16 -1 Cost-Volume- Profit Analysis: A Managerial Planning Tool CHAPTER.

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16 -1 Cost-Volume- Cost-Volume- Profit Profit Analysis: A Analysis: A Managerial Managerial Planning Planning Tool Tool CHAPTER CHAPTER

Transcript of 16 -1 Cost-Volume- Profit Analysis: A Managerial Planning Tool CHAPTER.

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Cost-Volume-Cost-Volume-Profit Profit

Analysis: A Analysis: A Managerial Managerial

Planning ToolPlanning Tool

CHAPTERCHAPTER

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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.

ObjectivesObjectivesObjectivesObjectives

After studying this After studying this chapter, you should chapter, you should

be able to:be able to:

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

ObjectivesObjectivesObjectivesObjectives

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Using Operating Income in CVP AnalysisUsing Operating Income in CVP AnalysisUsing 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 AnalysisUsing 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 AnalysisUsing 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 AnalysisUsing 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 = 600Proof

Sales (600 units) $240,000Less: Variable exp. 195,000Contribution margin $ 45,000Less: Fixed expenses 45,000 Operating income $ 0

ProofSales (600 units) $240,000Less: Variable exp. 195,000Contribution margin $ 45,000Less: Fixed expenses 45,000 Operating income $ 0

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Achieving a Targeted ProfitAchieving a Targeted ProfitAchieving 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

ProofSales (1,400 units) $560,000Less: Variable exp. 455,000Contribution margin $105,000Less: Fixed expenses 45,000 Operating income $ 60,000

ProofSales (1,400 units) $560,000Less: Variable exp. 455,000Contribution margin $105,000Less: 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)

After-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax 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)

After-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax 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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After-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax 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 = 1,600Proof

Sales (1,600 units) $640,000Less: Variable exp. 520,000Contribution margin $120,000Less: Fixed expenses 45,000Operating income $ 75,000Less: Income tax (35%) 26,250 Net income $ 48,750

ProofSales (1,600 units) $640,000Less: Variable exp. 520,000Contribution margin $120,000Less: Fixed expenses 45,000Operating income $ 75,000Less: Income tax (35%) 26,250 Net income $ 48,750

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Break-Even Point in Sales DollarsBreak-Even Point in Sales DollarsBreak-Even Point in Sales DollarsBreak-Even Point in Sales Dollars

First, the contribution margin ratio must be calculated.

First, the contribution margin ratio must be calculated.

Sales $400,000 100.00%Less: Variable expenses 325,000 81.25%Contribution margin $ 75,000 18.75%Less: Fixed exp. 45,000Operating income $ 30,000

Sales $400,000 100.00%Less: Variable expenses 325,000 81.25%Contribution margin $ 75,000 18.75%Less: Fixed exp. 45,000Operating income $ 30,000

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Break-Even Point in Sales DollarsBreak-Even Point in Sales DollarsBreak-Even Point in Sales DollarsBreak-Even 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) – $45,000Sales (0.1875) = $45,000

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Relationships Among Contribution Margin, Fixed Cost, and Profit

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

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

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 RevenueProfit 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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Multiple-Product AnalysisMultiple-Product AnalysisMultiple-Product AnalysisMultiple-Product Analysis

Mulching Riding Mower Mower Total

Sales $480,000 $640,000 $1,120,000Less: Variable expenses 390,000 480,000 870,000Contribution margin $ 90,000 $160,000 $ 250,000Less: Direct fixed expenses 30,000 40,000 70,000Product margin $ 60,000 $120,000 $ 180,000Less: Common fixed expenses 26,250 Operating income $ 153,750

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

Mulching RidingMulching Riding Mower Mower TotalMower Mower Total

Sales $184,800 $246,400 $431,200Less: Variable expenses 150,150 184,800 334,950Contribution margin $ 34,650 $ 61,600 $ 96,250Less: Direct fixed expenses 30,000 40,000 70,000Segment margin $ 4,650 $ 23,600 $ 26,250Less: Common fixed expenses 26,250 Operating income $ 0

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The profit-volume graph portrays the relationship between profits

and sales volume.

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 $100Variable costs per unit 5Selling price per unit 10

Total fixed costs $100Variable costs per unit 5Selling 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.

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 --

300 --

301 --

302 --

303 --

250 --

200 --

150 --

100 --

50 --

0 -- 5 10 15 20 25 30 35 40 45 50 55 60 | | | | | | | | | | | |

Total Revenue

Total Cost

Profit ($100)

Profit ($100)

LossLoss

Break-Even Point (20, $200)

Fixed Expenses ($100)

Variable Expenses ($5 per unit)

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Assumptions of C-V-P AnalysisAssumptions of C-V-P AnalysisAssumptions of C-V-P AnalysisAssumptions of C-V-P 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 THEINCREASEDINCREASED INCREASEDINCREASED

ADVERTISINGADVERTISING ADVERTISINGADVERTISING

Units sold 1,600 1,725Unit contribution margin x $75 x $75Total contribution margin $120,000 $129,375Less: Fixed expenses 45,000 53,000 Profit $ 75,000 $ 76,375

DIFFERENCE IN PROFITDIFFERENCE IN PROFIT

Change in sales volume 125Unit contribution margin x $75Change in contribution margin $9,375Less: Change in fixed expenses 8,000 Increase in profits $1,375

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BEFORE THEBEFORE THE WITH THEWITH THEPROPOSED PROPOSED

PROPOSEDPROPOSEDCHANGESCHANGESCHANGESCHANGESUnits sold 1,600 1,900

Unit contribution margin x $75 x $50Total contribution margin $120,000 $95,000Less: 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 $ -25,000Less: Change in fixed expenses -------- Decrease in profits $ -25,000

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BEFORE THEBEFORE THE WITH THEWITH THEPROPOSED PROPOSED

PROPOSEDPROPOSEDCHANGESCHANGES

CHANGESCHANGESUnits sold 1,600 2,600Unit contribution margin x $75 x $50Total contribution margin $120,000 $130,000Less: 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 $10,000Less: Change in fixed expenses 8,000 Increase in profit $ 2,000

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Margin of SafetyMargin of SafetyMargin of SafetyMargin of Safety

Assume that a company has the following projected income statement:

Sales $100,000Less: Variable expenses 60,000Contribution margin $ 40,000Less: Fixed expenses 30,000Income before taxes $ 10,000

Break-even point in dollars (R):

R = $30,000 ÷ .4 = $75,000Safety 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 $125,000Less: Variable expenses 75,000Contribution margin $ 50,000Less: Fixed expenses 30,000Income before taxes $ 20,000

Degree of Operating Leverage (DOL)

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CVP and ABCCVP and ABC

Assume the following:

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:

UnitLevel of

VariableActivity

Activity Driver CostsDriver

Setups $500100

Inspections 50600

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:

UnitLevel of

VariableActivity

Activity Driver CostsDriver

Setups $500100

Inspections 50600

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BEP = $180,000 ÷ $10

= 18,000 units

CVP and ABCCVP and ABC

1. What is the BEP under conventional analysis?

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CVP and ABCCVP 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 ABCCVP and ABC

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The EndThe EndThe EndThe End

Chapter SixteenChapter Sixteen

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