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# 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:

1. Materials price, mix, quantity and yield variance.
2. Labor rate, efficiency, and yield variance.
3. 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.

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:

2. Factory overhead idle capacity 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]

When two variance approach is used, the overhead variances are:

1. Controllable variance
2. Volume variance
3. 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].

## Relevant Articles:

 » Definition and Explanation of Standard Cost » Purposes and Advantages of Standard Costing System » Setting Standards » Materials Price Standard » Materials Price Variance » Materials Quantity Standard » Materials Quantity Variance » Direct Labor Rate Standard » Direct Labor Rate Variance » Direct Labor Efficiency Standard » Direct Labor Efficiency Variance » Factory Overhead Cost Standards » Overall or Net Factory Overhead Variance » Overhead Controllable Variance » Overhead Volume Variance » Overhead Spending Variance » Overhead Idle Capacity Variance » Overhead Efficiency Variance » Variable Overhead Efficiency Variance » Fixed Overhead Efficiency Variance » Mix and Yield Variance » Variance Analysis Example » Standard Costing and Variance Analysis Formulas » Management by Exception and Variance Analysis » International Uses of Standard Costing System » Advantages, Disadvantages, and Limitations of Standard Costing

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