chap 021

Chapter 21 - Other Variance Analysis

CHAPTER 21OTHER VARIANCE ANALYSIS

Changes from Twelfth Edition

All changes to Chapter 21 were minor.

Approach (also see “Approach” for Chapter 20)

The general message of the chapter is that differences between actual and budgeted production costs can be decomposed into price, quantity, mix, and volume variances. This general idea is applied to a variety of specific situations, but these details should not be permitted to obscure the general point. Illustration 21-1 helps keep the detailed calculations in perspective.

The computation of the mix variance is quite complicated and difficult to understand. However, students should have a general comprehension of the concept of mix because it comes up in a great many practical situations. We find it used more with respect to gross margin analysis than as a refinement of material price or labor rate variances.

Often there is miscommunication in class because students differ in the situations that they are implicitly thinking about. For example, the appropriateness of computing a gross margin variance rather than a selling variance depends on the nature of the company. If the job of the marketing organization is to obtain a certain gross margin above product costs, whatever the costs are, then attention should be focused on gross margin. If both the marketing organization and the production organization are responsible for the gross margin (one for the price component and the other for the cost component), then attention should be focused on selling price. It is not that one approach is generally better than the other, rather, each approach is appropriate for a certain situation and inappropriate for another situation. Students may not perceive that both situations exist, particularly if they have had experience in one type of company.

Cases

Campar Industries, Inc. is a problem set dealing with the variances that are introduced for the first time in this chapter.

Darius Company parallels the example in the “Complete Analysis” section of the chapter text.

Woodside Products, Inc. is a good variance analysis review case. It requires the use of last year’s actuals as the standards for analyzing this year’s performance.

Olympic Car Wash requires students to isolate the effects of an uncontrollable factor (rain) on the results of a car wash company. It can be framed as either a flexible budgeting or variance analysis case. (Note: This case was included in Chapter 25 in the Twelfth Edition. It fits equally well there.)

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Problems

Problem 21-1: Beta Division

Bdgt. Vol. @Bdgt Mix @

Bdgt. Margin

Act. Vol. @ Bdgt. Mix @ Bdgt. Margin

Act. Vol. @Act. Mix @

Bdgt. Margin

Act. Vol. @Act. Mix @Act. Margin

Sales Vol. Var. Mix Var. Unit Margin Var.

Product1 3,200 @ $10

= $32,0003,072 @ $10

= $30,7202,850 @ $10

= $28,5002,850 @ $10.20

= 29,070$1,280 U $ 2,220 U $ 570 F

2 1,700 @ $13= $22,100

1,632 @ $13= $21,216

2,500 @ $13= $32,500

2,500 @ $12.58= $31,450

884 U 11,284 F 1,050 U3 5,100 @ $9

= $45,9004,896 @ $9= $44,064

4,250 @ $9= $38,250

4,250 @ $8.80= $37,400

1,836 U 5,814 U 850 U

Total $4,000 U $ 3,250 F $1,330 U $2,080 U Net

Check: 10,000 x $10.00 – 9,600 x $10.20 = $2,080 U.

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Problem 21-2: Bradley Company

(all numbers are thousands, except per-unit amounts)

Calculation of Mix Variancea. Mix variance Product A Produce B

Actual quantity...........................................................................................................................................................................310 186Standard proportion of actual (1)...............................................................................................................................................298 198Difference...................................................................................................................................................................................+ 12 units - 12 units

Standard gross margin:...............................................................................................................................................................$5.90 - $4.00 std. cost..........................................................................................................................................................x $1.90$5.50 - $4.00 std. cost..........................................................................................................................................................______ x $1.50

Sale of more units of A than B gave a variance of.....................................................................................................................$22.80 -$18.00Or $ 4.80 F

b. Volume variance given as $47.3U reflects the fact that not as many units were produced as were expected to be produced. Net income would be higher if the expected units had been actually produced.

c. There would be no gross margin mix variance and no sales volume variance, but the gross margin would be lower by $21.3, due to the change in sales as illustrated below:

Sales.........................................................................................................................................................................................................300 @ $5.50 $1,650(2) 200 @ 5.45 1,090 $2,740

Change in gross marginActual310 ($5.50) = $1,705186 ($5.45) = $1013.7Actual $2718.70

BudgetedSales Units (2740.0)X ActualSelling $21.3

d. As illustrated below, a unit margin variance of -164.3 would have occurred:

Product A.................................................................................................................................................................................................($1.40 - $1.90) x 310 = -155.0Product B.................................................................................................................................................................................................($1.45 - $1.50) x 186 = -9.3 -164.3

1. Standard proportion: A 300/500 = .6B 200/500 = .4

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2. If Product A sells for $5.50 per unit, then 310 units would show total sales of $1,705, leaving Product B sales at $1,013.7, or $5.45/unit.

Problem 21-3: Delta Division

Gross margin variances:

Budgeted unit margin, A = $240 – ($60 + $50 + $60) = $70Budgeted unit margin, B = $148 – ($45 + $30 + $36) = $37Actual unit margin, A = ($427,000 1,750) - $170 = $74Actual unit margin, B = ($481,000 3,250) - $111 = $37

Sales volume variance: $0. This can be determined by inspection because both actual and budgeted total volumes were 5,000 units.

Mix variance:

A: (1,750 – 1,900) x $70 = $10,500UB: (3,250 – 3,100) x $37 = 5,550F

$ 4,950U

Unit margin variance:

A: ($74 - $70) x 1,750 = $7,000FB: (by inspection) = 0

$7,000F

Net margin variance = $4,950U + $7,000F = $2,050F

Labor variances:

Standard labor per unit, A: $50 $20/hr. = 2.5 hrs./unitStandard labor per unit, B: $30 $20/hr. = 1.5 hrs. unitEfficiency variance:

[(1,900 x 2.5 hr. + 3,100 x 1.5 hr.) – 9,450] x $20 = 1,000U

Rate variance:

[$20 – ($187,110 9,450 hr.] x 9,450] = 1,890FNet labor variance = $ 890F

Materials variances:

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Standard materials per unit, A: $60 $1.50/lb. = 40 lbs.Standard materials per unit, B: $45 $1.50/lb. = 30 lbs.

Usage variance:

[(1,900 x 40) + (3,100 x 30) – 180,000] x $1.50 = $16,500 U

Price variance:

[$1.50 - $275,400 180,000)] x 180,000 = 5,400UNet materials variance = $21,900U

Overhead variances:

Spending variance:$75,200 + $0.80 ($187,110) - $265,192 = $40,304U

Volume variance:1.2 ($187,110) - $224,888 = 356F

Net overhead variance = $39,948U

Sum of all variances (profit variance):

$2,050 F + $21,900 U + $890 F + $39,948 U = $58,908U

Statement of Budgeted and Actual Gross MarginBudget Actual

Revenues.................................................................................................................................................................................................$914,800 $908,000Cost of goods sold................................................................................................................................................................................... 667,100 658,250Gross margin @ std................................................................................................................................................................................. 247,700 249,750Production cost variances:

Materials usage................................................................................................................................................................................... -- (16,500)Materials price.................................................................................................................................................................................... -- (5,400)Labor efficiency.................................................................................................................................................................................. -- (1,000)Labor rate............................................................................................................................................................................................ -- 1,890Overhead volume................................................................................................................................................................................ -- 356Overhead spending............................................................................................................................................................................. -- (40,304)Total variances.................................................................................................................................................................................... -- (60,958)

Gross margin, actual................................................................................................................................................................................$247,700 $188,792

Standard gross margin increased by $2,050 because of a $4 per unit higher margin on Product A; but a shift in product mix toward lower-margin Product B more than eliminated this gain. The production cost variances are self-explanatory, except for the overhead volume variance; this $356 represents the amount our predetermined standard overhead cost per unit overcharged products for overhead, because our planned overhead was $1.20 per direct labor dollar, but our actual overhead was way overspent ($40,304). (Some students will offer details on the other production cost variances, which is fine.)

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Problem 21-4: Inman Company

a Comparison of Master Budget and Flexible BudgetNovember

Flexible Budgetat 19,000 Units

Variable per Unit Fixed Total

Master Budget Difference

Sales revenue...........................................................................................................................................................................................$20 $380,000 $400,000 $(20,000)Costs:Direct material......................................................................................................................................................................................... 3 57,000 $ 60,000 3,000Direct labor.............................................................................................................................................................................................. 3 57,000 60,000 3,000Manufacturing overhead.......................................................................................................................................................................... 4 $ 50,000 126,000 130,000 4,000Selling and administration....................................................................................................................................................................... 2 60,000 98,000 100,000 2,000Total costs................................................................................................................................................................................................$12 $110,000 338,000 350,000 12,000Operating income....................................................................................................................................................................................$ 42,000 $ 50,000 $ (8,000)

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b. (1) Sales volume variance:Act. vol. @ bdgtd. margin: 19,000 units x ($20 - $12.50*) = $142,500Bdgt. vol. @ bdgtd. margin: 20,000 units x ($20 - $12.50) = 150,000Unfavorable sales volume variance $ 7,500U

*Budgeted mfg. overhead per unit = $130,000 20,000 = $6.50; this plus budgeted direct material ($3.00) and direct labor ($3.00) gives a budgeted unit cost of $12.50.

(2) Unit margin variance:Act. vol. @ act. margin: 19,000 units x ($19* - $12.50) = $123,500Act. vol. @ bdgtd. margin (from l above) = 142,500Unfavorable unit margin variance = $ 19,000U

*$361,000 revenues 19,000 units = $19

(3) Direct material (net) variance:

Budgeted: $3 x 19,000 units = $57,000Actual (give)............................................................................................................................................................................................ 42,000Unfavorable direct material variance......................................................................................................................................................$15,000F

(4) Direct labor (net) variance:

Budgeted: $3 x 19,000 units = $57,000Actual (given).......................................................................................................................................................................................... 76,000Unfavorable direct labor variance...........................................................................................................................................................$19,000U

(5) Manufacturing overhead (net) variance:

Absorbed: $6.50 x 19,000 units = $123,500Actual (given) = 130,000Manufacturing overhead variance...........................................................................................................................................................$6,500U

(6) Selling ant administration (net) variance:

Budgeted (given) = $100,000Actual (given) = 99,000Favorable selling and administration variance........................................................................................................................................$1,000F

Sum of (l) through (6): $36,000 U = $14,000 actual - $50,000 budget

Note: Both (5) and (6) can be decomposed into volume and spending components. There is not enough information given to decompose (3) and (4) into price and usage components.

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CasesCase 21-1: Campar Industries, Inc.

Note: This case is unchanged from the Twelfth Edition.

ApproachThis problem set can be completed in one class session. Alpha is a straightforward calculation of gross margin variances. Beta introduces the gross margin mix variance. Gamma gives the student the opportunity to apply the mix concept to raw materials. Delta is a review problem, containing both margin and production cost variances.Alpha Division

Unit margin, budgeted:............................................................................................................................................................................$72 - $43 = $29Unit margin, actual:.................................................................................................................................................................................($1,658,250 / 22,000) - $43 = $75.38 - $43 - $32.38Unit margin variance = Unit margin * Actual volume

= ($32.38 - $29) * 22,000 = $74,360 FSales volume variance = Volume * Bdgt. unit margin

= (22,000 - 24,000) * $29 = $58,000 UNet gross margin variance = Act. gross margin – Bdgt. gross margin

= 22,000 * $32.38 - 24,000 * $29 = $16,360 FCheck: $74,360 F + $58,000 U = $16,360 F

The unfavorable volume variance is more than overcome by the favorable unit margin (also often called selling price) variance. I point out to students how this problem illustrates the importance of calculating margin variances rather than revenue variances.

Beta Division on following page.Gamma Division

Mix variance:(Standard Mix* - Actual Quantity) * Standard Price = Mix Variance

Material X................................................................................................................................................................................................(6,000 - 5,500) * $1.69 = $ 845 FMaterial Y................................................................................................................................................................................................(4,000 - 4,500) * $2.34 = 1,170 U

$ 325 U

*Actual quantity used at budgeted proportion (60/40).

Price variance:Standard Price - Actual Price) * Actual Quantity = Price Variance

Material X................................................................................................................................................................................................($1.69 - $1.69) * 5,500 = $0Material Y................................................................................................................................................................................................($2.34 - $2.53) * 4,500 = 855 U

$855 UUsage variance:

(Standard quantity - Actual quantity) * Standard Price = Usage variance(9,900 - 10,000) * $1.95 = $195 U

Net variance:

Mix variance + Price variance + Usage variance =$325 U + $855 U $195 U = $1,375 U

Check:

Actual cost = $20,680Standard cost = 9,900 lbs. * $1.95 = 19,305Net variance = $1,375U

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Beta Division

Bdgt. Vol. @ Act. Vol. @ Act. Vol. @ Act. Vol. @Bdgt Mix @ Bdgt. Mix @ Act. Mix @ Act. Mix @

Bdgt. Margin Bdgt. Margin Bdgt. Margin Act. Margin

Sales Vol. Var. Pdt. Mix Var. Unit Margin Var.

Pdt.1 3,200 @ $12

= $38,400 $1,536 U3,072 @ $12

= $36,864 $2,664 U2,850 @ $12

= $34,200 $684 F2,850 @ $12.24

=$34,884

2 1,700 @ $15.60= $26,520 $1,061 U

1,632 @ $15.60= $25,459 $13,541 F

2,500 @ $15.60= $39,000 $1,250 U

2,500 @ $15.10= $37,750

3 5,100 @ $10.80= $55,080 $2,203 U

4,896 @ $10.80= $52,877 $6,977 U

4,250 @ $10.80= $45,900 $1,020 U

4,250 @ $10.56= $44,880

Total $4,800 U + $3,900 F + $1,586 U = $2,486 U Net

Check: 9,600 x $12.241 – 10,000 x $12.00 = $2,486 U.The analysis indicates that if Beta explicitly changed its marketing program in order to produce the actual results, this was not a good move. The shift toward a “richer” mix did not generate enough additional margin to overcome the unfavorable sales volume and unit margin impacts.

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There are two mistakes students frequently make in this analysis. First, some forget to change the order of subtraction in the gross margin mix variance formula with the result that they show a favorable mix variance. A little discussion quickly reveals why it must be unfavorable, and reminds them again that whether a variance is favorable or unfavorable should be a matter of common sense (Will the phenomenon described tend to increase or decrease profit?) rather than algebraic sign. Second, some students calculate the mix variance this way

(Standard Mix - Actual Quantity) * Standard PriceX: (5,940 - 5,500) * $1.69 = $ 744 FY: (3,960 - 4,500) * $2.34 = 1,264 U

$ 520 U

Since 5,940 + 3,960 = 9,900 rather than 10,000, this approach changes both the mix and the quantity between the terms in parentheses. Thus, this would give a combined mix and usage variance; note that in the correct calculation, the sum of the mix and usage variance is in fact $520 unfavorable.

Delta Division

Gross margin variances:Budgeted unit margin, A = $300 - ($72 + $62.50 + $75) = $90.50Budgeted unit margin, B = $185 - ($54 + $37.50 + $45) = $48.50Actual unit margin, A = ($533,750 / 1,750) - $209.50 = $95.50Actual unit margin, B = ($601,250 / 3,250) - $136.50 = $48.50

Sales volume variance: $0. This can be determined by inspection because both actual and budgeted total volumes were 5,000 units.

Mix variance:A: (1,750 -1,900) * $90.50 = $13,575 UB: (3,250 - 3,100) * $48.50 = 7,275 F

$6,300 U

Unit margin variance:A: ($95.50 - $90.50) * 1,750 = $ 8,750FB: (by inspection) 0

$8,750 FNet margin variance = $6,300 U + $8,750 F = $2,450 F

Materials variances:Standard materials per unit, A: $72 / $l.80/lb. = 40 lbs.Standard materials per unit, B: $54 / $l.80/lb. = 30 lbs.

Usage variance:[(l,800 * 40) + (3,300 * 30) - 180,000] * $1.80 = $16,200 U

Price variance:[$1.80 - ($330,480 / 180,000)] * 180,000 = $ 6,480 UNet materials variances: = $22,680 U

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Labor variances:Standard labor per unit. A: $62.50 / $25/hr. = 2.5 hrs.Standard labor per unit, B: $37.50 / $25/hr. = 1.5 hrs.

Efficiency variance:[(1,800 * 2.5 + 3,300 * 1.5) - 9,450] * $25 = $0

Rate variance:[$25 - ($233,880 / 9,450)] * 9,450 = $2,370 FNet labor variance = $2,370 F

Overhead variances:Spending variance:$94,000 + $0.80 (233,880) - $320,000 = $38,896 U

Volume variance:$1.20 (233,880) - $281,104 = 448 UNet overhead variance $39,344 U

Sum of all variances (profit variance):$2,450F + $22,680U + $2,370F + $39,344U = $57,204 U

Delta Division Statement of Budgeted and Actual Gross MarginBudget Actual

Revenues.................................................................................................................................................................................................$1,143,500 $1,135,000Cost of goods sold @ standard................................................................................................................................................................ 821,200 810,250Gross margin @ standard........................................................................................................................................................................$ 322,300 $ 324,750Production cost variances:

Materials usage................................................................................................................................................................................... -- (16,200)Materials price.................................................................................................................................................................................... -- (6,480)Labor rate............................................................................................................................................................................................ -- 2,370Overhead spending............................................................................................................................................................................. -- (38,896

)Overhead volume................................................................................................................................................................................ -- (448)Total variances.................................................................................................................................................................................... -- (59,654)

Gross margin, actual................................................................................................................................................................................$ 322,300 $ 265,096

Standard gross margin increased by $8,750 because of a $5 per unit higher margin on Product A; but a shift in product mix toward lower-margin Product B eliminated $6,300 of this gain. The production cost variances are self-explanatory, except for the overhead volume variance; this represents the amount the predetermined standard overhead cost per unit undercharged products for overhead, because the overhead rate was based on a planned volume of 235,000 DL$, whereas the actual volume was slightly less, 233,880 DL$. (Some students will offer details on the other production cost variances, which is fine.)

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Case 21-2: Darius Company

Note: This case is unchanged from the Twelfth Edition. Please see the printed Instructor’s Resource Guide for the Harvard Teaching Note.

Case 21-3: Woodside Products, Inc. *

Note: This case is unchanged from the Twelfth Edition.

ApproachThis case provides a good summary—or good examination—of income variance analysis. Weaker students are thrown off balance at first because none of the costs given are labeled as being “standard.” However, because the task at hand is to explain 1992 results vis-a-vis those for 1993, the 1992 figures, although actual amounts, constitute the “standards” for analytical purposes. The case also asks the student to prepare a fairly intuitive summary analysis for a board meeting. I use this part of the assignment to emphasize the importance of communicating the results of quite complicated calculations in a straightforward, easy-to-grasp way to nonaccountants. The detailed analysis and a suggested summary follow.

A. Gross Margin VariancesSince inventory was valued at $55 per unit in 1992, this is the number used to determine the unit margins for these calculations:

Unit margin variance = ($50 - $39) * 82,350 = $905,850FSales volume variance a (82,350 - 88,125) * $39 = 225,225U

Net gross margin $680,625

B. Selling and Administrative Variance

The text mentions that these variances sometimes are decomposed into volume and spending components. The data given makes this possible in this case:

Volume effect = (88,125 - 82,350) * $4.42 = $25,525FSpending effect (derived from volume effect and net) = 21,942F

Net variance = $2,086,810 - $2,039,343 $47,467F

This spending variance can be further analyzed

Variable costs: ($4.42 - $4.70) * 82,350 = $23,058UFixed costs $1,697,298 - $1,652,298 = 45,000F

Net spending effect $21,942F

C. Prime Cost Variances

Material price variance = ($2.50 - $2.90) * 626,200 = $250,480UMaterial usage variance = (648,8001 - 626,200) * $2.50 = 56,500F

Net material variance $193,980U

181,100 units produced @ 8 lbs per unit

*This teaching note was prepared by Professor James S. Reece. Copyright © by James S. Reece.

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Labor rate variance = ($16.00 - $16.80) * 64,860 = $ 51,888ULabor efficiency variance = (60,8252 - 64,860) * $16.00 = 64,560U

Nat labor variance $116,448U281,100 units * 0.75 hr./unit

D. Production Overhead Variances

These calculations are challenging: Enough information is given to calculate every variance except the fixed overhead component of the overhead spending variance. However, this can be deduced from the other variances and the total production cost variance.

Overhead production variance =

(81,100 - 88,125) * $19.003 = $133,475U

3This is the fixed overhead absorption rate (see Appendix of Chapter 20)

Overhead spending variance, variable costs =

(81,100 * $4.00) - $359,500 = $ 35,100UOverhead spending variance, fixed costs

derived as follows:= $ 247,135U

Cost of goods sold @ std. = 82,350 * $55 = $4,529,250Cost of goods sold, incl. pdn. cost variances = 5,255,388So total pdn. cost variances = $ 726,138U

of which:Material variance = 193,980ULabor variance = 116,448UO’hd. pdn. vol. var. = 133,475UO’hd. spending var., vbl. costs = 35,100U

So we have accounted for 479,003ULeaving as o’hd. spending var., fixed costs $ 247,135U

As a check, the variances in categories A-D calculated above total $680,625 F + 47,467 F + 193,980 U + 116,448 U + 133,475 U + 35,100 U + 247,135 U = $1,954F, which is the income variance to be explained.

As a summary for the board of directors, I would present the numbers as follows: (The explanation contains a few conjectures, which Marilyn Mynar would easily be able to validate; this is done simply to remind students that the report should contain some reasons for balances, not just the numbers.)

1. We increased our unit selling price by $11 (or 11.7%). If our production costs had not increased this would have increased our pretax profit by $905,850

2. However, this price increase caused our sales volume to decline by 5,775 units (6.6%). At last year’s price and cost levels, the impact of this decline was to reduce pretax profit by $225,225.

3. This decrease in unit sales did have a favorable impact on pretax profits in one respect based on last year’s per-unit selling cost, the volume decline saved us $25,525 in selling costs (primarily salespeople’s commissions).

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4.

5. Our variable selling cost per unit, however, increased by $0.28 (or 6.3%), primarily because of salespeople’s commissions related to the higher per-unit selling price. This increase caused pretax profit to decline by $23,058.

6. Other selling costs and administrative costs were reduced by $45,000, with a corresponding favorable impact on pretax profit.

7. Increases in the purchase price of materials and labor rates caused pretax profit to decline by $302,368. We were more efficient in using materials than last year, but our labor was less productive; the combined effect of material usage and labor efficiency decreased pretax profit by $8,060.

8. Our factory worked at less than its usual volume this year, which increased the production cost of each unit because fixed factory overhead was spread over a lower volume. This had the effect of reducing pretax profit by $133,475.

9. Our factory overhead costs also increased considerably, reducing pretax profit by $282,235.

10. To sum up, pretax profit increased $1,954 for these reasons:

Impact of higher selling price..................................................................................................................................................................$905,850Impact of lower sales volume.................................................................................................................................................................. (199,700)Impact of lower production volume........................................................................................................................................................ (133,475)Impact of all spending and efficiency changes....................................................................................................................................... (570,721)Net change in pretax income...................................................................................................................................................................$ 1,954

[A really brief report would include only this ninth item.]

For some reason, students often end up with a set of numbers that do not add up to $1,954. I stress that a good explanation will contain a set of numbers that can be added—or, better, have been added—to demonstrate that the $1,954 pretax profit variance has indeed been explained.

Case 21-4: Olympic Car Wash. *

Note: This case is unchanged from the Twelfth Edition, but it has been moved from Chapter 25 in the Twelfth Edition to Chapter 21 in the Thirteenth Edition.

Approach

This is a flexible budgeting or profit variance analysis case in a setting that the students will easily understand. They will figure out that they have to make adjustments for an uncontrollable factor that is important in this industry—the weather. But doing the calculations is a little tricky.

Calculations

How large should the bonus pool be for the Aalst location?

One possible solution

*This teaching note was prepared by Professors Kenneth A. Merchant and Wim A. Van der Stede. Copyright © by Kenneth A. Merchant and Wim A. Van der Stede.

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Flex the budget based on number of hours of good weather.

Budget Actual

“Flexible”

Budget

Controllable Variance

(Actual - Flex Budget)

Revenue €184,000 €124,080 €108,100 €15,980

Variable expenses (50% of revenue)

92,000 62,040 54,050 (7,990)

Fixed expenses 53,820 55,000 53,820 (1,180)

Total expenses 145,820 117,040 107,870 (9,170)

Profit 38,180 7,040 230 6,810

Size of the bonus pool = € 3,000 + 681 = 3,681

While this solution is simple and straightforward, it is far from the only possible solution to this case. Students might well be asked to judge whether zero is a possible correct answer to this case. It is. Jacques Van Raemdonck might well conclude that no adjustments should be made for the uncontrollable effects of weather for any of the following reasons:

1. The weather constantly varies. While the employees were unlucky during the Spring quarter of 2002, they have been lucky in prior quarters. It evens out.

2. The company perhaps cannot afford to pay bonuses in periods when it is not taking in healthy amounts of cash.

3. The costs of making these adjustments exceed the benefits of making them. In order to make these adjustments, someone has to keep track of periods of rain that will deter customers from getting their cars washed. Some difficult judgments might be required. For example, how much rain warrants an adjustment? More than “a drizzle”? A duration more than “a brief shower”? Is just the threat of rain a justifiable cause for an adjustment? Is it not possible that customers will just defer their car wash until a good weather period, resulting is no (or little) actual loss of business? And if an adjustment seems warranted, someone has to sit down and do the calculations.

Note that regardless of the reasons, this approach of not adjusting for this weather factor, or any other uncontrollable factor, forces employees to share some risk with the owners of the company. The employees will have to be compensated somehow for bearing this risk.

But even if it is decided to make adjustments for the unforeseen 330 hours of bad weather (the difference between budget and actual), many solutions are possible because of the effects of what textbooks describe as “joint variances.” A variance analysis is a systematic way to explain the difference between two numbers, such as an actual and a budget target. The variance ascribed to any particular factor will depend on the order in which the factors are introduced into the analysis. This can be illustrated graphically as is shown in Figure A:

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Figure AGraphical Representation of a Variance Analysis

Factor Budget (1) (2) (3) (4) Actual

Hours of good weather P A A A A A

Vehicles/hr. P P A A A ARevenue/vehicle P P P A A AVariable costs P P P P A AFixed costs P P P P P A

Figure A shows that the budget is based on planned assumptions about each of the factors that affect performance. This is shown with the letter P. The actuals are calculated based on the actual levels for each of those factors, here designated with the letter A. The effect of each of the factors on performance can be calculated by changing the factor from P to A, or A to P. The difference between the budget and column (1) can be called the “weather variance.” The difference between columns (1) and (2) is the “productivity variance.” The difference between columns (2) and (3) is the “price variance.” And so on. If the budget is the starting point, the analysis is known as “flexing” the budget. If the actuals are the starting point, the analysis is known as “adjusting actuals.”

The numerical solution shown on the first page of this teaching note took the budget as the starting point. It changed the hours-of-good-weather factor from the planned to the actual amount to calculate the performance effect of the poor forecasting of hours of good weather. Note that the “flexible budget” column in that solution left all of the other factors at their planned (or budgeted) levels. This is, in effect, the analysis shown as column (1) in Figure A.

If the factors had been introduced into the analysis in a different order, or if the actuals had been adjusted first for weather, the resulting answer would be different. Just as one example, consider the numbers that would result if the actuals were adjusted first for the effects of the mis-forecast hours of bad weather.1

1 Note that this is identical to “flexing the budget” but considering the effects of the hours-of-bad-weather factor last in the analysis.

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Budget Actual

“Adjusted

Actual” 2

Controllable Variance (Adjusted

Actual - Budget)

Revenue €184,000 €124,080 €211,200 €27,200

Variable expenses (50% of revenue)

92,000 62,040 105,600 (13,600)

Fixed expenses 53,820 55,000 55,000 (1,180)

Total expenses 145,820 117,040 160,600 (14,780)

Profit 38,180 7,040 50,600 12,420

Size of the bonus pool = € 3,000 + 1,242 = 4,242.

This answer is as theoretically correct as the €3,681 answer given on p. 1 of this teaching note. So too are all of the other answers that would result if the performance factors were introduced into the analysis in a different order. If the incentive plan promises that adjustments will be made for the effects of specific uncontrollable factors, care must be taken to explain just how those adjustments will be made.

This little case is not as simple as it might first seem.

2 What actual performance would have been if the hours of good weather had been as forecast in the budget.

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chap 021

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