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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