Chapter 11, Problem 48P

Rutherford Wheel and Axle, Inc. has an automated production process, and production activity is quantified in terms of machine hours. A standard-costing system is used. The annual static budget for 20x1 called for 6,000 units to be produced, requiring 30,000 machine hours. The standard overhead rate for the year was computed using this planned level of production. The 20x1 manufacturing cost report follows.

Rutherford develops flexible budgets for different levels of activity for use in evaluating performance. A total of 6,200 units was produced during 20x1, requiring 32,000 machine hours. The preceding

To determine

Calculate the given amounts of Company R and indicate whether the variances are favorable or unfavorable.

Explanation of Solution

Flexible Budget: A flexible budget is a budget that is prepared for different levels of the output. In other words, it is a budget that adjusts according to the changes in the volume of the activity. The main purpose of preparing flexible budget is to determine the differences among standard and actual result.

Variance: Variance refers to the difference level in the actual cost incurred and standard cost. The total cost variance is subdivided into separate cost variances; this cost variance indicates that the amount of variance that is attributable to specific casual factors.

Calculate the given amounts of Company R and indicate whether the variances are favorable or unfavorable as follows:

1. Standard number of machine hours allowed to produce one unit of product:

$\begin{array}{c}\begin{array}{l}\text{Standard machine}\\ \text{ hours per unit}\end{array}\}\text{ = }\frac{\text{Budgeted machine hours}}{\text{Budgeted production}}\\ =\frac{30,000\text{ hours}}{6,000\text{ units}}\\ =5\text{ hours per unit}\end{array}$

2. Actual cost of direct material used in one unit of product:

$\begin{array}{c}\begin{array}{l}\text{Actual cost of }\\ \text{direct material per unit}\end{array}\}\text{ = }\frac{\left(\begin{array}{l}\text{Actual cost of G27 aluminum + }\\ \text{Actual cost of M14 steel alloy}\end{array}\right)}{\text{Actual production}}\\ =\frac{\$270,000+\$30,000}{6,200\text{ units}}\\ =\$56.94\text{ per unit}\end{array}$

3. The cost of material that should be processed per machine hour:

$\begin{array}{c}\begin{array}{l}\text{Standard cost of direct }\\ \text{material per machine hour}\end{array}\}\text{ = }\frac{\left(\begin{array}{l}\text{Standard cost of G27 aluminum + }\\ \text{Standard cost of M14 steel alloy}\end{array}\right)}{\text{Standard machine hours}}\\ =\frac{\$252,000+\$78,000}{30,000\text{ machine hours}}\\ =\$11\text{ per machine hour}\end{array}$

4. Standard direct labor cost for each unit produced:

$\begin{array}{c}\begin{array}{l}\text{Standard direct }\\ \text{labor cost per unit}\end{array}\}\text{ = }\frac{\left(\begin{array}{l}\text{Standard cost for assembler + }\\ \text{Standard cost for grinder}\end{array}\right)}{\text{Standard units}}\\ =\frac{\$273,000+\$234,000}{\text{6,000 units}}\\ =\$84.50\text{ per unit}\end{array}$

5. The variable overhead rate per machine hour in flexible budget:

$\begin{array}{c}\begin{array}{l}\text{Standard variable }\\ \text{rate per machine hour}\end{array}\}\text{ = }\frac{\left(\begin{array}{l}\text{Production overhead for 32,000 machine hours}-\\ \text{Production overhead for 30,000 machine hours}\end{array}\right)}{32,000\text{ hours}-30,000\text{ hours}}\\ =\frac{\left[\begin{array}{l}\left(\begin{array}{l}\$25,600+\$137,600+\$84,000+\\ \$150,000+\$50,000+\$200,000\end{array}\right)-\\ \left(\begin{array}{l}\$24,000+\$129,000+\$80,000+\\ \$144,000+\$50,000+\$200,000\end{array}\right)\end{array}\right]}{2,000\text{ hours}}\\ =\frac{\$20,200}{2,0000}\\ =\$10.10\text{ per machine hour}\end{array}$

6. The standard fixed overhead rate per machine hour used for product costing:

$\begin{array}{c}\begin{array}{l}\text{Standard fixed overhead }\\ \text{rate per machine hour}\end{array}\}\text{ =}\frac{\text{Total budgeted fixed overhead}}{\text{Standard machine hours}}\\ \text{=}\frac{\$324,000(1)}{30,000\text{ hours}}\\ \text{=\$10}\text{.80 per hour}\end{array}$

7. The variable overhead spending variance:

$\begin{array}{c}\begin{array}{l}\text{Variable overhead}\\ \text{ spending variance }\end{array}\}\text{= }\left[\begin{array}{l}\left(\text{Actual variable overhad}\right)-\\ \left(\text{Actual quantity}\times \text{Standard variable rate}\right)\end{array}\right]\\ \text{=\$309,000 (2)}-\left(32,000\text{ hours}\times \text{\$10}\text{.10 per hour}\right)\\ \text{=\$14,200 Favorable}\end{array}$

8. The variable overhead efficiency variance:

$\begin{array}{c}\begin{array}{l}\text{Variable overhead }\\ \text{efficiency variance}\end{array}\}\text{ =}\left[\left(\begin{array}{l}\text{Actual quantity}\times \\ \text{Standard variable rate}\end{array}\right)-\left(\begin{array}{l}\text{Standard quantity}-\\ \text{Standard varaible rate}\end{array}\right)\right]\\ =\left[\begin{array}{l}\left(\text{32,000 hours}\times \text{\$10}\text{.10 per hour}\right)-\\ \left(31,000\text{ hours (3)}\times \text{\$10}\text{.10 per hour}\right)\end{array}\right]\\ =\$10,100\text{ Unfavorable}\end{array}$

9. The fixed overhead budget variance:

$\begin{array}{c}\begin{array}{l}\text{Fixed overhead }\\ \text{budget variance}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Actual fixed overhead}-\\ \text{Budgeted fixed overhead}\end{array}\right)\\ =\$324,000-\$324,000\\ =\$0\end{array}$

10. Fixed overhead volume variance:

$\begin{array}{c}\begin{array}{l}\text{Fixed overhead }\\ \text{volume variance}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Budgeted fixed overhead}-\\ \text{Applied fixed overhead}\end{array}\right)\\ =\$324,000-\left(31,000\text{ hours }\times \frac{\$324,000}{30,000\text{ hours}}\right)\\ =\$10,800\text{ Favorable}\end{array}$

11. The total budgeted manufacturing cost for 6,050 units:

$\begin{array}{c}\begin{array}{l}\text{Total budgeted }\\ \text{manufacturing cost}\end{array}\}\text{ = }\left[\begin{array}{l}\left[\begin{array}{l}\left(\begin{array}{l}\text{Budgeted variable overhead}\\ \text{ cost per hour}\end{array}\right)\\ \times \text{Total activity hours}\end{array}\right]-\\ \text{Budgeted fixed cost}\end{array}\right]\\ \text{=}\left(\$38\text{ per hour}\times \text{30,250 hours (5)}\right)+\$324,000(1)\\ =\$1,473,500\end{array}$

Working note (1):

Calculate the budgeted fixed overhead cost for 30,000 machine hours.

$\begin{array}{c}\begin{array}{l}\text{Budgeted fixed }\\ \text{overhead cost}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Total budgeted overhead for 30,000 hours}-\\ \left(\begin{array}{l}\text{Standard machine hours}\times \\ \text{Standard variable rate per machine hour}\end{array}\right)\end{array}\right)\\ =\left[\begin{array}{l}\left(\begin{array}{l}\$24,000+\$129,000+\$80,000+\\ \$144,000+\$50,000+\$200,000\end{array}\right)-\\ \left(30,000\text{ hours}\times \text{\$10}\text{.10}\right)\end{array}\right]\\ =\$627,000-\$303,000\\ =\$324,000\end{array}$

Working note (2):

Calculate the actual variable overhead cost.

$\begin{array}{c}\text{Variable overhead cost = }\left(\begin{array}{l}\text{Total actual overhead}-\\ \text{Total fixed overhead}\end{array}\right)\\ =\left(\begin{array}{l}\$25,000+\$130,000+\$81,000+\\ \$147,000+\$50,000+\$200,000\end{array}\right)-\$324,000\\ \$633,000-\$324,000\\ =\$309,000\end{array}$

Working note (3):

Calculate the standard allowed machine hours.

$\begin{array}{c}\begin{array}{l}\text{Standard allowed }\\ \text{machine hours}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Standard production units}\times \\ \text{Standard machine hour per unit}\end{array}\right)\\ =6,200\text{ units}\times \text{5 hours per unit}\\ \text{=31,000 hours}\end{array}$

Working note (4):

Calculate the variable cost per machine hour.

$\begin{array}{c}\begin{array}{l}\text{Variable rate }\\ \text{per machine hour}\end{array}\}\text{ = }\frac{\left(\begin{array}{l}\text{Total costs for 32,000 machine hours}-\\ \text{Total costs for 30,000 machine hours}\end{array}\right)}{32,000\text{ hours}-30,000\text{ hours}}\\ =\frac{\$1,540,000-\$1,464,000}{2,000\text{ hours}}\\ =\$38\text{ per machine hour}\end{array}$

Working note (5):

Calculate the total machine hours for 6,050 units.

$\begin{array}{c}\text{Total machine hours = Number of units}\times \text{Hours per unit}\\ \text{=6,050 units}\times \text{5 hours per unit}\\ \text{=30,250 hours}\end{array}$