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8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserve 2009 by The McGraw-Hill Companies, Inc. All rights reserve McGraw-Hill/Irwin McGraw-Hill/Irwin Fifth Edition

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Page 1: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-1

Fundamental Managerial Accounting ConceptsThomas P. Edmonds

Bor-Yi Tsay

Philip R. Olds

Copyright © Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.2009 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinMcGraw-Hill/Irwin

Fifth Edition

Page 2: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-2

Chapter 8

Performance Evaluation

Page 3: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-3

Learning Objective

LO1LO1

Describe flexible and static budgets.

Page 4: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-4

Preparing Flexible Budgets

The master budget, sometimes called a The master budget, sometimes called a static budget, is based solely on the planned static budget, is based solely on the planned

volume of activity. Flexible budgets differ volume of activity. Flexible budgets differ from static budgets in that they show from static budgets in that they show

expected revenues and costs at a variety of expected revenues and costs at a variety of volume levels.volume levels.

Page 5: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-5

Preparing Flexible BudgetsMelrose Manufacturing, a producer of small high-quality

trophies, plans to make and sell 18,000 trophies during 2006. Melrose uses a standard cost system as outlined below:

Page 6: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-6

Preparing Flexible Budgets

With very little effort, the accountant can With very little effort, the accountant can provide management with a flexible budget provide management with a flexible budget

for both budgeted and actual levels of activity. for both budgeted and actual levels of activity. The flexible budget is a critical tool in The flexible budget is a critical tool in

effective performance evaluation.effective performance evaluation.

With very little effort, the accountant can With very little effort, the accountant can provide management with a flexible budget provide management with a flexible budget

for both budgeted and actual levels of activity. for both budgeted and actual levels of activity. The flexible budget is a critical tool in The flexible budget is a critical tool in

effective performance evaluation.effective performance evaluation.

Page 7: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-7

Preparing Flexible Budgets

From the standard cost information, Melrose prepares the following static and flexible budgets.

18,000 18,000 × $80 = × $80 = $1,440,000$1,440,000

18,000 18,000 × $80 = × $80 = $1,440,000$1,440,000

Page 8: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-8

Learning Objective

LO2LO2

Classify variances as being favorable

or unfavorable.

Page 9: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-9

Determining Variances for Performance Evaluation

The differences between standard and actual The differences between standard and actual amounts are called variances. A variance may amounts are called variances. A variance may

bebe favorablefavorable or or unfavorableunfavorable. When actual . When actual sales sales are less thanare less than expected, an expected, an unfavorable unfavorable

sales variancesales variance exists. When actual sales exists. When actual sales revenue is greater than expected revenue, a revenue is greater than expected revenue, a

company has a favorable sales variance. company has a favorable sales variance.

The differences between standard and actual The differences between standard and actual amounts are called variances. A variance may amounts are called variances. A variance may

bebe favorablefavorable or or unfavorableunfavorable. When actual . When actual sales sales are less thanare less than expected, an expected, an unfavorable unfavorable

sales variancesales variance exists. When actual sales exists. When actual sales revenue is greater than expected revenue, a revenue is greater than expected revenue, a

company has a favorable sales variance. company has a favorable sales variance.

Page 10: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-10

Learning Objective

LO3LO3

Compute and interpret sales

volume variances.

Page 11: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-11

Sales Volume VariancesThe difference between the static budget sales amount and the flexible budget sales amount is a measure of

the sales volume variance.

Page 12: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-12

Interpreting the Volume Variances

In a standard cost system, marketing managers are usually responsible for the volume variance. Because sales volume drives production, production managers

have little control over volume variance.

In the case of Melrose, the marketing manager exceeded planned sales volume by 1,000 units, resulting in an

$80,000 favorable revenue variance ($80 × 1,000). The unfavorable cost variances are somewhat misleading.

Melrose incurred higher costs because it manufactured and sold more units than planned.

Page 13: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-13

Interpreting the Volume Variances

Because actual volume is not known until the end of the period, the selling price must be based on planned

volume. At the planned volume of 18,000 units, Melrose’s fixed cost per unit is expected to be as follows:

Fixed costs: Manufacturing cost 201,600$ General, selling, and administrative cost 90,000 Total fixed costs 291,600$ Divided by planned level of activity ÷ 18,000 Fixed cost per unit 16.20$

Fixed costs: Manufacturing cost 201,600$ General, selling, and administrative cost 90,000 Total fixed costs 291,600$ Divided by planned level of activity ÷ 18,000 Fixed cost per unit 16.20$

Based on actual volume, fixed cost per unit Based on actual volume, fixed cost per unit would be $15.35 ($291,600 would be $15.35 ($291,600 ÷ 19,000).÷ 19,000).

Page 14: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-14

Learning Objective

LO4LO4

Compute and interpret flexible

budget variances.

Page 15: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-15

Flexible Budget VariancesFor effective performance evaluation, management must

compare the actual results achieved to the flexible budget based on the actual volume of activity. Here is a comparison of the standard amount and actual amount

per unit for the current period.

Standard ActualSales price 80.00$ 78.00$ Variable material cost 12.00 11.78 Variable labor cost 16.80 17.25 Variable overhead cost 5.60 5.75 Variable GS&A cost 15.00 14.90

Standard ActualSales price 80.00$ 78.00$ Variable material cost 12.00 11.78 Variable labor cost 16.80 17.25 Variable overhead cost 5.60 5.75 Variable GS&A cost 15.00 14.90

Page 16: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-16

Flexible Budget VariancesNow we are comparing actual results achieved with the

results that should have been achieved at the activity level.

$78 $78 × 19,000 = × 19,000 = $1,482,000$1,482,000$78 $78 × 19,000 = × 19,000 = $1,482,000$1,482,000

Page 17: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-17

Calculating Sales Price Variance

Actual sales (19,000 × $78) 1,482,000$ Expected sales (18,000 × $80) 1,440,000 Favorable total sales variance 42,000$

Activity variance (volume) 80,000$ Sales price variance (38,000) Favorable total sales variance 42,000$

oror

Page 18: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-18

Learning Objective

LO5LO5

Explain standard cost systems.

Page 19: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-19

Standard Cost Systems

A standard represents the amount a price, cost, or quantity should be, based on certain anticipated

circumstances. Accountants, engineers, purchasing agents, and production managers

combine efforts to set standards that encourage efficient future production.

Page 20: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-20

Establishing Standards

Should we useideal standardsideal standards that represent what costsshould be under thebest circumstances?

Engineer ManagerialAccountant

I recommend using practical practical standardsstandards that an average

worker performing diligentlywould be able to achieve.

Page 21: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-21

Need for Standard Costs

Standard costs help managers plan and establish benchmarks against which actual performance can be judged. Management by exceptionManagement by exception focuses on material

differences between actual and expected results.

Standard costs help managers plan and establish benchmarks against which actual performance can be judged. Management by exceptionManagement by exception focuses on material

differences between actual and expected results.

Page 22: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-22

Selecting Variances to Investigate

Management by exception tells us to consider:Management by exception tells us to consider:

1.1. the materiality of a variance,the materiality of a variance,

2.2. how frequently it occurs,how frequently it occurs,

3.3. the capacity to control the variance, andthe capacity to control the variance, and

4.4. the characteristics of the items behind the variance.the characteristics of the items behind the variance.

Management by exception tells us to consider:Management by exception tells us to consider:

1.1. the materiality of a variance,the materiality of a variance,

2.2. how frequently it occurs,how frequently it occurs,

3.3. the capacity to control the variance, andthe capacity to control the variance, and

4.4. the characteristics of the items behind the variance.the characteristics of the items behind the variance.

Page 23: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-23

Manufacturing Cost VariancesWe will use the following information provided by

Melrose Manufacturing in 2009 to calculate manufacturing variances.

Standard ActualVariable Materials Cost Per Unit of Product 12.00$ 11.78$ Variable Labor Cost Per Unit of Product 16.80 17.25 Variable Overhead Cost Per Unit of Product 5.60 5.75 Total Per Unit Variable Manufacturing Cost (a) 34.40$ 34.78$ Total Units Produced (c) 19,000 19,000 Total Variable Manufacturing Cost (a × b) 653,600 660,820 Fixed Manufacturing Cost 201,600 210,000 Total Manufacturing Cost 855,200$ 870,820$

Standard ActualVariable Materials Cost Per Unit of Product 12.00$ 11.78$ Variable Labor Cost Per Unit of Product 16.80 17.25 Variable Overhead Cost Per Unit of Product 5.60 5.75 Total Per Unit Variable Manufacturing Cost (a) 34.40$ 34.78$ Total Units Produced (c) 19,000 19,000 Total Variable Manufacturing Cost (a × b) 653,600 660,820 Fixed Manufacturing Cost 201,600 210,000 Total Manufacturing Cost 855,200$ 870,820$

Standard ActualActual Production Volume 19,000 19,000 Pounds of Materials Per Unit of Product 6.0 6.2 Total Quantity of Materials 114,000 117,800

Page 24: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-24

Learning Objective

LO6LO6

Calculate price and usage variances.

Page 25: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-25

Materials Price and Usage Variances

Actual QuantityUsed

×Actual PricePer Pound

Actual QuantityUsed

×Standard Price

Per Pound

Standard Quantity

×Standard Price

Per Pound

117,800×

$1.90$223,820

117,800×

$2.00$235,600

Materials Price Variance$11,780 Favorable$11,780 Favorable

114,000×

$2.00$228,000

Materials Usage Variance$7,600 Unfavorable$7,600 Unfavorable

Total Variance$4,180 Favorable$4,180 Favorable

Actual CostActual CostColumnColumn

Variance DividingVariance DividingColumnColumn

Standard CostColumn

Page 26: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-26

Materials Price and Usage Variances

PriceVariance

=Actual

Quantity×

ActualPrice

StandardPrice

= $11,780 Favorable

= ×–($1.90 $2.00) 117,800

UsageVariance

=Standard

Price×

ActualQuantity

StandardQuantity

= $7,600 Unfavorable

= ×–(117,800 114,000) $2.00

Page 27: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-27

Responsibility for Materials Variances

I am not responsible forI am not responsible for this unfavorable material this unfavorable material

quantity variance.quantity variance.

You purchased inferiorYou purchased inferiormaterial, so my peoplematerial, so my peoplehad to use more of it.had to use more of it.

Production Manager

Your poor scheduling Your poor scheduling sometimes requires me to sometimes requires me to “rush order” material at a “rush order” material at a

higher price, causing higher price, causing unfavorable price variances. unfavorable price variances.

Purchasing Manager

Page 28: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-28

Calculating Labor Variances

Actual StandardPrice Per Hour 11.50$ 12.00$ Hours of Labor Per Unit of Product 1.5 1.4 Cost Per Unit of Product 17.25$ 16.80$

Actual StandardPrice Per Hour 11.50$ 12.00$ Hours of Labor Per Unit of Product 1.5 1.4 Cost Per Unit of Product 17.25$ 16.80$

Actual StandardActual Production Volume 19,000 19,000 Hours of Labor Per Unit of Product 1.5 1.4 Total Hours of Labor 28,500 26,600

Actual StandardActual Production Volume 19,000 19,000 Hours of Labor Per Unit of Product 1.5 1.4 Total Hours of Labor 28,500 26,600

Melrose has provided the following information about labor cost and usage during the period.

Page 29: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-29

Labor Price and Usage Variances

Actual HoursUsed

×Actual Price

Per Hour

Actual HoursUsed

×Standard Price

Per Hour

Standard Hours

×Standard Price

Per Hour

28,500×

$11.50$327,750

28,500×

$12.00$342,000

Labor Price Variance$14,250 Favorable$14,250 Favorable

26,600×

$12.00$319,200

Labor Usage Variance$22,800 Unfavorable$22,800 Unfavorable

Total Variance$8,550 Unfavorable$8,550 Unfavorable

Actual CostActual CostColumnColumn

Variance DividingVariance DividingColumnColumn

Standard CostColumn

Page 30: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-30

Labor Price and Usage Variances

PriceVariance

=ActualHours

×ActualPrice

StandardPrice

= $14,250 Favorable

= ×–($11.50 $12.00) 28,500

UsageVariance

=Standard

Price×

ActualHours

StandardHours

= $22,800 Unfavorable

= ×–(28,500 26,600) $12.00

Page 31: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-31

Responsibility for Labor Variances

Production Manager

Production managers areusually held accountable

for labor variancesbecause they can

influence the:

Mix of skill levelsMix of skill levelsassigned to work tasks. assigned to work tasks.

Mix of skill levelsMix of skill levelsassigned to work tasks. assigned to work tasks.

Level of employee Level of employee motivation.motivation.

Level of employee Level of employee motivation.motivation.

Quality of production Quality of production supervision.supervision.

Quality of production Quality of production supervision.supervision.

Quality of training Quality of training provided to employees.provided to employees.

Quality of training Quality of training provided to employees.provided to employees.

Page 32: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-32

Responsibility for Labor Variances

I am not responsible forI am not responsible for the unfavorable labor the unfavorable labor

efficiency variance!efficiency variance!

You purchased cheapYou purchased cheapmaterial, so it took morematerial, so it took more

time to process. time to process.

I think it took more time to I think it took more time to process the materials process the materials

because the Maintenance because the Maintenance Department has poorly Department has poorly

maintained your equipment.maintained your equipment.

Production ManagerPurchasing Manager

Page 33: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-33

Variable Overhead Variances

VariableOverheadVariance

= ActualUnits

×ActualCost

StandardCost

= $2,850 UnfavorableUnfavorable

= ×–($5.75 $5.60) 19,000

For Melrose’s Flexible BudgetFor Melrose’s Flexible Budget

Page 34: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-34

Learning Objective

LO7LO7

Calculate and interpret fixed manufacturing overhead cost

variances.

Page 35: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-35

Fixed Manufacturing Overhead Variances

Variable costs can have both price and usage variances. Fixed overhead costs can have a price variance. The difference between the actual fixed overhead cost and the budgeted fixed overhead cost is called the spending variance. At Melrose,

the spending variance was:

($210,000 actual - $201,600 budgeted)($210,000 actual - $201,600 budgeted) = $8,400 Unfavorable = $8,400 Unfavorable($210,000 actual - $201,600 budgeted)($210,000 actual - $201,600 budgeted) = $8,400 Unfavorable = $8,400 Unfavorable

Page 36: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-36

Fixed Manufacturing Overhead Variances

Overhead Volume Variance Rate

Budgeted Fixed Overhead Costs 201,600$ Planned Volume of Trophies 18,000 Predetermined Fixed Overhead Rate 11.20$

AllocationActual Volume of Trophies 19,000 Predetermined Fixed Overhead Rate 11.20$ Fixed Overhead Applied 212,800$

($201,600 budgeted ($201,600 budgeted – $212,800 applied) = $11,200 Favorable– $212,800 applied) = $11,200 Favorable($201,600 budgeted ($201,600 budgeted – $212,800 applied) = $11,200 Favorable– $212,800 applied) = $11,200 Favorable

Page 37: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-37

Fixed Manufacturing Overhead Variances

ActualActualFixedFixedCostCost

ActualActualFixedFixedCostCost

BudgetedBudgetedFixedFixedCostCost

BudgetedBudgetedFixedFixedCostCost

$210,000$210,000 $201,600$201,600

Spending Variance$8,400 UnfavorableUnfavorable

AppliedAppliedFixedFixedCostCost

AppliedAppliedFixedFixedCostCost

$212,800$212,800

Volume Variance$11,200 FavorableFavorable

Page 38: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-38

General, Selling & Administrative Cost Variances

Variable general, selling, and administrative Variable general, selling, and administrative (GS&A) costs can have price and usage (GS&A) costs can have price and usage

variances.variances.

Fixed GS&A costs are also subject to variance Fixed GS&A costs are also subject to variance analysis. We know that the flexible budget for analysis. We know that the flexible budget for 19,000 units sold shows GS&A expenses of 19,000 units sold shows GS&A expenses of

$90,000. The actual GS&A expenses incurred $90,000. The actual GS&A expenses incurred during the period were $85,000. There was a during the period were $85,000. There was a $5,000 ($90,000 $5,000 ($90,000 – $85,000) favorable fixed – $85,000) favorable fixed

GS&S variance.GS&S variance.

Variable general, selling, and administrative Variable general, selling, and administrative (GS&A) costs can have price and usage (GS&A) costs can have price and usage

variances.variances.

Fixed GS&A costs are also subject to variance Fixed GS&A costs are also subject to variance analysis. We know that the flexible budget for analysis. We know that the flexible budget for 19,000 units sold shows GS&A expenses of 19,000 units sold shows GS&A expenses of

$90,000. The actual GS&A expenses incurred $90,000. The actual GS&A expenses incurred during the period were $85,000. There was a during the period were $85,000. There was a $5,000 ($90,000 $5,000 ($90,000 – $85,000) favorable fixed – $85,000) favorable fixed

GS&S variance.GS&S variance.

Page 39: 8-1 Fundamental Managerial Accounting Concepts Thomas P. Edmonds Bor-Yi Tsay Philip R. Olds Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights

8-39

End of Chapter 8