# Helping students see the "big picture" of variance analysis: two case problems are presented to 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 prepared to handle and address variance issues when they arise in the real world.

Variances, or the differences between budgeted, 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 typically presented in cost/managerial accounting textbooks. Some textbook coverage is disjointed, with brief mentions of flexible budget variances just prior to discussing manufacturing cost variances. Then, in a much later chapter, sales-variance analysis may be covered with little or no reference to the earlier sections. Discussion of input mix and yield variances may be presented in appendices, if at all.In addition to these disjointed presentations, textbook 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 chapter, 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 computational aspects of some of the variances.

In my senior/graduate-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 calculate all variances typically presented in cost/managerial textbooks, they are continuously reminded of the numerous similarities in the computational aspects of these variances. Furthermore, they learn--and understand--alternative methods for computing variances and presenting their solutions.

The first case requires students to calculate all the traditional sales variances and the "flexible budget" variances for the Fernandez Company, which manufactures 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 Product 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 flexible budgeting. The Fernandez Company table, however, has additional columns to incorporate the sales mix variance and rows for both variable and fixed operating expenses. Because accurate completion of this table is vital for students to fulfill and better understand the remaining requirements, I provide "check figures" and "help" as necessary to ensure successful completion. Students may complete the table manually, but I encourage them to use a spreadsheet package so they may clearly observe the computational similarities of each number and, thus, are better prepared to understand the differences. Students comfortable with a spreadsheet package tend to use the copy command and then revise the formulas as needed. The completed table appears in Table 2.

Sales Volume, Sales 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 flexible 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 solution 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 average 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 commissions based on the higher average price) times 110,000 equals the $60,000 variable operating expense difference; 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 of the mix variance.

Sales Price Variance

The sales price variance is the $341,000 at the top of the flexible budget variance column in Table 2. It is the difference 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 average 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) multiplied 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 Labor Variances

The total materials variance may be broken down between price and efficiency (quantity) differences. While most textbooks present these horizontally, I typically 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 calculations involve costs, positive differences reflect unfavorable variances, and negative differences reflect favorable variances. The unfavorable material variance in Table 2 ($87,725) 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.

Variable Overhead Variances

When manufacturing overhead is allocated on the basis of direct labor hours, the variable overhead efficiency variance will be consistent with the labor efficiency variance. A quick way to calculate the overhead efficiency variance is to multiply the labor efficiency variance by 7/25 (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 ($137,500 x 7/25). Table 2 shows the total variable overhead variance is $13,750 unfavorable. Thus, the variable overhead spending variance must be $52,250 unfavorable. The variable overhead variances can be shown in a format similar to the materials and labor variances as in Table 7.

Fixed Overhead 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 overhead is $2,000,000. The difference of $150,000 is the unfavorable fixed overhead spending variance.

The fixed overhead volume variance represents the under (over) applied fixed overhead. It can be calculated 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 fixed overhead costs allocated than planned) and vice versa. Thus, the fixed overhead volume variance in this case is $200,000 favorable ($2,000,000 x 10%). Because the volume variance in this case would be closed to cost of goods sold (or gross margin), this variance does not reflect 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 $34,100 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 reconciling the difference between actual income and static budget income.

Market Size and Market Share Variances

Part 4 of the Fernandez Company case provides information about the budgeted market size (1,000,000 units) and the actual market size (880,000 units). Students 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 x (Actual market share - Budgeted market share) x Budgeted weighted average contribution margin per unit

880,000 x (.125-.10) x $36.00 = $792,000 favorable

Market size = (Actual market size-Budgeted market size) x Budgeted market share x Budgeted weighted average contribution margin per unit

(880,000 - 1,000,000) x .10 x $36.00 = $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 - 10% of actual market) x $36.00

(110,000 - 88,000) x $36.00

22,000 x $36.00 = $792,000 favorable

Market size = (10% of actual market - static budget units) x $36.00 (88,000 - 100,000) x $36.00 -12,000 x $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 contribution 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 ($3,600,000 - $432,000).

An even simpler presentation, representing just a minor modification, is:

Actual units 110,000 Budgeted share of actual market (10% of 880,000) 88,000 Static budget units 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 ($36.00). Likewise, the market size variance is the difference between the second and third numbers times the budgeted contribution margin (-12,000 x $36.00 = $492,000 unfavorable).

Part 5 asks students to discuss computational similarities between the variances calculated and the calculations involved with strategic analysis of operating income (growth component, price-recovery component, and productivity component). While strategic analysis is not "variance analysis" per se, certainly the computations involved in the growth and price-recovery components, 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 efficiency variances, then breaking down the materials efficiency variance into the materials mix and yield variances. I primarily use this case to provide alternative approaches to solving these types of problems and to demonstrate computational similarities with the Fernandez 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.

You can also calculate the total price variance by multiplying the actual input total by the difference in the actual and standard costs of the actual mix: 52,000 gallons 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 Table 10.

The materials mix and yield variances can be calculated 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 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 simply multiplying 52,000 by the difference in the average budgeted cost of the actual mix and the standard average budgeted costs: 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 calculations 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 Fernandez case.

EXPOSING STUDENTS TO A VARIETY OF APPROACHES

Obviously, all alternative approaches to derive the correct answer must be mathematically equivalent, so I often demonstrate mathematical equivalency when presenting alternative solutions. Also keep in mind that you can easily revise the Fernandez case to increase its complexity:

* Students could be required to prove the mathematical equivalency of alternative methods and, perhaps, challenged to offer their own alternatives.

* More labor variances could be added by including additional classes (and costs) of labor for each product and by having each product exhibit different efficiency variances for materials and labor.

* Students may provide logical explanations of possible causes of individual variances.

* Another requirement might be to label the "static budget" column as last year's numbers, and then have students perform strategic profitability analysis.

Complexity can be reduced by assuming the Fernandez Company produces only one product, thus eliminating 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 of the flexible budget and product cost variances stated almost unanimously that they gained a better understanding 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 sacrifice. Table 12 summarizes 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 confused" by optional methods, even if they are easier to apply. Others, especially those who recognize the mathematical 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.

Neal VanZante, Ph.D., CMA, CFM, CPA, CFE, is a professor of accounting at Texas A&M University-Kingsville. Starting in September, he will be a faculty member at the University of Texas Pan American, Edinburg, Texas. Neal can be contacted at (956) 381-2406 or nealvz@stx.rr.com.

Table 1: THE FERNANDEZ COMPANY CASE SALES UNITS SALES PRICES PRODUCT BUDGET ACTUAL BUDGET ACTUAL Good 60,000 55,000 $80.00 $82.00 Better 30,000 38,500 $120.00 $123.00 Best 10,000 16,500 $160.00 $167.00 Totals/Average 100,000 110,000 $100.00 $109.10 The average budgeted sales price based on actual mix is $106.00. BUDGET ACTUAL Fixed Costs-Overhead $2,000,000 $2,150,000 Fixed Costs-Operating Expenses $1,000,000 $1,050,000 Total $3,000,000 $3,200,000 COSTS FEET/HOURS PER FOOT/HOUR PER UNIT PRODUCT BUDGET ACTUAL BUDGET ACTUAL Materials Good $2.40 $2.30 5.0 5.5 Better $4.80 $4.50 5.0 5.5 Best $7.20 $6.80 5.0 5.5 All Budgeted and actual $3.00 per unit for a carrying case. Labor All $25.00 $26.00 1.0 0.95 Variable OVH All $7.00 $7.50 1.0 0.95 Variable Operating Budgeted and actual 10% sales commission and Expenses $1.00 per unit shipping. REQUIREMENTS First complete the following table. FLEX B. ACTUAL MIX MIX ACTUAL $ VARIANCE BUDGETED $ VARIANCE Units 110,000 110,000 Sales Materials Labor Variable Overhead Variable Operating Total Variable Costs Contribution Margin Fixed Costs Income BUDG. MIX/ QUANTITY STATIC BUDG. $ VARIANCE BUDGET Units 110,000 10,000 100,000 Sales Materials Labor Variable Overhead Variable Operating Total Variable Costs Contribution Margin Fixed Costs Income Assuming no beginning nor ending inventories of any kind, show the calculation of the following 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 Overhead efficiency and spending variances Fixed Overhead volume and spending variances Variable and Fixed Operating Expense variances Use the above variances to reconcile the difference between 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 cue market was anticipated to be 1,000,000 units. The actual total market size was only 880,000 units. Explain the Fernandez Company's Quantity 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). Table 2: COMPLETED CALCULATIONS--FERNANDEZ CASE FLEX B. ACTUAL MIX MIX ACTUAL $ VARIANCE BUDGETED $ VARIANCE Units 110,000 -- 110,000 -- Sales 12,001,000 341,000 11,660,000 660,000 Materials 2,595,725 87,725 2,508,000 198,000 Labor 2,717,000 -33,000 2,750,000 -- Variable Overhead 783,750 13,750 770,000 -- Variable Operating 1,310,100 34,100 1,276,000 66,000 Total Variable Costs 7,406,575 102,575 7,304,000 264,000 Contribution Margin 4,594,425 238,425 4,356,000 396,000 Fixed Costs 3,200,000 200,000 3,000,000 -- Income 1,394,425 38,425 1,356,000 396,000 BUDG. MIX/ QUANTITY STATIC BUDG. $ VARIANCE BUDGET Units 110,000 10,000 100,000 Sales 11,000,000 1,000,000 10,000,000 Materials 2,310,000 210,000 2,100,000 Labor 2,750,000 250,000 2,500,000 Variable Overhead 770,000 70,000 700,000 Variable Operating 1,210,000 110,000 1,100,000 Total Variable Costs 7,040,000 640,000 6,400,000 Contribution Margin 3,960,000 360,000 3,600,000 Fixed Costs 3,000,000 -- 3,000,000 Income 960,000 360,000 600,000 Table 3: VOLUME VARIANCE, MIX VARIANCE, AND QUANTITY VARIANCE--FERNANDEZ CASE BUDGETED QUANTITY CONT. MARGIN TOTALS Flexible Budget 110,000 $39.60 $4,356,000 Static Budget 100,000 $36.00 3,600,000 Differences 10,000 $3.60 Times $36.00 110,000 $360,000 $396,000.00 $756,000 Quantity Mix Volume Table 4: ALTERNATE VIEW OF VARIANCES--FERNANDEZ CASE ACTUAL UNITS AT C/M UNITS BUDG. MIX DIFFERENCE PER U. Good 55,000 66,000 -11,000 $24.00 $(264,000) Better 38,500 33,000 5,500 $48.00 264,000 Best 16,500 11,000 5,500 $72.00 396,000 110,000 110,000 $396,000 Table 5: UNFAVORABLE MATERIAL VARIANCE--FERNANDEZ CASE EFFICIENCY PRICE TOTAL Good Actual 302,500 $2.30 $695,750 Standard 275,000 2.40 660,000 Difference 27,500 $(0.10) Times $2.40 302,500 $66,000 $(30,250) $35,750 Better Actual 211,750 $4.50 $952,875 Standard 192,500 4.80 924,000 Difference 19,250 $(0.30) Times $4.80 211,750 $92,400 $(63,525) $28,875 Best Actual 90,750 $6.80 $617,100 Standard 82,500 7.20 594,000 Difference 8,250 $(0.40) Times $7.20 90,750 $59,400 $(36,300) $23,100 Total Flexible Budget Materials Variances $217,800 $(130,075) $87,725 Table 6: FAVORABLE LABOR VARIANCE--FERNANDEZ CASE EFFICIENCY PRICE TOTAL Labor Actual 104,500 $26.00 $2,717,000 Standard 110,000 25.00 2,750,000 Difference (5,500) $1.00 Times $25.00 104,500 $(137,500) $104,500 $(33,000) Table 7: VARIABLE OVERHEAD VARIANCES--FERNANDEZ CASE EFFICIENCY SPENDING TOTAL Var. O/H Actual 104,500 $7.50 $783,750 Standard 110,000 7.00 770,000 Difference (5,500) $0.50 Times $7.00 104,500 (38,500) $52,250 $13,750 Table 8: THE ROGER COMPANY CASE The Roger Company produces product NRV by heating materials X, Y, and Z. Normal evaporation loss is 20%; thus, 1,000 gallons of input are anticipated to yield an output of 800 gallons. STANDARDS for 800 gallons of NRV: GALLONS PRICE PER GALLON TOTAL Material X 600 $0.80 $480 Material Y 300 $1.20 360 Material Z 100 $1.60 160 Totals/Weighted Average 1,000 $1.00 $1,000 OUTPUT of 40,000 gallons, actual costs: GALLONS PRICE PER GALLON TOTAL Material X 26,000 $0.82 $21,320 Material Y 18,200 $1.23 22,386 Material Z 7,800 $1.67 13,026 Totals/Weighted Average 52,000 $1.09 $56,732 Use the above information to calculate the materials price and efficiency variances. Then break down the efficiency 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 VARIANCES--ROGER CASE OUTPUT of 40,000 gallons, actual costs: Material X 26,000 $0.82 $21,320 Material Y 18,200 $1.23 22,386 Material Z 7,800 $1.67 13,026 Totals/Weighted Average 52,000 $1.09 $56,732 STANDARD input costs for 52,000 gallons (actual mix): Material X 26,000 $0.80 $20,800 Material Y 18,200 $1.20 21,840 Material Z 7,800 $1.60 12,480 Totals/Weighted Average 52,000 $1.06 $55,120 STANDARD for 40,000 gallons of output: Material X 30,000 $0.80 $24,000 Material Y 15,000 $1.20 18,000 Material Z 5,000 $1.60 8,000 Totals/Average 50,000 $1.00 $50,000 Table 10: PRICE VARIANCE--ROGER CASE PRICE GALLONS DIFFERENCE TOTAL Material X 26,000 $0.020 $520 Material Y 18,200 $0.030 546 Material Z 7,800 $0.070 546 Totals/Weighted Average 52,000 $0.031 $1,612 Table 11: DETAILED APPROACH TO MIX VARIANCE--ROGER CASE ACTUAL TOTAL UNITS INPUT STAND. MIX DIFFERENCE Material X 26,000 31,200 (5,200) $0.80 $(4,160) Material Y 18,200 15,600 2,600 $1.20 3,120 Material Z 7,800 5,200 2,600 $1.60 4,160 Totals/Weighted Average 52,000 52,000 3,120 Table 12: SUMMARY OF VARIANCES Fernandez Company: Flexible Budget Variance: Sales Price Manufacturing Cost Variances Materials Efficiency Materials Price Labor Price Variable Overhead Efficiency Variable Overhead Price Fixed Overhead Spending Fixed Overhead Volume (does not affect "profitability" in this case) Operating Expenses Variable Spending (Sales Commission as % of Sales Price) Fixed Spending Sales Volume Variance: Mix Quantity Market Size Market Share Roger Company: Price Efficiency (or Quantity) Mix Yield