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[litigants Helping Students Spring 2007 See the "Big Picture" of Variance Analysis BY NEAL R. VANZANTE, PH.D., CMA, CFM, CPA TWO CASE PROBLEMS ARE PRESENTEDTO HELP PROVIDE STUDENTS WITH A DEEPER, MORE THOROUGH UNDERSTANDING OF VARIANCE ANALYSIS AND THE CALCULATIONS THAT ARE NEEDED. INCORPORATING THESE CASES INTO ADVANCED COST ACCOUNTING COURSES MAKES STUDENTS BETTER PREPAREDTO HANDLE AND ADDRESS VARIANCE ISSUES WHEN THEY ARISE IN THE REAL WORLD. ariances, or the differences between bud geted, planned, or standard amounts and the actual amounts incurred or sold, are a critical part of management accounting They give managers a basis for making informed decisions, yet many accounting students have difficulty with variance analysis. Part of this difficulty may be caused by the manner in which this topic is typ\" ically presented in costl'managetial accounting textw books. Some textbook coverage is disjointed, with brief mentions of exible budget variances just prior to dis- cussing manufacturing cost variances. Then, in a much later chapter, sales-variance analysis may be covered with little or no reference to the earlier sections. Dis~ cussion of input mix and yield variances may be pre sented in appendices, if at all. In addition to these disjointed presentations, text- book coverage is often heavily formula driven, offering no alternative methodology. Although some textbooks provide overview tables (and problems) showing the interrelationships of the variances in a particular chap ter, comprehensive coverage of variances in the entire textbook is lacking. in other words, there is typically no discussion of how variances covered in earlier chapters may be incorporated with the variances covered in the later chapters. Thus, many students fail to see how they are related, as well as the similarities between the comv putational aspects of some of the variances. [n my seniorfgraduate-level Advanced Cost! Managerial Accounting course, I use two cases to help students better understand variance analysis. The cases allow students to see the \"big picture\" without being overly complex. While students are required to calcu- late all variances typically presented in costfmanagerial textbooks, they are continuously reminded of the numerous similarities in the computational aspects of these variances. Furthermore, they learnand understandaltemative methods for computing vari- ances and presenting their solutions. The first case requires students to calculate all the MANAGEMENT ACCOUNTING l'lUARTERL'II @SPRINE 200?, VOL. 3, Nl'J.3 traditional sales variances and the \"flexible budget\" variances for the Fernandez Company, which manufacw tures three types of fine pool cues: good, better, and best. The only difference is the materials used in their production. The second case requires the calculation of materials price, mix, and yield variances for the Roger Company, which uses materials X, Y, and Z to manufacture Prodv uct NRV. The exercise concludes with a summary of the variances in both cases. THE FERNANDEZ COMPANY The Fernandez case (Table 1) has five parts. Part 1 requires students to make several detailed calculations in a table similar to those usually included in textbook coverage of exible budgeting. The Fernandez Compa- ny table, however, has additional columns to incorpo- rate the sales mix variance and rows for both variable and fixed operating expenses. Because accurate comv pletion of this table is vital for students to fulfill and better understand the remaining requirements, 1 pro- vide \"check figures\" and \"help\" as necessary to ensure successful completion Students may complete the table manually, but I encourage them to use a spread sheet package so they may clearly observe the compun tational similarities of each number and, thus, are better prepared to understand the differences. Students com- fortable with a spreadsheet package tend to use the copy command and then revise the formulas as needed. The completed table appears in "Fable 2. Saks l'hkrme, Series Mix. and Sales Quantity Variances Part 2 of the Fernandez case requires students to detail the Calculation of the variances. The sales volume variance is equal to the difference of contribution margin between the exible budget (based on actual sales mix) and the static budget (based on original budgeted sales mix). In Table 2, it is simply the difference between the contribution margins (and incomes) in the third column (actual mix at budgeted dollars) and the seventh column (the static budget). The volume variance may be broken down into a mix variance (column three minus column five) and the quantity variance (column five minus column seven). Some students calculate the respective weighted average contribution margins of $39.60 per unit (actual) and $36.00 per unit (budgeted). Using this information, the solution of the volume variance, mix variance, and quantity variance is presented in Table 3. The amounts, of course, agree with those in the soluw tion to Part 1. Students observe that all variable items (sales and all variable costs) increase by 10% because the \"quantity" increases by 10%. Some students will explain the \"mix" variance in a little more detail, noting that the $6.00 ($106.00 $100.00) increase in the aver- age budgeted sales price times 110,000 units equals the $660,000 sales difference. The variable operating expenses increase of $0.60 (for the 10% sales commis- sions based on the higher average price) times 110,000 equals the $60,000 variable operating expense differw ence', and the $1.80 increase in the average budgeted cost of materials due to the change in sales mix times 110,000 equals the $198,000 increase in materials cost. These differences account for the $3.60 per unit increase ($6.00 - $0.60 - $1.80) in average budgeted contribution margin. Table 4 shows another approach; it is not necessarily simpler, but it gives students a better view of the underlying cause ofthe mix variance. Sales Price Variance The sales price variance is the $341,000 at the top of the exible budget variance column in Table 2. [t is the difv ference between the actual sales (in the actual mix at the actual prices) and the budgeted sales (in the actual mix at the budgeted prices). Students are provided with the actual average selling price ($109.10) and the averv age budgeted selling price based on the actual mix ($106). The $341,000 sales price variance comes from the difference between these two averages ($3.10) mul- tiplied by 110,000 units. You could also require students to calculate this variance by multiplying the individual differences in actual and budgeted sales prices times the actual number of units sold and then have them prove the mathematical equivalency of the two approaches. Materials and Iabar Variances The total materials variance may be broken down between price and efficiency (quantity) differences. While most textbooks present these horizontally, I typi- MANAEEMENT ACCOUNTING l'lUARTERL'II @SPRINE 200?, VOL. 3, NU.3 Table 1: THE FERNANDEZ COMPANY CASE SALES UNITS SALES PRICES [111101101 5.1.1.0135]: AERIAL BEIGE! AERIAL Good 00,000 55,000 $ 00.00 $ 02.00 Better 30,000 30,500 $12000 $12300 Best 10,000 16,500 $160.00 $167.00 Tota Is/Av era ge 100,000 110,000 $1111.00 $1 011.10 The average budgeted sales price based on actual mix is $106.00. B ET A AL xed CostsOverhead $2,000,000 $2,150,000 xed CostsOperating Expenses $1,000,000 $1,050,000 Total $3,000,000 $3,200,011] 0081's Pm moment: FEEmtnuns PERlll'll'l' P001! CT BUICE'I' ACTUAL BllEE'l' m Materials Good $ 2.40 $ 2.30 5.0 5.5 Better 11 4.00 $ 4.50 5.0 5.5 Best $ 1.20 $ 6.00 5.0 5.5 All Budgeted and actual $3.00 perunitfor a carrying case. Labor All $25.00 $36.00 1.0 0.05 Variable UVH All $ 103 $ 150 1.0 0.95 Variable Uperating Expenses Budgeted and actual 10% sales commission and $1.00 per unit shipping. RECLI BWENTS rst c omplete the following table. FLEX B. ACTUAL MIX MEX Blll MW QUANTITY STATIC VARIANCE RUNCE'I'EC S VARIANCE HJIGJ VARIANCE BUICE'I' _ M____ m _._100 000 _______ ______ ______ _____ ______ ______ ___ ______ Assuming no beginning nor ending inventories of any kind, show the calculation of thefollowing variances: Sales Volume Variance Sale Mix Variance Sales Quantity Variance Sales Price Variance Materials efficiency and price variances for each of the three materials and the total material variance Labor efficiency and price variances Variable Uverhead eiciency and spending variances xed Overhead volume and spending variances Variable and xed Operating Expense variances Use the above variances to reconcile the difference bemaen the actual operating income and the static budget operating income. If any of the above variances are not used, explain why. Assume the total fine pool one market was anticipated to be 1,000,000 units. The actual total market size was only 880,000 units. Explain the Fernandez Company's Eluantity Variance in terms of market size and market share. Discuss any computational similarities between the above variances and the calculations involved in the strategic analysis of operating income [growth component, price-recovery component, and productivity component]. MANAGEMENT ACCOUNTING lIlUARTEFIL'tI @SPRINE 200?, VOL. 8, NELS Table 2: COMPLETED CALCULATIONSFERNANDEZ CASE HEX B. ACTUAL MIX MIX BlIIIG. MW QUANTITY STATIC mm mutter 000051105 W 311.011.} WE MEI Units 110,000 110,000 110,000 EM 100,000 Sales 12,001,000 341,000 11,060,000 060,000 11,000,000 1,000,000 10,000,000 Ma terials 2,595,125 81,125 2, 508.000 198,000 2,310,000 210,000 2,100,000 Labor 2,111,000 (33,000) 2,150,000 7 2,150,000 250,000 2,500,000 Variable Overhead 103,150 13,150 110,000 110,000 10,000 100,000 Variable Operating 1.310101 34.100 1,216,000 66.1111 1,210,0m 110.000 1.1 (11.0411 Total Variable Costs L406.515 102.515 1304,1110 2154,1111 1.31.000 econ Em Contribution Margin 4,504,425 238,425 4,356,000 396.1110 350,000 360,000 3,500,000 Hired C0513 3.311.041} more 3.310.010 - 3.011.001 - 3.0010111 Inc Dme 13% 425 10.425 1,356,010 396.001 96110111 30011 M Table 3: V0 LUME VARIANCE, MIX VARIANCE, AND QUANTITY VARIANCE FERNANDEZ CASE IIIIJGETEII 00mm com. meant TOTALS Flexible B min at 110,000 $ 39.60 $4,356,000 Static Budget 101.0301 M 3.011.011 Different: es 10,000 $ 3.60 Tll'l'lBS use MM $300.0 mm m nuanllly Mix Volume Table 4: ALTERNATE VIEW OF VARIANCES FERNANDEZ CASE acruar unusar can urrrrs summer BEERENCE Peru. Good 55,000 66,000 -1 1,000 $2400 $064,000 Better 38,500 33,000 5,500 $4800 264,000 Best 145.510 0.010 5,500 $72.00 530.011 00000 00000 sateen caIly present them vertically, with the actual quantity and prices on top (using the same format as with the sales mix and quantity variances.) Because the calcula- tions involve costs, positive differences reect unfavor- able variances, and negative differences reect favor able variances. The unfavorable material variance in \"able 2 ($81,725) is explained in Table 5. The labor variance can be presented using the same format as the material variances. Table 6 illustrates the $33,000 favorable labor variance. Wzrs'abie Overhead Variances When manufacturing overhead is allocated on the basis of direct labor hours, the variable overhead efciency variance will be consistent with the labor efficiency variance. A quick way to calculate the overhead effi- ciencyr variance is to multiplyr the labor efficiency vari~ ance by 7125 (the budgeted variable overhead per hour divided by the budgeted labor rate per hour). In this case, the answer would be a favorable $38,500 ($131,500 2; 1125). Table 2 shows the total variable over- head variance is $13,750 unfavorable. Thus, the variable overhead spending variance must be $52,250 unfavor- able. The variable overhead variances can be shown in a format similar to the materials and labor variances as in Table 7. Fixed Owrkead Variances The fixed overhead spending variance is typically the easiest to compute because both the actual amount and budgeted amount are known; it is simply a matter of subtracting. In the Fernandez case, the actual fixed overhead is $2,150,000, and the budgeted fixed over head is $2,000,000. The difference of $150,000 is the MANAGEMENT ACCOUNTING l'lUARTERL'Il @SPRINE 2001, VOL. 0, N0.3 Table 5: UNFAVO FIABLE MATERIAL VARIANCEFERNANDEZ CASE HIE?!\" Good Actual 302,500 Standard 25.1110 Difference 27,500 limes m M Batter Actual 211,150 Standard mm Difference 19.25 limes M M Best Actual 90.750 Standard 32.11111 Difference 8.250 limes M M Total Flexible Budget MaterialsVariances m Table 6: FAVO RAB LE LABOR VARIANCEFERNANDEZ CASE EFFICIENCY PRICE 10m Labor Actual 101.500 $ 26.00 $2317.00] Standard more 15411 2.151.011 Difference [5.5001 Si 1.01) limes c 25411 M 031.5111 3mm $133M Tahle'i: VARIABLE OVERHEAD VARIANCESFERNANDEZ CASE EFHGIEIIIW sntunmc Tom Var. 01H Actual 104,500 $ 15] $733350 Standard more L111 ELM Difference {5.500) $ 0.5] limes 1111 Mill! mam $52131 $13151 unfavorable xed overhead spending variance. The fixed overhead volume variance represents the under (over) applied fixed overhead. It can be calculat PRICE ram $2.30 $695,150 M more 310.101 312.511 amen $5.153! $4.50 $952,875 can more $0.301 211 7 artists $13.31!: $630 $611,100 m 31.11111 $01.40} 311131 assent $13.1!!! suntan 1 72 ed easily by multiplying the budgeted fixed overhead by the percentage difference in the number of actual units sold and the original number of units originally predicted. if units produced exceed the original budget, the variance is favorable (more xed overhead costs allocated than planned) and vice versa. Thus, the fixed overhead volume variance in this case is $200,000 favor- able ($2,000,000 x 10%). Because the volume variance in this case would be closed to cost ofgoods sold (or gross margin), this variance does not reect a difference in the actual income and the static budget income. Operating Expense Variances in this case, variable operating expenses were larger than anticipated because of higher sales commissions associated with higher sales prices. Because the sales commissions were 10% of sales prices, the unfavorable variable operating expense variance of $54,100 is equal to 10% of the favorable sales price variance of $341,000. The fixed operating expense variance is similar to the fixed overhead spending variance: It is calculated by subtracting the budgeted fixed operating expenses from the actual fixed operating expenses. in this case, the unfavorable fixed operating expense spending variance is $50,000 ($1,050,000 $1,000,000). Part 3 of the Fernandez case requires students to summarize Parts 1 and 2. As previously noted, the fixed overhead volume variance is the only one not used in MANAGEMENT ACCOUNTING l'lUARTERL'Il @SPRINE 200?. VOL. 8, NELS reconciling the difference between actual income and static budget income. Market Size and Market Share Variances Part 4of the Fernandez Company case provides infor: mation about the budgeted market size (1,000,000 units) and the actual market size (880,000 units). Stuw dents are asked to compute the market size and market share variances. Fernandez Company budgeted 100,000 units (10% of the budgeted market) but sold 110,000 units (12.5% of the actual market). Textbook solutions are traditionally much more complex than necessary. For example, using the data from this case, a typical solution would be: Market share = Actual market size it [Actual market share 7 Budgeted market sharelx Budgeted weighted average contribution margin per unit 300,000 x {.125 7 .10) it $30.00 = $792,111] favorable Market size =lAc1ual market size Budgeted market size) it Budgeted market share it Budgeted weighted average contribution margin per unit [880,000 71,000,0001x.10 x $3600 = $432,000 unfavorable Together the market share and market size variances account for the $360,000 favorable quantity variance. I prefer to simplify it by focusing on the causes of each variance. For example, one way to present it is: Market share = [Actual sales in units 710% of actual market) it $36.00 {110.0110 730.0111): $16.00 22,000 it $36.00 = $192,000 favora ble Market size = {10% of actual market 7 slabs budget units) it $315.00 [88,000 7 100.0001 it $46.00 42,000 it $36.00 = $432,000 unfavorable Another way to present the variances is to note that the market size variance is simply 12% (the decline in market size) times $3,600,000 (the static budget contri- bution margin), or $432,000 unfavorable. The market share variance is 25% (the percentage increase in the market share from 10% to 12.5%) times $3,168,000 ($5,600,000 $432,000). An even simpler presentation, representing just a minor modification, is: Actual units 110,000 Budgeted share of actual market 110% of $00,000) 38,000 Static budget unils 100,000 The market share variance ($792,000 favorable) is simply the difference between the first two numbers (22,000) times the budgeted contribution margin ($56.00). Likewise, the market size variance is the dif- ference between the second and third numbers times the budgeted contribution margin (-12,000 x $36.00 = $492,1X10 unfavorable). Part 5 asks Students to discuss computational similar- ities between the variances calculated and the calcula- tions involved with strategic analysis of operating income (growth component, pricewtecovety component, and productivity component). While strategic analysis is not \"variance analysis\" per se, certainly the computa- tions involved in the growth and price~recovery compo- nents, for example, are practically identical to the computations of the direct materials and direct labor efficiency and price variances. (I mention these again later when highlighting ways to increase or decrease the complexity of the cases.) THE ROGER COMPANY The Roger Company case (Table 8) is a straightforward problem involving the calculation of the materials price and efciency variances, then breaking down the mate- rials efficiency variance into the materials mix and yield variances. l primarily use this case to provide alternative approaches to solving these types of problems and to demonstrate computational similarities with the Fer- nandez Company case. The information provided for the Roger Company case can be used to create Table 9. In Table 9, the price variance is the difference between the total actual costs and the standard input costs for the actual mix: $56,732 - $55,120 = $1,612 unfavorable. The efficiency variance is the difference between the standard cost of the actual input and the standard cost of the actual output: $55,120 $50,000 = $5,120 unfavorable. MANAGEMENT ACCOUNTING l'lUARTERL'II @SPRINE 200?, VOL. 0, N0.3 Table 8: THE ROGER COMPANY CASE The Roger Company produces productNR'v' by heating materials X, Y. and 2. Normal evaporation loss is 31%; thus, 1,000 gallons of input are anticipated to yield an output orem gallons. STANDARDS for 000 gallons of NRVE Material X Material Y Material 2 Tota lsNVeighted Average UUTPUT of 40,000 gallons, actual costs: Material X Material Y Material 2 TatalsNVeighted Average Al. II 600 300 mg 1.013 ntwue 26,000 10,200 M ELM mm: PER canon m $0.00 $480 $1.20 360 m m1 M mm: PER game m $0.32 $21,320 31.23 22335 M 13.03; mm m Use the above information to calculate the materials price and elficiency variances. Then break down the efciency variance into the mix and yield variances. Explain any computational similarities as compared to the calculations of any of those variances you calculated for the Fernandez Company. Table 9: MIX AND YIELD VARIANCESHOGER CASE UUTPUT of 40,000 gallons, actual costs: Material X 26,000 Material Y 18,200 Material 2 T 000 TotaISMl'eig hted Average 52,5110 STANDARD input costs for 52,000 gallons {actual mix): Material X 25,000 Material Y 18,200 Material Z LEE! Totals/Weig hted Av era ge 521110 STANDARD for 40,000 gallons of output Material X 30,000 Material Y 15,030 Material Z M Totalsr'Average 50M $0320 $1 23] m M $0.00 $1.20 m m $0.00 $1.20 m m $21,320 22,306 EE $20,000 21,800 M m $24,000 18,000 3.53.0 Tablo1o: PRICE VARIANCE ROGER CASE PR E will m Material X 26,000 $0.020 $520 Material Y 18,200 $0.030 5-16 Material 2 1.3!!! m0 M TotalstWeighted Average seem sum $1.63 You can also calculate the total price variance by Inulw tiplying the actual input total by the difference in the actual and standard costs of the actual mix: 52,000 galw Ions times ($1.091 $1.060), or 52,000 x $0.031: $1,612. Of course, you can present the price variance in the more traditional fashion by multiplying each of the inputs by the difference in price, as shown in 'l'ahle 10. The materials mix and yield variances can be calcuw lated quite quickly by observing that the difference in the total input gallons and standard input gallons is 2,000 (52,000 50,000). Multiplying by the standard $1.00 average cost per gallon provides the unfavorable MANAGEMENT ACCOUNTING DUARTERLY @SPRINE 200?, VOL. 3, N0.3 Table 11: DETAILED APPROACH TO MIX VARIANCEROGER CASE ACTUAL INEII Material X 26,030 Material Y 13.2\"\" Material Z m Totals/Wain hted Av era ge 52.9110 Table12: SUMMARY OF VARIANCES Fernandez Dempany: Flexible Budget Varian ce: Sales Price Manufacturing CostVariances Materials Efficiency Materials Price Labor Price Variable Uverhead Efficiency Variable Overhead Price Fixed Overhead Spending erd Dverh ead Volu me {does not affect "profitability" in this case) perating Expenses Variable Spending [Sales Commission as % of Sales Price) xed Spending Sales Volume Variance: Mix uendty Ma rket Size Ma rket She re Efficiency [or Eluantity} Mix Yield TOTAL Ul'l'S HAMLIN! \"RENEE 31.200 {5.200) $0.30 $01.16!\" 1 5,600 2,600 $1.31 3,120 am 2,600 $1.00 5.010 52530 $11.20 yield variance of $2,000. That means the mix variance must be $3,120 unfavorable ($5,120 efficiency - $2,000 yield). The mix variance can also be calculated by simw ply multiplying 52,000 by the difference in the average budgeted cost of the actual mix and the standard aver- age budgeted coats: 52,000 x ($1.06 - $1.00) = $3,120 unfavorable. The more complete approach, which includes the individual causes of the mix variance, is shown in Table 11. The more detailed approach to the mix variance is identical to the illustration of the detailed sales mix variance in the Fernandez Company case, and the cal~ culations of the overall materials price variance is the same as for the sales price variance. The yield variance, using the weighted average standard budgeted cost per gallon, can be calculated in the same manner as the materials efficiency variances as shown in the Fernan- dez case. Exposlna STUDENTS TO A VARIETY OF APPROAC H 53 Obviously, all alternative approaches to derive the corw rect answer must be mathematically equivalent, so I often demonstrate mathematical equivalency when prew senting alternative solutions. Also keep in mind that you can easily revise the Fernandez case to increase its complexity: 6 Students could be required to prove the mathemati' cal equivalency ofalternative methods and, perhaps, challenged to offer their own alternatives. 6 More labor variances could be added by including additional classes (and costs) of labor for each prodw act and by having each product exhibit different efficiency variances for materials and labor. 0 Students may provide logical explanations of possi ble causes of individual variances. MANAGEMENT ACCOUNTING l'lUARTERL'Il @SPRINE 200?, VOL. 8, NELS 6 Another requirement might be to label the \"static budget" column as last year's numbers, and then have students perform strategic protability analysis. Complexity can be reduced by assuming the Fernan- dez Company produces only one product, thus elimir nating computations and discussions of the mix variances. The Roger Company case either can be expanded to include similar labor variances, or it can be eliminated. WHAT DO STUDENTS THINK? Overall student response to the two cases has been favorable. Students who struggled through the coverage ofthe exible budget and product cost variances stated almost unanimously that they gained a better under- standing by revisiting the material. While most agree that the cases are a lot of work they would prefer not to do, the majority appreciate being exposed to the \"big picture\" of variance analysis. The Vast majority indicate the benefit exceeded their sacrice. Table 12 summa- rizes the variances involved in the two cases. Reactions to the alternative approaches are mixed. Many students prefer to learn (memorize) whatever approach is offered in their textbook and \"not be con- fused\" by optional methods, even if they are easier to apply. Others, especially those who recognize the math~ ematical equivalencies of the methods, tend to prefer the easier approaches. I believe students should be exposed to a variety of approaches. This makes them more capable to solve problems that are presented in a slightly different manner than in their textbook, which is very useful in the real world. I Need VanZame, Pill, CMA, CFM, CPA, CFE, is a? pro femur afamaunfirg at Texas A8611! UHiveTsity-KigsvH/e. Smm'rtg in September, fie new be a family member a! {58 Usivem'gy of Texas Pam Amerr'wa, Ediebung, Texas. Neal can be (attracted at (956) 381-2406 or aegimrmmmm MANAGEMENT ACCOUNTING UUARTERLY @SPRING 200?, VOL. 3, Nl'J.3 Case Study Two 14-4: Helping Students See the 'Big Picture of Variance Analysis by Neal VanZante, Management Accounting Quarterly, Vol. 8, No. 3 (Spring 2007), pp. 3947. This paper presents two examples that can be used to reinforce concepts and procedures students learn in text Chapters 14 through 16. The rst example, Fernandez Company, can be used as a comprehensive review of all three chapters; the second example, Roger Company, can be used in conjunction with Chapter 14 if additional coverage of the joint price-quantity variance for direct materials (DM) is desired. The Fernandez Company example requires students to rst calculate the total flexible budget variance (in operating income) for a period and then breakdown this variance into its constituent parts (selling price variance, various cost variances, etc). Discussion Questions 1. What is meant by the total operating-income variance for a given accounting period? What alternative names are there to describe this variance. 2. What would be a rst-level breakdown of the total variance described above in (1)? 3. How can the total flexible-budget variance be broken down (i.e., what are the constituent parts of this total variance)? 4. Explain the total sales volume variance for a period. How can this total variance be decomposed