Management Accounting:
Concepts, Techniques & Controversial Issues

James R. Martin

Chapter 13
Profit Analysis: An Overall Performance Evaluation

MAAW's Book Main Page

 CONTENTS Introduction Profit Analysis Graphic Part I: Contribution Margin Analysis with Unit data Part I: Two Variance Approach Part I: Four Variance Approach Part I: Alternative Four Variance Approach with Sales Mix Variance Part I: Summary Exhibit Example 13-1 Part I: The Income Statement Approach Problems Problem Solutions Extra MC Questions

INTRODUCTION

Profit analysis refers to the techniques used to generate an overall performance evaluation from the financial perspective. It is a broader level of analysis than 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 sales prices, constant unit variable costs, and constant sales mix. This chapter shows how to analyze the differences between the static master 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 Chapter 7 for a discussion of the cost hierarchy. Each type of analysis involves explaining the difference between the actual and budgeted (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 profit analysis 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, the form of the data available to the analyst determines the specific calculations required. The data may be in the form of: 1) Units and dollars, or 2) 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 all four 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 sales prices, 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. The techniques are practically the same for both inventory valuation methods. As a result, the total amount to be learned is considerably less than it may appear when one first skims through the chapter. Profit analysis for direct costing is illustrated first. This is referred to as contribution margin analysis and is divided 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 are only 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 units and 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 that provides 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 the current period can also be compared with the actual data from a previous period. The illustrations below are based on a comparison of actual results against the budget.

As indicated above, a difference between budgeted and actual contribution margin may result because of the combined effects of four related but different factors. The purpose of this type of analysis is to isolate the specific cause and effect relationships by separating the 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 for individual products.
BP = Budgeted sales price for individual products.
AV = Actual unit variable cost for individual products.
BV = Budgeted unit variable cost for individual products.
MR = Budget mix ratio for individual products, i.e., budgeted units for
the
ACM = Actual contribution margin per unit for individual products.
BCM = Budgeted contribution margin per unit for individual products.
TAU = Total actual units sold.
AUA = Actual units adjusted to the budgeted mix = (TAU)(MR)

There are many different approaches to profit analysis. The analyst usually starts by determining the total variance in the profit measurement, in this case, contribution margin. This is the difference between actual total contribution margin and budgeted total contribution margin. Then this variance may be separated to show the effects of: 1) sales price and unit cost differences, and 2) 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 volume variance. This is accomplished in the following manner:

Price Cost or Flexible Budget Variance
= Actual total contribution margin - Flexible budget contribution margin based 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 frequently called the contribution margin per unit variance and is calculated like a price variance by multiplying the difference between the budgeted and actual contribution margin per 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 budget contribution 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 the effects of sales mix differences. It is favorable if the actual units sold are greater than budgeted unit sales. Budgeted contribution margin per unit is used in 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 contribution margin. 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 to show 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 effect that different prices had on sales revenue, contribution margin and net income. It is favorable if the actual sales price is greater than the budgeted sales price.

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 and selling and administrative expenses. It is favorable if the actual variable cost per unit is less than the budgeted variable cost per unit. Although it is frequently 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 per unit variance.

The Sales Volume Variance can be separated to show the effects that sales volume differences had on revenue and cost. This is done in the following manner:

Revenue Part of Sales Volume Variance
= Flexible Budget Sales Revenue for actual units sold - Master budget sales revenue

= (AU)(BP) - (BU)(BP) or (AU-BU)(BP)

Cost part of Sales Volume Variance
= Flexible budget variable costs for actual units sold - Master budget variable costs

= (AU)(BV) - (BU)(BV) or (AU-BU)(BV)

Notice that the total variance in sales revenue is caused by two factors: 1) the differences in sales prices, and 2) the differences in sales volume. This can be stated more specifically as follows:

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 sales volume. 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 Including Sales 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 and actual sales mix. The approach is similar to the calculations required for direct material mix and yield variances. In this case, the purpose is to determine the effect that a difference between the budgeted sales mix and the actual sales mix had on contribution margin and net income. The technique separates 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 the actual 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 actual units 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. Multiplying these 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 the same. 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 if the 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 the sales 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 are summarized in Exhibit 13-5 for easy reference.

 EXHIBIT 13-5 Two Variance Four Variance Alternative Four Variance Price Cost Variance  (ACM-BCM)(AU) Sales Price Variance (AP-BP)(AU) Sales Price Variance (AP-BP)(AU) Unit Cost Variance (AV-BV)(AU) Unit Cost Variance (AV-BV)(AU) Sales Volume Variance (AU-BU)(BCM) Revenue part of  Sales Volume Variance  (AU-BU)(BP) Sales Mix Variance (AU-AUA)(BCM) Cost part of  Sales Volume Variance   (AU-BU)(BV) Sales Quantity Variance (AUA-BU)(BCM)
 Where: AU = Actual units sold for individual products. BU = Budgeted units sold for individual products. AP = Actual average sales price for individual products. BP = Budgeted sales price for individual products. AV = Actual unit variable cost for individual products. BV = Budgeted unit variable cost for individual products. MR = Budget mix ratio for individual products, i.e., budgeted units for the product divided by total units budgeted for all products. ACM = Actual contribution margin per unit for individual products. BCM = Budgeted contribution margin per unit for individual products. TAU = Total actual units sold. AUA = Actual units adjusted to the budgeted mix = (TAU)(MR)

EXAMPLE 13-1

The following example includes three products so that all the variances can be illustrated, including the sale mix variances. To start with a less involved problem, see the Example in the Chapter 13 Summary for a simple single product illustration.

Assume that a firm produces a product line that includes three products, Economy, Regular and Deluxe. Budgeted and actual data are presented in Exhibit 13-6 and 13-7.

 Exhibit 13-6 Example 13-1: Budgeted and Actual Data Master Budget Data Economy Regular Deluxe Totals Units Sales 10,000 8,000 2,000 20,000 Sales Price per unit \$100.00 \$120.00 \$140.00 Variable Cost per unit:      Manufacturing      Selling & Administrative Total 55.00    5.00 60.00 61.00     5.00 66.00 65.00     5.00 70.00 Fixed Cost:      Manufacturing      Selling & Administrative Total \$360,000 164,000 \$524,000 Actual Data Economy Regular Deluxe Totals Units Sales 12,000 9,000 1,800 22,800 Sales Price per unit \$98.00 \$132.00 \$154.00 Variable Cost per unit:      Manufacturing      Selling & Administrative Total 53.80    5.00 58.80 67.60     5.00 72.60 72.00    5.00 77.00 Fixed Cost:      Manufacturing      Selling & Administrative Total \$361,380 164,220 \$525,600

 EXHIBIT 13-7 Example 13-1 Continued Direct Costing Comparative Income Statements Data Master Budget Actual Total Variance Sales:    Economy    Regular    Delux  Total \$1,000,000 960,000 280,000 2,240,000 \$1,176,000 1,188,000 277,200 2,641,200 \$176,000 f 228,000 f 2,800 u 401,200 f Variable Cost:   Economy    Regular    Delux  Total 600,000 528,000 140,000 1,268,000 705,600 653,400 138,600 1,497,600 105,600 u 125,400 u       1,400 f 229,600 u Contribution Margin:    Economy    Regular    Delux  Total 400,000 432,000 140,000 972,000 470,400 534,600 138,600 1,143,600 70,400 f 102,600 f       1,400 u 171,600 f Less Fixed Costs Net Income Before Taxes 524,000 \$448,000 ======= 525,600 \$618,000 ======= 1,600 u \$170,000 f ========

The comparative income statements in Exhibit 13-7 indicate that the actual performance is considerably better than the master budget. More specifically, actual net income before taxes was \$170,000 higher than budgeted and, after subtracting the variance for fixed costs, the total variance in contribution margin was \$171,600 higher than budgeted. However, it is not clear what caused these favorable results. What is needed is to separate the total variance to isolate the effects of sales price, cost, sales volume, and sales mix differences.

SOLUTION TO EXAMPLE 13-1

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

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

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

Assuming the three products are substitute products, then the sales mix variances may be useful is evaluating an attempt to improve the sales mix, i.e., trade customers up to the more expensive, higher margin products. In this example 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 budgeted mix ratios, then actual contribution margin would have been \$16,080 greater (as indicated by the unfavorable total sales mix variance) and the sales volume variance would have been \$136,080 favorable (as indicated by the total sales quantity variance).

The Income Statement Approach: A Convenient Alternative

The methods presented above are useful for isolating each specific variance, but the solution presented in Exhibit 13-8 is probably not the best method for presenting the analysis to management. The comparative income statement approach illustrated in Exhibit 13-9 generates the same results as the four variance method, and also provides a more revealing picture of the overall profit analysis. The approach is fairly simple. Start with the comparative income statements in Exhibit 13-7 and add a forth column by multiplying the actual units sold by the budgeted or standard prices and unit cost. This is a flexible budget based on the actual sales level. Then the price cost variances are the differences between the actual results and the flexible budget, i.e., columns 2 and 4. The sales volume variances are the differences between 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 the unit cost variances (compare with Exhibit 13-8). The total price-cost variance is in the contribution margin row of column 5. Also note that the variances in column 6 are the revenue and cost parts of the sales volume variances. The total sales volume variance is in the contribution margin row of column 6.

 Exhibit 13-9
 Data Static Master Budget 1 Actual 2 Total Variance 3 Flexible Budget: Actual units @standard* 4 Price-Cost (Flexible Budget) Variance  5 = 2 vs 4 Sales Volume (Planning) Variance  6 = 1 vs 4 Unit sales:     Economy     Regular     Delux 10,000  8,000 2,000 12,000 9,000 1,800 - 12,000 9,000 1,800 - - Sales \$1,000,000 960,000 280,000 2,240,000 \$1,176,000 1,188,000 277,200 2,641,200 \$176,000 f 228,000 f    2,800 u 401,200 f \$1,200,000 1,080,000 252,000 2,532,000 \$24,000 u 108,000 f 25,200 f 109,200 f \$200,000 f 120,000 f 28,000 u 292,000 f Variable    costs 600,000 528,000 140,000 1,268,000 705,600 653,400 138,600 1,497,600 105,600 u 125,400 u    1,400 f 229,600 u 720,000 594,000 126,000 1,440,000 14,400  f 59,400 u 12,600 u 57,600 u 120,000 u 66,000 u 14,000 f 172,000 u Contribution   margin 400,000 432,000 140,000 972,000 470,400 534,600 138,600 1,143,600 70,400 f 102,600 f   1,400 u 171,600 f 480,000 486,000 126,000 1,092,000 9,600 u 48,600 f 12,600 f 51,600 f 80,000 f 54,000 f 14,000 u 120,000 f Fixed Cost:  Manufact.  S & A 360,000 164,000 524,000 361,380 164,220 525,600 1,380 u 220 u  1,600 u 360,000 164,000 524,000 1,380 u 220 u 1,600 u - NIBT \$448,000 ======= \$618,000 ======= \$170,000 f ======== \$568,000 ======= \$50,000 f ======= \$120,000 f =======

* Column 4 represents 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 the original budget.

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

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

Why Multiple Approaches Are Presented

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

The other parts of this chapter, i.e., Parts I.B, II.A and  II.B will be added later.

 QUESTIONS

Some questions related 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. Budgeted and actual unit sales are indicated below as well as comparative income statements.

 Data Budget Actual Variance Unit Sales 10,000 11,000 1,000 F Sales \$200,000 \$209,000 \$9,000 F Variable costs 120,000 137,500 17,500 U Contribution margin \$80,000 \$71,500 \$8,500 U

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 the Demonstration problem

PROBLEM 13-2
Profit Analysis based on Gross Profit
Single Product, Data in Units

This problem will be added later with part IIA.

PROBLEM 13-3
Profit Analysis based on Contribution Margin
Two Products, Data in Units

 Data Product A Product B Budgeted unit sales Actual unit sales Budgeted sales prices Actual sales prices Budgeted variable cost per unit Actual variable cost per unit 5,000 7,200 \$10.00 \$11.00 \$6.00 \$6.05 2,500 2,400 \$20.00 \$22.00 \$8.00 \$10.34

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 direct material,