Question

question 11
shawi corporations variable overhead is applied on the basis of direct labor-hours. the standard cost card for product f02e specifies 5.5 direct labor-hours per unit of f02e. the standard variable overhead rate is $6.80 per direct labor-hour. during the most recent month, 1,560 units of product f02e were made, and 8,700 direct labor-hours were worked.
the actual variable overhead incurred was $52,635.
required:
a. what was the variable overhead rate variance for the month?
b. what was the variable overhead efficiency variance for the month?

Explanation:

Part A: Variable Overhead Rate Variance

Step 1: Recall the formula for variable overhead rate variance

The formula for variable overhead rate variance is:
\( \text{Variable Overhead Rate Variance} = (\text{Actual Rate} - \text{Standard Rate}) \times \text{Actual Hours} \)

First, calculate the actual variable overhead rate.
Actual Rate \( = \frac{\text{Actual Variable Overhead Incurred}}{\text{Actual Direct Labor - Hours}} \)

Step 2: Calculate the actual rate

Given:
Actual Variable Overhead Incurred \( = \$52,635 \)
Actual Direct Labor - Hours \( = 8,700 \) hours

Actual Rate \( = \frac{52635}{8700} = \$6.05 \) per direct labor - hour (Wait, no, let's recalculate: \( 52635\div8700 = 6.05? \) Wait, \( 8700\times6 = 52200 \), \( 52635 - 52200 = 435 \), \( 435\div8700 = 0.05 \), so actual rate is \( 6 + 0.05=6.05 \)? Wait, no, the standard rate is \( \$6.80 \) per direct labor - hour. Wait, I think I made a mistake. Let's do it correctly:

Actual Rate \(=\frac{\text{Actual Variable Overhead}}{\text{Actual Hours}}=\frac{52635}{8700} = 6.05? \) Wait, no, \( 8700\times6.80=8700\times6 + 8700\times0.80 = 52200+6960 = 59160 \). But actual overhead is \( 52635 \), which is less than the standard cost at actual hours. Wait, maybe I messed up the formula. Wait, the variable overhead rate variance formula can also be written as:

\( \text{Variable Overhead Rate Variance}=\text{Actual Variable Overhead}-(\text{Standard Rate}\times\text{Actual Hours}) \)

Let's use this alternative formula for simplicity.

Step 3: Apply the alternative formula

Standard Rate \( = \$6.80 \) per direct labor - hour
Actual Hours \( = 8,700 \) hours
Standard Rate \(\times\) Actual Hours \(=6.80\times8700 = 59160\)
Actual Variable Overhead \( = 52635 \)

\( \text{Variable Overhead Rate Variance}=52635 - (6.80\times8700) \)
\(=52635 - 59160=- 6525\) (Favorable, since actual cost is less than standard cost for actual hours)

Wait, but let's check with the first formula. Actual Rate \(=\frac{52635}{8700}=6.05\) (Wait, no, \( 52635\div8700 = 6.05 \)? Wait, \( 8700\times6.05 = 8700\times6+8700\times0.05=52200 + 435=52635 \), correct. Standard Rate is \( 6.80 \).

So, \( (\text{Actual Rate}-\text{Standard Rate})\times\text{Actual Hours}=(6.05 - 6.80)\times8700=(- 0.75)\times8700=-6525 \) (Favorable)

Part B: Variable Overhead Efficiency Variance

Step 1: Recall the formula for variable overhead efficiency variance

The formula for variable overhead efficiency variance is:
\( \text{Variable Overhead Efficiency Variance}=(\text{Actual Hours}-\text{Standard Hours}) \times \text{Standard Rate} \)

First, calculate the standard hours allowed for the actual production.

Step 2: Calculate standard hours allowed

Standard direct labor - hours per unit \( = 5.5 \) hours per unit
Actual production \( = 1,560 \) units

Standard Hours Allowed \(=\text{Standard Hours per Unit}\times\text{Actual Units}=5.5\times1560 = 8580 \) hours

Step 3: Apply the formula

Actual Hours \( = 8,700 \) hours
Standard Rate \( = \$6.80 \) per direct labor - hour

\( \text{Variable Overhead Efficiency Variance}=(8700 - 8580)\times6.80=120\times6.80 = 816 \) (Unfavorable, since actual hours are more than standard hours allowed)

Answer:

s:
A. The variable overhead rate variance is \(\boldsymbol{-\$6,525}\) (or \(\$6,525\) favorable).
B. The variable overhead efficiency variance is \(\boldsymbol{\$816}\) (unfavorable).