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SMChap 010 - Managerial Accounting 15th edition Solution

Manual
Audit and Assurance (Nanjing Audit University)

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Chapter 10
Standard Costs and Variances

Solutions to Questions

10-1 A quantity standard indicates how much labor rate variance. For example, skilled workers
of an input should be used to make a unit of with high hourly rates of pay can be given duties
output. A price standard indicates how much the that require little skill and that call for low hourly
input should cost. rates of pay, resulting in an unfavorable rate
variance. Or unskilled or untrained workers can
10-2 Separating an overall variance into a be assigned to tasks that should be filled by
price variance and a quantity variance provides more skilled workers with higher rates of pay,
more information. Moreover, price and quantity resulting in a favorable rate variance.
variances are usually the responsibilities of Unfavorable rate variances can also arise from
different managers. overtime work at premium rates.

10-3 The materials price variance is usually 10-8 If poor quality materials create
the responsibility of the purchasing manager. production problems, a result could be excessive
The materials quantity and labor efficiency labor time and therefore an unfavorable labor
variances are usually the responsibility of efficiency variance. Poor quality materials would
production managers and supervisors. not ordinarily affect the labor rate variance.

10-4 The materials price variance can be 10-9 If overhead is applied on the basis of
computed either when materials are purchased direct labor-hours, then the variable overhead
or when they are placed into production. It is efficiency variance and the direct labor efficiency
usually better to compute the variance when variance will always be favorable or unfavorable
materials are purchased because that is when together. Both variances are computed by
the purchasing manager, who has responsibility comparing the number of direct labor-hours
for this variance, has completed his or her work. actually worked to the standard hours allowed.
In addition, recognizing the price variance when That is, in each case the formula is:
materials are purchased allows the company to
Efficiency variance = SR(AH – SH)
carry its raw materials in the inventory accounts
at standard cost, which greatly simplifies Only the “SR” part of the formula, the standard
bookkeeping. rate, differs between the two variances.

10-5 This combination of variances may 10-10 If labor is a fixed cost and standards are
indicate that inferior quality materials were tight, then the only way to generate favorable
purchased at a discounted price, but the low- labor efficiency variances is for every
quality materials created production problems. workstation to produce at capacity. However, the
output of the entire system is limited by the
10-6 If standards are used to find who to capacity of the bottleneck. If workstations
blame for problems, they can breed resentment before the bottleneck in the production process
and undermine morale. Standards should not be produce at capacity, the bottleneck will be
used to find someone to blame for problems. unable to process all of the work in process. In
general, if every workstation is attempting to
10-7 Several factors other than the produce at capacity, then work in process
contractual rate paid to workers can cause a

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inventory will build up in front of the

workstations with the least capacity.

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The Foundational 15

1. The raw materials cost included in the planning budget is $1,000,000

(= 125,000 pounds × $8.00 per pound = $1,000,000).

2, 3, and 4.

The raw materials cost included in the flexible budget (SQ × SP =

$1,200,000), the materials price variance ($80,000 F), and the materials
quantity variance ($80,000 U), can be computed using the general model
for cost variances as follows:
Standard Quantity
Actual Quantity of Actual Quantity of Allowed
Input, Input, for Actual Output,
at Actual Price at Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
160,000 pounds × 160,000 pounds × 150,000 pounds* ×
$7.50 per pound $8.00 per pound $8.00 per pound
= $1,200,000 = $1,280,000 = $1,200,000
Materials price Materials quantity
variance = $80,000 F variance = $80,000 U
Spending variance = $0
*30,000 units × 5 pounds per unit = 150,000 pounds

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)

= 160,000 pounds ($7.50 per pound – $8.00 per pound)
= $80,000 F
Materials quantity variance = SP (AQ – SQ)
= $8.00 per pound (160,000 pounds – 150,000 pounds)
= $80,000 U

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The Foundational 15 (continued)

5. and 6.

The materials price variance ($85,000 F) and the materials quantity

variance ($80,000 U) can be computed as follows:

Standard Quantity
Actual Quantity Actual Quantity Allowed for Actual
of Input, of Input, Output,
at Actual Price at Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
170,000 pounds × 170,000 pounds × 150,000 pounds* ×
$7.50 per pound $8.00 per pound $8.00 per pound
= $1,275,000 = $1,360,000 = $1,200,000
Materials price variance
= $85,000 F
160,000 pounds ×
$8.00 per pound
= $1,280,000
Materials quantity
variance = $80,000 U
*30,000 units × 5 pounds per unit = 150,000 units

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)

= 170,000 pounds ($7.50 per pound – $8.00 per pound)
= $85,000 F
Materials quantity variance = SP (AQ – SQ)
= $8.00 per pound (160,000 pounds – 150,000 pounds)
= $80,000 U

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The Foundational 15 (continued)

7. The direct labor cost included in the planning budget is $700,000 (=

50,000 hours × $14.00 per hour = $700,000).

8, 9, 10, and 11.

The direct labor cost included in the flexible budget (SH × SR = $840,000),
the labor rate variance ($55,000 U), the labor efficiency variance ($70,000
F), and the labor spending variance ($15,000 F) can be computed using
the general model for cost variances as follows:
Standard Hours Allowed
Actual Hours of Input,
Actual Hours of Input, for Actual Output,
at Actual Rate at Standard Rate at Standard Rate
(AH × AR) (AH × SR) (SH × SR)
55,000 hours × 55,000 hours × 60,000 hours* ×
$15 per hour $14.00 per hour $14.00 per hour
= $825,000 = $770,000 = $840,000
Labor efficiency
Labor rate variance variance
= $55,000 U = $70,000 F
Spending variance = $15,000 F
*30,000 units × 2.0 hours per unit = 60,000 hours

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)

= 55,000 hours ($15.00 per hour – $14.00 per hour)
= $55,000 U
Labor efficiency variance = SR (AH – SH)
= $14.00 per hour (55,000 hours – 60,000 hours)
= $70,000 F

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The Foundational 15 (continued)

12. The variable manufacturing overhead cost included in the planning

budget is $250,000 (= 50,000 hours × $5.00 per hour = $250,000).

13, 14, and 15.

The variable overhead cost included in the flexible budget (SH × SR =

$300,000), the variable overhead rate variance ($55,000 U), and the
variable overhead efficiency variance ($25,000 F) can be computed using
the general model for cost variances as follows:
Standard Hours Allowed
Actual Hours of Input,
Actual Hours of Input, for Actual Output,
at Actual Rate at Standard Rate at Standard Rate
(AH × AR) (AH × SR) (SH × SR)
55,000 hours × 55,000 hours × 60,000 hours* ×
$5.10 per hour** $5.00 per hour $5.00 per hour
= $280,500 = $275,000 = $300,000
Variable overhead
Variable overhead rate efficiency variance
variance = $5,500 U = $25,000 F
Spending variance = $19,500 F
*30,000 units × 2.0 hours per unit = 60,000 hours
** $280,500 ÷ 55,000 hours = $5.10 per hour

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR* – SR)

= 55,000 hours ($5.10 per hour – $5.00 per hour)
= $5,500 U

*$280,500 ÷ 55,000 hours = $5.10 per hour

Variable overhead efficiency variance = SR (AH – SH)

= $5.00 per hour (55,000 hours – 60,000 hours)
= $25,000 F

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Exercise 10-1 (20 minutes)

1. Number of helmets............................................ 35,000
Standard kilograms of plastic per helmet............. × 0.6
Total standard kilograms allowed....................... 21,000
Standard cost per kilogram................................ × $8
Total standard cost............................................ $168,000
Actual cost incurred (given)............................... $171,000
Total standard cost (above)............................... 168,000
Total material variance—unfavorable.................. $ 3,000

2. Actual Quantity Standard Quantity

of Input, at Actual Quantity of Input, Allowed for Output, at
Actual Price at Standard Price Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
22,500 kilograms × 21,000 kilograms* ×
$8 per kilogram $8 per kilogram
$171,000 = $180,000 = $168,000
  
Price Variance, Quantity Variance,
$9,000 F $12,000 U
Spending Variance,
$3,000 U
*35,000 helmets × 0.6 kilograms per helmet = 21,000 kilograms

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
22,500 kilograms ($7.60 per kilogram* – $8.00 per kilogram)
= $9,000 F
* $171,000 ÷ 22,500 kilograms = $7.60 per kilogram
Materials quantity variance = SP (AQ – SQ)
$8 per kilogram (22,500 kilograms – 21,000 kilograms)
= $12,000 U

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Exercise 10-2 (20 minutes)

1. Number of meals prepared.................... 4,000
Standard direct labor-hours per meal..... × 0.25
Total direct labor-hours allowed............. 1,000
Standard direct labor cost per hour........ × $9.75
Total standard direct labor cost............. $9,750
Actual cost incurred.............................. $9,600
Total standard direct labor cost (above). 9,750
Total direct labor variance..................... $ 150 Favorable

2. Actual Hours of Standard Hours

Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH×AR) (AH×SR) (SH×SR)
960 hours × 960 hours × 1,000 hours ×
$10.00 per hour $9.75 per hour $9.75 per hour
= $9,600 = $9,360 = $9,750
  
Rate Variance, Efficiency Variance,
$240 U $390 F
Spending Variance,
$150 F

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH(AR – SR)
= 960 hours ($10.00 per hour – $9.75 per hour)
= $240 U
Labor efficiency variance = SR(AH – SH)
= $9.75 per hour (960 hours – 1,000 hours)
= $390 F

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Exercise 10-3 (20 minutes)

1. Number of items shipped................................. 120,000
Standard direct labor-hours per item................ × 0.02
Total direct labor-hours allowed....................... 2,400
Standard variable overhead cost per hour......... × $3.25
Total standard variable overhead cost.............. $ 7,800
Actual variable overhead cost incurred.............. $7,360
Total standard variable overhead cost (above). . 7,800
Total variable overhead variance...................... $ 440 Favorable

2. Actual Hours of Standard Hours

Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH×AR) (AH×SR) (SH×SR)
2,300 hours × 2,300 hours × 2,400 hours ×
$3.20 per hour* $3.25 per hour $3.25 per hour
= $7,360 = $7,475 = $7,800
  
Variable Overhead
Variable Overhead Rate Efficiency Variance,
Variance, $115 F $325 F
Spending Variance,
$440 F
*$7,360 ÷ 2,300 hours = $3.20 per hour

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance:
AH(AR – SR) = 2,300 hours ($3.20 per hour – $3.25 per hour)
= $115 F
Variable overhead efficiency variance:
SR(AH – SH) = $3.25 per hour (2,300 hours – 2,400 hours)
= $325 F

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Exercise 10-4 (30 minutes)

1. Number of units manufactured............................. 20,000
Standard labor time per unit
(18 minutes ÷ 60 minutes per hour).................. × 0.3
Total standard hours of labor time allowed............ 6,000
Standard direct labor rate per hour....................... × $12
Total standard direct labor cost............................. $72,000
Actual direct labor cost......................................... $73,600
Standard direct labor cost.................................... 72,000
Total variance—unfavorable.................................. $ 1,600

2. Actual Hours of Standard Hours Allowed

Input, at the Actual Hours of Input, for Output, at the
Actual Rate at the Standard Rate Standard Rate
(AH × AR) (AH × SR) (SH × SR)
5,750 hours × 6,000 hours* ×
$12.00 per hour $12.00 per hour
$73,600 = $69,000 = $72,000
  
Rate Variance, Efficiency Variance,
$4,600 U $3,000 F
Spending Variance,
$1,600 U
*20,000 units × 0.3 hours per unit = 6,000 hours

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
5,750 hours ($12.80 per hour* – $12.00 per hour) = $4,600 U
*$73,600 ÷ 5,750 hours = $12.80 per hour
Labor efficiency variance = SR (AH – SH)
$12.00 per hour (5,750 hours – 6,000 hours) = $3,000 F

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Exercise 10-4 (continued)

3. Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
5,750 hours × 6,000 hours ×
$4.00 per hour $4.00 per hour
$21,850 = $23,000 = $24,000
  
Rate Variance, Efficiency Variance,
$1,150 F $1,000 F
Spending Variance,
$2,150 F

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR – SR)
5,750 hours ($3.80 per hour* – $4.00 per hour) = $1,150 F
*$21,850 ÷ 5,750 hours = $3.80 per hour

Variable overhead efficiency variance = SR (AH – SH)

$4.00 per hour (5,750 hours – 6,000 hours) = $1,000 F

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Exercise 10-5 (20 minutes)

1. If the labor spending variance is $93 unfavorable, and the rate variance
is $87 favorable, then the efficiency variance must be $180 unfavorable,
because the rate and efficiency variances taken together always equal
the spending variance. Knowing that the efficiency variance is $180
unfavorable, one approach to the solution would be:
Efficiency variance = SR (AH – SH)
$9.00 per hour (AH – 125 hours*) = $180 U
$9.00 per hour × AH – $1,125 = $180**
$9.00 per hour × AH = $1,305
   AH = $1,305 ÷ $9.00 per hour
   AH = 145 hours
*50 jobs × 2.5 hours per job = 125 hours
**When used with the formula, unfavorable variances are positive and
favorable variances are negative.

2. Rate variance = AH (AR – SR)

145 hours (AR – $9.00 per hour) = $87 F
145 hours × AR – $1,305 = –$87*
145 hours × AR = $1,218
       AR = $1,218 ÷ 145 hours
       AR = $8.40 per hour
*When used with the formula, unfavorable variances are positive and
favorable variances are negative.

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Exercise 10-5 (continued)

An alternative approach would be to work from known to unknown data
in the columnar model for variance analysis:
Standard Hours
Actual Hours of Input, Actual Hours of Input, Allowed for Output, at
at the Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
145 hours × 145 hours × 125 hours§ ×
$8.40 per hour $9.00 per hour* $9.00 per hour*
= $1,218 = $1,305 = $1,125
  
Rate Variance, Efficiency Variance,
$87 F* $180 U
Spending Variance,
$93 U*
§
50 tune-ups* × 2.5 hours per tune-up* = 125 hours
*Given

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Exercise 10-6 (20 minutes)

1. Actual Quantity Actual Quantity Standard Quantity
of Input, at of Input, at Allowed for Output,
Actual Price Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
20,000 pounds × 20,000 pounds × 18,400 pounds* ×
$2.35 per pound $2.50 per pound $2.50 per pound
= $47,000 = $50,000 = $46,000
  
Price Variance, Quantity Variance,
$3,000 F $4,000 U
Spending Variance,
$1,000 U
*4,000 units × 4.6 pounds per unit = 18,400 pounds

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
20,000 pounds ($2.35 per pound – $2.50 per pound) = $3,000 F
Materials quantity variance = SP (AQ – SQ)
$2.50 per pound (20,000 pounds – 18,400 pounds) = $4,000 U

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Exercise 10-6 (continued)

2. Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
750 hours × 800 hours* ×
$12.00 per hour $12.00 per hour
$10,425 = $9,000 = $9,600
  
Rate Variance, Efficiency Variance,
$1,425 U $600 F
Spending Variance,
$825 U
*4,000 units × 0.2 hours per unit = 800 hours

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
750 hours ($13.90 per hour* – $12.00 per hour) = $1,425 U
*10,425 ÷ 750 hours = $13.90 per hour

Labor efficiency variance = SR (AH – SH)

$12.00 per hour (750 hours – 800 hours) = $600 F

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Exercise 10-7 (15 minutes)

Notice in the solution below that the materials price variance is
computed for the entire amount of materials purchased, whereas the
materials quantity variance is computed only for the amount of materials
used in production.

Actual Quantity Standard Quantity

Actual Quantity of of Input, at Allowed for Output,
Input, at Actual Price Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
20,000 pounds × 20,000 pounds × 13,800 pounds* ×
$2.35 per pound $2.50 per pound $2.50 per pound
= $47,000 = $50,000 = $34,500
  
Price Variance,
$3,000 F
14,750 pounds × $2.50 per pound = $36,875

Quantity Variance,
$2,375 U
*3,000 units × 4.6 pounds per unit = 13,800 pounds

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
20,000 pounds ($2.35 per pound – $2.50 per pound) = $3,000 F
Materials quantity variance = SP (AQ – SQ)
$2.50 per pound (14,750 pounds – 13,800 pounds) = $2,375 U

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Exercise 10-8 (30 minutes)

1. a. Notice in the solution below that the materials price variance is
computed on the entire amount of materials purchased, whereas the
materials quantity variance is computed only on the amount of
materials used in production.
Actual Quantity Standard Quantity
of Input, at Actual Quantity of Allowed for Output, at
Actual Price Input, at Standard Price Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
25,000 microns × 25,000 microns × 18,000 microns* ×
$0.48 per micron $0.50 per micron $0.50 per micron
= $12,000 = $12,500 = $9,000
  
Price Variance,
$500 F
20,000 microns × $0.50 per micron
= $10,000

Quantity Variance,
$1,000 U
*3,000 toys × 6 microns per toy = 18,000 microns

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
25,000 microns ($0.48 per micron – $0.50 per micron) = $500 F
Materials quantity variance = SP (AQ – SQ)
$0.50 per micron (20,000 microns – 18,000 microns) = $1,000 U

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Exercise 10-8 (continued)

b. Direct labor variances:
Actual Hours of Standard Hours Allowed
Input, at the Actual Hours of Input, for Output, at the
Actual Rate at the Standard Rate Standard Rate
(AH × AR) (AH × SR) (SH × SR)
4,000 hours × 3,900 hours* ×
$8.00 per hour $8.00 per hour
$36,000 = $32,000 = $31,200
  
Rate Variance, Efficiency Variance,
$4,000 U $800 U
Spending Variance,
$4,800 U
*3,000 toys × 1.3 hours per toy = 3,900 hours

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
4,000 hours ($9.00 per hour* – $8.00 per hour) = $4,000 U
*$36,000 ÷ 4,000 hours = $9.00 per hour
Labor efficiency variance = SR (AH – SH)
$8.00 per hour (4,000 hours – 3,900 hours) = $800 U

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Exercise 10-8 (continued)

2. A variance usually has many possible explanations. In particular, we
should always keep in mind that the standards themselves may be
incorrect. Some of the other possible explanations for the variances
observed at Dawson Toys appear below:
Materials Price Variance Since this variance is favorable, the actual price
paid per unit for the material was less than the standard price. This could
occur for a variety of reasons including the purchase of a lower grade
material at a discount, buying in an unusually large quantity to take
advantage of quantity discounts, a change in the market price of the
material, or particularly sharp bargaining by the purchasing department.
Materials Quantity Variance Since this variance is unfavorable, more
materials were used to produce the actual output than were called for by
the standard. This could also occur for a variety of reasons. Some of the
possibilities include poorly trained or supervised workers, improperly
adjusted machines, and defective materials.
Labor Rate Variance Since this variance is unfavorable, the actual
average wage rate was higher than the standard wage rate. Some of the
possible explanations include an increase in wages that has not been
reflected in the standards, unanticipated overtime, and a shift toward
more highly paid workers.
Labor Efficiency Variance Since this variance is unfavorable, the actual
number of labor hours was greater than the standard labor hours allowed
for the actual output. As with the other variances, this variance could have
been caused by any of a number of factors. Some of the possible
explanations include poor supervision, poorly trained workers, low-quality
materials requiring more labor time to process, and machine breakdowns.
In addition, if the direct labor force is essentially fixed, an unfavorable
labor efficiency variance could be caused by a reduction in output due to
decreased demand for the company’s products.
It is worth noting that all of these variances could have been caused by
the purchase of low quality materials at a cut-rate price.

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Problem 10-9 (45 minutes)

This problem is more difficult than it looks. Allow ample time for discussion.

1. Actual Quantity Standard Quantity

Actual Quantity of of Input, at Allowed for Output,
Input, at Actual Price Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
12,000 yards × 11,200 yards** ×
$4.00 per yard* $4.00 per yard*
$45,600 = $48,000 = $44,800
  
Price Variance, Quantity Variance,
$2,400 F $3,200 U
Spending Variance,
$800 U
* $22.40 ÷ 5.6 yards = $4.00 per yard
** 2,000 sets × 5.6 yards per set = 11,200 yards

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
12,000 yards ($3.80 per yard* – $4.00 per yard) = $2,400 F
*$45,600 ÷ 12,000 yards = $3.80 per yard

Materials quantity variance = SP (AQ – SQ)

$4.00 per yard (12,000 yards – 11,200 yards) = $3,200 U

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Problem 10-9 (continued)

2. Many students will miss parts 2 and 3 because they will try to use
product costs as if they were hourly costs. Pay particular attention to
the computation of the standard direct labor time per unit and the
standard direct labor rate per hour.
Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
2,800 hours × 3,000 hours** ×
$6.00 per hour* $6.00 per hour*
$18,200 = $16,800 = $18,000
  
Rate Variance, Efficiency Variance,
$1,400 U $1,200 F
Spending Variance,
$200 U

* 2,850 standard hours ÷ 1,900 sets = 1.5 standard hours per set,
$9.00 standard cost per set ÷ 1.5 standard hours per set =
$6.00 standard rate per hour.
** 2,000 sets × 1.5 standard hours per set = 3,000 standard hours.

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
2,800 hours ($6.50 per hour* – $6.00 per hour) = $1,400 U
*$18,200 ÷ 2,800 hours = $6.50 per hour

Labor efficiency variance = SR (AH – SH)

$6.00 per hour (2,800 hours – 3,000 hours) = $1,200 F

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Problem 10-9 (continued)

3. Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
2,800 hours × 3,000 hours ×
$2.40 per hour* $2.40 per hour*
$7,000 = $6,720 = $7,200
  
Rate Variance, Efficiency Variance,
$280 U $480 F
Spending Variance,
$200 F
*$3.60 standard cost per set ÷ 1.5 standard hours per set
= $2.40 standard rate per hour

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR – SR)
2,800 hours ($2.50 per hour* – $2.40 per hour) = $280 U
*$7,000 ÷ 2,800 hours = $2.50 per hour

Variable overhead efficiency variance = SR (AH – SH)

$2.40 per hour (2,800 hours – 3,000 hours) = $480 F

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Problem 10-10 (45 minutes)

1.
Standard
Quantity Standard Price Standard
or Hours or Rate Cost
Alpha6:
Direct materials—X442...... 1.8 kilos $3.50 per kilo $ 6.30
Direct materials—Y661...... 2.0 liters $1.40 per liter 2.80
Direct labor—Sintering....... 0.20 hours $19.80 per hour 3.96
Direct labor—Finishing....... 0.80 hours $19.20 per hour 15.36
Total................................ $28.42
Zeta7:
Direct materials—X442...... 3.0 kilos $3.50 per kilo $10.50
Direct materials—Y661...... 4.5 liters $1.40 per liter 6.30
Direct labor—Sintering....... 0.35 hours $19.80 per hour 6.93
Direct labor—Finishing....... 0.90 hours $19.20 per hour 17.28
Total................................ $41.01

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Problem 10-10 (continued)

2. The computations to follow will require the standard quantities allowed

for the actual output for each material.
Standard Quantity Allowed
Material X442:
Production of Alpha6 (1.8 kilos per unit × 1,500 units)...... 2,700 kilos
Production of Zeta7 (3.0 kilos per unit × 2,000 units)........ 6,000 kilos
Total............................................................................... 8,700 kilos
Material Y661:
Production of Alpha6 (2.0 liters per unit × 1,500 units)...... 3,000 liters
Production of Zeta7 (4.5 liters per unit × 2,000 units)....... 9,000 liters
Total............................................................................... 12,000 liters

Direct Materials Variances—Material X442:

Materials quantity variance = SP (AQ – SQ)
= $3.50 per kilo (8,500 kilos – 8,700 kilos)
= $700 F
Materials price variance = AQ (AP – SP)
= 14,500 kilos ($3.60 per kilo* – $3.50 per kilo)
= $1,450 U
*$52,200 ÷ 14,500 kilos = $3.60 per kilo

Direct Materials Variances—Material Y661:

Materials quantity variance = SP (AQ – SQ)
= $1.40 per liter (13,000 liters – 12,000 liters)
= $1,400 U
Materials price variance = AQ (AP – SP)
= 15,500 liters ($1.35 per liter* – $1.40 per liter)
= $775 F
*$20,925 ÷ 15,500 liters = $1.35 per liter

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Problem 10-10 (continued)

3. The computations to follow will require the standard quantities allowed

for the actual output for direct labor in each department.
Standard Hours Allowed
Sintering:
Production of Alpha6 (0.20 hours per unit × 1,500 units)... 300 hours
Production of Zeta7 (0.35 hours per unit × 2,000 units).... 700 hours
Total............................................................................... 1,000 hours
Finishing:
Production of Alpha6 (0.80 hours per unit × 1,500 units)... 1,200 hours
Production of Zeta7 (0.90 hours per unit × 2,000 units).... 1,800 hours
Total............................................................................... 3,000 hours

Direct Labor Variances—Sintering:

Labor efficiency variance = SR (AH – SH)
= $19.80 per hour (1,200 hours – 1,000 hours)
= $3,960 U
Labor rate variance = AH (AR – SR)
= 1,200 hours ($22.50 per hour* – $19.80 per hour)
= $3,240 U
*$27,000 ÷ 1,200 hours = $22.50 per hour

Direct Labor Variances—Finishing:

Labor efficiency variance = SR (AH – SH)
= $19.20 per hour (2,850 hours – 3,000 hours)
= $2,880 F
Labor rate variance = AH (AR – SR)
= 2,850 hours ($21.00 per hour* – $19.20 per hour)
= $5,130 U
*$59,850 ÷ 2,850 hours = $21.00 per hour

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Problem 10-11 (45 minutes)

1. a. Materials quantity variance = SP (AQ – SQ)
$5.00 per foot (AQ – 9,600 feet*) = $4,500 U
$5.00 per foot × AQ – $48,000 = $4,500**
$5.00 per foot × AQ = $52,500
AQ = 10,500 feet
* $3,200 units × 3 foot per unit
** When used with the formula, unfavorable variances are
positive and favorable variances are negative.
Therefore, $55,650 ÷ 10,500 feet = $5.30 per foot

b. Materials price variance = AQ (AP – SP)

10,500 feet ($5.30 per foot – $5.00 per foot) = $3,150 U
The total variance for materials is:
Materials price variance.................. $3,150 U
Materials quantity variance............. 4,500 U
Total variance................................. $7,650 U

Alternative approach to parts (a) and (b):

Actual Quantity Standard Quantity
Actual Quantity of of Input, at Allowed for Output, at
Input, at Actual Price Standard Price Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
10,500 feet × 10,500 feet × 9,600 feet** ×
$5.30 per foot $5.00 per foot* $5.00 per foot*
= $55,650* = $52,500 = $48,000
  
Price Variance, Quantity Variance,
$3,150 U $4,500 U*
Spending Variance,
$7,650 U
* Given
** 3,200 units × 3 foot per unit = 9,600 feet

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Problem 10-11 (continued)

2. a. Labor rate variance = AH (AR – SR)
4,900 hours ($7.50 per hour* – SR) = $2,450 F**
$36,750 – 4,900 hours × SR = –$2,450***
4,900 hours × SR = $39,200
SR = $8.00

* $36,750 ÷ 4,900 hours

** $1,650 F + $800 U.
*** When used with the formula, unfavorable variances are
positive and favorable variances are negative.

b. Labor efficiency variance = SR (AH – SH)

$8 per hour (4,900 hours – SH) = $800 U
$39,200 – $8 per hour × SH = $800*
$8 per hour × SH = $38,400
SH = 4,800 hours

* When used with the formula, unfavorable variances are positive

and favorable variances are negative.

Alternative approach to parts (a) and (b):

Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output,
Actual Rate at the Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
4,900 hours* × 4,800 hours ×
$8.00 per hour $8.00 per hour
$36,750* = $39,200 = $38,400
  
Rate Variance, Efficiency Variance,
$2,450 F $800 U*
Spending Variance,
$1,650 F*
*Given.

c. The standard hours allowed per unit of product are:

4,800 hours ÷ 3,200 units = 1.5 hours per unit
Problem 10-12 (45 minutes)
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1. The standard quantity of plates allowed for tests performed during the
month would be:
Blood tests................................... 1,800
Smears........................................ 2,400
Total............................................ 4,200
Plates per test.............................. × 2
Standard quantity allowed............. 8,400

The variance analysis for plates would be:

Actual Quantity Standard Quantity
Actual Quantity of of Input, at Allowed for Output,
Input, at Actual Price Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
12,000 plates × 8,400 plates ×
$2.50 per plate $2.50 per plate
$28,200 = $30,000 = $21,000
  
Price Variance,
$1,800 F
10,500 plates ×
$2.50 per plate =
$26,250

Quantity Variance,
$5,250 U

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
12,000 plates ($2.35 per plate* – $2.50 per plate) = $1,800 F
*$28,200 ÷ 12,000 plates = $2.35 per plate.
Materials quantity variance = SP (AQ – SQ)
$2.50 per plate (10,500 plates – 8,400 plates) = $5,250 U

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Problem 10-12 (continued)

Note that all of the price variance is due to the hospital’s 6% quantity
discount. Also note that the $5,250 quantity variance for the month is
equal to 25% of the standard cost allowed for plates.

2. a. The standard hours allowed for tests performed during the month
would be:
Blood tests: 0.3 hour per test × 1,800 tests........... 540 hours
Smears: 0.15 hour per test × 2,400 tests.............. 360 hours
Total standard hours allowed................................ 900 hours

The variance analysis would be:

Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
1,150 hours × 900 hours ×
$14.00 per hour $14.00 per hour
$13,800 = $16,100 = $12,600
  
Rate Variance, Efficiency Variance,
$2,300 F $3,500 U
Spending Variance,
$1,200 U

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
1,150 hours ($12.00 per hour* – $14.00 per hour) = $2,300 F
*$13,800 ÷ 1,150 hours = $12.00 per hour
Labor efficiency variance = SR (AH – SH)
$14.00 per hour (1,150 hours – 900 hours) = $3,500 U

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Problem 10-12 (continued)

b. The policy probably should not be continued. Although the hospital is
saving $2 per hour by employing more assistants than senior
technicians, this savings is more than offset by other factors. Too
much time is being taken in performing lab tests, as indicated by the
large unfavorable labor efficiency variance. And, it seems likely that
most (or all) of the hospital’s unfavorable quantity variance for plates
is traceable to inadequate supervision of assistants in the lab.

3. The variable overhead variances follow:

Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output,
Actual Rate at the Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
1,150 hours × 900 hours ×
$6.00 per hour $6.00 per hour
$7,820 = $6,900 = $5,400
  
Rate Variance, Efficiency Variance,
$920 U $1,500 U
Spending Variance,
$2,420 U

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR – SR)
1,150 hours ($6.80 per hour* – $6.00 per hour) = $920 U
*$7,820 ÷ 1,150 hours = $6.80 per hour
Variable overhead efficiency variance = SR (AH – SH)
$6.00 per hour (1,150 hours – 900 hours) = $1,500 U
Yes, the two variances are closely related. Both are computed by
comparing actual labor time to the standard hours allowed for the
output of the period. Thus, if the labor efficiency variance is favorable
(or unfavorable), then the variable overhead efficiency variance will also
be favorable (or unfavorable).

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Problem 10-13 (45 minutes)

1. a.
Standard Quantity
Actual Quantity of Allowed
Actual Quantity of Input, Input, for Actual Output,
at Actual Price at Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
21,600 feet** × 21,600 feet** × 21,600 feet* ×
$3.30 per foot $3.00 per foot $3.00 per foot
= $71,280 = $64,800 = $64,800
Materials price variance = Materials quantity
$6,480 U variance = $0
Spending variance = $6,480 U
* 12,000 units × 1.80 feet per unit = 21,600 feet
** 12,000 units × 1.80 feet per unit = 21,600 feet

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)

= 21,600 feet ($3.30 per foot – $3.00 per foot)
= $6,480 U
Materials quantity variance = SP (AQ – SQ)
= $3.00 per foot (21,600 feet – 21,600 feet)
= $0

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Problem 10-13 (continued)

1. b.
Standard Hours Allowed
Actual Hours of Input,
Actual Hours of Input, for Actual Output,
at Actual Rate at Standard Rate at Standard Rate
(AH × AR) (AH × SR) (SH × SR)
11,040 hours** × 11,040 hours** × 10,800 hours* ×
$17.50 per hour $18.00 per hour $18.00 per hour
= $193,200 = $198,720 = $194,400
Labor efficiency
Labor rate variance variance
= $5,520 F = $4,320 U
Spending variance = $1,200 F
* 12,000 units × 0.90 hours per unit = 10,800 hours
** 12,000 units × 0.92 hours per unit = 11,040 hours

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)

= 11,040 hours ($17.50 per hour – $18.00 per hour)
= $5,520 F
Labor efficiency variance = SR (AH – SH)
= $18.00 per hour (11,040 hours – 10,800 hours)
= $4,320 U

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Problem 10-13 (continued)

1. c.
Standard Hours Allowed
Actual Hours of Input,
Actual Hours of Input, for Actual Output,
at Actual Rate at Standard Rate at Standard Rate
(AH × AR) (AH × SR) (SH × SR)
11,040 hours** × 11,040 hours** × 10,800 hours* ×
$4.50 per hour $5.00 per hour $5.00 per hour
= $49,680 = $55,200 = $54,000
Variable overhead
Variable overhead rate efficiency variance
variance = $5,520 F = $1,200 U
Spending variance = $4,320 F
* 12,000 units × 0.90 hours per unit = 10,800 hours
** 12,000 units × 0.92 hours per unit = 11,040 hours

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR – SR)

= 11,040 hours ($4.50 per hour – $5.00 per hour)
= $5,520 F
Variable overhead efficiency variance = SR (AH – SH)
= $5.00 per hour (11,040 hours – 10,800 hours)
= $1,200 U
2.
Materials:
Price variance ($6,480 ÷ 12,000 units)........... $0.54 U
Quantity variance ($0 ÷ 12,000 units)............ 0.00 $0.54 U
Labor:
Rate variance ($5,520 ÷ 12,000 units)............ 0.46 F
Efficiency variance ($4,320 ÷ 12,000 units).... 0.36 U 0.10 F
Variable overhead:
Rate variance ($5,520 ÷ 12,000 units)............ 0.46 F
Efficiency variance ($1,200 ÷ 12,000 units).... 0.10 U 0.36 F
Excess of actual over standard cost per unit........ $0.08 U

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Problem 10-13 (continued)

3. Both the labor efficiency and variable overhead efficiency variances are
affected by inefficient use of labor time.
Excess of actual over standard cost per unit........ $0.08 U
Less portion attributable to labor inefficiency:
Labor efficiency variance.................................... 0.36 U
Variable overhead efficiency variance.................. 0.10 U 0.46 U
Portion due to other variances............................ $0.38 F
In sum, had it not been for the apparent inefficient use of labor time,
the total variance in unit cost for the month would have been favorable
by $0.38 rather than unfavorable by $0.08.

4. Although the excess of actual cost over standard cost is only $0.08 per
unit, the details of the variances are significant. The materials price
variance is $6,480 U and it warrants further investigation. The labor
efficiency variance is $4,320 U and the variable overhead efficiency
variance is $1,200 U. Taken together, these latter two variances
highlight an opportunity for the company to pursue process
improvement opportunities that would improve efficiency.

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Problem 10-14 (45 minutes)

1. a. In the solution below, the materials price variance is computed on the
entire amount of materials purchased whereas the materials quantity
variance is computed only on the amount of materials used in
production:
Actual Quantity of Actual Quantity Standard Quantity
Input, at of Input, at Allowed for Output, at
Actual Price Standard Price Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
12,000 ounces × 9,375 ounces* ×
$20.00 per ounce $20.00 per ounce
$225,000 = $240,000 = $187,500
  
Price Variance,
$15,000 F
9,500 ounces × $20.00 per ounce
= $190,000

Quantity Variance,
$2,500 U
*3,750 units × 2.5 ounces per unit = 9,375 ounces

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
12,000 ounces ($18.75 per ounce* – $20.00 per ounce) = $15,000 F
*$225,000 ÷ 12,000 ounces = $18.75 per ounce

Materials quantity variance = SP (AQ – SQ)

$20.00 per ounce (9,500 ounces – 9,375 ounces) = $2,500 U

b. Yes, the contract probably should be signed. The new price of $18.75
per ounce is substantially lower than the old price of $20.00 per
ounce, resulting in a favorable price variance of $15,000 for the
month. Moreover, the material from the new supplier appears to
cause little or no problem in production as shown by the small
materials quantity variance for the month.

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Problem 10-14 (continued)

2. a.
Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output, at
Actual Rate Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
5,600 hours* × 5,600 hours × 5,250 hours** ×
$12.00 per hour $12.50 per hour $12.50 per hour
= $67,200 = $70,000 = $65,625
  
Rate Variance, Efficiency Variance,
$2,800 F $4,375 U
Spending Variance,
$1,575 U
*35 technicians × 160 hours per technician = 5,600 hours
**3,750 units × 1.4 hours per technician = 5,250 hrs

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
5,600 hours ($12.00 per hour – $12.50 per hour) = $2,800 F
Labor efficiency variance = SR (AH – SH)
$12.50 per hour (5,600 hours – 5,250 hours) = $4,375 U

b. No, the new labor mix probably should not be continued. Although it
decreases the average hourly labor cost from $12.50 to $12.00,
thereby causing a $2,800 favorable labor rate variance, this savings is
more than offset by a large unfavorable labor efficiency variance for
the month. Thus, the new labor mix increases overall labor costs.

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Problem 10-14 (continued)

3. Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
5,600 hours* × 5,250 hours** ×
$3.50 per hour $3.50 per hour
$18,200 = $19,600 = $18,375
  
Rate Variance, Efficiency Variance,
$1,400 F $1,225 U
Spending Variance,
$175 F
* Based on direct labor hours:
35 technicians × 160 hours per technician = 5,600 hours
** 3,750 units × 1.4 hours per unit = 5,250 hours

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR – SR)
5,600 hours ($3.25 per hour* – $3.50 per hour) = $1,400 F
*$18,200 ÷ 5,600 hours = $3.25 per hour

Variable overhead efficiency variance = SR (AH – SH)

$3.50 per hour (5,600 hours – 5,250 hours) = $1,225 U

Both the labor efficiency variance and the variable overhead efficiency
variance are computed by comparing actual labor-hours to standard
labor-hours. Thus, if the labor efficiency variance is unfavorable, then
the variable overhead efficiency variance will be unfavorable as well.

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Problem 10-15 (45 minutes)

1. a.
Actual Quantity Standard Quantity
Actual Quantity of of Input, at Allowed for Output,
Input, at Actual Price Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
60,000 pounds × 60,000 pounds × 45,000 pounds* ×
$1.95 per pound $2.00 per pound $2.00 per pound
= $117,000 = $120,000 = $90,000
  
Price Variance,
$3,000 F
49,200 pounds × $2.00 per pound = $98,400

Quantity Variance,
$8,400 U
*15,000 pools × 3.0 pounds per pool = 45,000 pounds

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
60,000 pounds ($1.95 per pound – $2.00 per pound) = $3,000 F
Materials quantity variance = SP (AQ – SQ)
$2.00 per pound (49,200 pounds – 45,000 pounds) = $8,400 U

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Problem 10-15 (continued)

b.
Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output,
Actual Rate at the Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
11,800 hours × 11,800 hours × 12,000 hours* ×
$7.00 per hour $6.00 per hour $6.00 per hour
= $82,600 = $70,800 = $72,000
  
Rate Variance, Efficiency Variance,
$11,800 U $1,200 F
Spending Variance,
$10,600 U
*15,000 pools × 0.8 hours per pool = 12,000 hours

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
11,800 hours ($7.00 per hour – $6.00 per hour) = $11,800 U
Labor efficiency variance = SR (AH – SH)
$6.00 per hour (11,800 hours – 12,000 hours) = $1,200 F

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Problem 10-15 (continued)

c.
Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
5,900 hours × 6,000 hours* ×
$3.00 per hour $3.00 per hour
$18,290 = $17,700 = $18,000
  
Rate Variance, Efficiency Variance,
$590 U $300 F
Spending Variance,
$290 U
*15,000 pools × 0.4 hours per pool = 6,000 hours

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR – SR)
5,900 hours ($3.10 per hour* – $3.00 per hour) = $590 U
*$18,290 ÷ 5,900 hours = $3.10 per hour

Variable overhead efficiency variance = SR (AH – SH)

$3.00 per hour (5,900 hours – 6,000 hours) = $300 F

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Problem 10-15 (continued)

2. Summary of variances:
Material price variance........................... $ 3,000 F
Material quantity variance...................... 8,400 U
Labor rate variance............................... 11,800 U
Labor efficiency variance....................... 1,200 F
Variable overhead rate variance............. 590 U
Variable overhead efficiency variance..... 300 F
Net variance......................................... $16,290 U
The net unfavorable variance of $16,290 for the month caused the
plant’s variable cost of goods sold to increase from the budgeted level of
$180,000 to $196,290:
Budgeted cost of goods sold at $12 per pool.......... $180,000
Add the net unfavorable variance, as above........... 16,290
Actual cost of goods sold...................................... $196,290
This $16,290 net unfavorable variance also accounts for the difference
between the budgeted net operating income and the actual net
operating income for the month.
Budgeted net operating income............................ $36,000
Deduct the net unfavorable variance added to cost
of goods sold for the month............................... 16,290
Net operating income........................................... $19,710

3. The two most significant variances are the materials quantity variance
and the labor rate variance. Possible causes of the variances include:
Materials quantity variance: Outdated standards, unskilled workers,
poorly adjusted machines,
carelessness, poorly trained workers,
inferior quality materials.
Labor rate variance: Outdated standards, change in pay
scale, overtime pay.

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Problem 10-16 (60 minutes)

1. Standard cost for March production:
Materials...................................................................... $16,800
Direct labor.................................................................. 10,500
Variable manufacturing overhead................................... 4,200
Total standard cost (a).................................................. $31,500
Number of backpacks produced (b)................................ 1,000
Standard cost of a single backpack (a) ÷ (b).................. $31.50

Standard cost of a single backpack (above).................... $31.50

Deduct difference between standard and actual cost....... 0.15
Actual cost per backpack............................................... $31.35

Total standard cost of materials allowed during March

3. (a)............................................................................ $16,800
Number of backpacks produced during March (b).......... 1,000
Standard materials cost per backpack (a) ÷ (b)............. $16.80
Standard materials cost per backpack $16.80 per backpack
=
Standard materials cost per yard $6.00 per yard
= 2.8 yards per backpack

4. Standard cost of material used............ $16,800

Actual cost of material used................ 15,000
Total variance..................................... $ 1,800 F
The price and quantity variances together equal the total variance. If
the quantity variance is $1,200 U, then the price variance must be
$3,000 F:
Price variance..................................... $ 3,000 F
Quantity variance............................... 1,200 U
Total variance..................................... $ 1,800 F

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Problem 10-16 (continued)

Alternative Solution:
Actual Quantity Actual Quantity Standard Quantity
of Input, at of Input, at Allowed for Output,
Actual Price Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
3,000 yards × 3,000 yards × 2,800 yards** ×
$5.00 per yard $6.00 per yard* $6.00 per yard*
= $15,000* = $18,000 = $16,800*
  
Price Variance, Quantity Variance,
$3,000 F $1,200 U*
Spending Variance,
$1,800 F
* Given.
** 1,000 units × 2.8 yards per unit = 2,800 yards

5. The first step in computing the standard direct labor rate is to determine
the standard direct labor-hours allowed for the month’s production. The
standard direct labor-hours can be computed by working with the
variable manufacturing overhead costs, because they are based on
direct labor-hours worked:
Standard variable manufacturing overhead cost for March (a). $4,200
Standard variable manufacturing overhead rate per direct
labor-hour (b).................................................................... $3.00
Standard direct labor-hours for March (a) ÷ (b)...................... 1,400

Total standard direct labor cost for March $10,500

=
Total standard direct labor-hours for March 1,400 DLHs
= $7.50 per DLH

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Problem 10-16 (continued)

6. Before the labor variances can be computed, it is necessary to compute
the actual direct labor cost for the month:
Actual cost per backpack produced (part 2)......... $ 31.35
Number of backpacks produced.......................... × 1,000
Total actual cost of production............................ $31,350
Less: Actual cost of materials.............................. $15,000
Actual cost of variable manufacturing
overhead................................................ 3,600 18,600
Actual cost of direct labor................................... $12,750
With this information, the variances can be computed:
Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
1,500 hours* ×
$7.50 per hour
$12,750 = $11,250 $10,500*
  
Rate Variance, Efficiency Variance,
$1,500 U $750 U
Spending Variance,
$2,250 U
*Given.

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Problem 10-16 (continued)

7. Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output,
Actual Rate at the Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
1,500 hours* ×
$3.00 per hour*
$3,600* = $4,500 $4,200*
  
Rate Variance, Efficiency Variance,
$900 F $300 U
Spending Variance,
$600 F
*Given.

8.
Standard Standard Standard
Quantity or Price or
Hours Rate Cost
1
Direct materials............... 2.8 yards $6 per yard $16.80
2 3
Direct labor..................... 1.4 hours $7.50 per hour 10.50
Variable manufacturing
overhead...................... 1.4 hours $3 per hour 4.20
Total standard cost.......... $31.50
1
From part 3.
2
1,400 standard hours (from part 5) ÷ 1,000 backpacks = 1.4
hours per backpack.
3
From part 5.

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Case 10-17 (60 minutes)

1. The number of units produced can be computed by using the total
standard cost applied for the period for any input—direct materials,
direct labor, or variable manufacturing overhead. Using the standard
cost applied for direct materials, we have:
Total standard cost applied for the period $405,000
=
Standard cost per unit $18 per unit
= 22,500 units
The same answer can be obtained by using direct labor or variable
manufacturing overhead.

2. 138,000 pounds; see below for a detailed analysis.

3. $2.95 per pound; see below for a detailed analysis.

4. 19,400 direct labor-hours; see below for a detailed analysis.

5. $15.75 per direct labor-hour; see below for a detailed analysis.

6. Standard variable overhead cost applied $54,000

Add: Overhead efficiency variance......... 4,200 U (see below)
Deduct: Overhead rate variance............ 1,300 F
Actual variable overhead cost incurred... $56,900

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Case 10-17 (continued)

Direct materials analysis:
Actual Quantity of Actual Quantity Standard Quantity
Inputs, at Actual of Inputs, at Allowed for Output,
Price Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
138,000 pounds 138,000 pounds** 135,000 pounds*
× $2.95 per pound*** × $3 per pound × $3 per pound
= $407,100 = $414,000 = $405,000

Price Variance, Quantity Variance,

$6,900 F $9,000 U
Spending Variance,
$2,100 U
* 22,500 units × 6 pounds per unit = 135,000 pounds
** $414,000 ÷ $3 per pound = 138,000 pounds
*** $407,100 ÷ 138,000 pounds = $2.95 per pound

Direct labor analysis:

Actual Hours of Standard Hours

Actual Hours of Input, Input, at the Allowed for Output,
at the Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
19,400 DLHs × 19,400 DLHs** × 18,000 DLHs* ×
$15.75 per DLH*** $15 per DLH $15 per DLH
= $305,550 = $291,000 = $270,000
  
Rate Variance, Efficiency Variance,
$14,550 U $21,000 U
Spending Variance,
$35,550 U
* 22,500 units × 0.8 DLHs per unit = 18,000 DLHs
** $291,000 ÷ $15 per DLH = 19,400 DLHs
*** $305,550 ÷ 19,400 DLHs = $15.75 per DLH

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Case 10-17 (continued)

Variable overhead analysis:
Actual Hours of Standard Hours
Actual Hours of Input, Input, at the Allowed for Output,
at the Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
$56,900** 19,400 DLHs × 18,000 DLHs ×
$3 per DLH $3 per DLH
= $58,200 = $54,000

Rate Variance, Efficiency Variance,

$1,300 F $4,200 U*
* Computed using 19,400 actual DLHs at the $3 per DLH standard rate.
** $58,200 – $1,300 = $56,900.

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Appendix 10A
Predetermined Overhead Rates and Overhead
Analysis in a Standard Costing System

Exercise 10A-1 (15 minutes)

1. Fixed overhead
Fixed portion of the =
predetermined overhead rate Denominator level of activity
$250,000
=
25,000 DLHs
= $10.00 per DLH

2.
Budget = Actual fixed - Budgeted fixed
variance overhead overhead

= $254,000 - $250,000
= $4,000 U
Fixed portion of
variance overhead rate hours allowed (
Volume = the predetermined × Denominator - Standard hours
)
= $10.00 per DLH × (25,000 DLHs - 26,000 DLHs)
= $10,000 F

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Exercise 10A-2 (20 minutes)

1. Predetermined = $3 per MH × 60,000 MHs + $300,000
overhead rate 60,000 MHs
$480,000
=
60,000 MHs
= $8 per MH

Variable portion of $3 per MH × 60,000 MHs

the predetermined =
overhead rate 60,000 MHs

$180,000
=
60,000 MHs
= $3 per MH
Fixed portion of $300,000
the predetermined =
overhead rate 60,000 MHs

= $5 per MH

2. The standard hours per unit of product are:

60,000 hours ÷ 40,000 units = 1.5 hours per unit
Given this figure, the standard hours allowed for the actual production
would be:
42,000 units × 1.5 hours per unit = 63,000 standard hours allowed.

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Exercise 10A-2 (continued)

3. Variable overhead rate variance:
Variable overhead rate variance = (AH × AR) – (AH × SR)
($185,600) – (64,000 hours × $3 per hour) = $6,400 F
Variable overhead efficiency variance:
Variable overhead efficiency variance = SR (AH – SH)
$3 per hour (64,000 hours – 63,000 hours) = $3,000 U
The fixed overhead variances are as follows:
Actual Fixed Budgeted Fixed Fixed Overhead Applied to
Overhead Overhead Work in Process
$302,400 $300,000* 63,000 hours × $5 per hour
= $315,000
  
Budget Variance, Volume Variance,
$2,400 U $15,000 F
*As originally budgeted.

Alternative approach to the budget variance:

Budget = Actual fixed - Budgeted fixed
variance overhead overhead

= $302,400 - $300,000
= $2,400 U
Alternative approach to the volume variance:
Fixed portion of æ Standardö
Volume = the predetermined ´ ç
çDenominator - hours ÷ ÷
Variance ç hours ÷
÷
overhead rate ç
ç
è ÷
allowed ø

= $5 per hour ´ (60,000 hours - 63,000 hours)

= $15,000 F

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Exercise 10A-3 (15 minutes)

1. The total overhead cost at the denominator level of activity must be
determined before the predetermined overhead rate can be computed.
Total fixed overhead cost per year................................. $250,000
Total variable overhead cost
($2 per DLH × 40,000 DLHs)....................................... 80,000
Total overhead cost at the denominator level of activity. . $330,000

Predetermined = Overhead at the denominator level of activity

overhead rate Denominator level of activity
$330,000
= = $8.25 per DLH
40,000 DLHs

2. Standard direct labor-hours allowed for

the actual output (a)........................... 38,000 DLHs
Predetermined overhead rate (b)............ $8.25 per DLH
Overhead applied (a) × (b).................... $313,500

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Exercise 10A-4 (10 minutes)

Company A: This company has a favorable volume variance because the
standard hours allowed for the actual production are greater
than the denominator hours.
Company B: This company has an unfavorable volume variance because
the standard hours allowed for the actual production are less
than the denominator hours.
Company C: This company has no volume variance because the standard
hours allowed for the actual production and the denominator
hours are the same.

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Exercise 10A-5 (15 minutes)

1. 9,500 units × 4 hours per unit = 38,000 hours.

2. and 3.
Actual Fixed Budgeted Fixed Fixed Overhead Applied to
Overhead Overhead Work in Process
$198,700* $200,000 38,000 hours × $5 per hour*
= $190,000
  
Budget Variance, Volume Variance,
$1,300 F $10,000 U*
*Given.

4. Fixed element of the Budgeted fixed overhead

=
predetermined overhead rate Denominator activity

$200,000
=
Denominator activity

= $5 per hour

Therefore, the denominator activity is: $200,000 ÷ $5 per hour =

40,000 hours.

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Exercise 10A-6 (15 minutes)

1. Total overhead at the
Predetermined = denominator activity
overhead rate Denominator activity

$1.90 per DLH × 30,000 per DLH + $168,000

=
30,000 DLHs
$225,000
=
30,000 DLHs
= $7.50 per DLH

Variable element: ($1.90 per DLH × 30,000 DLHs) ÷ 30,000 DLHs =

$57,000 ÷ 30,000 DLHs = $1.90 per DLH

Fixed element: $168,000 ÷ 30,000 DLHs = $5.60 per DLH

2. Direct materials, 2.5 yards × $8.60 per yard...................... $21.50

Direct labor, 3 DLHs* × $12.00 per DLH............................ 36.00
Variable manufacturing overhead, 3 DLHs × $1.90 per DLH 5.70
Fixed manufacturing overhead, 3 DLHs × $5.60 per DLH.... 16.80
Total standard cost per unit............................................... $80.00
*30,000 DLHs ÷ 10,000 units = 3 DLHs per unit.

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Exercise 10A-7 (15 minutes)

1. 14,000 units produced × 3 MHs per unit = 42,000 MHs

2. Actual fixed overhead incurred................. $267,000

Add: Favorable budget variance............... 3,000
Budgeted fixed overhead cost.................. $270,000
Fixed element of the Budgeted fixed overhead
=
predetermined overhead rate Denominator activity

$270,000
=
45,000 MHs
= $6 per MH

3. Fixed portion of æ Standardö÷

Volume = the predetermined ç
çDenominator - hours ÷
Variance ç hours ÷
÷
overhead rate ç ç
è ÷
allowed ø

= $6 per MH (45,000 MHs - 42,000 MHs)

= $18,000 U

Alternative solution to parts 1-3:

Actual Fixed Budgeted Fixed Fixed Overhead Applied
Overhead Overhead to Work in Process
$267,000* $270,0001 42,000 MHs2 × $6 per MH3
= $252,000
  
Budget Variance, Volume Variance,
$3,000 F* $18,000 U
1
$267,000 + $3,000 = $270,000.
2
14,000 units × 3 MHs per unit = 42,000 MHs
3
$270,000 ÷ 45,000 denominator MHs = $6 per MH
*Given.

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Problem 10A-8 (45 minutes)

1. $600,000
Total rate: = $10 per DLH
60,000 DLHs
$120,000
Variable rate: = $2 per DLH
60,000 DLHs
$480,000
Fixed rate: = $8 per DLH
60,000 DLHs

2. Direct materials: 3 pounds at $7 per pound........... $21

Direct labor: 1.5 DLHs at $12 per DLH.................. 18
Variable overhead: 1.5 DLHs at $2 per DLH........... 3
Fixed overhead: 1.5 DLHs at $8 per DLH............... 12
Standard cost per unit.......................................... $54

3. a. 42,000 units × 1.5 DLHs per unit = 63,000 standard DLHs.

b. Manufacturing Overhead
Actual costs 606,500 Applied costs 630,000 *
Overapplied overhead 23,500
*63,000 standard DLHs × $10 per DLH = $630,000.

4. Variable overhead variances:

Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
$123,500 65,000 DLHs × 63,000 DLHs ×
$2 per DLH $2 per DLH
= $130,000 = $126,000
  
Rate Variance, Efficiency Variance,
$6,500 F $4,000 U

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Problem 10A-8 (continued)

Alternative solution:
Variable overhead rate variance = (AH × AR) – (AH × SR)
($123,500) – (65,000 DLHs × $2 per DLH) = $6,500 F
Variable overhead efficiency variance = SR (AH – SH)
$2 per DLH (65,000 DLHs – 63,000 DLHs) = $4,000 U

Fixed overhead variances:

Actual Fixed Budgeted Fixed Fixed Overhead
Overhead Overhead Applied to Work in Process
$483,000 $480,000* 63,000 DLHs × $8 per DLH
= $504,000
  
Budget Variance, Volume Variance,
$3,000 U $24,000 F
*Can be expressed as: 60,000 denominator DLHs × $8 per DLH =
$480,000

Alternative solution:
Budget variance:
Budget = Actual fixed - Budgeted fixed
variance overhead overhead

= $483,000 - $480,000
= $3,000 U
Volume variance:
Fixed portion of æ Standardö÷
Volume = the predetermined ç
çDenominator - hours ÷
Variance ç hours ÷
÷
overhead rate ç ç
è ÷
allowed ø

= $8 per DLH ´ (60,000 DLHs - 63,000 DLHs)

= $24,000 F

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Problem 10A-8 (continued)

The company’s overhead variances can be summarized as follows:
Variable overhead:
Rate variance................................. $ 6,500 F
Efficiency variance.......................... 4,000 U
Fixed overhead:
Budget variance.............................. 3,000 U
Volume variance............................. 24,000 F
Overapplied overhead—see part 3...... $23,500 F

5. Only the volume variance would have changed. It would have been
unfavorable because the standard DLHs allowed for the year’s
production (63,000 DLHs) would have been less than the denominator
DLHs (65,000 DLHs).

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Problem 10A-9 (45 minutes)

1. $297,500
Total rate: = $8.50 per hour
35,000 hours
$87,500
Variable rate: = $2.50 per hour
35,000 hours
$210,000
Fixed rate: = $6.00 per hour
35,000 hours

2. 32,000 standard hours × $8.50 per hour = $272,000.

3. Variable overhead variances:

Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
$78,000 30,000 hours × 32,000 hours ×
$2.50 per hour $2.50 per hour
= $75,000 = $80,000
  
Rate Variance, Efficiency Variance,
$3,000 U $5,000 F

Alternative solution:
Variable overhead rate variance = (AH × AR) – (AH × SR)
($78,000) – (30,000 hours × $2.50 per hour) = $3,000 U
Variable overhead efficiency variance = SR (AH – SH)
$2.50 per hour (30,000 hours – 32,000 hours) = $5,000 F

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Problem 10A-9 (continued)

Fixed overhead variances:
Actual Fixed Budgeted Fixed Fixed Overhead Applied to
Overhead Overhead Work in Process
$209,400 $210,000 32,000 hours ×
$6 per hour = $192,000
  
Budget Variance, Volume Variance,
$600 F $18,000 U

Alternative solution:
Budget variance:
Budget = Actual fixed - Budgeted fixed
variance overhead overhead

= $209,400 - $210,000

= $600 F
Volume variance:
Fixed portion of æ Standardö÷
Volume = the predetermined ç
çDenominator - hours ÷
Variance ç hours ÷
÷
overhead rate ç ç
è ÷
allowed ø

= $6.00 per hour (35,000 hours - 32,000 hours)

= $18,000 U

Verification:
Variable overhead rate variance........ $ 3,000 U
Variable overhead efficiency variance 5,000 F
Fixed overhead budget variance........ 600 F
Fixed overhead volume variance....... 18,000 U
Underapplied overhead..................... $15,400 U

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Problem 10A-9 (continued)

4. Variable overhead
Rate variance: This variance includes both price and quantity elements.
The overhead spending variance reflects differences between actual and
standard prices for variable overhead items. It also reflects differences
between the amounts of variable overhead inputs that were actually
used and the amounts that should have been used for the actual output
of the period. Because the variable overhead spending variance is
unfavorable, either too much was paid for variable overhead items or
too many of them were used.
Efficiency variance: The term “variable overhead efficiency variance” is a
misnomer, because the variance does not measure efficiency in the use
of overhead items. It measures the indirect effect on variable overhead
of the efficiency or inefficiency with which the activity base is utilized. In
this company, the activity base is labor-hours. If variable overhead is
really proportional to labor-hours, then more effective use of labor-hours
has the indirect effect of reducing variable overhead. Because 2,000
fewer labor-hours were required than indicated by the labor standards,
the indirect effect was presumably to reduce variable overhead spending
by about $5,000 ($2.50 per hour × 2,000 hours).

Fixed overhead
Budget variance: This variance is simply the difference between the
budgeted fixed cost and the actual fixed cost. In this case, the variance
is favorable which indicates that actual fixed costs were lower than
anticipated in the budget.
Volume variance: This variance occurs as a result of actual activity being
different from the denominator activity in the predetermined overhead
rate. In this case, the variance is unfavorable, so actual activity was less
than the denominator activity. It is difficult to place much of a
meaningful economic interpretation on this variance. It tends to be
large, so it often swamps the other, more meaningful variances if they
are simply netted against each other.

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Problem 10A-10 (45 minutes)

1. Direct materials price and quantity variances:
Materials price variance = AQ (AP – SP)
64,000 feet ($8.55 per foot – $8.45 per foot) = $6,400 U
Materials quantity variance = SP (AQ – SQ)
$8.45 per foot (64,000 feet – 60,000 feet*) = $33,800 U
*30,000 units × 2 feet per unit = 60,000 feet

2. Direct labor rate and efficiency variances:

Labor rate variance = AH (AR – SR)
43,500 DLHs ($15.80 per DLH – $16.00 per DLH) = $8,700 F
Labor efficiency variance = SR (AH – SH)
$16.00 per DLH (43,500 DLHs – 42,000 DLHs*) = $24,000 U
*30,000 units × 1.4 DLHs per unit = 42,000 DLHs

3. a. Variable overhead spending and efficiency variances:

Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
$108,000 43,500 DLHs 42,000 DLHs
× $2.50 per DLH × $2.50 per DLH
= $108,750 = $105,000
  
Rate Variance, Efficiency Variance,
$750 F $3,750 U

Alternative solution:
Variable overhead rate variance = (AH × AR) – (AH × SR)
($108,000) – (43,500 DLHs × $2.50 per DLH) = $750 F
Variable overhead efficiency variance = SR (AH – SH)
$2.50 per DLH (43,500 DLHs – 42,000 DLHs) = $3,750 U

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Problem 10A-10 (continued)

b. Fixed overhead budget and volume variances:
Actual Fixed Budgeted Fixed Fixed Overhead Applied to
Overhead Overhead Work in Process
$211,800 $210,000* 42,000 DLHs × $6 per DLH
= $252,000
  
Budget Variance, Volume Variance,
$1,800 U $42,000 F
*As originally budgeted. This figure can also be expressed as: 35,000
denominator DLHs × $6 per DLH = $210,000.

Alternative solution:
Budget variance:
Budget = Actual fixed - Budgeted fixed
variance overhead overhead

= $211,800 - $210,000
= $1,800 U
Volume variance:
Fixed portion of æ Standardö÷
Volume = the predetermined ç
çDenominator - hours ÷
Variance ç hours ÷
÷
overhead rate ç ç
è ÷
allowed ø

= $6.00 per DLH ´ (35,000 DLHs - 42,000 DLHs)

= $42,000 F

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Problem 10A-10 (continued)

4. The total of the variances would be:
Direct materials variances:
Price variance............................................. $ 6,400 U
Quantity variance........................................ 33,800 U
Direct labor variances:
Rate variance.............................................. 8,700 F
Efficiency variance....................................... 24,000 U
Variable manufacturing overhead variances:
Rate variance.............................................. 750 F
Efficiency variance....................................... 3,750 U
Fixed manufacturing overhead variances:
Budget variance.......................................... 1,800 U
Volume variance.......................................... 42,000 F
Total of variances........................................... $18,300 U
Note that the total of the variances agrees with the $18,300 variance
mentioned by the president.
It appears that not everyone should be given a bonus for good cost
control. The materials quantity variance and the labor efficiency variance
are 6.7% and 3.6%, respectively, of the standard cost allowed and thus
would warrant investigation.
The company’s large unfavorable variances (for materials quantity and
labor efficiency) do not show up more clearly because they are offset by
the favorable volume variance. This favorable volume variance is a result
of the company operating at an activity level that is well above the
denominator activity level used to set predetermined overhead rates.
(The company operated at an activity level of 42,000 standard hours;
the denominator activity level set at the beginning of the year was
35,000 hours.) As a result of the large favorable volume variance, the
unfavorable quantity and efficiency variances have been concealed in a
small “net” figure. The large favorable volume variance may have been
achieved by building up inventories.

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Problem 10A-11 (30 minutes)

1. Direct materials, 3 yards × $4.40 per yard.............................. $13.20
Direct labor, 1 DLH × $12.00 per DLH.................................... 12.00
Variable manufacturing overhead, 1 DLH × $5.00 per DLH*.... 5.00
Fixed manufacturing overhead, 1 DLH × $11.80 per DLH**.... 11.80
Standard cost per unit........................................................... $42.00
* $25,000 ÷ 5,000 DLHs = $5.00 per DLH.
** $59,000 ÷ 5,000 DLHs = $11.80 per DLH.

2. Materials variances:
Materials price variance = AQ (AP – SP)
24,000 yards ($4.80 per yard – $4.40 per yard) = $9,600 U
Materials quantity variance = SP (AQ – SQ)
$4.40 per yard (18,500 yards – 18,000 yards*) = $2,200 U
*6,000 units × 3 yards per unit = 18,000 yards

Labor variances:
Labor rate variance = AH (AR – SR)
5,800 DLHs ($13.00 per DLH – $12.00 per DLH) = $5,800 U
Labor efficiency variance = SR (AH – SH)
$12.00 per DLH (5,800 DLHs – 6,000 DLHs*) = $2,400 F
*6,000 units × 1 DLH per unit = 6,000 DLHs

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Problem 10A-11 (continued)

3. Variable overhead variances:
Actual DLHs of Actual DLHs of Standard DLHs
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
$29,580 5,800 DLHs 6,000 DLHs
× $5.00 per DLH × $5.00 per DLH
= $29,000 = $30,000
  
Rate Variance, Efficiency Variance,
$580 U $1,000 F
Spending Variance,
$420 F

Alternative solution for the variable overhead variances:

Variable overhead rate variance = (AH × AR) – (AH × SR)
($29,580) – (5,800 DLHs × $5.00 per DLH) = $580 U
Variable overhead efficiency variance = SR (AH – SH)
$5.00 per DLH (5,800 DLHs – 6,000 DLHs) = $1,000 F

Fixed overhead variances:

Fixed Overhead
Actual Fixed Budgeted Fixed Applied to
Overhead Overhead Work in Process
$60,400 $59,000 6,000 DLHs
× $11.80 per DLH
= $70,800
  
Budget Variance, Volume Variance,
$1,400 U $11,800 F

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Problem 10A-11 (continued)

Alternative approach to the budget variance:
Budget = Actual fixed - Budgeted fixed
variance overhead overhead

= $60,400 - $59,000

= $1,400 U
Alternative approach to the volume variance:
Fixed portion of æ Standardö
Volume = the predetermined ç
çDenominator - hours ÷ ÷
Variance ç hours ÷
÷
overhead rate ç ç
è allowed ÷
ø

= $11.80 per DLH ´ (5,000 DLHs - 6,000 DLHs)

= $11,800 F

4. The choice of a denominator activity level affects standard unit costs in

that the higher the denominator activity level chosen, the lower
standard unit costs will be. The reason is that the fixed portion of
overhead costs is spread over more units as the denominator activity
rises.
The volume variance cannot be controlled by controlling spending. The
volume variance simply reflects whether actual activity was greater than
or less than the denominator activity. Thus, the volume variance is
controllable only through activity.

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Problem 10A-12 (45 minutes)

1. and 2. Per Direct Labor-Hour

Variable Fixed Total
Denominator of 30,000 DLHs:
$135,000 ÷ 30,000 DLHs................. $4.50 $ 4.50
$270,000 ÷ 30,000 DLHs................. $9.00 9.00
Total predetermined rate..................... $13.50

Denominator of 40,000 DLHs:

$180,000 ÷ 40,000 DLHs................. $4.50 $ 4.50
$270,000 ÷ 40,000 DLHs................. $6.75 6.75
Total predetermined rate..................... $11.25

3.
Denominator Activity: Denominator Activity:
30,000 DLHs 40,000 DLHs
Direct materials, 4 feet ×
$8.75 per foot............... $35.00 Same............................ $35.00
Direct labor, 2 DLHs ×
$15 per DLH................. 30.00 Same............................ 30.00
Variable overhead, 2
DLHs × $4.50 per DLH. . 9.00 Same............................ 9.00
Fixed overhead, 2 DLHs × Fixed overhead, 2 DLHs
$9.00 per DLH.............. 18.00 × $6.75 per DLH......... 13.50
Standard cost per unit..... $92.00 Standard cost per unit... $87.50

4. a. 18,000 units × 2 DLHs per unit = 36,000 standard DLHs.

b. Manufacturing Overhead
Actual costs 446,400 Applied costs 486,000 *
Overapplied
overhead 39,600
*36,000 standard DLHs × $13.50 predetermined rate per DLH =
$486,000.

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Problem 10A-12 (continued)

c. Variable overhead variances:
Actual DLHs of Actual DLHs of Standard DLHs
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
$174,800 38,000 DLHs × 36,000 DLHs ×
$4.50 per DLH $4.50 per DLH
= $171,000 = $162,000
  
Rate Variance, Efficiency Variance,
$3,800 U $9,000 U

Alternative solution:
Variable overhead rate variance = (AH × AR) – (AH × SR)
($174,800) – (38,000 DLHs × $4.50 per DLH) = $3,800 U
Variable overhead efficiency variance = SR (AH – SH)
$4.50 per DLH (38,000 DLHs – 36,000 DLHs) = $9,000 U

Fixed overhead variances:

Actual Fixed Budgeted Fixed Fixed Overhead Applied to
Overhead Overhead Work in Process
$271,600 $270,000* 36,000 DLHs × $9 per DLH
= $324,000
  
Budget Variance, Volume Variance,
$1,600 U $54,000 F
*Can be expressed as: 30,000 denominator DLHs × $9 per DLH =
$270,000.

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Problem 10A-12 (continued)

Alternative solution:
Budget variance:
Budget = Actual fixed - Budgeted fixed
variance overhead overhead

= $271,600 - $270,000

= $1,600 U
Volume variance:
Fixed portion of æ Standardö÷
Volume = the predetermined ç
çDenominator - hours ÷
Variance ç hours ÷
÷
overhead rate ç ç
è ÷
allowed ø

= $9.00 per DLH ´ (30,000 DLHs - 36,000 DLHs)

= $54,000 F
Summary of variances:
Variable overhead rate variance................. $ 3,800 U
Variable overhead efficiency variance......... 9,000 U
Fixed overhead budget variance................ 1,600 U
Fixed overhead volume variance................ 54,000 F
Overapplied overhead............................... $39,600 F

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Problem 10A-12 (continued)

5. The major disadvantage of using normal activity is the large volume
variance that ordinarily results. This occurs because the denominator
activity used to compute the predetermined overhead rate is different
from the activity level that is anticipated for the period. In the case at
hand, the company has used a long-run normal activity figure of 30,000
DLHs to compute the predetermined overhead rate, whereas activity for
the period was expected to be 40,000 DLHs. This has resulted in a large
favorable volume variance that may be difficult for management to
interpret. In addition, the large favorable volume variance in this case
has masked the fact that the company did not achieve the budgeted
level of activity for the period. The company had planned to work
40,000 DLHs, but managed to work only 36,000 DLHs (at standard).
This unfavorable result is concealed due to using a denominator figure
that is out of step with current activity.
On the other hand, using long-run normal activity as the denominator
results in unit costs that are stable from year to year. Thus,
management’s decisions are not clouded by unit costs that jump up and
down as the activity level rises and falls.

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Appendix 11B
Journal Entries to Record Variances

Exercise 10B-1 (20 minutes)

1. The general ledger entry to record the purchase of materials for the
month is:
Raw Materials
(12,000 meters at $3.25 per meter)................... 39,000
Materials Price Variance
(12,000 meters at $0.10 per meter F)........ 1,200
Accounts Payable
(12,000 meters at $3.15 per meter)........... 37,800

2. The general ledger entry to record the use of materials for the month is:
Work in Process
(10,000 meters at $3.25 per meter)................... 32,500
Materials Quantity Variance
(500 meters at $3.25 per meter U)..................... 1,625
Raw Materials
(10,500 meters at $3.25 per meter)........... 34,125

3. The general ledger entry to record the incurrence of direct labor cost for
the month is:
Work in Process (2,000 hours at $12.00 per hour). 24,000
Labor Rate Variance
(1,975 hours at $0.20 per hour U)...................... 395
Labor Efficiency Variance
(25 hours at $12.00 per hour F)................ 300
Wages Payable
(1,975 hours at $12.20 per hour).............. 24,095

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Exercise 10B-2 (45 minutes)

1. a.
Actual Quantity Actual Quantity Standard Quantity
of Input, at of Input, at Allowed for Output,
Actual Price Standard Price at Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
10,000 yards × 10,000 yards × 7,500 yards* ×
$13.80 per yard $14.00 per yard $14.00 per yard
= $138,000 = $140,000 = $105,000
  
Price Variance,
$2,000 F
8,000 yards × $14.00 per yard
= $112,000

Quantity Variance,
$7,000 U
*3,000 units × 2.5 yards per unit = 7,500 yards

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
10,000 yards ($13.80 per yard – $14.00 per yard) = $2,000 F
Materials quantity variance = SP (AQ – SQ)
$14.00 per yard (8,000 yards – 7,500 yards) = $7,000 U

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Exercise 10B-2 (continued)

b. The journal entries would be:
Raw Materials
(10,000 yards × 14.00 per yard).................. 140,000
Materials Price Variance
(10,000 yards × $0.20 per yard F)....... 2,000
Accounts Payable
(10,000 yards × $13.80 per yard)........ 138,000
Work in Process
(7,500 yards × $14.00 per yard).................. 105,000
Materials Quantity Variance
(500 yards U × $14.00 per yard).................. 7,000
Raw Materials
(8,000 yards × $14.00 per yard).......... 112,000

2. a.
Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output, at
Actual Rate Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
5,000 hours × 4,800 hours* ×
$8.00 per hour $8.00 per hour
$43,000 = $40,000 = $38,400
  
Rate Variance, Efficiency Variance,
$3,000 U $1,600 U
Spending Variance,
$4,600 U

*3,000 units × 1.6 hours per unit = 4,800 hours

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Exercise 10B-2 (continued)

Alternative Solution:
Labor rate variance = AH (AR – SR)
5,000 hours ($8.60 per hour* – $8.00 per hour) = $3,000 U
*$43,000 ÷ 5,000 hours = $8.60 per hour
Labor efficiency variance = SR (AH – SH)
$8.00 per hour (5,000 hours – 4,800 hours) = $1,600 U

b. The journal entry would be:

Work in Process
(4,800 hours × $8.00 per hour)..................... 38,400
Labor Rate Variance
(5,000 hours × $0.60 per hour U).................. 3,000
Labor Efficiency Variance
(200 hours U × $8.00 per hour)..................... 1,600
Wages Payable
(5,000 hours × $8.60 per hour)............. 43,000

3. The entries are: entry (a), purchase of materials; entry (b), issue of
materials to production; and entry (c), incurrence of direct labor cost.

Raw Materials Work in Process

(a) 140,000 (b) 112,000 (b) 105,000
Bal.* 28,000 (c) 38,400

Accounts Payable Wages Payable

(a) 138,000 (c) 43,000

Materials Price Variance Materials Quantity Variance

(a) 2,000 (b) 7,000

Labor Rate Variance Labor Efficiency Variance

(c) 3,000 (c) 1,600

*2,000 yards of material at a standard cost of $14.00 per yard

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Problem 10B-3 (60 minutes)

1. a.
Actual Quantity Standard Quantity
Actual Quantity of of Input, at Allowed for Output, at
Input, at Actual Price Standard Price Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
32,000 feet × 32,000 feet × 29,600 feet* ×
$4.80 per foot $5.00 per foot $5.00 per foot
= $153,600 = $160,000 = $148,000
  
Price Variance, Quantity Variance,
$6,400 F $12,000 U
Spending Variance,
$5,600 U
*8,000 footballs × 3.7 ft. per football = 29,600 feet

Alternatively, the variances can be computed using the formulas:

Materials price variance = AQ (AP – SP)
32,000 feet ($4.80 per foot – $5.00 per foot) = $6,400 F
Materials quantity variance = SP (AQ – SQ)
$5.00 per foot (32,000 feet – 29,600 feet) = $12,000 U

b. Raw Materials (32,000 feet × $5.00 per foot).. 160,000

Materials Price Variance
(32,000 feet × $0.20 per foot F)......... 6,400
Accounts Payable
(32,000 feet × $4.80 per foot)............ 153,600
Work in Process
(29,600 feet × $5.00 per foot)..................... 148,000
Materials Quantity Variance
(2,400 feet U × $5.00 per foot)................... 12,000
Raw Materials
(32,000 feet × $5.00 per foot)............ 160,000

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Problem 10B-3 (continued)

2. a.
Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
6,400 hours* × 6,400 hours × 7,200 hours** ×
$8.00 per hour $7.50 per hour $7.50 per hour
= $51,200 = $48,000 = $54,000
  
Rate Variance, Efficiency Variance,
$3,200 U $6,000 F
Spending Variance,
$2,800 F
* 8,000 footballs × 0.8 hours per football = 6,400 hours
** 8,000 footballs × 0.9 hours per football = 7,200 hours

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
6,400 hours ($8.00 per hour – $7.50 per hour) = $3,200 U
Labor efficiency variance = SR (AH – SH)
$7.50 per hour (6,400 hours – 7,200 hours) = $6,000 F

b. Work in Process (7,200 hours × $7.50 per hour). . 54,000

Labor Rate Variance
(6,400 hours × $0.50 per hour U).................... 3,200
Labor Efficiency Variance
(800 hours F × $7.50 per hour) .............. 6,000
Wages Payable
(6,400 hours × $8.00 per hour)............... 51,200

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Problem 10B-3 (continued)

3. Actual Hours of Actual Hours of Standard Hours
Input, at the Input, at the Allowed for Output,
Actual Rate Standard Rate at the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
6,400 hours × 6,400 hours × 7,200 hours ×
$2.75 per hour $2.50 per hour $2.50 per hour
= $17,600 = $16,000 = $18,000
  
Rate Variance, Efficiency Variance,
$1,600 U $2,000 F
Spending Variance,
$400 F

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR – SR)
6,400 hours ($2.75 per hour – $2.50 per hour) = $1,600 U
Variable overhead efficiency variance = SR (AH – SH)
$2.50 per hour (6,400 hours – 7,200 hours) = $2,000 F

4. No. He is not correct in his statement. The company has a large,

unfavorable materials quantity variance that should be investigated.
Also, the overhead rate variance equals 10% of standard, which should
also be investigated.
It appears that the company’s strategy to increase output by giving
raises was effective. Although the raises resulted in an unfavorable rate
variance, this variance was more than offset by a large, favorable
efficiency variance.

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Problem 10B-3 (continued)

5. The variances have many possible causes. Some of the more likely
causes include the following:

Materials variances:
Favorable price variance: Good price, inferior quality materials, unusual
discount due to quantity purchased, drop in market price, less costly
method of freight, outdated or inaccurate standards.
Unfavorable quantity variance: Carelessness, poorly adjusted machines,
unskilled workers, inferior quality materials, outdated or inaccurate
standards.

Labor variances:
Unfavorable rate variance: Use of highly skilled workers, change in pay
scale, overtime, outdated or inaccurate standards.
Favorable efficiency variance: Use of highly skilled workers, high-quality
materials, new equipment, outdated or inaccurate standards.

Variable overhead variances:

Unfavorable rate variance: Increase in costs, waste, theft, spillage,
purchases in uneconomical lots, outdated, or inaccurate standards.
Favorable efficiency variance: Same as for labor efficiency variance.

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Problem 10B-4 (75 minutes)

1. a. Before the variances can be computed, we must first compute the
standard and actual quantities of material per hockey stick. The
computations are:
Direct materials added to work in process (a). . $115,200
Standard direct materials cost per foot (b)....... $3.00
Standard quantity of direct materials (a) ÷ (b). 38,400 feet

Standard quantity of direct materials (a).......... 38,400 feet

Number of sticks produced (b)........................ 8,000
Standard quantity per stick (a) ÷ (b)............... 4.8 feet
Actual quantity of direct materials used per stick last year:
4.8 feet + 0.2 feet = 5.0 feet.

With these figures, the variances can be computed as follows:

Actual Quantity Standard Quantity
of Input, at Actual Quantity of Allowed for Output, at
Actual Price Input, at Standard Price Standard Price
(AQ × AP) (AQ × SP) (SQ × SP)
60,000 feet × 38,400 feet ×
$3.00 per foot $3.00 per foot
$174,000 = $180,000 = $115,200
  
Price Variance,
$6,000 F
40,000 feet* × $3.00 per foot
= $120,000

Quantity Variance,
$4,800 U
*8,000 units × 5.0 feet per unit = 40,000 feet

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Problem 10B-4 (continued)

Alternatively, the variances can be computed using the formulas:
Materials price variance = AQ (AP – SP)
60,000 feet ($2.90 per foot* – $3.00 per foot) = $6,000 F
*$174,000 ÷ 60,000 feet = $2.90 per foot

Materials quantity variance = SP (AQ – SQ)

$3.00 per foot (40,000 feet – 38,400 feet) = $4,800 U

b. Raw Materials (60,000 feet × $3.00 per foot)...... 180,000

Materials Price Variance
(60,000 feet × $0.10 per foot F)................. 6,000
Accounts Payable
(60,000 feet × $2.90 per foot).................... 174,000
Work in Process (38,400 feet × $3.00 per foot)... 115,200
Materials Quantity Variance
(1,600 feet U × $3.00 per foot)....................... 4,800
Raw Materials (40,000 feet × $3.00 per foot). 120,000

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Problem 10B-4 (continued)

2. a. Before the variances can be computed, we must first determine the
actual direct labor hours worked for last year. This can be done
through the variable overhead efficiency variance, as follows:

Variable overhead efficiency variance = SR (AH – SH)

$1.30 per hour × (AH – 16,000 hours*) = $650 U
$1.30 per hour × AH – $20,800 = $650**
$1.30 per hour × AH = $21,450
AH = $21,450 ÷ $1.30 per hour
AH = 16,500 hours
* 8,000 units × 2.0 hours per unit = 16,000 hours
** When used in the formula, an unfavorable variance is positive.

We must also compute the standard rate per direct labor hour. The
computation is:
Labor rate variance = (AH × AR) – (AH × SR)
$79,200 – (16,500 hours × SR) = $3,300 F
$79,200 – 16,500 hours × SR = –$3,300*
16,500 hours × SR = $82,500
SR = $82,500 ÷ 16,500 hours
SR = $5.00 per hour
* When used in the formula, a favorable variance is negative.

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Problem 10B-4 (continued)

Given these figures, the variances are:

Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
16,500 hours × 16,000 hours ×
$5.00 per hour $5.00 per hour
$79,200 = $82,500 = $80,000
  
Rate Variance, Efficiency Variance,
$3,300 F $2,500 U
Spending Variance,
$800 F

Alternatively, the variances can be computed using the formulas:

Labor rate variance = AH (AR – SR)
16,500 hours ($4.80 per hour* – $5.00 per hour) = $3,300 F
*79,200 ÷ 16,500 hours = $4.80 per hour
Labor efficiency variance = SR (AH – SH)
$5.00 per hour (16,500 hours – 16,000 hours) = $2,500 U

b. Work in Process
(16,000 hours × $5.00 per hour)..................... 80,000
Labor Efficiency Variance
(500 hours U × $5.00 per hour)....................... 2,500
Labor Rate Variance
(16,500 hours × $0.20 per hour F).............. 3,300
Wages Payable
(16,500 hours × $4.80 per hour)................ 79,200

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Problem 10B-4 (continued)

3. Actual Hours of Standard Hours
Input, at the Actual Hours of Input, Allowed for Output, at
Actual Rate at the Standard Rate the Standard Rate
(AH × AR) (AH × SR) (SH × SR)
16,500 hours × 16,000 hours ×
$1.30 per hour $1.30 per hour
$19,800 = $21,450 = $20,800
  
Rate Variance, Efficiency Variance,
$1,650 F $650 U
Spending Variance,
$1,000 F

Alternatively, the variances can be computed using the formulas:

Variable overhead rate variance = AH (AR – SR)
16,500 hours ($1.20 per hour* – $1.30 per hour) = $1,650 F
*$19,800 ÷ 16,500 hours = $1.20 per hour
Variable overhead efficiency variance = SR (AH – SH)
$1.30 per hour (16,500 hours – 16,000 hours) = $650 U

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Problem 10B-4 (continued)

4. For materials:
Favorable price variance: Decrease in outside purchase price; fortunate
buy; inferior quality materials; unusual discounts due to quantity
purchased; less costly method of freight; inaccurate standards.
Unfavorable quantity variance: Inferior quality materials; carelessness;
poorly adjusted machines; unskilled workers; inaccurate standards.

For labor:
Favorable rate variance: Unskilled workers (paid lower rates);
piecework; inaccurate standards.
Unfavorable efficiency variance: Poorly trained workers; poor quality
materials; faulty equipment; work interruptions; fixed labor and
insufficient demand to fill capacity; inaccurate standards.

For variable overhead:

Favorable rate variance: Decrease in supplier prices; less usage of
lubricants or indirect materials than planned; inaccurate standards.
Unfavorable efficiency variance: See comments under direct labor
efficiency variance above.
5.
Standard
Quantity or Standard Price Standard
Hours or Rate Cost
Direct materials............. 4.8 feet $3.00 per foot $14.40
Direct labor................... 2.0 hours $5.00 per hour 10.00
Variable overhead.......... 2.0 hours $1.30 per hour 2.60
Total standard cost........ $27.00

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Case 10B-5 (30 minutes)

This case may be difficult for some students to grasp because it requires
looking at standard costs from an entirely different perspective. In this
case, standard costs have been inappropriately used as a means to
manipulate reported earnings rather than as a way to control costs.

1. Lansing has evidently set very loose standards in which the standard
prices and standard quantities are far too high. This guarantees that
favorable variances will ordinarily result from operations. If the standard
costs are set artificially high, the standard cost of goods sold will be
artificially high and thus the division’s net operating income will be
depressed until the favorable variances are recognized. If Lansing saves
the favorable variances, he can release just enough in the second and
third quarters to show some improvement and then he can release all of
the rest in the last quarter, creating the annual “Christmas present.”

2. Lansing should not be permitted to continue this practice for several

reasons. First, it distorts the quarterly earnings for both the division and
the company. The distortions of the division’s quarterly earnings are
troubling because the manipulations may mask real signs of trouble. The
distortions of the company’s quarterly earnings are troubling because
they may mislead external users of the financial statements. Second,
Lansing should not be rewarded for manipulating earnings. This sets a
moral tone in the company that is likely to lead to even deeper trouble.
Indeed, the permissive attitude of top management toward the
manipulation of earnings may indicate the existence of other, even more
serious, ethical problems in the company. Third, a clear message should
be sent to division managers like Lansing that their job is to manage
their operations, not their earnings. If they keep on top of operations
and manage well, the earnings should take care of themselves.

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Case 10B-5 (continued)

3. Stacy Cummins does not have any easy alternatives available. She has
already taken the problem to the President, who was not interested. If
she goes around the President to the Board of Directors, she will be
putting herself in a politically difficult position with little likelihood that it
will do much good if, in fact, the Board of Directors already knows what
is going on.
On the other hand, if she simply goes along, she will be violating the
Credibility standard of ethical conduct for management accountants. The
Home Security Division’s manipulation of quarterly earnings does distort
the entire company’s quarterly reports. And the Credibility standard
clearly stipulates that management accountants have a responsibility to
“disclose all relevant information that could reasonably be expected to
influence an intended user’s understanding of the reports, analyses, or
recommendations.” Apart from the ethical issue, there is also a very
practical consideration. If Merced Home Products becomes embroiled in
controversy concerning questionable accounting practices, Stacy
Cummins will be viewed as a responsible party by outsiders and her
career is likely to suffer dramatically and she may even face legal
problems.
We would suggest that Ms. Cummins quietly bring the manipulation of
earnings to the attention of the audit committee of the Board of
Directors, carefully laying out in a non-confrontational manner the
problems created by Lansing’s practice of manipulating earnings. If the
President and the Board of Directors are still not interested in dealing
with the problem, she may reasonably conclude that the best alternative
is to start looking for another job.

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