Variance Analysis Example:
(A Comprehensive
illustration of all variances)
The Springmint Company, a manufacturer of
chewing gum, uses a standard cost system. Standard product and cost
specifications for 1,000 lbs. of chewing gum are as follows:

Quantity 
× 
Price 
= 
Cost 

Gum base 
800 

$0.25 

$200 
Corn
syrup 
200 

$0.40 

80 
Sugar 
200 

$0.10 

20 






Input 
1,200 lbs 



$300 
$300 / 1,200 lbs = $0.25
per lb.* 







Output 
1,000 lbs 



$300 
$300 / 1,000 lbs = $0.30
per lb.* 







*Weighted
average.
The production of 1,000 lbs. of chewing gum
required 1,200 lbs of raw materials. Hence the yield is 1,000 lbs / 1,200lbs. or
5/6 of input. Materials records indicate.
Materials 
Beginning Inventory 
Purchases in January 
Ending Inventory 
Gum base 
10,000 lbs 
162,000 lbs@ 0.24 
15,000 lbs 
Corn Syrup 
12,000 lbs 
30,000 lbs @ 0.42 
4,000 lbs 
Sugar 
15,000 lbs 
32,000 lbs @ 0.11 
11,000 lbs 
To convert 1,200 lbs. of raw materials into
1,000 lbs of finished product required 20 hours at $6.00 per hour or $0.12 per
lbs. of finished product. Actual direct labor hours and cost for January are
3,800 hours at $23,104. Factory overhead is applied on a direct labor hour basis
at a rate of $5 per hour ($3 fixed , $2 variable), or $ 0.1 per lb. of finished
product. Normal overhead is $20,000 with 4,000 direct labor hours. Actual
overhead for the month is $22,000, Actual finished production for January is
200,000 lbs.
The standard cost per pound of finished
chewing gum is:
Materials 
$0.30 per lb. 
Labor 
$0.12 per lb. 
Factory overhead 
$0.10 per lb 
Required:
Calculate:

Materials price, mix, quantity and yield variance.
 Labor rate, efficiency, and yield
variance.
 Overhead yield variance using two and
three variance methods.
Calculation of Materials Variance:
The materials variances for January consists of
price variance, mix variance, yield variance, and quantity variance.
Materials Price Variance:
The company
calculates the materials price variance using the
procedure explained on "direct
materials price variance" page and recognizes
variances when materials are purchased.
Materials 
Quantity 
Actual Price 
Standard Price 
Unit Price Variance 
Price variance 
Gum base 
$162,000 
$0.24 
$0.25 
$(0.01) 
(1,620)$ 
Corn syrup 
30,000 
$0.42 
$0.40 
$0.02 
$600 
Sugar 
32,000 
$0.11 
$0.10 
$0.01 
$320 






materials price variance 




$(700) fav. 
Materials Mix Variance:
The materials mix variance results from
combining materials in a ratio different from the standard materials
specifications. It is computed as follows:
Actual quantities at
individual standard materials costs: 


Gum base 157,000 @ $0.25

$39,250 

Corn syrup 38,000 @ $0.40 
$15,200 

Sugar 36,000 @ $0.10 
$3,600 



$58,050 
Actual quantity at
weighted average of standard materials cost input 231,000 lbs × $0.25 

$57,750 



Materials mix variance
(unfavorable) 

$300U 



Materials Yield Variance:
Material yield variance is computed as follows:
Actual quantity at weighted average of
standard materials cost input 231,000 lbs × $0.25 
$57,750 
Actual out put quantity at standard materials
cost (200,000 lbs × $0.30) 
$60,000 


Material yield variance (Favorable) 
$(2,250)F 


F = Favorable
U = Unfavorable
The yield variance occurred because the actual
production of 200,000 lbs. exceeded the expected output of 192,500 lbs. (5/6 of
231,000) by 7,500 lbs. The yield difference multiplied by the standard weighted
materials cost of $0.30 per output pound equals the favorable yield variance of
$2,250.
The materials quantity variance can be
calculated for each item as follows, using the procedure explained on direct
materials quantity variance page.


Unit 
× 
Standard
unit cost 
= 
Amount 
Materials quantity variance 
Gum base: 
Actual quantity used 
157,000 lbs 

$0.25 

$39,250 


Standard
quantity allowed 
160,000 lbs* 

$0.25 

40,000 








$ (750)
Favorable 
Corn Syrup: 
Actual
quantity used 
38,000 lbs 

$0.40 

$15,200 


Standard
quantity allowed 
40,000 lbs** 

$0.40 

16,000 








$ (800)
Favorable 
Sugar: 
Actual
quantity used 
36,000 lbs 

$0.10 

$3,600 


Standard
quantity allowed 
4,000 lbs*** 

$0.10 

4,000 








$ (400)
Favorable 








Total materials quantity variance
 
$ (1,950)
Favorable 


 *An
output of 200,000 lbs. should require and output of 240,000 lbs., with a
standard yield of 1,000 lbs. output for each 1,200 lbs input. Then the
240,000 lbs. × (800 lbs. / 1,200 lbs ) gum base portion of the formula =
160,000 lbs.
 **The
240,000 lbs. × (200lbs. / 1,200 lbs.) corn syrup portion of the formula
= 40,000 lbs
 ***The
240,000 lbs. × (200lbs. / 1,200 lbs.) sugar portion of the formula =
40,000 lbs.
The total materials quantity variance can
also be determined by comparing actual quantities at standard prices,
$58,050 ($39250 + $15,200 + $3,600), to actual output quantity at standard
materials cost, $60,000 (200,000 lbs × $0.30) for a total favorable variance
of $1,950. The mix and yield variances separate the materials quantity
variance into two parts:
Materials mix variance 
$300 unfavorable 
Materials yield variance 
(2,250) favorable 


Materials quantity
variance 
$(1,950) favorable 
The influence of individual raw materials
on the total materials mix variance can be calculated in the following
manner:
Materials 
Actual quantity 
Standard Formula 
× 
Total Actual Quantity 
= 
Actual quantity Using Standard Formula 
Quantity Variation 
× 
Standard Unit Price 
= 
Materials Mix Variance 
Gum base 
157,000 lbs 
800 / 1,200 

231,000 lbs. 

154,000 lbs 
3,000 lbs 

$0.25 

$750 
Corn syrup 
38,000 lbs 
200 / 1,200 

231,000 lbs. 

38,500 lbs 
(500) 

$0.40 

(200) 
Sugar 
36,000 lbs 
200 / 1,200 

231,000 lbs. 

38,500 lbs 
(2,500) 

$0.10 

(250) 













231,000 lbs 




231,000 lbs 
0 



$300 












The expected output
of 192,500 lbs. of chewing gum should require 3,850
standard labor hours (20 hours per thousand pounds
of chewing gum produced). Similarly, the actual out
put of 200,000 lbs. of chewing gum should require
4,000 standard labor hours.
The labor variances are labor rate
variance, labor efficiency variance and labor yield variance.
Calculation of Labor Variances:
Labor Rate Variance:
labor rate variance is calculated as
explained on "direct
labor rate variance" page.
Actual payroll 
$23,104 
Actual hours (3,800) ×
Standard labor hours ($6) 
$22,800 


Labor rate variance 
$304 unfavorable 


Labor Efficiency Variance:
Actual hours (3,800) ×
Standard labor hours ($6) 
$22,800 
Standard hours allowed for
expected output (3,850) × Standard labor rate ($6) 
$23,100 


Labor efficiency variance 
$(300) favorable 


The traditional labor efficiency variance,
as explained on
direct labor efficiency variance page, is calculated as follows:

Time 
× 
Rate 
= 
Amount 
Actual hours worked 
3,800 

$6 

$22,800 
Standard hours allowed 
4,000 

$6 

$24,000 






Labor efficiency variance 
(200) 

$6 

$(1,200) favorable 






Labor Yield Variance:
Standard hours allowed for expected output
(3,850) × Standard labor rate ($6) 
$23,100 
Standard hours allowed for actual output
(4,000) × Standard labor rate ($6) 
24,000 


Labor yield variance 
$(900) favorable 


The labor yield variance identifies the
portion of the labor efficiency variance attributable to obtaining an
unfavorable or, as in this example, a favorable yield [(3,850 standard hours
allowed for expected output – 4,000 standard hours allowed for actual
output) × $6 standard labor rate = $900].
The favorable labor efficiency variance of
$300 is the portion of the traditional labor efficiency variance that is
attributable to factors other than yield. The sum of the two variances, $900
plus $300, equals the $1,200 traditional labor efficiency variance.
Factory Overhead Variances:
Three Variance Method Adapted to Calculate
Overhead Yield Variance:
A yield variance can be calculated for
factory overhead. When three variance method is used to calculate overhead
yield variance, the overhead variances consist of the:
 Factory overhead spending variance
 Factory overhead idle capacity variance
 Factory overhead efficiency variance
 Factory overhead yield variance
These variances are computed as follows:
Actual factory overhead 

$22,000 
Budgeted allowance based on actual hours worked: 


Fixed
expenses budgeted 
$12,000 

Variable
expenses: 3,800 actual hours × $2 variable standard overhead rate 
$7,600 



$19,600 



Overhead spending variance 

$2,400 U 



Budgeted allowance based
on actual hours worked 

$19,600 
Actual hours (3,800) ×
Standard overhead rate ($5) 

$19,000 



Overhead idle capacity variance 

$600 U 



Actual hours (3,800) ×
Standard overhead rate ($5) 

$19,000 
Standard hours allowed for
expected out put (3,850) × Standard overhead rate ($5) 

$19,250 



Overhead efficiency variance 

$(250) F 



Standard hours allowed for
expected output (3,850) × Standard overhead rate ($5) 

$19,250 
Standard hours allowed for
actual output (4,000) × Standard overhead rate ($5) 

$20,000 



Overhead yield variance 

$(750) F 



F = Favorable
U = Unfavorable 


The spending and idle capacity variances
are calculated in the same manner as explained on factory overhead spending
variance page and factory overhead idle capacity variance page respectively.
The overhead efficiency variance calculated here and the overhead yield
variance when combined , equal the traditional overhead efficiency variance
discussed on overhead efficiency variance page. The overhead yield variance
measures that portion of the total overhead variance resulting from a
favorable yield. [(3,850 hours – 4000hours) × $5.00 = $750]
Two Variance Method Adopted to Calculate Overhead Yield Variance:
When two variance approach is used, the
overhead variances are:
 Controllable variance
 Volume variance
 Yield variance
These variances are calculated as follows:
Actual factory overhead 

$22,000 
Budgeted allowance based on standard hours
allowed: 


Fixed overhead budgeted 
$12,000 

Variable expenses (3,850 standard hours ×
$2 standard rate) 
$7,700 



$19,700 



Controllable variance 

$2,300 U 



Budgeted allowance based on standard hours
allowed 

$19,700 
Standard hours allowed for expected output
(3,850) × standard overhead rate ($5) 

$19,250 



Volume variance 

$450 U 



Standard hours allowed for expected output
(3,850) × standard overhead rate ($5) 

$19,250 
Standard hours allowed for actual output
(4,000) × standard overhead rate ($5) 

$20,000 



Overhead yield variance 

$ (750) F 
F = Favorable
U = Unfavorable 


The favorable overhead yield variance is
the same as for the three variance approach and can be viewed as consisting
of $300 variable cost [(3,850 standard hours allowed for expected output –
4,000 standard hours allowed for actual output) × $2], and $450 fixed cost
[(3,850 – 4,000) × $3].
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