James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida
Citation: Martin, J. R. Not dated. Chapter 13: Profit Analysis: An Overall Performance Evaluation  Part I. Management Accounting: Concepts, Techniques & Controversial Issues. Management And Accounting Web. https://maaw.info /Chapter13.htm
CONTENTS
Part I: Contribution Margin Analysis with Unit data
Part I: Four Variance Approach
Part I: Alternative Four Variance Approach with Sales Mix Variance
Part I: The Income Statement Approach
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.1. Sales prices,
2. Unit costs,
3. Sales volume, and
4. Sales mix.
Remember the underlying assumptions in the master budget and conventional linear costvolumeprofit 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 131 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
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)
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.
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 (ACMBCM)(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 (AUBU)(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 132.
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 (APBP)(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 (AVBV)(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 (AUBU)(BP)
Cost part of Sales Volume Variance = Flexible budget variable costs for actual units sold  Master budget variable
costs
= (AU)(BV)  (BU)(BV) or (AUBU)(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 133 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 134 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 รท Total budgeted unit sales
Sales Mix Variance = (AUAUA)(BCM)
Sales Quantity Variance = (AUABU)(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 135 for easy reference.
Exhibit 135  
Two Variance  Four Variance  Alternative Four Variance 
Price Cost Variance (ACMBCM)(AU) 
Sales Price Variance (APBP)(AU) 
Sales Price Variance (APBP)(AU) 
Unit Cost Variance (AVBV)(AU) 
Unit Cost Variance (AVBV)(AU) 

Sales Volume Variance (AUBU)(BCM) 
Revenue part of Sales Volume Variance (AUBU)(BP)  Sales Mix Variance (AUAUA)(BCM) 
Cost part of Sales Volume Variance (AUBU)(BV) 
Sales Quantity Variance (AUABU)(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) 
Exhibit 136 Example 131: 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 137 Example 131 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 
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
Exhibit 139  
Data 
Static Master Budget 1 
Actual 2 
Total Variance 3 
Flexible Budget: Actual units @standard* 4 
PriceCost (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:  
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 
$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:  
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 1,400f 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:  
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 
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 Total 
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 139 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 pricecost variance is $50,000 rather than $51,600. In other words, the total pricecost variance is the last amount in column 5. When we limit the analysis to contribution margin, it is $51,600 (see Exhibit 138), but if we carry the analysis down to net income, it is $50,000 (see Exhibit 139).
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 (Pricecost 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.
QUESTIONS
Some questions related to profit analysis.
PROBLEM 131
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. Pricecost 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 132
Profit Analysis based on Gross Profit  Single Product, Data in Units
This problem is not included because it goes with part IIA.
PROBLEM 133
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. Pricecost 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, direct labor, and variable overhead?