Chapter 21, Problem 5PSA

1.

To determine

The variable overhead spending and efficiency variance.

Explanation of Solution

Given,
The actual hours are 265,000.
The variable overhead costs are $2,200,000.
The standard direct labor hours at 80% capacity is 240,000.
The variable overhead costs at 80% capacity are $1,920,000.

Compute variable overhead spending variance.

The formula to calculate the variable overhead spending variance is,

     $\text{Spending}\text{variance}=\left[\begin{array}{c}\left(\text{Actual}\text{hours}\times \text{Actual}\text{variable}\text{rate}\right)\\ -\left(\text{Actual}\text{hours}\times \text{Standard}\text{variable}\text{rate}\right)\end{array}\right]$

Substitute 265,000 for actual hours, $8.30 for actual variable rate and $8 for standard variable rate (refer working note).

     $\begin{array}{c}\text{Spending}\text{variance}=\left(265,000\times \$8.30\right)-\left(265,000\times \$8\right)\\ =\$2,199,500-\$2,120,000\\ =\$79,500\text{U}\end{array}$

The variable overhead spending variance is $79,500 (unfavorable).

Calculation of variable overhead efficiency variance:

The formula to calculate the variable overhead efficiency variance is,

     $\text{Efficiency}\text{variance}=\left[\begin{array}{c}\left(\text{Actual}\text{hours}\times \text{Standard}\text{variable}\text{rate}\right)\\ -\left(\text{Standard}\text{hours}\times \text{Standard}\text{variable}\text{rate}\right)\end{array}\right]$

Substitute 265,000 for the actual hours, 240,000 for standard hours and $8 for the standard variable rate.

     $\begin{array}{c}\text{Efficiency}\text{variance}=\left(265,000\times \$8\right)-\left(240,000\times \$8\right)\\ =\$2,120,000-\$1,920,000\\ =\$200,000\text{U}\end{array}$

The variable overhead efficiency variance is $200,000 (unfavorable).

Working note:

Calculation of the actual variable rate,

     $\begin{array}{c}\text{Actual}\text{variable}\text{rate}=\frac{\text{Actual}\text{variable}\text{overhead}\text{costs}}{\text{Actual}\text{hours}}\\ =\frac{\$2,200,000}{265,000}\\ =\$8.30\end{array}$

The actual variable rate is $8.30.

Calculation of the standard variable rate,

     $\begin{array}{c}\text{Standard}\text{variable}\text{rate}=\frac{\text{Standard}\text{variable}\text{overhead}\text{costs}}{\text{Standard}\text{hours}}\\ =\frac{\$1,920,000}{240,000}\\ =\$8.00\end{array}$

The standard variable rate is $8.00.
Hence, the variable overhead spending variance and variable overhead efficiency variance is $79,500 (unfavorable), and $200,000 (favorable).

2.

To determine

The fixed overhead spending and volume variances.

Explanation of Solution

Given,
The actual overhead is $2,350,000.
The budgeted overhead is $2,400,000.
The standard direct labor hours at 80% capacity is 240,000.
The actual hours are 265,000 hours.

Compute the fixed overhead spending variance.

The formula to calculate the fixed overhead spending variance is,

     $\text{Spending}\text{variance}=\text{Actual}\text{overhead}-\text{Budgeted}\text{overhead}$

Substitute $2,350,000 for actual overhead and $2,400,000 for budgeted overhead.

     $\begin{array}{c}\text{Spending}\text{variance}=\$2,350,000-\$2,400,000\\ =\$50,000\text{F}\end{array}$

The fixed overhead spending variance is $50,000 (favorable).

Compute fixed overhead volume variance.

The formula to calculate the fixed overhead volume variance is,

     $\text{Fixed}\text{overhead}\text{volume}\text{variance}=\text{Budgeted}\text{overhead}-\text{Applied}\text{overhead}$

Substitute $2,400,000 for the budgeted overhead and $2,650,000 for the applied overhead (refer working note).

     $\begin{array}{c}\text{Fixed}\text{overhead}\text{volume}\text{variance}=\text{\$2,400,000}-\$2,650,000\\ =\$250,000\text{F}\end{array}$

The fixed overhead volume variance is $250,000 (favorable).

Working note:

Calculation of the applied overhead,

     $\begin{array}{c}\text{Applied}\text{overhead}=\frac{\text{Budgeted}\text{overhead}}{\text{Standard}\text{direct}\text{labor}\text{hours}}\times \text{Actual}\text{hours}\\ =\frac{\$2,400,000}{240,000\text{hours}}\times 265,000\text{hours}\\ =\text{\$2,650,000}\end{array}$

The applied overhead is $2,650,000.

Hence, the fixed overhead spending variance and fixed overhead volume variance is $50,000 (favorable) and $250,000 (favorable).

3.

To determine

The total overhead controllable variance.

Explanation of Solution

Given,
The variable overhead spending variance is $79,500 (unfavorable).
The variable overhead efficiency variance is $200,000 (unfavorable).
The fixed overhead spending variance is $50,000 (favorable).

Compute the overhead controllable variance.

The formula to calculate the overhead controllable variance is,

     $\text{Controllable}\text{variance}=\left(\begin{array}{l}\text{Variable}\text{overhead}\text{spending}\text{variance}\\ +\text{Variable}\text{overhead}\text{efficiency}\text{variance}\\ +\text{Fixed}\text{overhead}\text{spending}\text{variance}\end{array}\right)$

Substitute $79,500 for variable overhead spending variance, $200,000 for variable overhead efficiency variance and $50,000 for fixed overhead spending variance.

     $\begin{array}{c}\text{Controllable}\text{variance}=\left(\$79,500\text{U}+\$200,000\text{U}+\$50,000\text{F}\right)\\ =\$229,500\text{U}\end{array}$

The overhead controllable variance is $229,500 (unfavorable).

Thus, the total overhead controllable variance is $229,500 (unfavorable).