# Management Accounting - Hansen Mowen CH16

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CHAPTER

Cost-VolumeProfit Analysis: A Managerial Planning Tool

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Objectives1. Determine the number of units that must be After studying this sold to break even oryou should profit. earn a target chapter, 2. Calculate the amount of to: be able 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 costvolume-profit graph, and explain the meaning of each.

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Objectives5. 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

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Using Operating Income in CVP AnalysisNarrative Equation

Sales revenue

Variable expenses Fixed expenses

= Operating income

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Using Operating Income in CVP AnalysisSales (1,000 units @ \$400)Less: Variable expenses Contribution margin

\$400,000325,000 \$ 75,000

Less: Fixed expensesOperating income

45,000\$ 30,000

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Using Operating Income in CVP AnalysisBreak Even in Units0 = (\$400 x Units) (\$325 x Units) \$45,000

\$400,000 1,000

\$325,000 1,000

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Using Operating Income in CVP AnalysisBreak 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) Less: Variable exp. Contribution margin Less: Fixed expenses Operating income \$240,000 195,000 \$ 45,000 45,000 \$ 0

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Achieving a Targeted ProfitDesired Operating Income of \$60,000 \$60,000 = (\$400 x Units) (\$325 x Units) \$45,000 \$105,000 = \$75 x Units Units = 1,400Proof Sales (1,400 units) Less: Variable exp. Contribution margin Less: Fixed expenses Operating income \$560,000 455,000 \$105,000 45,000 \$ 60,000

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Targeted Income as a Percent of Sales RevenueDesired Operating Income of 15% of Sales Revenue0.15(\$400)(Units) = (\$400 x Units) (\$325 x Units) \$45,000

\$60 x Units = (\$400 x Units) \$325 x Units) \$45,000\$60 x Units = (\$75 x Units) \$45,000 \$15 x Units = \$45,000 Units = 3,000

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After-Tax Profit TargetsNet income = Operating income Income taxes= Operating income (Tax rate x Operating income) = Operating income (1 Tax rate)Or

Operating income =

Net income (1 Tax rate)

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After-Tax Profit TargetsIf the tax rate is 35 percent and a firm wants to achieve a profit of \$48,750. How much is the necessary operating income? \$48,750 = Operating income (0.35 x Operating income)\$48,750 = 0.65 (Operating income) \$75,000 = Operating income

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After-Tax Profit TargetsHow 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 Proof Sales (1,600 units) \$640,000 Units = 1,600Less: 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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Break-Even Point in Sales DollarsFirst, the contribution margin ratio must be calculated.Sales Less: Variable expenses Contribution margin Less: Fixed exp. Operating income \$400,000 100.00%325,000 81.25%

\$ 75,000 18.75% 45,000 \$ 30,000

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Break-Even Point in Sales DollarsGiven 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 \$0 = Sales (1 0.8125) \$45,000 Sales (0.1875) = \$45,000Sales = \$240,000

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Relationships Among Contribution Margin, Fixed Cost, and ProfitFixed Cost = Contribution MarginFixed Cost Contribution Margin

RevenueTotal Variable Cost

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Relationships Among Contribution Margin, Fixed Cost, and ProfitFixed Cost < Contribution MarginFixed Cost Contribution Margin Profit

RevenueTotal Variable Cost

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Relationships Among Contribution Margin, Fixed Cost, and ProfitFixed Cost > Contribution MarginFixed Cost Contribution Margin Loss

RevenueTotal Variable Cost

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Profit Targets and Sales RevenueHow 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 AnalysisSales Less: Variable expenses Contribution margin Less: Direct fixed expenses Product margin Less: Common fixed expenses Operating income Mulching Mower \$480,000 390,000 \$ 90,000 30,000 \$ 60,000 Riding Mower Total \$640,000 \$1,120,000 480,000 870,000 \$160,000 \$ 250,000 40,000 70,000 \$120,000 \$ 180,000 26,250 \$ 153,750

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Income Statement: B/E SolutionMulching Mower Sales Less: Variable expenses Contribution margin Less: Direct fixed expenses Segment margin Less: Common fixed expenses Operating income \$184,800 150,150 \$ 34,650 30,000 \$ 4,650 Riding Mower \$246,400 184,800 \$ 61,600 40,000 \$ 23,600

Total\$431,200 334,950 \$ 96,250 70,000 \$ 26,250 26,250 \$ 0

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The profit-volume graph portrays the relationship between profits and sales volume.

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ExampleThe Tyson Company produces a single product with the following cost and price data: Total fixed costs Variable costs per unit Selling price per unit \$100 5 10

Profit-Volume GraphProfit \$100 or Loss 80 (40, \$100) I = \$5X - \$100

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6040 20 Break-Even Point (20, \$0)

0 | | | | | | | | | | 5 10 15 20 25 30 35 40 45 50 - 20 Units Sold - 40 Loss-60 -80 -100 (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 GraphRevenue \$500 -450 -400 -350 -300 -250 -200 -150 -100 -Loss 50 -| 0 -- | 5 10 Total Revenue

Total Cost

Break-Even Point (20, \$200)

Variable Expenses (\$5 per unit)

Fixed Expenses (\$100)| | | | | | | | | |

15

20

25

30

35 40

45 50 55 Units Sold

60

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Assumptions of C-V-P Analysis1. 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.

Relevant Range\$

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Total Revenue

Total Cost

UnitsRelevant Range

Alternative 1: If advertising expenditures increase by 16 -28 \$8,000, sales will increase from 1,600 units to 1,725 units.BEFORE THE INCREASED ADVERTISING WITH THE INCREASED ADVERTISING

Units sold Unit contribution margin Total contribution margin Less: Fixed expenses Profit

1,600 x \$75 \$120,000 45,000 \$ 75,000

1,725 x \$75 \$129,375 53,000 \$ 76,375

DIFFERENCE IN PROFIT

Change in sales volume Unit contribution margin Change in contribution margin Less: Change in fixed expenses Increase in profits

125 x \$75 \$9,375 8,000 \$1,375

Alternative 2: A price decrease from \$400 to \$375 per 16 -29 lawn mower will increase sales from 1,600 units to 1,900 units.BEFORE THE PROPOSED CHANGES WITH THE PROPOSED CHANGES

Units sold Unit contribution margin Total contribution margin Less: Fixed expenses Profit

1,600 x \$75 \$120,000 45,000 \$ 75,000

1,900 x \$50 \$95,000 45,000 \$50,000

DIFFERENCE IN PROFIT

Change in contribution margin Less: Change in fixed expenses Decrease in profits

\$ -25,000 -------\$ -25,000

Alternative 3: Decreasing price to \$375and increasing 16 -30 advertising expenditures by \$8,000 will increase sales from 1,600 units to 2,600 units.BEFORE THE PROPOSED CHANGES WITH THE PROPOSED CHANGES

Units sold Unit contribution margin Total contribution margin Less: Fixed expenses Profit

1,600 x \$75 \$120,000 45,000 \$ 75,000

2,600 x \$50 \$130,000 53,000 \$ 77,000

DIFFERENCE IN PROFIT

Change in contribution margin Less: Change in fixed expenses Increase in profit

\$10,000 8,000 \$ 2,000

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Margin of SafetyAssume that a company has the following projected income statement:

Sales Less: Variable expenses Contribution margin Less: Fixed expenses Income before taxes Break-even point in dollars (R):

\$100,000 60,000 \$ 40,000 30,000 \$ 10,000

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 = 4.0Now 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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Degree of Operating Leverage (DOL)Proof: Sales Less: Variable expenses Contribution margin Less: Fixed expenses Income before taxes \$125,000 75,000 \$ 50,000 30,000 \$ 20,000

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CVP and ABCAssume 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: Unit Level of Variable Activity Activity Driver Costs Driver Setups \$500 100 Inspections 50 600

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CVP and ABC1. What is the BEP under conventional analysis? BEP = \$180,000 \$10 = 18,000 units

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CVP and ABC2. What is the BEP under ABC analysis? BEP = [\$100,000 + (100 x \$500) + (600 x \$50)]/\$10 = 18,000 units

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CVP and ABC3. What is the BEP if setup cost could be reduced to \$450 and inspection cost reduced to \$40?BEP = [\$100,000 + (100 x \$450) + (600 x \$40)]/\$10 = 16,900 units

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Chapter Sixteen

The End

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