Chapter 9, Problem 22P

Variance Analysis In a Hospital

John Fleming, chief administrator for Valley View Hospital. is concerned about the costs for tests in the hospital’s lab.
Charges for lab tests are consistently higher at Valley View than at other hospitals and have resulted in many complaints.
Also, because of strict regulations on amounts reimbursed for lab tests, payments received from insurance companies and
governmental units have not been high enough to cover lab costs.
Mr. Fleming has asked you to evaluate costs in the hospital’s lab for the past month. The following information is available:
a. Two types of tests are performed in the lab−blood tests and smears. During the past month, 1.800 blood tests and 2,400 smears were performed in the lab.
b. Small glass plates are used in both types of tests. During the past month, the hospital purchased 12.000 plates at a cost of S56.400. 1.500 of these plates were unused at the end of the month: no plates were on hand at the beginning of the month.
c. During the past month. 1,150 hours of labor time were recorded in the lab at a cost of S2 1.850.
d. The lab’s variable overhead cost last month totaled S7,820.
Valley View Hospital has never used standard costs. By searching industry literature, however, you have determined the following nationwide averages for hospital labs:
Plates: Two plates are required per lab test. These plates cost S5.00 each and are disposed of after the test is completed.
Labor: Each blood test should require 0.3 hours to complete, and each smear should require 0.15 hours to complete. The average cost of this lab time is $20 per hour.
Overhead: Overhead cost is based on direct labor-hours. The average rate for variable overhead is $6 per hour.

Required:
1. Compute a materials price variance for the plates purchased last month and a materials quantity variance for the plates used last month.
2. For labor cost in the lab:
a. Compute a labor rate variance and a labor efficiency variance.
b. In most hospitals. one-half of the workers in the lab arc senior technicians and one-half arc assistants. In an effort to reduce costs, Valley View Hospital employs only one-fourth senior technicians and three-fourths assistants. would you recommend that this policy be continued? Explain.
3. Compute the variable overhead rate and efficiency variances. Is there any relation between the variable overhead efficiency variance and the labor efficiency variance? Explain.

To determine

Material price variance

This variance shows the difference between actual cost of materials and budgeted cost of purchasing materials.

Material quantity variance

This variance shows the difference between the actual value of materials used inmanufacturing process and value that was calculated to be used.

To calculate: Amount of material price variance for plates purchased and quantity variance for plates used.

Answer to Problem 22P

Calculated material price variance is $3,600 favorable and quantity variance is $10,500 unfavorable.

Explanation of Solution

Formula to calculate material price variance is

  $\text{Material price variance = (Standard price - Actual price)}\times \text{Actual quantity}$

Here, actual quantity is given as 12,000, actual price is $4.7 per plate ($56,400/12,000) and standard price is $5 per plate. So, the variance will be:

  $\begin{array}{l}\text{Material price variance = (Standard price - Actual price)}\times \text{Actual quantity}\\ \text{ = (\$5 - \$4}\text{.7)}\times 12,000\\ \text{ = \$3,600 favorable}\end{array}$

Formula to calculate material quantity variance is

  $\text{Material quanitity variance = (Standard quantity - Actual quantity)}\times \text{standard price}$

Here, actual quantity of plates used is 10,500 plates (12,000-1,500),standard price is $5 per plate and standard quantity is,

  $\begin{array}{l}\text{Standard quantity = Total of both the tests }\times \text{ Plates used per test }\\ \text{ = (1,800 + 2,400)}\times \text{2}\\ \text{ = 4,200 }\times \text{ 2}\\ \text{ = 8,400 plates }\end{array}$

So, the variance will be:

  $\begin{array}{l}\text{Material quanitity variance = (Standard quantity - Actual quantity)}\times \text{standard price}\\ \text{ = (8,400 - 10,500)}\times \$5\\ \text{ = \$10,500 Unfavorable}\end{array}$

So, material price variance is $3,600 favorable and material quantity variance is $10,500 unfavorable.

To determine

Labor rate variance

This variance shows the difference between actual amount paid to workers and amount that was budgeted to be paid.

Labor efficiency variance

This variance shows the difference between actual labor hours used in production and labor hours that were budgeted to be used.

To compute: Alabor rate and efficiency variance and whether current policy should be continued.

Answer to Problem 22P

Labor rate variance is calculated as $1,150 Favorable and efficiency variance is $5,000 Unfavorable.

Explanation of Solution

Part a

Formula to calculate labor rate variance is

  $\text{Labor rate variance = (Standard rate - Actual rate)}\times \text{Actual hours}$

Here, actual hours are given as 1,150, actual rate is $19 per hour ($21,850/1,150) and standard rate is $20 per hour. So, the variance will be:

  $\begin{array}{l}\text{Labor rate variance = (Standard rate - Actual rate)}\times \text{Actual hours}\\ \text{ = (\$20 - \$19)}\times 1,150\\ \text{ = \$1,150 Favorable}\end{array}$

Formula to calculate labor efficiency variance is

  $\text{Labor efficiency variance = (Standard hours - Actual hours)}\times \text{Standard rate}$

Here, standard rate is $20 per hour, actual hours are 1,150 and standard hours are:

  $\begin{array}{l}\text{Standard hours = Standard hours for blood tests + Standard hours for blood smears }\\ \text{ = (1,800}\times \text{0}\text{.3) + (2,400}\times \text{0}\text{.15)}\\ \text{ = 900 hours }\end{array}$

So, the variance will be:

  $\begin{array}{l}\text{Labor efficiency variance = (Standard hours - Actual hours)}\times \text{Standard rate }\\ \text{ = (900 - 1,150)}\times \$20\\ \text{ = \$5,000 Unfavorable}\end{array}$

Labor rate variance is calculated as $1,150 favorable and efficiency variance is $5,000 unfavorable.

Part b

Current policy which is used by the hospital should not be continued. Policy should be discontinued because value of labor efficiency variance is unfavorable and actual cost is more than the cost that was budgeted to be incurred (standard cost). Standard cost is calculated by using certain standards, it represents the ideal cost that should be incurred. Currently, hospital is incurring more than its standard cost and therefore, policy should be discontinued.

To determine

Variable overhead rate variance

This variance shows the difference between the actual value spent on variable overheads and the value that was expected to be spent.

Variable overhead efficiency variance

This variance shows the difference between actual hours used in production and hours that were budgeted to be used.

To calculate: Amount of variable overhead rate and efficiency variances. To explain the relation between variable overhead efficiency and labor efficiency variances.

Answer to Problem 22P

Overhead rate variance is calculated as $920unfavorable and efficiency variance is $1,500unfavorable.

Explanation of Solution

Formula to calculate variable overhead rate variance is

  $\text{Variable overhead rate variance = (Standard rate - Actual rate)}\times \text{Actual hours}$

Here, actual labor hours are 1,150, actual rate is $6.8 per hour ($7,820/1,150) and standard rate is $6 per hour. So, the variance will be:

  $\begin{array}{l}\text{Variable overhead rate variance = (Standard rate - Actual rate)}\times \text{Actual hours }\\ \text{ = (\$6 - \$6}\text{.8)}\times 1,150\\ \text{ = \$920 Unfavorable}\end{array}$

Formula to calculate variable overhead efficiency variance is:

  $\text{Variable overhead efficiency variance = (Standard hours - Actual hours)}\times \text{Standard rate }$

Here, standard rate is $6 per hour, actual hours are 1,150 and standard hours are 900 (computed above). So, the variance will be:

  $\begin{array}{l}\text{Variable overhead efficiency variance = (Standard hours - Actual hours)}\times \text{Standard rate }\\ \text{ = (900 - 1,150)}\times 6\\ \text{ = \$1,500 Unfavorable}\end{array}$

Therefore, variable overhead rate variance is $920 unfavorable and variable overhead efficiency variance is $1,500 unfavorable.

Yes, there is a close relation between labor efficiency variance and variable overhead efficiency variance. Only difference in the calculation of both the variance is that, labor efficiency variance uses standard labor rate while variable overhead efficiency variance uses per hour standard rate for variable overheads. Both the variance uses same standard hours and actual hours.