6. cost volume-profit analysis

Universidad CuauhtémocCampus Aguascalientes

Cost Behavior & Cost-Volume-Profit

AnalysisAnálisis de Costos

Maestría en Administración

Cost BehaviorCost Behavior

Jason Inc. produces stereo sound systems under the brand name of J-Sound. The parts for the stereo are purchased from an outside supplier for $10 per unit (a variable cost).

Variable CostVariable Cost

Total Variable Cost GraphT

otal

Cos

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

10 20 300Units Produced (in thousands)

Variable CostVariable Cost

Unit Variable Cost Graph

$20

$15

$10

$5

0

Cos

t p

er U

nit

10 20 30Units Produced

(000)

Variable CostVariable Cost

Tot

al C

osts

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

10 20 300

$20$15$10

$5

0

Cos

t per

Uni

t

10 20 30

Number ofUnits

Produced

Units Produced (000)

Units Produced (000)

Direct Materials

Cost per Unit

Total Direct Materials

Cost

5,000 units $10 $ 50,00010,000 10 l00,00015,000 10 150,00020,000 10 200,00025,000 10 250,00030,000 10 300,000

Variable CostVariable Cost

The production supervisor for Minton

Inc.’s Los Angeles plant is Lupita Marmolejo.

She is paid $75,000 per year. The plant

produces from 50,000 to 300,000 bottles of

perfume.

La Fleur

Fixed CostsFixed Costs

Number ofBottles

Produced

Total Salary for Jane Sovissi

50,000 bottles $75,000 $1.500100,000 75,000 0.750150,000 75,000 0.500200,000 75,000 0.375250,000 75,000 0.300300,000 75,000 0.250

Salary per Bottle

Produced

Fixed CostsFixed Costs

Fixed Costs

Total Fixed Cost GraphT

otal

Cos

ts

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

$25,000

100 200 3000

Unit Fixed Cost Graph

Bottles Produced (000)

Number ofBottles

Produced

Cos

t per

Uni

t $1.50$1.25$1.00

$.75$.50

$.25

100 200 3000

Units Produced (000)

Total Salary for Jane Sovissi

50,000 bottles $75,000 $1.500100,000 75,000 0.75015,000 75,000 0.50020,000 75,000 0.37525,000 75,000 0.30030,000 75,000 0.250

Salary per Bottle

Produced

Simpson Inc. manufactures sails using rented equipment.

The rental charges are $15,000 per year, plus $1 for each machine hour used over

10,000 hours.

Mixed CostsMixed Costs

Total Mixed Cost Graph

Tot

al C

osts

0

Total Machine Hours (000)

$45,000$40,000 $35,000$30,000$25,000$20,000$15,000$10,000 $5,000

10 20 30 40

Mixed costs are usually separated into

their fixed and variable components

for management analysis.

Mixed costs are usually separated into

their fixed and variable components

for management analysis.

Mixed costs are sometimes called semivariable or semifixed costs.

Mixed costs are sometimes called semivariable or semifixed costs.

The high-low method is a simple way to separate mixed costs into their fixed and variable components.

Mixed CostsMixed Costs

Low

High

Actual costs incurred

ProductionTotal(Units) Cost

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

High-Low Method

Variable cost per unit =

Highest level of activity ($) minus lowest level of activity ($)

Highest level of activity (n) minus lowest level of activity (n)

What month has the highest level

of activity in terms of cost?

Actual costs incurred

ProductionTotal(Units) Cost

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

Variable cost per unit =

$61,500 minus lowest level of activity ($)

What month has the highest level

of activity in terms of cost?

Highest level of activity (n) minus lowest level of activity (n)

High-Low Method

Actual costs incurred

ProductionTotal(Units) Cost

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

Variable cost per unit =

$61,500 minus lowest level of activity ($)

For the highest level of cost,

what is the level of production?

Highest level of activity (n) minus lowest level of activity (n)

2,100 minus lowest level of activity (n)

High-Low Method

Actual costs incurred

ProductionTotal(Units) Cost

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

Variable cost per unit =

$61,500 minus lowest level of activity ($)

What month has the lowest level of activity in terms

of cost?

$61,500 – $41,250 2,100 minus lowest level of

activity (n)2,100 – 750

High-Low Method

2,100 – 750

Actual costs incurred

ProductionTotal(Units) Cost

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

What is the variable cost per

unit?

$57,500 – $41,250

High-Low Method

$20,250

1,350Variable cost per unit = $15

Actual costs incurred

ProductionTotal(Units) Cost

Variable cost per unit = $15

What is the total fixed cost (using the

highest level)?

Total cost = (Variable cost per unit x Units of production) + Fixed cost

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

$61,500 = ($15 x 2,100) + Fixed cost

$61,500 = ($15 x 2,100) + $30,000

High-Low Method

Actual costs incurred

ProductionTotal(Units) Cost

Variable cost per unit = $15

The fixed cost is the same at the lowest level.

Total cost = (Variable cost per unit x Units of production) + Fixed cost

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

$41,250 = ($15 x 750) + Fixed cost

$41,250 = ($15 x 750) + $30,000

High-Low Method

Variable Costs

Total Fixed Costs

Total Units Produced

Tota

l Cos

ts

Total Units Produced

Per

Uni

t Cos

t

Total Variable Costs

Total Units Produced

Unit Variable Costs

Total Units Produced

Tota

l Cos

tsPe

r U

nit C

ost

Fixed Costs

ReviewUnit Fixed CostsTotal costs remain the same regardless of

activity.

Unit Costs increase and decreases with

activity level.Total costs increase and

decreases proportionately with activity level.

Unit costs remain the same per unit regardless

of activity.

Contribution Margin Income Statement

Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000

The contribution margin is

available to cover the fixed costs

and income from operations.

The contribution margin is

available to cover the fixed costs

and income from operations.

FIXED COSTS

Contribution margin

Income from Operations

Contribution Margin Income Statement

Sales Variablecosts

Fixedcosts

Income from

operations = + +

Sales Variablecosts

Contribution

margin

– =

Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000

Contribution Margin Ratio

100% 60%

40% 30%

10%

Contribution margin ratio =Sales – Variable costs

Sales

Contribution margin ratio =$1,000,000 – $600,000

$1,000,000

Contribution margin ratio = 40%

Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000

100% 60%

40% 30%

10%

The contribution margin can be expressed three ways:1. Total contribution margin in dollars.3. Contribution margin ratio (percentage).3. Unit contribution margin (dollars per unit).

The contribution margin can be expressed three ways:1. Total contribution margin in dollars.3. Contribution margin ratio (percentage).3. Unit contribution margin (dollars per unit).

$20 12$ 8

Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000

Contribution Margin Ratio

What is the break-even

point?

What is the break-even

point?

Revenues Costs=

Break-even

Calculating the Break-Even PointCalculating the Break-Even Point

At the break-even point, fixed costs and the contribution

margin are equal.

At the break-even point, fixed costs and the contribution

margin are equal.

Sales (? units) $ ?Variable costs ?Contribution margin $ 90,000 Fixed costs 90,000Income from operations $ 0

$25 15$10

Sales ($25 x ? units) $ ?Variable costs ($15 x ? units) ?Contribution margin $ 90,000 Fixed costs 90,000Income from operations $ 0

$25 15$10

Break-even sales (units) =Unit contribution margin

Fixed costs$90,000

$109,000 units

Sales ($25 x 9,000) $225,000Variable costs ($15 x 9,000) 135,000Contribution margin $ 90,000Fixed costs 90,000Income from operations $ 0

PROOF!PROOF!

Calculating the Break-Even PointCalculating the Break-Even PointIn UnitsIn Units

Sales ($250 x ? units) $ ?Variable costs ($145 x ? units) ?Contribution margin $ ? Fixed costs 840,000Income from operations $ 0

$250 145$105

Break-even sales (units) =Unit contribution margin

Fixed costs$840,000

$1058,000 units

Calculating the Break-Even PointCalculating the Break-Even PointIn UnitsIn Units

The unit selling price is $250 and unit variable cost is $145. Fixed costs are $840,000.

Sales ($25 x ? units) $ ?Variable costs ($15 x ? units) ?Contribution margin $ ? Fixed costs 840,000Income from operations $ 0

$250 145$105

Break-even sales (units) =Unit contribution margin

Fixed costs$840,000

$1008,400 units

$250 150$100

Next, assume variable costs is increased by $5.

Next, assume variable costs is increased by $5.

Calculating the Break-Even PointCalculating the Break-Even PointIn UnitsIn Units

The unit selling price is $250 and unit variable cost is $145. Fixed costs are $840,000.

Sales $ ?Variable costs ?Contribution margin $ ? Fixed costs $600,000Income from operations $ 0

Break-even sales (units) =Unit contribution margin

Fixed costs$600,000

$2030,000 units

$50 30

$20

Calculating the Break-Even PointCalculating the Break-Even PointIn UnitsIn Units

A firm currently sells their product at $50 per unit and it has a related unit variable cost of

$30. The fixed costs are $600,000.

Sales $ ?Variable costs ?Contribution margin $ ? Fixed costs $600,000Income from operations $ 0

Break-even sales (units) =Unit contribution margin

Fixed costs$600,000

$3020,000 units

$50 30

$20

$60 30$30

Calculating the Break-Even PointCalculating the Break-Even PointIn UnitsIn Units

Management increases the selling price from

$50 to $60.

Management increases the selling price from

$50 to $60.

Summary of Effects of Changes on Break-Even Point

Summary of Effects of Changes on Break-Even Point

Target ProfitTarget Profit

Fixed costs are estimated at $200,000, and the desired profit is $100,000. The unit selling

price is $75 and the unit variable cost is $45. The firm wishes to make a $100,000 profit.

Sales (? units) $ ?Variable costs ?Contribution margin $ ? Fixed costs 200,000Income from operations $ 0

$75 45$30

In Units

In Units

Sales (? units) $ ?Variable costs ?Contribution margin $ ? Fixed costs 200,000Income from operations $ 0

Sales (units) =Unit contribution margin

Fixed costs + target profit$200,000 + $100,000

$3010,000 units

Target ProfitTarget Profit In Units

In Units

$75 45$30

Target profit is used here to refer to “Income from

operations.”

Target profit is used here to refer to “Income from

operations.”

$75 45$30

Sales (10,000 units x $75) $750,000Variable costs (10,000 x $45) 450,000Contribution margin $300,000Fixed costs 200,000Income from operations $100,000

Proof that sales of 10,000 units will provide a profit of $100,000.Proof that sales of 10,000 units

will provide a profit of $100,000.

Target ProfitTarget Profit

Graphic Approach to Cost-Volume-Profit

Analysis

Cost-Volume-Profit ChartSa

les

and

Cos

ts (

$000

)

0

Units of Sales (000)

$500$450$400$350$300$250$200$150$100$ 50

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

60%

Total Sales

Variable Costs

1 2 3 4 5 6 7 8 9 10

Cost-Volume-Profit ChartSa

les

and

Cos

ts (

$000

)

0

Units of Sales (000)

$500$450$400$350$300$250$200$150$100$ 50

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

60%

40%

Contribution Margin

100% 60%

40%

1 2 3 4 5 6 7 8 9 10

Cost-Volume-Profit ChartSa

les

and

Cos

ts (

$000

)

0

Units of Sales (000)

$500$450$400$350$300$250$200$150$100$ 50

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

Fixed Costs

100% 60%

40%

TotalCosts

1 2 3 4 5 6 7 8 9 10

Cost-Volume-Profit ChartSa

les

and

Cos

ts (

$000

)

0

$500$450$400$350$300$250$200$150$100$ 50

1 2 3 4 5 6 7 8 9 10

Break-Even Point

Units of Sales (000)

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

100% 60%

40%$100,000

$20= 5,000 units

Cost-Volume-Profit ChartSa

les

and

Cos

ts (

$000

)

0

Units of Sales (000)

$500$450$400$350$300$250$200$150$100$ 50

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

100% 60%

40%

Operating Profit Area

Operating Loss Area

$100$75$50$25$ 0

$(25)$(50)$(75)

$(100)

Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000

Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000

Operating profit $100,000

Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000

Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000

Operating profit $100,000

Units of Sales (000’s)

1 2 3 4 5 6 7 8 9 10

Relevant range is

10,000 units

Relevant range is

10,000 units

Op

erat

ing

Pro

fit

(Los

s) $

000’

s

Units of Sales (000’s)

1 2 3 4 5 6 7 8 9 10

Maximum loss is equal to the

total fixed costs.

Maximum loss is equal to the

total fixed costs.

Profit Line

Operating loss

Operating profit

$100$75$50$25$ 0

$(25)$(50)$(75)

$(100)

Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000

Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000

Operating profit $100,000

Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000

Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000

Operating profit $100,000

Maximum profit within the relevant

range.

Maximum profit within the relevant

range.

Op

erat

ing

Pro

fit

(Los

s) $

000’

s

Op

erat

ing

Pro

fit

(Los

s) $

000’

s

Units of Sales (000’s)

1 2 3 4 5 6 7 8 9 10

Operating loss

Operating profit

Break-Even Point

Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000

Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000

Operating profit $100,000

Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000

Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000

Operating profit $100,000

$100$75$50$25$ 0

$(25)$(50)$(75)

$(100)

Sales Mix Considerations

Cascade Company sold 8,000 units of Product A and 2,000 units of Product B during the past year. Cascade Company’s fixed costs are $200,000. Other relevant data are as follows:

Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix 80% 20%

Products A B

Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix 80% 20%

Sales Mix Considerations Sales Mix Considerations

Products A B

Product contribution margin $16 $ 9

$25

Fixed costs, $200,000

Sales Mix Considerations Sales Mix Considerations

Products A BProduct contribution

margin $16 $ 9

$25

Break-even sales units

$200,000

$25

Fixed costs, $200,000

Sales Mix Considerations Sales Mix Considerations

Products A BProduct contribution

margin $16 $ 9

$25

Break-even sales units

$200,000

$25

Fixed costs, $200,000

= 8,000 units

Sales Mix Considerations Sales Mix Considerations

Products A BProduct contribution

margin $16 $ 9

$25

A: 8,000 units x Sales Mix (80%) = 6,400B: 8,000 units x Sales Mix (20%) = 1,600

PROOF

Product A Product B Total

Sales:6,400 units x $90 $576,000 $576,0001,600 units x $140 $224,000 224,000Total sales $576,000 $224,000 $800,000

Variable costs:6,400 x $70 $448,000 $448,0001,600 x $95 $152,000 152,000Total variable costs $448,000 $152,000 $600,000

Contribution margin $128,000 $ 72,000 $200,000

Fixed costs 200,000Income from operations $ 0Break-even point

Margin of Safety

Margin of Safety =Sales – Sales at break-even point

Sales

The margin of safety indicates the possible decrease in sales that may occur

before an operating loss results.

Margin of Safety =$250,000 – $200,000

$250,000

Margin of Safety = 20%

Universidad CuauhtémocCampus Aguascalientes

Questions?

Análisis de Costos

Maestría en Administración