cost volume profit analysis

Cost Volume Profit Analysis

Chapter 16

2

Chapter Overview

Contribution Margin Income Statement and the Break-Even

Formula

Sales MixGraphical

Representation of Break-Even

Margin of Safety

Operating Leverage

Break-even defined

Derivation of the break-even formula

Break-even pointEffect of changes

in the break-even formula variables

Target profitAfter tax profit

targets

Profit volume graph

Cost volume profit graph

Assumptions of cost volume profit analysis

Effect on earnings volatility

3

Chapter Overview

Cost Structures Today

4

Chapter Overview


Formula

Sales MixGraphical


Margin of Safety

Operating Leverage

Break-even defined




Target profit After tax profit

targets

Profit volume graph




5

Break-Even Defined

At break-even: total revenue = total costs.

The contribution margin income statement can be used to derive the break-even formula.

Revenues Costs=Break-even

6

Break-Even Defined

At break-even: total revenue = total costs.

The contribution margin income statement can be used to derive the break-even formula.

Revenues Costs=Break-even

7

Sales– Variable Costs= Contribution margin

= Net income

ManufacturingSellingAdministrative


VARIABLE COSTING (CONTRIBUTION MARGIN)

INCOME STATEMENT

– Fixed Costs

SP x Q– VC x Q= Contribution margin

= Net income




INCOME STATEMENT

– FC

Derivation of the Break-Even Formula

8

Sales– Variable Costs= Contribution margin

= Net income




INCOME STATEMENT

– Fixed Costs

SP x Q– VC x Q= Contribution margin

= Net income




INCOME STATEMENT

– FC


9

The contribution margin income statement written as an algebraic equation is as follows:

(SP x Q) – (VC x Q) – FC = NIAt break-even net income is zero:

(SP x Q) – (VC x Q) – FC = 0Add fixed costs to both sides of the equation

(SP x Q) – (VC x Q) = FCFactor out quantity:

Q(SP – VC) = FCDivided both sides of the equation by (SP – VC):

Q = = FCSP – VC

FCCM


10

Contribution Margin Ratio

Contribution margin ratio – percentage of each sales dollar available to cover fixed costs and provide income from operations.

Measures the effect of an increase/decrease in sales volume on income from operations:

Sales – Variable CostsSales

Contribution Margin Ratio =

11

Break-Even Point

Blazin-Boards CompanyCost Data

Sales Price/Unit $ 400Variable Costs:

Direct materials $ 80Direct labor 125Variable overhead 15Variable selling expenses 20 240

Fixed Costs:Factory overhead $800,000Selling & administrative expense 400,000 $1,200,000

12

Break-Even Point

Blazin-Boards CompanyIncome Statement

Sales (7,500 x $400) $3,000,000 100%Less: Variable expenses (7,500 x $240) 1,800,000 60Contribution margin $1,200,000 40%Less: Fixed expenses 1,200,000 Operating income $ 0





13

Break-Even Point in Units

$1,200,000 $400 – $240Break-Even Sales (Units) =

Fixed Costs UCMBreak-Even Sales (Units) =

Break-Even Sales (Units) = 7,500





14

Break-Even Point in Dollars

Contribution Margin Ratio = 40%

$400 − $240 $400Contribution Margin Ratio =

Break-Even Sales = $3,000,000

$1,200,000 40% Break Even Sales =






Sales (7,500 units x $400) $3,000,000Less: Variable expenses (7,500 x $240) 1,800,000

Contribution margin $1,200,000Less: Fixed expenses

1,200,000 Operating income $ 0

Effect of Changes in Break-Even in the Formula Variables

15

16

Effect of Changes in Fixed Costs

There is a direct

relationship between fixed

costs and break-even

units.

FixedCosts

BreakEvenIf Then

FixedCosts

BreakEven

ThenIf

17


How would a $200,000 increase in fixed costs affect the break-even sales units?

18


Before a $200,000 increase in fixed costs:•Unit Contribution Margin = $160•Fixed Costs = $1,200,000•$1,200,000/$160 = 7,500 units needed to break even

After a $200,000 increase in fixed costs:•Unit Contribution Margin = $160•Fixed Costs = $1,400,000•$1,400,000/$160 = 8,750 units needed to break even

A 1/6 increase in fixed costs equals a 1/6 increase in the unit break-even point.

19

Effect of Changes in Unit Variable Costs

There is a direct

relationship between unit variable costs

and break-even units.

UnitVariable

Cost

BreakEvenIf Then

UnitVariable

Cost

BreakEven

ThenIf

20


How would an extra 2% commission (increase in

variable cost per unit) affect the break-even sales units?

21


Before a 2% increase in variable costs•Unit Contribution Margin = 400 – 240 = $160•Fixed Costs = $1,200,000•$1,200,000/$160 = 7,500 units needed to break even

After a 2% increase in variable costs•Unit CM = 400 – (240 + (400 x .02) = $152•Fixed Costs = $1,200,000•$1,200,000/$152 = 7,895 units needed to break even

When unit variable cost increases by $8, break-even units increases by 395.

22

Effect of Changes in Unit Selling Price

There is an inverse

relationship between unit selling price and break-even units.

UnitSellingPriceIf Then

BreakEven

BreakEven

UnitSellingPrice

ThenIf

23


How would a $80 selling price increase affect the break-even

sales units?

24


Before a $80 selling price increase:•Unit Contribution Margin = 400 – 240= $160•Fixed Costs = $1,200,000•$1,200,00/$160 = 7,500 units needed to break even

After a $80 selling price increase:•Unit Contribution Margin = 480 – 240 = $240•Fixed Costs = $1,200,000•$1,200,000/$240 = 5,000 units needed to break even

When unit selling price increases by $10, break-even units decreases by 10,000.

25

Target Profit

To find units needed to attain a certain target profit, add the target profit to the fixed costs in the break-even formula:

The number of units Blazin-Boards Company must sell to achieve a target profit of $300,000:

Fixed Costs + Target Profit Unit Contribution Margin

Target Profit (Units) =

$1,2000,000 + $300,000 $160

Target Profit (Units) =

Target Profit (Units) = 9,375

Net income = Operating income – Income taxes= Operating income – (Operating income x Tax rate)= Operating income (1 – Tax rate)

Or

Operating income = Net income (1 – Tax rate)

After Tax Profit Targets

26

$422,500 = Operating income – 0.35(Operating income) $422,500 = 0.65(Operating income)

$650,000 = Operating income

Blazin-Boards Company wants to earn $422,500 in net income and its income tax rate is 35 percent.

Units = ($1,200,000 + $650,000)/$160Units = $1,850,000/$160Units = 11,563 (rounded)

27



Per Total UnitSales (11,563 x $400) $4,625,200 $400Less: Variable expenses (11,563 x $240) 2,775,120 240Contribution margin $1,850,080 $160Less: Fixed expenses 1,200,000 Operating income $ 650,080Less: income taxes ($650,080 x 0.35) 227,528 Net income $ 422,552


How much sales revenue must Blazin-Boards generate to earn a before-tax profit of $650,080?

Sales = ($1,200,000 + $650,080)/0.40

= $1,850,080/0.40

= $4,625,200

29

Profit Targets

ContributionMargin

30

Chapter Overview


Formula

Sales MixGraphical


Margin of Safety

Operating Leverage

Break-even defined





target

Profit volume graph




31

Sales Mix

Blazin-Boards Company plans to sell 10,000 regular snowboards and 2,500 deluxe snowboards in the coming year.

Product price and cost information includes:

Common fixed selling and administrative expenses total $200,000.

Regular Deluxe Snowboards Snowboards

Price $ 400 $ 600Unit variable cost 240 300Direct fixed cost 400,000 200,000

32

Sales Mix

Individual products , regular snowboards and deluxe snowboards , may be thought of as one package product P.

Unit selling price, unit variable cost, and unit contribution margin of P equal the unit selling prices, variable costs, and unit contribution margins of regular snowboards and deluxe snowboards multiplied by the sales mix ratios:

Unit selling price of P ($400 x 4) + ($600 x 1) $2,200Unit variable cost of P ($240 x 4) + ($300 x 1) 1,260Unit contribution margin of P $ 940

Contribution margin of P

33

Sales Mix

The break-even sales of package, P, is calculated by dividing total fixed costs (direct and common) by the weighted average contribution margin:

Total fixed costs $800,000Product P contribution margin $940Break-even sales of individual products: Regular snowboards (851 x 4) 3,404 Deluxe snowboards (851 x 1) 851

Break-even sales units of P

= 851 units of P

34

Chapter Overview


Formula

Sales MixGraphical


Margin of Safety

Operating Leverage

Break-even defined





target

Profit volume graph




35

Profit Volume Graph

Focuses on profits.Plots the difference between profits and sales volumeConstruct a profit-volume chart assuming:

Unit selling price $10Unit variable cost 5Unit contribution margin $ 5

Fixed costs $100

Break-even = $100/$5 = 20 units

Maximum loss is $100 in fixed costs (if no sales). Assume maximum profit is $100 (based on 40 maximum sales).

36

Profit Volume Graph

Profit or Loss

$100—

80—

60—

40—

20—

0—

- 20—

- 40—

-60—- 80—- 100—

5 10 15 20 25 30 35 40 45 50 | | | | | | | | | |

Units Sold

Relevant range is 50 units.

37

Profit Volume Graph

Profit or Loss

$100—

80—

60—

40—

20—

0—

- 20—

- 40—

-60—- 80—- 100—

5 10 15 20 25 30 35 40 45 50 | | | | | | | | | |

Units Sold

Sales (40 units x $10) $400 Variable costs (40 units x $5) 200 Contribution margin $200 Fixed costs 100 Operating profit $100

Maximum profit within the

relevant range.

Maximum loss is equal to the total

fixed costs.

38

Profit Volume Graph

Profit or Loss

$100—

80—

60—

40—

20—

0—

- 20—

- 40—

-60—- 80—- 100—

5 10 15 20 25 30 35 40 45 50 | | | | | | | | | |

Units Sold


Break-Even Point(20, $0)

Profit Line

(40, $100)

39

Profit Volume Graph

Profit or Loss

$100—

80—

60—

40—

20—

0—

- 20—

- 40—

-60—- 80—- 100—

5 10 15 20 25 30 35 40 45 50 | | | | | | | | | |

Units Sold


Break-Even Point(20, $0)

Profit Line

OperatingProfit

Focus on units to determine profit or loss at different levels of operations. At sales of 25 units, operating profit will be $25 (5 units above the 20 break-even point times $5).

OperatingLoss

OperatingProfit

40

Cost Volume Profit Graph

The cost-volume-profit graph depicts the relationships among cost, volume, and profits

Necessary to graph two separate lines:1. The total revenue line: revenue = price x units

2. The total cost line: (unit variable cost x units) + Fixed costs

The vertical axis is measured in dollars and the horizontal axis is measured in units sold

Profit ($100)

Revenue

Units Sold

$500 --450 --400 --350 --300 -- 250 -- 200 -- 150 --100 -- 50 -- 0 --

5 10 15 20 25 30 35 40 45 50 55 60 | | | | | | | | | | | |

Total Revenue

Total Cost

Loss

Break-Even Point (20, $200)

Fixed Expenses ($100)

Variable Expenses ($200, or $5 per unit)

41

Cost Volume Profit Graph

42

Assumptions of Cost Volume Profit Analysis

1. The analysis assumes a linear revenue function and a linear cost function.

2. The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range.

3. The analysis assumes that what is produced is sold.4. For multiple-product analysis, the sales mix is assumed

to be known.5. The selling price and costs are assumed to be known

with certainty.

43

It Gets Even Worse:Sprohge’s Analysis

SCHEIN UND SEIN (appearance and reality)

Expenditures for capacity costs are incurred before the capacity is used.

The matching principle requires the capitalized expenditures to be matched with future reporting periods by treating a portion of the capitalized cost as an expense (depreciation expense).

Depreciation expense does not involve any cash outflow.Sales revenue and variable costs do involve cash flow.

44



So, to calculate of the number of units to break even, a fictitious number in the numerator is divided by net unit contribution margin which represents cash inflow from sale minus cash outflow to recover variable costs:

This does not make any sense.

Fixed Costs UCMBreak-Even Sales (Units) =

45



What makes break even analysis even more nonsensical is that the numerator can be arbitrarily changed:

The matching of capitalized costs with future reporting periods can be based on different depreciation methods:

straightlinedouble declining balancesum of the years’ digits

After a depreciation method has been selected and used for some time, it can be changed to another method.

46



Such information is of limited use because the following factors, among others, are not known:

Physical life of the assetEconomic life of the assetFuture demand for the productFuture selling pricesFuture variable costs

47



Land is purchased as a site for a factory provides manufacturing capacity.

The expenditure for land like all capacity expenditures must be recovered.

Land is not depreciable.The capitalized expenditures for land are not matched with future periods of benefit.

So, can the cost of land enter into break even analysis in a way that makes sense?

48



Break even analysis can be used to calculate the number of units needed to recover the initial expenditure for capacity costs, including the cost of land.

The numerator is the amount of the expenditure to acquire capacity and the denominator equals contribution margin:

Cost of capacity UCM

Units needed to recover cost =

49



Accumulated depreciation represents the cumulative cost of capacity of depreciable assets recovered to date.

Book value is the amount of the initial expenditure that still needs to be recovered.

Textbooks on cost/managerial accounting do not provide any evidence that firms use break even analysis.

50



Break even analysis can be used to calculate the number of units needed to recover the initial expenditure for capacity costs, including the cost of land.

The numerator is the amount of the expenditure to acquire capacity and the denominator equals contribution margin:

Cost of capacity UCM

Units needed to recover cost =

51

Chapter Overview


Formula

Sales MixGraphical


Margin of Safety

Operating Leverage

Break-even defined




Target profitAfter tax target

profit

Profit volume graph




52

Margin of Safety

Margin of safety is used to assess risk.

Margin of safety measures how much sales revenue can drop before an operating loss occurs.

Assume current sales and break even sales in dollars and units are as follows:

Dollars UnitsSales $400,000 10,000Break-even sales 300,000 7,500Excess $100,000 2,500

53

Margin of Safety

A Dollars Units

Sales $400,000 10,000Break-even sales 300,000 7,500Excess $100,000 2,500

Actual sales level.

54

B

Margin of Safety

A Dollars Units

Sales $400,000 10,000Break-even sales 300,000 7,500Excess $100,000 2,500

Excess of actual sales over the break-even sales.

Margin of safety expressed in units.

What is the margin of safety as a percentage?

55

Margin of Safety

B

Sales – Sales at break-even pointSales

A Dollars Units

Sales $400,000 10,000Break-even sales 300,000 7,500Excess $100,000 2,500Margin of safety (B/A) 25% 25%

56

Margin of Safety

B

Sales – Sales at break-even pointSales

A

Margin of safety indicates the decrease in sales that may occur before an operating

loss results.

Dollars UnitsSales $400,000 10,000Break-even sales 300,000 7,500Excess $100,000 2,500Margin of safety (B/A) 25% 25%

57

Chapter Overview


Formula

Sales MixGraphical


Margin of Safety

Operating Leverage

Break-even defined





target

Profit volume graph




58

Operating Leverage

Operating leverage is the use of fixed costs to magnify the effects of changes in sales on the firm’s net income:

The degree of operating leverage is a measure of the relative mix of variable costs and fixed costs.

Total contribution marginIncome from operations

59

Operating Leverage

Companies with high fixed costs (capital intensive) have high operating leverage. Companies with low fixed costs (labor intensive) have low Operating leverage.

Operating leverage measures how changes in sales affect changes in income from operations.

$ Total Revenue

Volume

Total Costs

$ Total Revenue

Volume

Total Costs

Break Even

Break Even

60

Automated System Manual System

Operating Leverage


Contribution marginOperating income

61

Sales $1,000,000 $1,000,000 Automated System Manual System

Operating Leverage



62

Sales $1,000,000 $1,000,000Variable costs 500,000 800,000


Operating Leverage



63

Sales $1,000,000 $1,000,000Variable costs 500,000 800,000Contribution margin $ 500,000 $ 200,000


Operating Leverage



64

Sales $1,000,000 $1,000,000Variable costs 500,000 800,000Contribution margin $ 500,000 $ 200,000Less: total fixed expenses 375,000 100,000


A

Operating Leverage



65

Sales $1,000,000 $1,000,000Variable costs 500,000 800,000Contribution margin $ 500,000 $ 200,000Less: total fixed expenses 375,000 100,000Operating income $ 125,000 $ 100,000


A

B

Operating Leverage



66

Sales $1,000,000 $1,000,000Variable costs 500,000 800,000Contribution margin $ 500,000 $ 200,000Less: total fixed expenses 375,000 100,000Operating income $ 125,000 $ 100,000Operating leverage (A/B)


A

B

Operating Leverage

4 2



67

Sales $1,000,000 $1,000,000Variable costs 500,000 800,000Contribution margin $ 500,000 $ 200,000Less: total fixed expenses 375,000 100,000Operating income $ 125,000 $ 100,000Operating leverage (A/B)


A

B

High FixedCosts

Low Fixed Costs

Operating Leverage

4 2



For each percentage point change in sales, income from operations will change by the operating leverage times that change

68Time Time

Net

inco

me

Net

inco

me

Company A Company B

Earnings volatility determines company risk and, hence, value.

Which of the following companies is riskier than the other?

The Effect of Operating Leverage on Earnings Volatility

69

VariableCosts

FixedCosts

Do companieswith higher levels of

fixed costs experiencemore earnings

volatility?


70

Units Sold 10 10 10

Selling Price Per Unit 10$ 10$ 10$

Variable Cost Per Unit 0 3 6 Sales Revenue 100$ 100$ 100$ Total Variable Cost 0 30 60 Total Fixed Cost 60 30 0Net Income 40$ 40$ 40$

All Fixed Company

Combination Company

All Variable Company


71

Units Sold 10 10 10



All Fixed Company

Combination Company


Now Let’s see what happens when the number of units sold increases by 10%.


72

%5.1740

4047

Units Sold 11 11 11



All Fixed Company

Combination Company


The percentage increased in income is greatest in the All Fixed Company.

%2540

4050

%5.17

404047

%10

404044

When all costs are fixed, selling 1 additional unit increases gross profit by the selling price


73

VariableCosts

FixedCosts

If sales decrease by 10%, will the income

decrease be greaterin the All Fixed

Company?


74

Units Sold 9 9 9



All Fixed Company

Combination Company


Yes, the income decrease is greater in the All Fixed Company.

%2540

4030

%5.17

404037

%1040

4036


75

VariableCosts

FixedCosts

Level of Fixed Cost

Earnings Volatility

High High

Low Low

Risk may be reduced byconverting fixed costs

into variable costs.


76

Chapter Overview


77

The composition of manufacturing costs has changed substantially in recent years

Many formal cost systems were first implemented in the early 1900’s:

Direct labor represented a large proportion, sometimes 50% or more, of the total manufacturing costs

Direct material costs were also substantialCapacity-related (fixed) costs generally represented a small

fraction of total manufacturing costs


78

Today, direct labor is only a small portion of manufacturing costs

The cost of direct materials remains important, representing 40% to 60% of the costs in many plants

The big change has been the vastly increased share of total costs from capacity-related costs


79

The increase in fixed costs results from:The shift toward greater automation, which requires more

production engineering, scheduling, and machine setup activities

The emphasis on better customer serviceThe increase in support activities required by a proliferation of

multiple productsBoth variable and fixed costs associated with design,

product development, distribution, selling, marketing, and administrative activities have increased


80

Changing cost structures have caused cost systems allocating indirect costs using volume measures to become increasingly inaccurate in computing product costs

Many costing systems take costs that did not vary proportionally with volume, accumulate them, and then allocate them using a measure of volume

These systems often underallocate costs to cost objects (e.g., product lines) produced in low volumes


End of Chapter 16

That’s it for today!

cost volume profit analysis

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