Let's take a step-by-step approach to calculate the fixed overhead budget variance and the fixed overhead volume variance for Acme Company, and indicate their effects (favorable or unfavorable).
### Step 1: Understand the Given Data
- Budgeted Production: 19,500 units
- Actual Production: 21,450 units
- Budgeted Fixed Overhead: \$52,000
- Actual Fixed Overhead: \$55,500
- Standard Fixed Overhead Application Rate: \$2.6 per unit (each unit corresponds to 1 machine hour)
### Step 2: Calculate the Fixed Overhead Budget Variance
The formula for the Fixed Overhead Budget Variance is:
[tex]\[ \text{Fixed Overhead Budget Variance} = \text{Actual Fixed Overhead} - \text{Budgeted Fixed Overhead} \][/tex]
Using the given data:
[tex]\[ \text{Fixed Overhead Budget Variance} = \[tex]$55,500 - \$[/tex]52,000 = \$3,500 \][/tex]
Next, we determine if this variance is favorable (F) or unfavorable (U). Since the actual fixed overhead (\[tex]$55,500) is higher than the budgeted fixed overhead (\$[/tex]52,000), the variance is unfavorable (U).
### Step 3: Calculate the Fixed Overhead Volume Variance
The formula for the Fixed Overhead Volume Variance is:
[tex]\[ \text{Fixed Overhead Volume Variance} = (\text{Actual Production} - \text{Budgeted Production}) \times \text{Standard Overhead Rate} \][/tex]
Using the data:
[tex]\[ \text{Fixed Overhead Volume Variance} = (21,450 - 19,500) \times \$2.6 \][/tex]
[tex]\[ \text{Fixed Overhead Volume Variance} = 1,950 \times \$2.6 \][/tex]
[tex]\[ \text{Fixed Overhead Volume Variance} = \$5,070 \][/tex]
Next, we determine if this variance is favorable (F) or unfavorable (U). Since the actual production (21,450 units) is higher than the budgeted production (19,500 units), and we are applying a standard rate, the variance results in more efficient use of fixed overhead. Therefore, the variance is favorable (F).
### Summary of Variances
[tex]\[
\begin{array}{|l|l|l|}
\hline \text{Fixed overhead budget variance} & \$3,500 & \text{U} \\
\hline \text{Fixed overhead volume variance} & \$5,070 & \text{F} \\
\hline
\end{array}
\][/tex]
In conclusion:
- The Fixed Overhead Budget Variance is \$3,500 and it is unfavorable (U).
- The Fixed Overhead Volume Variance is \$5,070 and it is favorable (F).
