Cost Volume - Profit Relationships - NELY BACHSIN BLOG · PDF fileCost – Volume - Profit...

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CostCost –– VolumeVolume --

Profit Profit

RelationshipsRelationships

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1. Determine the number of units that must be

sold to break even or earn a target profit.

2. Calculate the amount of revenue required to

break even or to earn a targeted profit.

3. Apply cost-volume-profit analysis in a

multiple-product setting.

4. Prepare a profit-volume graph and a cost-

volume-profit graph, and explain the meaning

of each.

ObjectivesObjectives

After studying this After studying this

chapter, you should chapter, you should

After studying this After studying this

chapter, you should chapter, you should

be able to:be able to:

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5. Explain the impact of risk, uncertainty, and

changing variables on cost-volume-profit

analysis.

6. Discuss the impact of activity-based costing

on cost-volume-profit analysis

ObjectivesObjectives

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Using Operating Income in CVP AnalysisUsing Operating Income in CVP Analysis Using Operating Income in CVP AnalysisUsing Operating Income in CVP Analysis

Narrative Equation

Sales revenue

– Variable expenses

– Fixed expenses

= Operating income

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Using Operating Income in CVP AnalysisUsing Operating Income in CVP Analysis Using Operating Income in CVP AnalysisUsing Operating Income in CVP Analysis

Sales (1,000 units @ $400) $400,000

Less: Variable expenses 325,000

Contribution margin $ 75,000

Less: Fixed expenses 45,000

Operating income $ 30,000

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Using Operating Income in CVP AnalysisUsing Operating Income in CVP Analysis Using Operating Income in CVP AnalysisUsing Operating Income in CVP Analysis

$400,000 ÷

1,000

$325,000 ÷

1,000

0 = ($400 x Units) – ($325 x Units) – $45,000

Break Even in Units

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Using Operating Income in CVP AnalysisUsing Operating Income in CVP Analysis Using Operating Income in CVP AnalysisUsing Operating Income in CVP Analysis

Break Even in Units

0 = ($400 x Units) – ($325 x Units) – $45,000

0 = ($75 x Units) – $45,000

$75 x Units = $45,000

Units = 600 Proof Proof

Sales (600 units) $240,000

Less: Variable exp. 195,000

Contribution margin $ 45,000

Less: Fixed expenses 45,000

Operating income $ 0

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Achieving a Targeted ProfitAchieving a Targeted Profit Achieving a Targeted ProfitAchieving a Targeted Profit

Desired Operating Income of $60,000

$60,000 = ($400 x Units) – ($325 x Units) – $45,000

$105,000 = $75 x Units

Units = 1,400 Proof Proof

Sales (1,400 units) $560,000

Less: Variable exp. 455,000

Contribution margin $105,000

Less: Fixed expenses 45,000

Operating income $ 60,000

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Desired Operating Income of

15% of Sales Revenue

0.15($400)(Units) = ($400 x Units) – ($325 x Units) – $45,000

$60 x Units = ($400 x Units) – $325 x Units) – $45,000

Units = 3,000

Targeted Income as a Percent of Sales RevenueTargeted Income as a Percent of Sales Revenue

$60 x Units = ($75 x Units) – $45,000

$15 x Units = $45,000

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Net income = Operating income – Income taxes

= Operating income – (Tax rate x Operating income)

AfterAfter--Tax Profit TargetsTax Profit Targets

= Operating income (1 – Tax rate)

Or

Operating income = Net income

(1 – Tax rate)

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$48,750 = Operating income – (0.35 x Operating income)

$48,750 = 0.65 (Operating income)

AfterAfter--Tax Profit TargetsTax Profit Targets

$75,000 = Operating income

If the tax rate is 35 percent and a firm wants

to achieve a profit of $48,750. How much is

the necessary operating income?

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AfterAfter--Tax Profit TargetsTax Profit Targets

How many units would have to be sold to

earn an operating income of $48,750?

Units = ($45,000 + $75,000)/$75

Units = $120,000/$75

Units = 1,600 Proof Proof

Sales (1,600 units) $640,000

Less: Variable exp. 520,000

Contribution margin $120,000

Less: Fixed expenses 45,000

Operating income $ 75,000

Less: Income tax (35%) 26,250

Net income $ 48,750

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BreakBreak--Even Point in Sales DollarsEven Point in Sales Dollars BreakBreak--Even Point in Sales DollarsEven Point in Sales Dollars

First, the contribution margin

ratio must be calculated.

Sales $400,000 100.00%

Sales $400,000 100.00%

Less: Variable

expenses 325,000 81.25%

Contribution

margin $ 75,000 18.75%

Less: Fixed exp. 45,000

Operating income $ 30,000

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BreakBreak--Even Point in Sales DollarsEven Point in Sales Dollars BreakBreak--Even Point in Sales DollarsEven Point in Sales Dollars

Given a contribution margin ratio of 18.75%, how

much sales revenue is required to break even?

Operating income = Sales – Variable costs – Fixed costs

$0 = Sales – (Variable costs ratio x Sales)

– $45,000

Sales = $240,000

$0 = Sales (1 – 0.8125) – $45,000

Sales (0.1875) = $45,000

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Relationships Among Contribution

Margin, Fixed Cost, and Profit

Contribution MarginContribution Margin

Total Variable CostTotal Variable Cost

Revenue

Fixed CostFixed Cost

Fixed Cost = Contribution Margin

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Relationships Among Contribution

Margin, Fixed Cost, and Profit

Contribution MarginContribution Margin

Total Variable CostTotal Variable Cost

Revenue

Fixed CostFixed Cost

Fixed Cost < Contribution Margin

ProfitProfit

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Relationships Among Contribution

Margin, Fixed Cost, and Profit

Contribution MarginContribution Margin

Total Variable CostTotal Variable Cost

Revenue

Fixed CostFixed Cost

Fixed Cost > Contribution Margin

LossLoss

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Profit Targets and Sales Revenue Profit Targets and Sales Revenue

How much sales revenue must a firm generate to

earn a before-tax profit of $60,000. Recall that

fixed costs total $45,000 and the contribution

margin ratio is .1875.

Sales = ($45,000 + $60,000)/0.1875

= $105,000/0.1875

= $560,000

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MultipleMultiple--Product AnalysisProduct Analysis MultipleMultiple--Product AnalysisProduct Analysis

Mulching Riding

Mower Mower Total

Sales $480,000 $640,000 $1,120,000

Less: Variable expenses 390,000 480,000 870,000

Contribution margin $ 90,000 $160,000 $ 250,000

Less: Direct fixed expenses 30,000 40,000 70,000

Product margin $ 60,000 $120,000 $ 180,000

Less: Common fixed expenses 26,250

Operating income $ 153,750

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Income Statement: B/E SolutionIncome Statement: B/E Solution Income Statement: B/E SolutionIncome Statement: B/E Solution

Mulching RidingMulching Riding

Mower Mower TotalMower Mower Total

Sales $184,800 $246,400 $431,200

Less: Variable expenses 150,150 184,800 334,950

Contribution margin $ 34,650 $ 61,600 $ 96,250

Less: Direct fixed expenses 30,000 40,000 70,000

Segment margin $ 4,650 $ 23,600 $ 26,250

Less: Common fixed expenses 26,250

Operating income $ 0

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The profit-volume graph portrays

the relationship between profits

and sales volume.

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Example

The Tyson Company produces a single product

with the following cost and price data:

Total fixed costs $100

Variable costs per unit 5

Selling price per unit 10

Total fixed costs $100

Variable costs per unit 5

Selling price per unit 10

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Profit-Volume Graph

Profit

or Loss

Loss

(40, $100) I = $5X - $100

Break-Even Point

(20, $0)

$100—

80—

60—

40—

20—

0—

- 20—

- 40—

-60—

-80—

-100—

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

Units Sold

(0, -$100)

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The cost-volume-profit graph

depicts the relationship among

costs, volume, and profits.

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Cost-Volume-Profit Graph

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

LossLoss

Break-Even Point

(20, $200)

Fixed Expenses ($100)

Variable Expenses

($5 per unit)

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Assumptions of CAssumptions of C--VV--P AnalysisP Analysis Assumptions of CAssumptions of C--VV--P AnalysisP 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.

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$

Units

Total Cost

Total Revenue

Relevant Range

Relevant Range

16 -28 Alternative 1: If advertising expenditures increase by

$8,000, sales will increase from 1,600 units to 1,725 units.

BEFORE THEBEFORE THE WITH THEWITH THE

INCREASEDINCREASED INCREASEDINCREASED

ADVERTISINGADVERTISING ADVERTISINGADVERTISING

Units sold 1,600 1,725

Unit contribution margin x $75 x $75

Total contribution margin $120,000 $129,375

Less: Fixed expenses 45,000 53,000

Profit $ 75,000 $ 76,375

DIFFERENCE IN PROFITDIFFERENCE IN PROFIT

Change in sales volume 125

Unit contribution margin x $75

Change in contribution margin $9,375

Less: Change in fixed expenses 8,000

Increase in profits $1,375

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BEFORE THEBEFORE THE WITH THEWITH THE

PROPOSED PROPOSED PROPOSEDPROPOSED

CHANGESCHANGES CHANGESCHANGES

Units sold 1,600 1,900

Unit contribution margin x $75 x $50

Total contribution margin $120,000 $95,000

Less: Fixed expenses 45,000 45,000

Profit $ 75,000 $50,000

Alternative 2: A price decrease from $400 to $375 per

lawn mower will increase sales from 1,600 units to 1,900

units.

DIFFERENCE IN PROFITDIFFERENCE IN PROFIT

Change in contribution margin $ -25,000

Less: Change in fixed expenses --------

Decrease in profits $ -25,000

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BEFORE THEBEFORE THE WITH THEWITH THE

PROPOSED PROPOSED PROPOSEDPROPOSED

CHANGESCHANGES CHANGESCHANGES

Units sold 1,600 2,600

Unit contribution margin x $75 x $50

Total contribution margin $120,000 $130,000

Less: Fixed expenses 45,000 53,000

Profit $ 75,000 $ 77,000

Alternative 3: Decreasing price to $375and increasing

advertising expenditures by $8,000 will increase sales from

1,600 units to 2,600 units.

DIFFERENCE IN PROFITDIFFERENCE IN PROFIT

Change in contribution margin $10,000

Less: Change in fixed expenses 8,000

Increase in profit $ 2,000

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Margin of SafetyMargin of Safety

Assume that a company has the following projected income statement:

Sales $100,000

Less: Variable expenses 60,000

Contribution margin $ 40,000

Less: Fixed expenses 30,000

Income before taxes $ 10,000 Break-even point in dollars (R):

R = $30,000 ÷ .4 = $75,000

Safety margin = $100,000 - $75,000 = $25,000

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Degree of Operating Leverage (DOL)

DOL = $40,000/$10,000 = 4.0

Now suppose that sales are 25% higher than projected. What is

the percentage change in profits?

Percentage change in profits = DOL x percentage change in

sales

Percentage change in profits = 4.0 x 25% = 100%

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Proof:

Sales $125,000

Less: Variable expenses 75,000

Contribution margin $ 50,000

Less: Fixed expenses 30,000

Income before taxes $ 20,000

Degree of Operating Leverage (DOL)

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CVP and ABC CVP and ABC

Assume the following:

Sales price per unit $15

Variable cost

Fixed costs (conventional) $180,000

Fixed costs (ABC)

Other Data:

Sales price per unit $15

Variable cost 5

Fixed costs (conventional) $180,000

Fixed costs (ABC) $100,000 with $80,000 subject to ABC analysis

Other Data:

Unit Level of

fixed Activity

Activity Driver Costs Driver

Setups $500 100

Inspections 50 600

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BEP = $180,000 ÷ $10

= 18,000 units

CVP and ABC CVP and ABC

1. What is the BEP under conventional

analysis?

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CVP and ABC CVP and ABC

2. What is the BEP under ABC analysis?

BEP = [$100,000 + (100 x $500) + (600 x

$50)]/$10

= 18,000 units

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BEP = [$100,000 + (100 x $450) + (600 x $40)]/$10

= 16,900 units

3. What is the BEP if setup cost could be reduced to

$450 and inspection cost reduced to $40?

CVP and ABC CVP and ABC

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The EndThe End The EndThe End

Chapter SixteenChapter Sixteen

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