Math Problem Statement

the budgeted variable overhead rate and the actual variable overhead cost are per unit, not per machine hour.

Solution

Thank you for the clarification. If both the budgeted variable overhead rate and the actual variable overhead cost are per unit rather than per machine hour, we’ll need to adjust how we interpret the overhead variance. Here’s how this affects calculations for variable overhead:

  1. Variable Overhead Spending Variance: This will now compare the actual variable overhead cost per unit against the budgeted rate per unit, multiplied by the actual units produced.

    Variable Overhead Spending Variance=(Actual Cost per UnitBudgeted Cost per Unit)×Actual Units Produced\text{Variable Overhead Spending Variance} = (\text{Actual Cost per Unit} - \text{Budgeted Cost per Unit}) \times \text{Actual Units Produced}

  2. Variable Overhead Efficiency Variance: Since it is based on units produced, we’ll now use the total standard variable overhead cost for the actual units produced and compare it to the actual cost. The calculation formula is:

    Variable Overhead Efficiency Variance=(Actual Units ProducedBudgeted Units)×Budgeted Variable Overhead Rate per Unit\text{Variable Overhead Efficiency Variance} = (\text{Actual Units Produced} - \text{Budgeted Units}) \times \text{Budgeted Variable Overhead Rate per Unit}

By using units rather than machine hours, we directly link variable overhead to production levels on a per-unit basis, simplifying the calculation when there’s no allocation to machine hours.

Would you like further details or have any specific questions about these variances?


Expanding on This Explanation

  1. How does using units instead of machine hours impact the overall variance analysis?
  2. What scenarios would require shifting from a per-unit to a per-hour overhead calculation?
  3. Can we compare the efficiency variance more easily with direct labor variances now?
  4. How does this affect interpreting budget performance in high-volume vs. low-volume production?
  5. What changes might we expect if fixed overhead rates were also on a per-unit basis?

Tip

When analyzing variances, always ensure that the cost drivers (like units or hours) match between budgeted and actual costs for accurate comparisons.

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Math Problem Analysis

Mathematical Concepts

Variance Analysis
Budgeting
Overhead Cost Allocation

Formulas

Variable Overhead Spending Variance = (Actual Cost per Unit - Budgeted Cost per Unit) × Actual Units Produced
Variable Overhead Efficiency Variance = (Actual Units Produced - Budgeted Units) × Budgeted Variable Overhead Rate per Unit

Theorems

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Suitable Grade Level

Undergraduate Accounting or Finance