Martin's Management Accounting Textbook: Chapter 13 (2024)

Chapter 13
Profit Analysis: An Overall Performance Evaluation

Chapter Contents

INTRODUCTION

Profit analysis refers to the techniques usedto generate an overall performance evaluation from the financial perspective. It is a broader level of analysisthan the standard cost variance analysis for manufacturing costs and includes those variances as well as several others.

There are four factors that affect any type of multi-product profit measurement. These include:

1. Sales prices,
2. Unit costs,
3. Sales volume, and
4. Sales mix.

Remember the underlying assumptions in the master budget and conventional linear cost-volume-profit analysis, i.e., constant salesprices, constant unit variable costs, and constant sales mix. This chapter shows how to analyze the differences between the staticmaster budget and actual performance recognizing that prices, costs and sales mix are not constant.

Profit measurements that can be analyzed include manufacturing margin, contribution margin, gross profit, throughput and net income.Measurements based on the ABC cost hierarchy could also be used such the contributions at the unit, batch, product and facility levels. See Chapter7 for a discussion of the cost hierarchy. Each type of analysis involves explaining the difference between the actual andbudgeted (or some previous period's) profit measurements in terms of sales price, unit cost, sales volume and, when applicable, sales mix. An overall view of profitanalysis appears in the graphic illustration presented in Exhibit 13-1 below.

The approach to profit analysis is essentially the same regardless of the type of profit measurement involved. However, theform of the data available to the analyst determines the specific calculations required. The data may be in the form of: 1) Units and dollars, or2) Dollars only. If the data are in the form of units and dollars, i.e., unit sales, unit prices, and unit costs, then the effects of allfour elements , i.e., sales price, unit cost, sales volume, and sales mix can be determined. However, if the data are in the form of dollars only, then only the effects of salesprices, unit costs, and sales volume can be accurately determined. This is usually not a problem however,since the sales mix variances are only useful when the products involved may be purchased as substitutes for each other. This point will be explained below.

The profit analysis techniques applicable to both direct and full absorption costing are illustrated in this chapter. Thetechniques are practically the same for both inventory valuation methods. As a result, the total amount to be learned is considerably less than it may appearwhen one first skims through the chapter. Profit analysis for direct costing is illustrated first. This is referred to as contribution margin analysis and isdivided into two sections: I.A) contribution margin analysis when the data are in units and dollars, and I.B) contribution margin analysis when the available data areonly stated in dollars. Then profit analysis for full absorption costing is illustrated in two sections including: II.A) gross profit analysis when the data are in unitsand dollars, and II.B) gross profit analysis when the data are stated only in dollars. At the end of each section, an income statement approach is presented thatprovides an alternative way to calculate the variances and a more revealing picture of performance.

I. PROFIT ANALYSIS FOR DIRECT COSTING

A. CONTRIBUTION MARGIN ANALYSIS WHEN DATA ARE IN UNITS AND DOLLARS

Profit analysis is usually based on a comparison of the actual data with the budget, but the actual data for thecurrent period can also be compared with the actual data from a previous period. The illustrations below are based on a comparison of actualresults against the budget.

As indicated above, a difference between budgeted and actual contribution margin may result because of the combinedeffects of four related but different factors. The purpose of this type of analysis is to isolate the specific cause and effect relationships by separatingthe total variance into various parts. The following symbols are used to illustrate the techniques:

AU = Actual units sold for individual products.
BU = Budgeted units sold for individual products.
AP = Actual average sales price forindividual products.
BP = Budgeted sales price for individualproducts.
AV = Actual unit variable cost forindividual products.
BV = Budgeted unit variable cost forindividual products.
MR = Budget mix ratio for individualproducts, i.e., budgeted units for theproduct divided by total units budgeted for all products.
ACM = Actual contribution margin per unitfor individual products.
BCM = Budgeted contribution margin per unitfor individual products.
TAU = Total actual units sold.
AUA = Actual units adjusted to the budgetedmix = (TAU)(MR)

There are many different approaches to profit analysis. The analyst usually starts by determining the total variance in theprofit measurement, in this case, contribution margin. This is the difference between actual total contributionmargin and budgeted total contribution margin. Then this variance may be separated to show the effects of: 1) sales price and unit cost differences, and2) sales volume differences.

Two Variance Approach

In the two variance approach the total variance is divided into a combined price cost (or flexible budget) variance, and a sales volumevariance. This is accomplished in the following manner:

Price Cost or Flexible Budget Variance = Actual total contribution margin - Flexible budget contribution marginbased on actual units
= (ACM)(AU) - (BCM)(AU) or (ACM-BCM)(AU)

The price cost variance combines the effects of both sales price differences and unit cost differences. It is also frequentlycalled the contribution margin per unit variance and is calculated like a price variance by multiplying the difference between the budgeted and actual contribution marginper unit by the actual units sold. The variance is favorable if the actual contribution margin per unit is greater than the budgeted contribution per unit.

Sales Volume Variance = Flexible budget contribution margin based on actual units - Master budgetcontribution margin
= (AU) (BCM) - (BU)(BCM) or (AU-BU)(BCM)

The sales volume variance combines the effects that sales volume differences have on revenue and costs. It also includes theeffects of sales mix differences. It is favorable if the actual units sold are greater than budgeted unit sales. Budgeted contribution margin per unit is usedin the calculation to isolate the sales volume effects, i.e., to keep the price and cost effects out of the calculation.

Note that when combined, the Price Cost Variance and the Sales Volume Variance must be equal to the Total Variance in contributionmargin. This is illustrated by the combined two variance flexible budget approach illustrated in Exhibit 13-2.

Four Variance Approach

The two variances above can be separated in several ways to provide a clearer picture. A useful technique is to separate the Price Cost Variance toshow the effects of sales price and unit cost differences. This is done in the following manner:

Sales Price Variance= Actual sales revenue - Flexible budget sales revenue for actual units sold
= (AP)(AU) - (BP)(AU) or (AP-BP)(AU)

The actual sales prices in these calculations are average prices for the period involved. The sales price variance measures the effectthat different prices had on sales revenue, contribution margin and net income. It is favorable if the actual sales price is greater than the budgeted salesprice.

Unit Cost Variance = Actual variable costs - Flexible budget variable costs for actual units sold
= (AV)(AU) - (BV)(AU) or (AV-BV)(AU)

The unit cost variance measures the differences between budgeted variable cost and actual variable cost for both product costs andselling and administrative expenses. It is favorable if the actual variable cost per unit is less than the budgeted variable cost per unit. Although it isfrequently referred to as a cost price variance, it includes both input price differences (i.e., for direct materials,direct labor, variable overhead and variable selling and administrative cost) and any quantity differences for the various inputs.

Note that when combined, the sales price variance and the unit cost variance must be equal to the price cost or contribution margin perunit variance.

Total Variance in Sales Revenue = Sales price variance + Revenue part of sales volume variance

The combined flexible budget approach presented in Exhibit 13-3 illustrates these relationships.

Also note that the total variance in variable costs is caused by two factors: 1) the differences in unit cost, and 2) the differences in salesvolume. Specifically, this is stated in the following manner:

Total Variance in Variable Costs = Unit cost variance + Cost part of sales volume variance

The combined flexible budget approach presented in Exhibit 13-4 emphasizes these cost relationships.

Alternative Four Variance Approach IncludingSales Mix Variances

When products may be purchased as substitutes for each other, it may be useful to measure the effect of a difference between the budgeted andactual sales mix. The approach is similar to the calculations required for direct material mix and yield variances. In this case, the purpose is todetermine the effect that a difference between the budgeted sales mix and the actual sales mix had on contribution margin and net income. The techniqueseparates the sales volume variance into two parts: 1) the sales mix variance, and 2) the sales quantity variance. One way to do this is to determine theactual units of each product that would have been sold if the actual sales mix had been the same as the budgeted sales mix. These measurements are referred to as actualunits adjusted to the budgeted mix (AUA). The differences between these adjusted units and the actual units sold provides the mix variations in terms of units. Multiplyingthese differences by the budgeted contribution margin per unit provides the sales mix variance that shows of the effect the sales mix differences had on contribution margin.The calculations are as follows for each product:

Actual Units Adjusted to the Budgeted Mix or AUA= (Total Actual Units Sold)(Budgeted Mix Ratio)= (TAU)(MR)

Where the Budgeted Mix Ratios = Budgeted units sales for each product ÷ Total budgeted unit sales

Sales Mix Variance= (AU-AUA)(BCM)

Sales Quantity Variance = (AUA-BU)(BCM)

The sales quantity variance represents what the sales volume variance would have been if the budgeted sales mix and actual sales mix were thesame. It is easy to see this because the sum of the sales mix variance and sales quantity variance has to equal the sales volume variance. Notice also that ifthe budgeted sales mix and actual sales mix are the same, then actual units and actual units adjusted would be the same quantity. This would cause thesales mix variance to be zero, and the sales quantity variance would be equal to the sales volume variance.

Summary Exhibit - The profit analysis equations illustrated in Part I. A aresummarized in Exhibit 13-5 for easy reference.

The comparative income statements in Exhibit 13-7 indicatethat the actual performance is considerably better than the master budget. Morespecifically, actual net income before taxes was $170,000 higher than budgetedand, after subtracting the variance for fixed costs, the total variance incontribution margin was $171,600 higher than budgeted. However, it is not clearwhat caused these favorable results. What is needed is to separate the totalvariance to isolate the effects of sales price, cost, sales volume, and salesmix differences.

SOLUTION TO EXAMPLE 13-1

The calculations for each variance are illustrated in Exhibit 13-8. A discussion of the meaning of the variancesappears below the exhibit.

AUA = (Total Actual Units)(Mix Ratio)
Economy (22,800)(10/20) = 11,400
Regular (22,800)(8/20) = 9,120
Delux (22,800)(2/20) = 2,280
Total units = 22,800

The two variance approach presented in the left-hand column of Exhibit13-8 indicatesthat sales price and unit cost differences accounted for $51,600 of thisfavorable variance and sales volume differences accounted for the other$120,000. But notice from Exhibit 13-7 that there is a $401,200 favorablevariance in sales revenue. The four variance approach in the center of Exhibit13-8 reveals that$109,200 of this variance was caused by sales price differences, and $292,000was caused by sales volume differences. Also observe that there is a $229,600unfavorable variance in variable costs. Exhibit 13-8 indicates that $57,600 ofthis variance was caused by unit cost differences and $172,000 was caused bysales volume differences.

Assuming the three products are substitute products, then thesales mix variances may be useful is evaluating an attempt to improve the salesmix, i.e., trade customers up to the more expensive, higher margin products. In thisexample there is a larger proportion of the less profitable products in the actual mix.If the firm had sold the same actual total units, but in proportion to the budgetedmix ratios, then actual contribution margin would have been $16,080 greater (asindicated by the unfavorable total sales mix variance) andthe sales volume variance would have been $136,080 favorable (as indicated bythe total sales quantity variance).

The Income Statement Approach: A Convenient Alternative

The methods presented above are useful for isolating eachspecific variance, but the solution presented in Exhibit 13-8 is probably notthe best method for presenting the analysis to management. The comparative incomestatement approach illustrated in Exhibit 13-9 generates the same resultsas the four variance method, and also provides a morerevealing picture of the overall profit analysis. The approach is fairly simple. Startwith the comparative income statements in Exhibit 13-7 and add a forth column bymultiplying the actual units sold by the budgeted or standard prices and unitcost. This is a flexible budget based on the actual sales level. Then the pricecost variances are the differences between the actual results and the flexiblebudget, i.e., columns 2 and 4. The sales volume variances are the differencesbetween the static master budget and the flexible budget, i.e., columns 1 and 4.Observe that the variances in column 5 are the sales price variances and theunit cost variances (compare with Exhibit 13-8). The total price-cost varianceis in the contribution margin row of column 5. Also note that the variances incolumn 6 are the revenue and cost parts of the sales volume variances. The totalsales volume variance is in the contribution margin row of column 6.

* Column 4represents a flexible budget based on actual units sold, i.e., Sales: E =(12,000)($100), R = (9,000)($120), D = (1,800)($140); Variable Cost: E =(12,000)($60), R = (9,000)($66), D = (1,800)($70). Fixed costs are from theoriginal budget.

The sales mix and sales quantity variances could be added tothe presentation for all rows, by adding a seventh column calculated bymultiplying actual units adjusted to the budgeted mix, i.e., AUA, by thebudgeted prices and unit costs. Then the revenue and cost parts of the sales mixvariances would be the differences between columns 4 and 7. The revenue and costparts of the sales quantity variances would be the difference between columns 1and 7.

Before moving on to the next section, observe from Exhibit13-9 that fixed costs can also be included in the analysis. Note, that the fixedcosts that appear in column 4 are the same amounts that appear in column 1 sincefixed costs are not affected by sales volume. For this reason any variances forfixed costs will appear in column 5 an represent mixed price/quantity variances.Also notice that when fixed costs are included in the analysis, the totalprice-cost variance is $50,000 rather than $51,600. In other words, the totalprice-cost variance is the last amount in column 5. When we limit the analysisto contribution margin, it is $51,600 (see Exhibit 13-8), but if we carry theanalysis down to net income, it is $50,000 (see Exhibit 13-9).

Why Multiple Approaches Are Presented

The different approaches provide different perspectives thattends to strengthen our understanding of the techniques. The equation approachcombines the effects of sales prices and unit cost into one variance (Price-costvariance) and then shows how this variance can be separated into sales price andunit cost variances. It also combines the volume effects into one variance(Sales volume variance) and then shows how this can be separated to show thesales volume effects on revenue and cost. The diagram approach emphasizes thetotal variance in sales dollars and the separate price and volume effects (i.e.,sales price variance and revenue part of sales volume variance). It alsoemphasizes the total variance in costs and the separate unit cost and volumeeffects (i.e., unit cost variance and cost part of sales volume variance). Theincome statement approach shows all of this an more. The sales price and unitcost effects are emphasized in column 5, while the volume effects on revenue andcost are emphasized in column 6. On the other hand, the sales rows emphasize theseparate price and volume effects on revenue, and the cost rows emphasize theseparate unit cost and volume effects on costs. Learning how to use all threeapproaches will help insure that you understand the concepts involved.

QUESTIONS

Some questionsrelated to profit analysis.

PROBLEMS

PROBLEM 13-1
Profit Analysis based on Contribution Margin: Single Product, Data in Units

Assume the Riley Company manufactures and sells a single product. Budgetedand actual unit sales are indicated below as well as comparative income statements.

Calculate the following variances and indicate if each variance is favorable or unfavorable.

1. Sales price variance.
2. Unit cost variance.
3. Price-cost variance or flexible budget variance.
4. Sales volume variance or planning variance.
5. Revenue part of the sales volume variance.
6. Cost part of the sales volume variance.
7. Show how two of the variances explain the total variance in sales dollars.
8. Show how two of the variances explain the total variance in variable cost.

For the solution to this problem see theDemonstration problem.

PROBLEM 13-2

Profit Analysis based on Gross Profit - Single Product, Data in Units

This problem is not included because it goes with part IIA.

PROBLEM 13-3

Profit Analysis based on Contribution Margin - Two Products, Data in Units

Required:

1. Sales price variances.
2. Unit cost variances.
3. Price-cost variances or contribution margin per unit variances.
4. Sales volume variances.
5. Revenue part of the sales volume variances.
6. Cost part of the sales volume variances.
7. Sales mix variances.
8. Sales quantity variances.
9. Which two variances explain the total variance in sales dollars?
10. Which two variances explain the total variance in variable costs?
11. Which two variances explain the total variance in contribution margin?
12. Which two variances include the manufacturing cost variances for directmaterial, direct labor, and variable overhead?

Problem Solutions

Extra MC Questions