Cost-Volume-Profit AnalysisChapter 18

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Wild, Shaw, and ChiappettaFinancial & Managerial Accounting6th Edition

Wild, Shaw, and ChiappettaFinancial & Managerial Accounting6th Edition

18-C1: Fixed Costs

2

Identifying Cost Behavior Cost-volume-profit analysis is used to answer questions

such as:

– How much does income increase if we install a new machine to reduce labor costs?

– What is the change in income if selling prices decline and sales volume increases?

– How will income change if we change the sales mix of our products or services?

– What sales volume is needed to earn a target income?

C 13

Fixed Costs

C 14

Variable Costs

C 15

Mixed Costs

C 16

Step-Wise Costs

Total cost increases to a new higher cost for the next higher range of activity, but remains constant within a range of activity.

C 17

Curvilinear Costs

Costs that increase when activityincreases, but in a nonlinear manner.C 1

8

NEED-TO-KNOW

Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.

Rubber used to manufacture tennis balls $0.50 per tennis ball Variable costDepreciation (straight-line method) Electricity cost Supervisory salariesA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

0 2,000 4,000 6,000 8,000 10,000

Tota

l Cos

t

Units Produced

$0.50 per tennis ball - Variable

C 19

NEED-TO-KNOW

Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.

Rubber used to manufacture tennis balls $0.50 per ball Variable costDepreciation (straight-line method) $2,000 per month Fixed costElectricity cost Supervisory salariesA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000

$0

$500

$1,000

$1,500

$2,000

$2,500

0 2,000 4,000 6,000 8,000 10,000

Tota

l Cos

t

Units Produced

$2,000 per month - Fixed

C 110

NEED-TO-KNOW

Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.

Rubber used to manufacture tennis balls $0.50 per ball Variable costDepreciation (straight-line method) $2,000 per month Fixed costElectricity cost $500 + $0.10 per ball Mixed costSupervisory salariesA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000

$0

$200

$400

$600

$800

$1,000

$1,200

$1,400

$1,600

0 2,000 4,000 6,000 8,000 10,000

Tota

l Cos

t

Units Produced

$500 + $0.10 per unit- Mixed

C 111

NEED-TO-KNOW

Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.

Rubber used to manufacture tennis balls $0.50 per ball Variable costDepreciation (straight-line method) $2,000 per month Fixed costElectricity cost $500 + $0.10 per ball Mixed costSupervisory salaries 4,000 units per shift $5,000 per mo. per supervisor Step-wise costA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

$16,000

0 2,000 4,000 6,000 8,000 10,000

Units Produced

$5,000 per supervisor per month - Step-wise

Tota

l Cos

t

C 112

NEED-TO-KNOW

Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinearcost with respect to product units.

Rubber used to manufacture tennis balls $0.50 per ball Variable costDepreciation (straight-line method) $2,000 per month Fixed costElectricity cost $500 + $0.10 per ball Mixed costSupervisory salaries 4,000 units per shift $5,000 per mo. per supervisor Step-wise cost

Curvilinear costA salesperson’s commission is 7% for sales of up to $100,000, and 10% of sales for sales above $100,000

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

$0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000

Sales $

Sales Commissions - Curvilinear

Tota

l Cos

t

C 113

18-P1: Measuring Cost Behavior

14

Measuring Cost Behavior

The objective is to classify all costs as either fixed or variable. We will look at three methods:

1. Scatter diagrams.2. The high-low method.3. Least–squares regression.

A scatter diagram is a plot of cost data points on a graph. It is almost always helpful to plot cost data to be able to observe a visual picture of the relationship

between cost and activity.

P 115

Scatter Diagrams

P 116

The High-Low MethodThe following relationships between units

produced and total cost are observed:

Using these two levels of activity, compute: the variable cost per unit.

the total fixed cost. P 117

Units Cost

High activity level - October 67,500 29,000$ Low activity level - February 17,500 20,500 Change in activity 50,000 8,500$

The High-Low Method

Total cost = $17,525 + $0.17 per unit producedP 1

18

The objective of the cost analysis remains the

same: determination of total fixed cost and the

variable unit cost.

Least-Squares RegressionLeast-squares regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs

or calculators.

P 119

Comparison of Cost Estimation Methods

P 120

NEED-TO-KNOW

Using the information below, use the high-low method to determine the cost equation (total fixed costs plus variable costs per unit).

Activity Level

Units Produced

Total Cost

Lowest 1,600 $9,800Highest 4,000 17,000

Variable Cost = $7,2002,400

$3 per unit produced

Fixed Costs (at high point) Total cost = Fixed costs + $3 per unit$17,000 = Fixed costs + ($3 x 4,000)$5,000 = Fixed costs

Fixed Costs (at low point) Total cost = Fixed costs + $3 per unit$9,800 = Fixed costs + ($3 x 1,600)$5,000 = Fixed costs

Cost at high point - Cost at low pointUnits at high point - Units at low point

($17,000 - $9,800)(4,000 - 1,600)

Total costs = $5,000 + $3 per unit

P 121

NEED-TO-KNOW

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

$16,000

$18,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500

Tota

l Cos

t

Units Produced

Total Cost

Slope = Variable Cost $3 per unity-intercept = Fixed Costs $5,000

(1,600 units, $9,800)

(4,000 units, $17,000)

(0 units, $5,000)

= $5,000 + $3 per unit

P 122

18-A1: Contribution Margin and Its Measures

23

Contribution Margin and Its Measures

A 124

18-P2: Computing the Break-Even Point

25

Using Break-Even Analysis

The break-even point (expressed in units of product or dollars of sales) is

the unique sales level at which a company earns neither a profit nor

incurs a loss.

P 226

Computing the Break-Even Point

P 227

P 2

Computing the Margin of Safety

28

NEED-TO-KNOW

A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next

year.1. Compute the contribution margin per unit.2. Compute the break-even point (in units).3. Compute the margin of safety (in dollars).

Contribution margin per unit, or unit contribution margin, is the amount by which a product’s unit selling price exceeds its total variable cost per unit.

Sales $170 per unit Variable costs 150 per unit Contribution margin $ 20 per unit

$20 per unit

P 229

NEED-TO-KNOW

A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next

year.1. Compute the contribution margin per unit.2. Compute the break-even point (in units).3. Compute the margin of safety (in dollars).

Break-even point in units = Fixed costs Contribution margin per unit

$400,000 $20 per unit

20,000 units to break-even

Units per unit TotalSales 20,000 $170 $3,400,000Variable costs 20,000 $150 3,000,000Contribution margin $20 400,000Fixed costs 400,000Net income $0

$20 per unit20,000 units

P 230

NEED-TO-KNOW

A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next

year.1. Compute the contribution margin per unit.2. Compute the break-even point (in units).3. Compute the margin of safety (in dollars).

The excess of expected sales over the break-even sales level is called a company’s margin of safety

$20 per unit20,000 units

Units per unit TotalExpected sales 25,000 $170 $4,250,000Break-even sales 20,000 $170 3,400,000Margin of safety $850,000

$850,000

P 231

18-P3: Preparing a Cost-Volume-Profit Chart

32

Preparing a CVP Chart

P 333

Working with Changesin Estimates

P 334

18-C2: Applying Cost-Volume-Profit Analysis

35

Computing Income from Sales and Costs

C 236

Computing Salesfor a Target Income

C 237

Computing Salesfor a Target Income

C 238

Computing Salesfor a Target Income

C 239

NEED-TO-KNOWA manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,

and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.1. Compute the contribution margin ratio.2. Compute the dollar sales needed to yield the target income.3. Compute the unit sales needed to yield the target income.

The contribution margin ratio is the percent of a unit’s selling price that exceeds total unit variable cost.

Contribution margin ratio = Contribution margin per unit Selling price per unit

$180 - $126 $54 $180 $180

30%

30%

per unit Ratio

Sales $180 100%Variable costs 126 70%Contribution margin $54 30%

C 240

NEED-TO-KNOW

Dollar sales to achieve target income = Fixed costs + Pretax Income Contribution margin ratio

$502,000 + $200,000 .30

$2,340,000

A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.

1. Compute the contribution margin ratio.2. Compute the dollar sales needed to yield the target income.3. Compute the unit sales needed to yield the target income.

30%

per unit Ratio TotalSales $180 100% $2,340,000Variable costs $126 70% 1,638,000Contribution margin $54 30% 702,000Fixed costs 502,000Net income $200,000

$2,340,000

C 241

NEED-TO-KNOW

Break-even point in units = Fixed costs Contribution margin per unit

A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.

1. Compute the contribution margin ratio.2. Compute the dollar sales needed to yield the target income.3. Compute the unit sales needed to yield the target income.

30%$2,340,000

Units to yield target income = Fixed costs + target (pretax) income Contribution margin per unit

$502,000 + $200,000 $702,000 $180 - $126 $54

13,000 units

Units per unit Total

Sales 13,000 $180 $2,340,000Variable costs 13,000 $126 1,638,000Contribution margin $54 702,000Fixed costs 502,000Net income $200,000

13,000 units (or $2,340,000 / $180)

C 242

Using Sensitivity Analysis

C 243

18-P4: Computing a

Multiproduct Break-Even Point

44

Computing a MultiproductBreak-Even Point

The CVP formulas can be modified for use when a company sells more than one product. The unit contribution margin is replaced with the

contribution margin for a composite unit. A composite unit is composed of specific numbers

of each product in proportion to the product sales mix.

Sales mix is the ratio of the volumes of the various products.

P 445

Computing a MultiproductBreak-Even Point

The resulting break-even formulafor composite unit sales is:

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

ContinueP 4

46

Haircuts Basic Ultra Budget

Selling Price 20.00$ 32.00$ 16.00$ Variable Cost 13.00 18.00 8.00 Unit Contribution 7.00$ 14.00$ 8.00$ Sales Mix Ratio 4 2 1

Hair-Today offers three cuts as shown below. Annual fixed costs are $192,000. Compute the break-even point in

composite units and in number of units for each haircut at the given sales mix.

Computing a MultiproductBreak-Even Point

P 447

Computing a MultiproductBreak-Even Point

P 4

Haircuts Basic Ultra Budget

Selling Price 20.00$ 32.00$ 16.00$ Sales Mix Ratio 4.00 2.00 1.00 Selling Price/cut 80.00$ 64.00$ 16.00$ Total Selling Price/Composite Unit 160.00$

48

Computing a MultiproductBreak-Even Point

P 4

Haircuts Basic Ultra Budget

Variable Costs 13.00$ 18.00$ 8.00$ Sales Mix Ratio 4.00 2.00 1.00 Selling Price/cut 52.00$ 36.00$ 8.00$ Total Variable Cost/Composite Unit 96.00$

49

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Break-even pointin composite units

$192,000$64.00 per

composite unit

=

Break-even pointin composite units

= 3,000 composite units

Computing a MultiproductBreak-Even Point

P 450

Sales CompositeProduct Mix Cuts HaircutsBasic 4 × 3,000 = 12,000Ultra 2 × 3,000 = 6,000Budget 1 × 3,000 = 3,000

Total 21,000

Computing a MultiproductBreak-Even Point

P 451

Multiproduct Break-EvenIncome Statement

P 452

NEED-TO-KNOWThe sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both productsare $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.

1. What is the contribution margin per composite unit?2. What is the break-even point in composite units?3. How many units of X and how many units of Y will be sold at the break-even point?

Selling price per composite unit Units per unit TotalProduct X 2 $5 $10Product Y 1 $4 4Total 3 $14

Variable cost per composite unit Units per unit TotalProduct X 2 $2 $4Product Y 1 $2 2Total 3 $6

Contribution margin per composite unit ($14 - $6) $8

$8

P 453

NEED-TO-KNOWThe sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both productsare $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.

1. What is the contribution margin per composite unit?2. What is the break-even point in composite units?3. How many units of X and how many units of Y will be sold at the break-even point?

$8

Break-even point in composite units = Fixed costs Contribution margin per composite unit

$640,000 $8 per composite unit

80,000 composite units to break even

80,000 composite units

P 454

NEED-TO-KNOWThe sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both productsare $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.

1. What is the contribution margin per composite unit?2. What is the break-even point in composite units?3. How many units of X and how many units of Y will be sold at the break-even point?

$880,000 composite units

Units of each product at break-even TotalProduct X 80,000 composite units x 2 units per composite unit 160,000Product Y 80,000 composite units x 1 unit per composite unit 80,000

240,000

Total Sales Units per unit TotalProduct X 160,000 $5 $800,000Product Y 80,000 $4 320,000Total 240,000 $1,120,000

Total Variable Costs Units per unit TotalProduct X 160,000 $2 $320,000Product Y 80,000 $2 160,000Total 240,000 $480,000

Composite units per unit Total

Sales $14 $1,120,000Variable costs $6 480,000Contribution margin $8 640,000Fixed costs 640,000Net income $0

80,00080,000

P 455

Global View

Over 90 percent of German companies surveyed report their cost accounting systems focus on contribution margin. This focus helps

German companies like Volkswagen control costs and plan their production levels.

56

18-A2: Degree of Operating Leverage

57

Degree of Operating Leverage

A measure of the extent to which fixed costs are being used in an organization.

A measure of the extent to which fixed costs are being used in an organization.

A measure of how a percentage change in sales will affect profits.

A measure of how a percentage change in sales will affect profits.

A 258

Rydell Company

Sales (1,200 units) 120,000$ Less: variable expenses 84,000 Contribution margin 36,000 Less: fixed expenses 24,000 Pretax income 12,000$

If Rydell increases sales by 10 percent, what will the percentage increase in income be?

Operating Leverage

A 259

Appendix 18A: Using Excel toEstimate Least-Squares Regression

60

End of Chapter 18

61