM Ratio for Tasty Bagel?a. 1.319b. 0.758c. 0.242d. 4.139

Practice…

(a) (b) (c) (d) (e) (f) Per Unit Var. Cost Total Total Total Operating Selling Per Units CM Fixed Income Price Unit Sold Costs $30 120,000 $720,000 $640,000

$10 $6 100,000 $320,000

$9 80,000 $160,000 $120,000

Contribution Margin Method to Determine Break-even

The contribution margin method is a variation of the equation method.

Fixed expensesUnit contribution margin =

Break-even pointin units sold

Pop Quiz Tasty Bagel is a snack shop in a strip mall. The average

selling price of a bagel is $1.49 and the average variable expense per bagel is $0.36. The average fixed expense per month is $1,300. 2,100 bagels are sold each month on average. What is the break-even sales in units?a. 872 bagelsb. 3,611 bagelsc. 1,200 bagelsd. 1,150 bagels

-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

- 100 200 300 400 500 600 700 800

CVP Graph

Fixed expenses

Units

Dol

lar s Total Expenses

Total Sales

-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

- 100 200 300 400 500 600 700 800

Units

Dol

lar s

CVP Graph

Break-even point

Profit Area

Loss Area

Break-even Reduction• Micro is currently selling 500 ovens per month.

Break-even units are 400 per month under the current cost structure.

• What would be the break-even units if fixed costs decrease to $70,000?

• What would be the break-even units if variable costs were reduced to $250?

• What would be the break-even units if selling price was increased to $513.33?

Sensitivity Analysis – Fixed Costs

• Micro Wave Co. is currently selling 500 ovens per month

• The sales manager believes that an increase of $10,000 in the monthly advertising budget would increase sales of ovens to 540 per month

• Should the increase in advertising be made?

Change in Variable Costs and Sales Volume

• Micro Wave management is contemplating the use of higher-quality components, which would increase variable costs by $15 per oven. However, the sales manager predicts that the overall higher quality would increase sales to 600 ovens per month. Should the higher quality components be used?

Change in Fixed Cost, Sales Price, and Sales Volume

• To increase sales, the sales manager would like to cut the selling price by $40 per oven and increase the advertising budget by $30,000 per month. The sales manager believes that if these two steps are taken, unit sales will increase by 60% to 800 ovens per month. Should the changes be made?

Target Operating Profit - CM Approach

Original contribution margin formula:

Target operating profit modification:

Units Sold to Earn Target Profit = Fixed Expenses +Target Op. Profit Contribution Margin per Unit

Break Even Point in Units = Fixed Expenses Contribution Margin per Unit

Pop QuizTasty Bagel is a snack shop in a strip mall. The

average selling price of a bagel is $1.49 and the average variable expense per bagel is $0.36. The average fixed expense per month is $1,300.

How many bagels would have to be sold to attain target profits of $2,500 per month?a. 3,363 bagelsb. 2,212 bagelsc. 1,150 bagelsd. 4,200 bagels

The Margin of SafetyExcess of actual sales over the break-even volume of sales. The amount by which sales can drop before losses begin to be incurred.

Margin of safety = Total sales - Break-even sales

Let’s calculate the margin of safety for Micro

Pop Quiz

Tasty Bagel is a snack shop in a strip mall. The average selling price of a bagel is $1.49 and the average variable expense per bagel is $0.36. The average fixed expense per month is $1,300. 2,100 bagels are sold each month on average.

What is the margin of safety?a. 3,250 bagelsb. 950 bagelsc. 1,150 bagelsd. 2,100 bagels

Cost Structure and ProfitabilityAlpha Beta Gamma

Amount % Amount % Amount %

Sales $800,000 100% $800,000 100% $800,000 100%

Variable Expenses

400,000 50% 300,000 37.5% 200,000 25%

Contribution Margin

400,000 50% 500,000 62.5% 600,000 75%

Fixed Expenses

300,000 400,000 500,000

Op. Income $ 100,000 $ 100,000 $ 100,000

Effect on Profit of 10% Increase in Sales Revenue

Increase in Sales

Revenue

Contribution Margin Ratio

Increase in Op.Income

Alpha $80,000 X 50% = $40,000 +40%

Beta $80,000 X 62.5% = $50,000 +50%

Gamma $80,000 X 75% = $60,000 +60%

Definition of Operating Leverage

The relative mix of a firm’s fixed and variable costs determines its operating leverage.

At a given level of sales: Operating leverage = Contribution Margin• factor Operating Income

Operating leverage is greatest in firm’s that have a high proportion of fixed costs in relation to variable costs.

Let’s calculate the operating leverage for each firm.

Application of Operating Leverage

At a given level of sales, the operating leverage is a measure of how a given percentage change in sales will affect operating profits.

In fact, the operating profit will increase by the operating leverage times the percentage change in sales.

For a 10% increase in sales , Firm Alpha’s operating income increased 40% (4 times 10%).

For a 10% increase in sales , Firm Beta’s operating income increased 50% (5 times 10%).

For a 10% increase in sales , Firm Gamma’s operating income increased 60% (6 times 10%).

Pop Quiz Tasty Bagel is an snack shop in a strip mall. The average selling price

of a bagel is $1.49 and the average variable expense per bagel is $0.36. The average fixed expense per month is $1,300. 2,100 bagels are sold each month on average. What is the operating leverage?

a. 2.21b. 0.45c. 0.34d. 2.92

Pop QuizAt Tasty Bagel the average selling price of a bagel is $1.49, the average variable expense per bagel is $0.36, and the average fixed expense per month is $1,300. 2,100 bagels are sold each month on average.

If sales increase by 20%, by how much should operating income increase?

a. 30.0%b. 20.0%c. 22.1%d. 44.2%

Break-even Analysis (in Units) with Multiple Products

Curl Company provides us with the following information:

Fixed cost is $120,000. What is the break-even point in units? What are the sales of Surfboards and Sailboards at the break-even point?

Mark Corporation produces two models of calculators. The Business model sells for $60, and the Math model sells for $40. The variable expenses are given below:

Business Math

Model Model

Variable production costs per unit $15 $16

Variable selling and administrative expenses per unit $9 $6

The fixed expenses are $75,000 per month. The expected monthly sales of each model are: Business, 1,000 units; Math, 500 units.

The break-even point for the expected sales mix is (round to nearest whole unit):

A) 833 of each B) 1,667 Business and 833 Math C) 1,667 of each D) 833 Business and 1,667 Math

POP QUIZ

Assumptions Underlying CVP Analysis

• Selling price is constant throughout the entire relevant range

• Costs are linear over the relevant range (costs can be divided into variable and fixed)

• In multi-product companies, the sales mix is constant• In manufacturing firms, inventories do not change (units

produced = units sold)