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Sagot :
Let's go through each part of the question step-by-step.
1. Determine the Allocation Order:
The sequential method (or step method) of cost allocation allocates costs from support departments to production departments and other support departments in a step-wise manner. The typical rule is to start with the support department that uses the least services from other support departments.
Given the options:
a. It has the lowest departmental cost with no accurate cost driver.
b. It has the highest departmental cost with no accurate cost driver.
c. It has the lowest departmental cost with an accurate cost driver.
d. It has the highest departmental cost with an accurate cost driver.
Based on this, the statement corresponding to the Personnel Department having the lowest departmental cost with no accurate cost driver (option a) is correct. Therefore, the Personnel Department should be allocated first.
2. Determine the Cost Allocations:
Let's allocate the costs using the sequential method. Here are the provided departmental data:
- Personnel Department: [tex]\( \$15,000 \)[/tex]
- Maintenance Department: [tex]\( \$11,400 \)[/tex]
- Production Departments:
- Molding: [tex]\( \$72,000 \)[/tex]
- Assembly: [tex]\( \$69,000 \)[/tex]
First, we need to allocate the Personnel Department costs. The allocation will be based on the number of employees:
### Personnel Department Cost Allocation:
- Total employees: [tex]\( 28 + 10 + 41 + 49 = 128 \)[/tex]
The allocation to each department:
- Maintenance: [tex]\( \frac{10}{128} \times 15000 \approx 1171.88 \)[/tex]
- Molding: [tex]\( \frac{41}{128} \times 15000 \approx 4804.69 \)[/tex]
- Assembly: [tex]\( \frac{49}{128} \times 15000 \approx 5742.19 \)[/tex]
So, our allocation will be:
- Maintenance: \[tex]$1,171.88 - Molding: \$[/tex]4,804.69
- Assembly: \[tex]$5,742.19 Now, we add this allocated cost to the respective department costs. As per the question: After Personnel Department allocation: - Maintenance: \( \$[/tex]11,400 + 1171.88 = \[tex]$12,571.88 \) ### Maintenance Department Cost Allocation: Allocate the Maintenance Department costs to the production departments based on the number of service calls. - Total service calls: \( 57 + 41 + 168 + 112 = 378 \) The allocation to each department: - Molding: \( \frac{168}{378} \times 12571.88 \approx 5592.08 \) - Assembly: \( \frac{112}{378} \times 12571.88 \approx 3725.80 \) ### Summary of Cost Allocations: 1. Personnel Department Costs allocated: - Maintenance: \$[/tex]1,171.88
- Molding: \[tex]$4,804.69 - Assembly: \$[/tex]5,742.19
2. Maintenance Department Costs allocated:
- Molding: \[tex]$5,592.08 - Assembly: \$[/tex]3,725.80
Combining both allocations:
- Molding Department Total Costs:
- Initial Cost: \[tex]$72,000 - Allocation from Personnel: \$[/tex]4,804.69
- Allocation from Maintenance: \[tex]$5,592.08 - Total: \$[/tex]72,000 + \[tex]$4,804.69 + \$[/tex]5,592.08 = \[tex]$82,396.77 - Assembly Department Total Costs: - Initial Cost: \$[/tex]69,000
- Allocation from Personnel: \[tex]$5,742.19 - Allocation from Maintenance: \$[/tex]3,725.80
- Total: \[tex]$69,000 + \$[/tex]5,742.19 + \[tex]$3,725.80 = \$[/tex]78,468.00
Therefore, the total costs allocated to each production department are:
- Molding: \[tex]$82,396.77 - Assembly: \$[/tex]78,468.00
3. Most Accurate Allocation Method:
Typically, the most accurate allocation method is the Direct Method, Step Method (sequential), or Reciprocal Method, with each having its own advantages:
- Direct Method: Simple, ignores service department interactions.
- Step Method: Recognizes partial interactions but still simplifies some relationships.
- Reciprocal Method: Most accurate, considers all inter-departmental interactions.
Among these, the Reciprocal Method is usually considered the most accurate as it takes into account the reciprocal services provided among all support departments.
Answer for statement:
The Personnel Department is allocated first because it has the lowest departmental cost with no accurate cost driver.
The sequential method is used here for:
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline \multirow[b]{2}{*}{ Personnel Department cost allocation } & \multicolumn{2}{|c|}{Maintenance Department} & \multicolumn{2}{|c|}{Molding Department} & \multicolumn{2}{|c|}{Assembly Department} \\
\hline & [tex]$1,171.88$[/tex] & [tex]$x$[/tex] & [tex]$4,804.69$[/tex] & [tex]$x$[/tex] & [tex]$5,742.19$[/tex] & [tex]$x$[/tex] \\
\hline Maintenance Department cost allocation & & & [tex]$5,592.08$[/tex] & [tex]$x$[/tex] & [tex]$3,725.80$[/tex] & [tex]$x$[/tex] \\
\hline
\end{tabular}
1. Determine the Allocation Order:
The sequential method (or step method) of cost allocation allocates costs from support departments to production departments and other support departments in a step-wise manner. The typical rule is to start with the support department that uses the least services from other support departments.
Given the options:
a. It has the lowest departmental cost with no accurate cost driver.
b. It has the highest departmental cost with no accurate cost driver.
c. It has the lowest departmental cost with an accurate cost driver.
d. It has the highest departmental cost with an accurate cost driver.
Based on this, the statement corresponding to the Personnel Department having the lowest departmental cost with no accurate cost driver (option a) is correct. Therefore, the Personnel Department should be allocated first.
2. Determine the Cost Allocations:
Let's allocate the costs using the sequential method. Here are the provided departmental data:
- Personnel Department: [tex]\( \$15,000 \)[/tex]
- Maintenance Department: [tex]\( \$11,400 \)[/tex]
- Production Departments:
- Molding: [tex]\( \$72,000 \)[/tex]
- Assembly: [tex]\( \$69,000 \)[/tex]
First, we need to allocate the Personnel Department costs. The allocation will be based on the number of employees:
### Personnel Department Cost Allocation:
- Total employees: [tex]\( 28 + 10 + 41 + 49 = 128 \)[/tex]
The allocation to each department:
- Maintenance: [tex]\( \frac{10}{128} \times 15000 \approx 1171.88 \)[/tex]
- Molding: [tex]\( \frac{41}{128} \times 15000 \approx 4804.69 \)[/tex]
- Assembly: [tex]\( \frac{49}{128} \times 15000 \approx 5742.19 \)[/tex]
So, our allocation will be:
- Maintenance: \[tex]$1,171.88 - Molding: \$[/tex]4,804.69
- Assembly: \[tex]$5,742.19 Now, we add this allocated cost to the respective department costs. As per the question: After Personnel Department allocation: - Maintenance: \( \$[/tex]11,400 + 1171.88 = \[tex]$12,571.88 \) ### Maintenance Department Cost Allocation: Allocate the Maintenance Department costs to the production departments based on the number of service calls. - Total service calls: \( 57 + 41 + 168 + 112 = 378 \) The allocation to each department: - Molding: \( \frac{168}{378} \times 12571.88 \approx 5592.08 \) - Assembly: \( \frac{112}{378} \times 12571.88 \approx 3725.80 \) ### Summary of Cost Allocations: 1. Personnel Department Costs allocated: - Maintenance: \$[/tex]1,171.88
- Molding: \[tex]$4,804.69 - Assembly: \$[/tex]5,742.19
2. Maintenance Department Costs allocated:
- Molding: \[tex]$5,592.08 - Assembly: \$[/tex]3,725.80
Combining both allocations:
- Molding Department Total Costs:
- Initial Cost: \[tex]$72,000 - Allocation from Personnel: \$[/tex]4,804.69
- Allocation from Maintenance: \[tex]$5,592.08 - Total: \$[/tex]72,000 + \[tex]$4,804.69 + \$[/tex]5,592.08 = \[tex]$82,396.77 - Assembly Department Total Costs: - Initial Cost: \$[/tex]69,000
- Allocation from Personnel: \[tex]$5,742.19 - Allocation from Maintenance: \$[/tex]3,725.80
- Total: \[tex]$69,000 + \$[/tex]5,742.19 + \[tex]$3,725.80 = \$[/tex]78,468.00
Therefore, the total costs allocated to each production department are:
- Molding: \[tex]$82,396.77 - Assembly: \$[/tex]78,468.00
3. Most Accurate Allocation Method:
Typically, the most accurate allocation method is the Direct Method, Step Method (sequential), or Reciprocal Method, with each having its own advantages:
- Direct Method: Simple, ignores service department interactions.
- Step Method: Recognizes partial interactions but still simplifies some relationships.
- Reciprocal Method: Most accurate, considers all inter-departmental interactions.
Among these, the Reciprocal Method is usually considered the most accurate as it takes into account the reciprocal services provided among all support departments.
Answer for statement:
The Personnel Department is allocated first because it has the lowest departmental cost with no accurate cost driver.
The sequential method is used here for:
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline \multirow[b]{2}{*}{ Personnel Department cost allocation } & \multicolumn{2}{|c|}{Maintenance Department} & \multicolumn{2}{|c|}{Molding Department} & \multicolumn{2}{|c|}{Assembly Department} \\
\hline & [tex]$1,171.88$[/tex] & [tex]$x$[/tex] & [tex]$4,804.69$[/tex] & [tex]$x$[/tex] & [tex]$5,742.19$[/tex] & [tex]$x$[/tex] \\
\hline Maintenance Department cost allocation & & & [tex]$5,592.08$[/tex] & [tex]$x$[/tex] & [tex]$3,725.80$[/tex] & [tex]$x$[/tex] \\
\hline
\end{tabular}
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