PROFIT VARIANCE ANALYSIS
Profit variance analysis, often called gross profit analysis, deals with how to analyze the profit variance which constitutes the departure between actual profit and the previous year`s income or the budgeted figure. The primary goal of profit variance analysis is to improve performance and profitability in the future.
Profit, whether it is gross profit in absorption costing or contribution margin in direct costing, is affected by at least three basic items: sales price, sales volume, and costs. In addition, in a multiproduct firm, if not all products are equally profitable, profit is affected by the mix of products sold.
The difference between budgeted and actual profits are due to one or more of the following:
(1) Changes in unit sales price and cost, called sales price and cost price variances, respectively. The difference between sales price variance and cost price variance is often called a contributionmarginperunit variance or a grossprofitperunit variance, depending upon what type of costing system being referred to, that is absorption costing or direct costing. Contribution margin is considered, however, a better measure of product profitability because it deducts from sales revenue only the variable costs that are controllable in terms of fixing responsibility. Gross profit does not reflect costvolumeprofit relationships. Nor does it consider directly traceable marketing costs.
(2) Changes in the volume of products sold summarized as the sales volume variance and the cost volume variance. The difference between the two is called the total volume variance.
(3) Changes in the volume of the more profitable or less profitable items referred to as the sales mix variance.
Detailed analysis is critical to management when multiproducts exist. The volume variances may be used to measure a change in volume (while holding the mix constant) and the mix may be employed to evaluate the effect of a change in sales mix (while holding the quantity constant). This type of variance analysis is useful when the products are substituted for each other, or when products which are not necessarily substitutes for each are marketed through the same channel.
Types of Standards in Profit Variance Analysis
To determine the various causes for a favorable variance (an increase) or an unfavorable variance (a decrease) in profit we need some kind of yardsticks to compare against the actual results. The yardsticks may be based on the prices and costs of the previous year, or any year selected as the base periods. Some companies are summarizing profit variance analysis data in their annual report by showing departures from the previous year`s reported income. However, one can establish a more effective control and budgetary method rather than the previous year`s data. Standard or budgeted mix can be determined using such sophisticated techniques as linear and goal programming.
Single Product Firms
Profit variance analysis is simplest in a single product firm, for there is only one sales price, one set of costs (or cost price), and a unitary sales volume. An unfavorable profit variance can be broken down into four components: a sales price variance, a cost price variance, a sales volume variance, and a cost volume variance.
The sales price variance measures the impact on the firm`s contribution margin (or gross profit) of changes in the unit selling price. It is computed as:
Sales price variance = (actual price  budget price) x actual sales
If the actual price is lower than the budgeted price, for example, this variance is unfavorable; it tends to reduce profit. The cost price variance, on the other hand, is simply the summary of price variances for materials, labor and overhead. (This is the sum of material price, labor rate, and factory overhead spending variances). It is computed as:
Cost price variance = (actual cost  budget cost) x actual sales
If the actual unit cost is lower than budgeted cost, for example, this variance is favorable; it tends to increase profit. We simplify the computation of price variances by taking the sales price variance less the cost price variance and call it the grossprofitperunit variance or contributionmarginperunit variance.
The sale volume variance indicates the impact on the firm`s profit of changes in the unit sales volume. This is the amount by which sales would have varied from the budget if nothing but sales volume had changed. It is computed as:
Sales volume variance = (actual sales  budget sales) x budget price
If actual sales volume is greater than budgeted sales volume, this is favorable; it tends to increase profit. The cost volume variance has the same interpretation. It is:
(Actual sales  budget sales) x budget cost per unit.
The difference between the sales volume variance and the cost volume variance is called the total volume variance.
Multi  Product Firms
When a firm produces more than one product, there is a fourth component of the profit variance. This is the sales mix variance, the effect on profit of selling a different proportionate mix of products than that which has been budgeted. This variance arises when different products have different contribution margins. In a multiproduct firm, actual sales volume can differ from that budgeted in two ways. The total number of units sold could differ from the target aggregate sales. In addition, the mix of the products actually sold may not be proportionate to the target mix. Each of these two different types of changes in volume is reflected in a separate variance.
The total volume variance is divided into the two: the sales mix variance and the sales quantity variance. These two variances should be used to evaluate the marketing department of the firm. The sales mix variance shows how well the department has done in terms of selling the more profitable products while the sales quantity variance measures how well the firm has done in terms of its overall sales volume. They are computed as:
Sales Mix Variance
(Actual Sales at budget mix  Actual Sales at actual mix) x Budget CM (or gross profit / unit)
Sales Quantity Variance
(Actual Sales at budget mix  Budget Sales at budget mix) x Budget CM (or gross profit / unit)
Sales Volume Variance
(Actual Sales at actual mix  Budget Sales at budget mix) x Budget CM ( or gross profit / unit)
EXAMPLE 2
The Lake Tahoe Ski Store sells two ski models  Model X and Model Y. For the years 20x1 and 20x2, the store realized a gross profit of $246,640 and only $211,650, respectively. The owner of the store was astounded since the total sales volume in dollars and in units was higher for 20x2 than for 20x1 yet the gross profit achieved actually declined. Given below are the store`s unaudited operating results for 20x1 and 20x2. No fixed costs were included in the cost of goods sold per unit.

Model X 



Model Y 


Selling 
Costs of Go ods 
Sales in 
Sales 
Selling 
Costs of Go ods 
Sales in 
Sales 
YEAR 
Price 
Sold per unit 
Units 
Revenue 
Price 
Sold per unit 
Units 
Reve nue 
1 
$150 
$110 
2,800 
420,000 
$172 
$121 
2,640 
454,080 
2 
160 
125 
2,650 
424,000 
176 
135 
2,900 
510,400 
Explain why the gross profit declined by $34,990. Include a detailed variance analysis of price changes and changes in volume both for sales and cost. Also subdivide the total volume variance into change in price and changes in quantity.
Sales price and sales volume variances measure the impact on the firm`s CM (or GM) of changes in the unit selling price and sales volume. In computing these variances, all costs are held constant in order to stress changes in price and volume. Cost price and cost volume variances are computed in the same manner, holding price and volume constant. All these variances for the take Tahoe Ski Store are computed below.
Sales Price Variance
Actual sales for 20x2: 
$896,300 
Model X 2,650 x $160 = $424,000 

Model Y 2,900 x $179 = $510,400 
$934,400 
Actual 20x2 sales at 20x1 prices: 

Model X 2,650 x $150 = $397,500 

Model Y 2,900 x $172 = $498,800 
896,300 

$38,100 F 
Sales Volume Variance
Actual 20x2 sales at 20x1 prices: 
$896,300 
Actual 20x1 sales (at 20x1 prices): 

Model X 2,800 x $150 = $420,000 

Model Y 2,640 x 172 = 454,080 
874,080 

$22,220 F 
Cost Price Variance
Actual cost of goods sold for 20x2: 
$896,300 
Model X 2,650 x $125 = $331,250 

Model Y 2,900 x $135 = $391,500 

Actual 20x2 sales at 20x1 costs: 

Model X 2,650 x $110 = $291,500 

Model Y 2,900 x $121 = $350,900 
$642,400 

$80,350 U 
Cost Volume Variance
Actual 20x2 sales at 20x1 costs: 
$642,400 
Actual 20x1 sales (at 20x1 costs): 

Model X 2,800 x $110 = $308,000 

Model Y 2,640 x 121 = 319,440 
627,440 

$14,960 U 
Total volume variance 
= sales volume variance  cost volume variance 

= $22,220 F  $14,960 U = $7,260 F 
The total volume variance is computed as the sum of a sales mix variance and a sales quantity variance as follows:
Sales Mix Variance

20x2 Actual Sale at 
20x2 Actual Sale at 

20x1 Gross 


Profit 
Variance 

20x1 Mix* 
20x2 Mix 
Diff. 
per Unit 
($) 

Model X 
2,857 
2,650 
207 U 
$40 
$8,280 U 
Model Y 
2,693 
2,900 
207 F 
51 
10,557 F 

5,500 
5,550 


$2,277 F 
*This is the 20x1 mix (used as standard or budget) proportions of 51.47% (or 2,800/5,440 = 51.47%) and 48.53% (or 2,640/5,440 = 48.53%) applied to the actual 20x2 sales figure of 5,550 units.
Sales Quantity Variance

20x2 Actual Sale at 
20x2 Actual Sale at 

20x1 Gross 


Profit 
Variance 

20x1 Mix* 
20x1 Mix 
Diff. 
per Unit 
($) 

Model X 
2,857 
2,800 
57 F 
$40 
$2,280 F 
Model Y 
2,693 
2,640 
52 F 
51 
2,703 F 

5,550 
5,440 


$4,983 F 
A favorable total volume variance is due to a favorable shift is the sales mix (that is from Model X to Model Y) and also to a favorable increase in sales volume (by 110 units) which is shown as follows.
Sale mix variance 
$2,277 F 
Sales quantity 
4,983 F 

$7,260 F 
However, there remains the decrease in gross profit. The decrease in gross profit of $34,990 can be explained as follows.

Gains 
Losses 
Gain due to increased sales price 
$38,100 F 
80,350 
Loss due to increased cost 


Gain due to increase in units sold 
4,983 F 

Gain due to shift in sales mix 
2,277 F 


$45,360 F 
$80,350 
Hence, net decrease in gross profit 
= $80,350  $45,360 = $34,990U 
Hence, net decrease in gross profit = $80,350  $45,360 = $34,990U 
Despite the increase in sales price and volume and the favorable shift in sales mix, the Lake Tahoe Ski Store ended up losing $34,990 compare to 20x1. The major reason for this comparative loss was the tremendous increase in cost of goods sold, as costs for both Model X and Model Y went up quite significantly over 20x1. The store has to take a close look at the cost picture. Even though only variable and fixed costs should be analyzed in an effort to cut down on controllable costs. In doing that, it is essential that responsibility be clearly fixed to given individuals. In a retail business like the Lake Tahoe Ski Store, operating expenses such as advertising and payroll of store employees must also be closely scrutinized.
EXAMPLE 3
Shim and Siegel, Inc. sells two products, C and D. Product C has a budgeted unit CM (contribution Margin) of $3 and Product D has a budgeted Unit CM of $6. The budget for a recent month called for sales of 3,000 units of C and 9,000 units of D, for a total of 12,000 units. Actual sales totaled 12,200 units, 4,700 of C and 7,500 of D. Compute the sales volume variance and break this variance down into the (a) sales quantity variance and (b) sales mix variance.
Shim and Siegel`s sales volume variance is computed below. As we can see, while total unit sales increased by 200 units, the shift in sales mix resulted in a $3,900 unfavorable sales volume variance.
Sale Volume Variance
Actual Sales at Actual Mix  Standard Sales at Budgeted Mix  
Bud geted  Variance  
Difference  CM per Unit  ($)  
Pro duct C  4,700  3,000  1,700 F  $3  $5,100 F 
Pro duct D  7,500  9,000  1,500 U  6  9,000 U 
12,200  12,000  $3,900 U 
In multiproduct firms, the sales volumes variance is further divided into a sales quantity variance and a sales mix variance. The computations of these variances are shown below.
Sales Quantity Variance

Actual Sales at Budgeted Mix 
Standard Sales at Budgeted Mix 



Standard 
Variance 

Difference 
CM per Unit 
($) 

Pro duct C 
3,050 
3,000 
50 F 
$3 
$ 150 F 
Pro duct D 
9,150 
9,000 
150 F 
6 
900 F 

12,200 
12,000 


$ 1,050F 
Sale Mix Variance

Actual Sales at Budgeted Mix 
Standard Sales at Actual Mix 



Standard 
Variance 

Diffe rence 
CM per Unit 
($) 

Pro duct C 
3,050 
4,700 
1,650 F 
$3 
$4,950 F 
Pro duct D 
9,150 
7,500 
1,650 U 
6 
9,900 U 

12,200 
12,200 


$4,950 U 
The sales quantity variance reflects the impact on the CM or GM (gross margin) of deviations from the standard sales volume, whereas the sales mix variance measures the impact on the CM of deviations from the budgeted mix. In the case of Shim and Siegel, Inc., the sales quantity variance came out to be favorable, i.e., $1,050 F and the sales mix variance came out to be unfavorable, i.e., $4,950 U. These variances indicate that while there was a favorable increase in sales volume by 200 units, it was obtained by an unfavorable shift in the sales mix, that is, a shift from Product D, with a high margin, to Product C, with a low margin.
Note that the sales volume variance of $3,900 U is the algebraic sum of the following two variances.
Sales quantity variance 
$1,050 F 
Sales mix variance 
4,950 U 

$3,900 U

In conclusion, the product emphasis on high margin sales is often a key to success for multiproduct firms. Increasing sales volume is one side of the story; selling the more profitable products is another.
Managerial Planning and Decision Making
In view of the fact that Shim and Siegel, Inc. experienced an unfavorable sales volume variance of $3,900 due to an unfavorable (or less profitable) mix in the sales volume, the company is advised to put more emphasis on increasing the sales of Product D.
In doing that the company might wish to:
 Increase the advertising budget for succeeding periods to boost Product D sales;
 Set up a bonus plan in such a way that the commission is based on quantities sold rather than higher rates for higher margin items such as Product D or revise the bonus plan to consider the sale of product D;
 Offer a more lenient credit term for Product D to encourage its sale;
 Reduce the price of Product D enough to maintain the present profitable mix while increasing the sale of the product. This strategy must take into account the price elasticity of demand for Product D.
Sales Mix Analysis
Many product lines include a lowermargin price leader model, and often a highmargin deluxe model. For example, the automobile industry includes in its product line lowmargin energyefficient small cars and highermargin deluxe models. In an attempt to increase overall profitability, management would wish to emphasize the highermargin expensive items, but salesmen might find it easier to sell lower margin cheaper models. Thus, a salesman might meet his unit sales quota with each item at its budgeted price, but because of mix shifts he could be far short of contributing his share of budgeted profit.
Management should realize that

Greater proportions of more profitable products mean higher profits.
Higher proportions of lower margin sales reduce overall profit despite the increase in overall sales volume. That is to say that an unfavorable mix may easily offset a favorable increase in volume, and vice versa.
Performance Reports
Profit variance analysis aids in fixing responsibility by separating the causes of the change in profit into price, volume, and mix factors. With responsibility resting in different places, the segregation of the total profit variance is essential. The performance reports based on the analysis of profit variances must be prepared for each responsibility center, indicating the following:

Is it controllable?

Is it favorable or unfavorable?

If it is unfavorable, is it significant enough for further investigation?

Who is responsible for what portion of the total profit variance?

What are the causes for an unfavorable variance?

What is the remedial action to take?
The performance report must address these types of questions. The report is useful in two ways: (1) in focusing attention on situations in need of management action and (2) in increasing the precision of planning and control of sales and costs. The report should be produced as part of the overall standard costing and responsibility accounting system.