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Sagot :
Certainly! Let's break down the solution step-by-step:
### Given Data:
1. Standard Rates and Information:
- Standard variable overhead rate per unit: \( \$6.0 \)
- Each unit is allowed a standard of 1 hour of machine time.
2. Actual Information for August:
- Actual variable overhead cost: \( \$136,032 \)
- Actual machine hours used: \( 21,255 \)
### Calculations:
1. Standard Variable Overhead Rate Per Hour:
- The standard variable overhead rate per unit given is \( \[tex]$6.0 \). Since each unit is allowed 1 hour of machine time, the standard rate per hour is also \( \$[/tex]6.0 \).
2. Standard Variable Overhead Cost for Actual Hours:
- We calculate this by multiplying the actual machine hours by the standard variable overhead rate per hour.
[tex]\[ \text{Standard Cost} = \text{Actual Machine Hours} \times \text{Standard Variable Overhead Rate} \][/tex]
[tex]\[ \text{Standard Cost} = 21,255 \text{ hours} \times \[tex]$6.0 \text{ per hour} = \$[/tex]127,530
\][/tex]
3. Variable Overhead Spending Variance:
- The spending variance tells us if there was a difference between the actual overhead costs and what was expected given the actual hours worked.
[tex]\[ \text{Spending Variance} = \text{Actual Variable Overhead Cost} - \text{Standard Cost} \][/tex]
[tex]\[ \text{Spending Variance} = \[tex]$136,032 - \$[/tex]127,530 = \$8,502
\][/tex]
- The variance is \( \$8,502 \). Since the actual costs are higher than the standard costs, this variance is unfavorable.
[tex]\[ \text{Spending Variance Effect} = 'U' \][/tex]
4. Variable Overhead Efficiency Variance:
- Efficiency variance measures the efficiency in using the machine hours based on the standard allowed hours. Given that each unit is allowed 1 hour and all 21,255 hours matched the standard rate, the efficiency variance is zero.
[tex]\[ \text{Efficiency Variance} = 0 \][/tex]
- This is because the standard allowed hours match the actual hours used. Hence, there is no variance.
[tex]\[ \text{Efficiency Variance Effect} = 'None' \][/tex]
### Final Results:
[tex]\[ \begin{array}{|l|l|l|} \hline \text{Variable overhead spending variance} & \$8,502 & U \\ \hline \text{Variable overhead efficiency variance} & 0 & None \\ \hline \end{array} \][/tex]
To summarize:
- The variable overhead spending variance is \$8,502 and it is unfavorable (U).
- The variable overhead efficiency variance is 0, indicating no effect (None).
### Given Data:
1. Standard Rates and Information:
- Standard variable overhead rate per unit: \( \$6.0 \)
- Each unit is allowed a standard of 1 hour of machine time.
2. Actual Information for August:
- Actual variable overhead cost: \( \$136,032 \)
- Actual machine hours used: \( 21,255 \)
### Calculations:
1. Standard Variable Overhead Rate Per Hour:
- The standard variable overhead rate per unit given is \( \[tex]$6.0 \). Since each unit is allowed 1 hour of machine time, the standard rate per hour is also \( \$[/tex]6.0 \).
2. Standard Variable Overhead Cost for Actual Hours:
- We calculate this by multiplying the actual machine hours by the standard variable overhead rate per hour.
[tex]\[ \text{Standard Cost} = \text{Actual Machine Hours} \times \text{Standard Variable Overhead Rate} \][/tex]
[tex]\[ \text{Standard Cost} = 21,255 \text{ hours} \times \[tex]$6.0 \text{ per hour} = \$[/tex]127,530
\][/tex]
3. Variable Overhead Spending Variance:
- The spending variance tells us if there was a difference between the actual overhead costs and what was expected given the actual hours worked.
[tex]\[ \text{Spending Variance} = \text{Actual Variable Overhead Cost} - \text{Standard Cost} \][/tex]
[tex]\[ \text{Spending Variance} = \[tex]$136,032 - \$[/tex]127,530 = \$8,502
\][/tex]
- The variance is \( \$8,502 \). Since the actual costs are higher than the standard costs, this variance is unfavorable.
[tex]\[ \text{Spending Variance Effect} = 'U' \][/tex]
4. Variable Overhead Efficiency Variance:
- Efficiency variance measures the efficiency in using the machine hours based on the standard allowed hours. Given that each unit is allowed 1 hour and all 21,255 hours matched the standard rate, the efficiency variance is zero.
[tex]\[ \text{Efficiency Variance} = 0 \][/tex]
- This is because the standard allowed hours match the actual hours used. Hence, there is no variance.
[tex]\[ \text{Efficiency Variance Effect} = 'None' \][/tex]
### Final Results:
[tex]\[ \begin{array}{|l|l|l|} \hline \text{Variable overhead spending variance} & \$8,502 & U \\ \hline \text{Variable overhead efficiency variance} & 0 & None \\ \hline \end{array} \][/tex]
To summarize:
- The variable overhead spending variance is \$8,502 and it is unfavorable (U).
- The variable overhead efficiency variance is 0, indicating no effect (None).
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