MANAGEMENT ACCOUNTING
CONCEPTS AND TECHNIQUES
By Dennis Caplan, University
at Albany (State University of New York)
CHAPTER
7: Cost Variances for Direct Materials
and Labor
Chapter Contents:
 Introduction
 Notation
 Derivation of the direct materials variances
 Geometric representation of the direct materials variances
 Timing of recognition of the price variance
 Cost variances and external reporting
 Cost variances for direct labor
 The Blue Moose restaurant
 Exercises and problems
Introduction:
In the previous chapter, we saw that the static budget variance measures the difference between budgeted costs and actual costs (or budgeted revenues and actual revenues). We also saw that when the actual volume of output (sales or production) differs from the budgeted volume of output, this difference contributes to the static budget variance. We saw that a flexible budget adjusts the static budget to reflect what the budget would have looked like, if the actual output volume could have been known in advance. The flexible budget variance measures the difference between the flexible budget and actual results.
As stated in the previous chapter, there can be only two explanations for the flexible budget variance for variable costs. First, there can be a difference between budgeted input prices and actual input prices: the company paid more per yard of fabric, or less per pound of steel, than planned. Second, there can be an efficiency piece: the company used more fabric per pair of pants, or fewer pounds of steel per widget, than planned. In this chapter, we separate the flexible budget variance for direct materials into these two pieces: the “price” piece, and the “efficiency” piece. At the end of the chapter, we extend the discussion to other variable costs: direct labor and variable overhead.
Notation:
The following concepts and abbreviations are used:
Inputs are the materials used in the production process (fabric or steel).
Outputs are the units of finished product (pairs of pants, or widgets).
Abbreviation 
Definition 
Explanation 
Q P AP SP AQ SQ 
Quantity Price Actual Price Standard Price Actual Quantity Standard Quantity 
The total quantity of inputs used in production (the inputs for all output units, not the inputs for one unit of output) The price per unit of input The actual price paid per unit of input The budgeted price paid per unit of input The actual quantity of inputs used in production The quantity of inputs that “should have been used” for the actual output produced 
Sometimes Q refers to the total quantity of inputs purchased, not used in production. We will return to this possibility later in this chapter, but for now, Q refers to the quantity used in production.
The most important concept identified above is the Standard Quantity (SQ). SQ is a flexible budget concept: it is the quantity of inputs that would have been budgeted had the budget correctly anticipated the actual volume of output.
Derivation
of the Direct Materials Variances:
Given these definitions, the flexible budget can be expressed as
SQ x SP;
and the flexible budget variance can be expressed as
(AQ x AP) – (SQ x SP) (1)
We introduce the following expression:
(AQ x SP)
This expression measures what the company “should have spent” for the actual quantity of inputs used. We can insert this expression into Equation (1) in order to separate the flexible budget variance into two pieces:
(AQ x AP) – (AQ x SP) – (SQ x SP) (2)
The first term minus the second term in Equation (2) can be rewritten as follows:
(AQ x AP) – (AQ x SP) = AQ x (AP – SP)
This expression is the price variance. It is the actual inputs used in production (AQ) multiplied by the difference between the budgeted price (SP) and the actual price (AP) paid per unit of input. The price variance is abbreviated PV. Hence:
PV = AQ x (AP – SP)
If the term in parenthesis
is positive, the factory paid more per unit of input than budgeted, and the
price variance is unfavorable. If the term in parenthesis is negative, the
factory paid less per unit of input than budgeted, and the price variance is
favorable. In either case, the price variance can be interpreted as answering
the following question: What was the
total impact on the cost of production caused by the fact that the actual price
per unit of input differed from the budgeted price.
The second term minus the third term in Equation (2) can be rewritten as follows:
(AQ x SP) – (SQ x SP) = SP x (AQ – SQ)
This expression is the quantity variance (also called the usage variance). It is the budgeted price per unit of input (SP) multiplied by the difference between the quantity of inputs that should have been used for the output units produced (SQ) and the quantity of inputs actually used (AQ). The quantity variance is abbreviated QV. Hence:
QV = SP x (AQ – SQ)
If the term in parenthesis is positive, the factory used more inputs than it should have used for the amount of output units produced, and the quantity variance is unfavorable. If the term in parenthesis is negative, the factory used fewer inputs than it should have used for the amount of output units produced, and the quantity variance is favorable. In either case, the quantity variance can be interpreted as answering the following question: What was the total impact on the cost of production caused by the fact that the quantity of inputs used to make each unit of output differed from budget.
Geometric
Representation of the Direct Materials Variances:
The following table shows the price and quantity variances graphically, when both variances are negative. The area of the yellow box represents the flexible budget. The area of the “outer” box (the union of the three colored boxes) represents the actual amount incurred for direct materials. The price variance is the area of the orange box, and the quantity variance is the area of the green box. It is easy to see from this geometric representation that the difference between the flexible budget and actual costs consists of two variances: the price variance and the quantity variance.
AP 
Price Variance 

SP 
Flexible Budget 
Quantity Variance 

SQ 
AQ 
The following table is identical to the one shown above except for the upper righthand corner. This table shows that the formula for the price variance includes an “interactive” variance that only exists when both AP ¹ SP and AQ ¹ SQ. If AQ = SQ, this interactive variance box collapses from the right. If AP = SP, this box collapses from the top.
AP 
Price Variance 
Interactive
Price/Quantity Variance 
SP 
Flexible Budget 
Quantity Variance 

SQ 
AQ 
There is no theoretical justification for treating this interactive variance as part of the price variance instead of part of the quantity variance, but it is customarily assigned to the price variance or else reported separately.
Timing
of Recognition of the Price Variance:
Some firms recognize the price variance for direct materials when the raw materials are purchased, rather than waiting until the raw materials are put into production. In this case, the AQ in the price variance will generally differ from the AQ in the quantity variance, which is denoted in the following expressions for these variances:
PV = AQ _{Purchased} x (AP – SP)
QV = SP x (AQ _{Used} – SQ)
Where usually, AQ _{Purchased }¹ AQ _{Used}
Recognizing the price variance when raw materials are purchased provides more timely information to management about the cost of direct materials and the performance of the purchasing department. Hence, this method for calculating the price variance has much to commend it. However, in this situation, the sum of the price variance and quantity variance will not equal the flexible budget variance, except by coincidence or when beginning and ending quantities of raw materials are zero.
Cost
Variances and External Reporting:
Cost variances are not reported separately in the external financial statements of a firm, but are implicitly incorporated in one or more lineitems on the balance sheet and income statement, such as Cost of Goods Sold and ending Finished Goods Inventory. However, for internal reporting, cost variances are frequently reported as separate lineitems on divisional income statements and productspecific profit statements.
Cost
Variances for Direct Labor:
The formulas for splitting the flexible budget variance into a “price” variance and “quantity” variance are the same for direct labor as direct materials. However, the terminology differs slightly. What is called the price variance for direct materials is called the rate variance or wage rate variance for direct labor. However, we retain the same abbreviations:
PV = AQ x (AP – SP)
where AQ is the actual labor hours used in production, AP is the actual wage rate, and SP is the budgeted wage rate.
What is called the quantity or usage variance for direct materials is called the efficiency variance for direct labor. We abbreviate this variance as EV:
EV = SP x (AQ – SQ)
where SP and AQ are the same as above, and SQ is the flexible budget quantity of labor hours (the labor hours the factory should have used for the volume of output units produced).
The issue discussed earlier in this chapter regarding the timing of the recognition of the price variance for direct materials does not arise for direct labor. Consequently, for direct labor, the sum of the wage rate variance and efficiency variance always equals the flexible budget variance.
The
Blue Moose Restaurant:
The Blue Moose Restaurant makes and sells sandwiches. The Restaurant makes and sells a lot of sandwiches. Following is the restaurant’s budget for making a peanut butter and jelly sandwich:
Direct
Materials
Bread
Quantity: 2 slices of bread (you probably knew this)
Price: $0.10 per slice of bread
Peanut butter
Quantity: 3 tablespoons
Price: $0.05 per tablespoon
Jelly
Quantity: 4 tablespoons
Price: $0.03 per tablespoon
Direct labor
Quantity: two minutes of labor
Wage rate: $12 per hour ($0.20 per minute)
The static budget for May indicated a production and sales level of 1,100 peanut butter and jelly sandwiches. In fact, the restaurant made and sold 1,000 peanut butter and jelly sandwiches. The total cost in direct materials and labor to make these 1,000 sandwiches was $520 for ingredients and $450 for labor.
Required:
1. What is the budgeted cost per unit for making a peanut butter and jelly sandwich?
2. What would the static budget show, in total, for the cost of production for all peanut butter and jelly sandwiches?
3. What would the flexible budget show, in total, for the cost of production for all peanut butter and jelly sandwiches? Show materials separately from labor.
4. What is the flexible budget variance? Show this variance separately for materials and labor. Is the flexible budget variance favorable or unfavorable?
5. Each loaf of bread contains 20 slices of bread. 105 loafs of bread were used to make all of the peanut butter and jelly sandwiches. The actual price paid per loaf was $2.20. Calculate the quantity (usage) variance for bread. Provide a possible explanation for this variance.
6. What is the price variance for bread? Is it favorable or unfavorable?
7. 30 labor hours were spent making peanut butter and jelly sandwiches, at an average wage rate of $15 per hour. What is the efficiency variance for labor?
8. What is the wage rate variance?
Solutions:
1. What is the budgeted cost per unit for making a peanut butter and jelly sandwich?
Bread Peanut butter Jelly Labor Total budgeted cost per unit 
$0.20 $0.15 $0.12 $0.40 $0.87 
2. What would the static budget show, in total, for the cost of production for all peanut butter and jelly sandwiches?
$0.87 per sandwich x 1,100 sandwiches = $957.
3. What would the flexible budget show, in total, for the cost of production for all peanut butter and jelly sandwiches? Show materials separately from labor.
Ingredients Labor Total 
$0.47 x 1,000 = $0.40 x 1,000 = 
$470 $400 $870 
4. What is the flexible budget variance? Show this variance separately for materials and labor. Is the flexible budget variance favorable or unfavorable?
Ingredients Labor Total 
$520 actual  $470 budgeted = $450 actual  $400 budgeted = 
$ 50 unfavorable $ 50 unfavorable $100 unfavorable 
5. Each loaf of bread contains 20 slices of bread. 105 loafs of bread were used to make all of the peanut butter and jelly sandwiches. The actual price paid per loaf was $2.20. Calculate the quantity (usage) variance for bread. Provide a possible explanation for this variance.
SP x (AQ – SQ)
= $0.10 per slice x (2,100 actual slices – 2,000 flexible budget slices)
= $10 unfavorable
Possible reasons for the unfavorable usage variance for bread include the following:
1. Some of the bread was stale.
2. Some bread was dropped on the floor and not used
3. The 20 slices per loaf includes the heels, which are not used.
6. What is the price variance for bread? Is it favorable or unfavorable?
AQ x (AP – SP)
= 2,100 slices of bread x ($0.11 per slice  $0.10 per slice)
= $21 unfavorable
7. 30 labor hours were spent making peanut butter and jelly sandwiches, at an average wage rate of $15 per hour. What is the efficiency variance for labor?
SP x (AQ – SQ)
= $12 per hour x (30.00 actual hours – 33.33 flexible budget hours)
= $40 favorable
8. What is the wage rate variance?
AQ x (AP – SP)
= 30 actual hours x ($15 actual wage rate – $12 budgeted wage rate)
= $90 unfavorable
Go
to the EndofChapter Exercises and Problems
Return
to the Table of Contents
Management
Accounting Concepts and Techniques; copyright 2006; most recent update:
November 2010
For a printerfriendly version, contact Dennis Caplan at dcaplan@uamail.albany.edu