Let's solve this step by step! The most important thing to understand is that Apex Company uses two different methods to allocate its copy department costs:
- Fixed costs are allocated 40% to Sales and 60% to Administration.
- Variable costs are allocated based on the actual number of copies each department makes, at $0.02 per copy.
We need to calculate the total amount allocated to each department.
Step 1: Calculate Total Fixed Costs
The problem provides four fixed expenses:
Salaries = $108,500
Employee benefits = $13,600
Depreciation = $12,800
Utilities = $4,400
Add them together:
Total Fixed Costs = 108,500 + 13,600 + 12,800 + 4,400
Total Fixed Costs = $139,300
These costs are considered fixed because they do not change directly with the number of copies made within the relevant activity range.
Step 2: Allocate Fixed Costs to Sales
The Sales Department is responsible for 40% of the fixed costs.
Fixed Costs Allocated to Sales = Total Fixed Costs × 40%
= $139,300 × 0.40
Sales Fixed Cost Allocation = $55,720
Step 3: Allocate Fixed Costs to Administration
The Administrative Department is responsible for 60% of the fixed costs.
Fixed Costs Allocated to Administration = Total Fixed Costs × 60%
= $139,300 × 0.60
Administration Fixed Cost Allocation = $83,580
Let's verify:
$55,720 + $83,580 = $139,300
Perfect! All fixed costs have been allocated.
Step 4: Determine the Variable Cost per Copy
The problem tells us:
Paper = $0.01 per copy
Toner = $0.01 per copy
Therefore:
Variable Cost per Copy = $0.01 + $0.01
Variable Cost per Copy = $0.02
This means every copy made creates an additional 2 cents in variable costs.
Unlike fixed costs, variable costs are allocated based on actual copying activity.
Step 5: Calculate Variable Costs for Sales
The Sales Department made 2,489,100 copies.
Variable Costs = Number of Copies × Variable Cost per Copy
= 2,489,100 × $0.02
Sales Variable Cost Allocation = $49,782
Step 6: Calculate Variable Costs for Administration
The Administrative Department made 2,297,200 copies.
Variable Costs = Number of Copies × Variable Cost per Copy
= 2,297,200 × $0.02
Administration Variable Cost Allocation = $45,944
Step 7: Calculate Total Costs Allocated to Sales
Now add Sales' fixed and variable costs.
Fixed Costs = $55,720
Variable Costs = $49,782
Total Sales Allocation = 55,720 + 49,782
Total Costs Allocated to Sales = $105,502
Step 8: Calculate Total Costs Allocated to Administration
Now add Administration's fixed and variable costs.
Fixed Costs = $83,580
Variable Costs = $45,944
Total Administration Allocation = 83,580 + 45,944
Total Costs Allocated to Administration = $129,524
Step 9: Verify Our Answers
Let's make sure the allocated costs add up correctly.
Total Fixed Costs = $139,300
Total Actual Copies = 4,786,300
Total Variable Costs = 4,786,300 × $0.02
Total Variable Costs = $95,726
Therefore:
Total Actual Costs = $139,300 + $95,726
Total Actual Costs = $235,026
Now check our departmental allocations:
Sales = $105,502
Administration = $129,524
Total = $105,502 + $129,524
Total = $235,026
Our totals match exactly!
Final Answers:
Costs Allocated to Sales = $105,502
Costs Allocated to Administration = $129,524
Important Concept to Remember
Notice that the company originally budgeted for 4,986,300 copies but actually produced only 4,786,300 copies.
Why didn't we use the budgeted number of copies to allocate the variable costs?
Because the problem specifically states that variable costs are assigned at a rate of $0.02 per copy.
Therefore, we multiply that rate by the actual number of copies produced by each department.
The fixed costs, however, remain allocated according to the predetermined 40%/60% percentages.
This is an example of a dual-rate cost allocation method, in which fixed and variable costs are allocated using different bases.
Final Check:
Sales: $55,720 fixed + $49,782 variable = $105,502
Administration: $83,580 fixed + $45,944 variable = $129,524
Both allocations are correct, and together they account for the entire $235,026 allocated cost.
