End of Chapter: Allocation of Support-Department Costs, Common Costs, and Revenues

Problem for Self-Study

This problem illustrates how costs of two corporate support departments are allocated to operating divisions using the dual-rate method. Fixed costs are allocated using budgeted costs and budgeted hours used by other departments. Variable costs are allocated using actual costs and actual hours used by other departments.

Computer Horizons reports the following budgeted and actual amounts for its two central corporate support departments (legal and personnel) that support each other and two manufacturing divisions: the laptop division (LTD) and the work station division (WSD):

Details of the spreadsheet are as follows:

Support Division: Legal Department
1. Budgeted usage
  - Legal hours: Nil
  - Legal percentages: Nil
  - Personnel hours: 2,500
  - Personnel percentages: 5%
2. Actual usage
  - Legal hours: Nil
  - Legal percentages: Nil
  - Personnel hours: 2,000
  - Personnel percentages: 5%
  - Budgeted fixed overhead costs before any interdepartment cost allocations: $360,000
  - Actual variable overhead costs before any interdepartment cost allocations: $200,000
Support Division: Personnel Department
1. Budgeted usage
  - Legal hours: 250
  - Legal percentages: 10%
  - Personnel hours: Nil
  - Personnel percentages: Nil
2. Actual usage
  - Legal hours: 400
  - Legal percentages: 20%
  - Personnel hours: Nil
  - Personnel percentages: Nil
  - Budgeted fixed overhead costs before any interdepartment cost allocations: $475,000
  - Actual variable overhead costs before any interdepartment cost allocations: $600,000
Operating Division: Laptop division
1. Budgeted usage
  - Legal hours: 1,500
  - Legal percentages: 60%
  - Personnel hours: 22,500
  - Personnel percentages: 45%
2. Actual usage
  - Legal hours: 400
  - Legal percentages: 20%
  - Personnel hours: 26,600
  - Personnel percentages: 66.5%
  - Budgeted fixed overhead costs before any interdepartment cost allocations: Nil
  - Actual variable overhead costs before any interdepartment cost allocations: Nil
Operating Division: Work station division
1. Budgeted usage
  - Legal hours: 750
  - Legal percentages: 30%
  - Personnel hours: 25,000
  - Personnel percentages: 50%
2. Actual usage
  - Legal hours: 1,200
  - Legal percentages: 60%
  - Personnel hours: 11,400
  - Personnel percentages: 28.5%
  - Budgeted fixed overhead costs before any interdepartment cost allocations: Nil
  - Actual variable overhead costs before any interdepartment cost allocations: Nil
Total
1. Budgeted usage
  - Legal hours: 2,500
  - Legal percentages: 100%
  - Personnel hours: 50,000
  - Personnel percentages: 100%
2. Actual usage
  - Legal hours: 2,000
  - Legal percentages: 100%
  - Personnel hours: 40,000
  - Personnel percentages: 100%
  - Budgeted fixed overhead costs before any interdepartment cost allocations: $835,000
  - Actual variable overhead costs before any interdepartment cost allocations: $800,000

Required

What amount of support-department costs for legal and personnel will be allocated to LTD and WSD using (1) the direct method, (2) the step-down method (allocating the legal department costs first), and (3) the reciprocal method using linear equations?

Solution

Exhibit 16-8 presents the computations for allocating the fixed and variable support-department costs. A summary of these costs follows:

The table depicts fixed and variable costs under the direct, step-down, and reciprocal methods for the laptop division and the work station division. The details of the table are as follows:

1. Direct method, fixed costs

• Laptop division: 465,000 dollars

• Work station division: 370,000 dollars

2. Direct method, variable costs

• Laptop division: 470,000 dollars

• Work station division: 330,000 dollars

3. Total costs for direct method

• Laptop division: 935,000 dollars

• Work station division: 700,000 dollars

4. Step-down method, fixed costs

• Laptop division: 458,053 dollars

• Work station division: 376,947 dollars

5. Step-down method, variable costs

• Laptop division: 488,000 dollars

• Work station division: 312,000 dollars

6. Total costs for step-down method

• Laptop division: 946,053 dollars

• Work station division: 688,947 dollars

7. Reciprocal method, fixed costs

• Laptop division: 462,513 dollars

• Work station division: 372,487 dollars

8. Reciprocal method, variable costs

• Laptop division: 476,364 dollars

• Work station division: 323,636 dollars

9. Total costs for reciprocal method

• Laptop division: 938,877 dollars

• Work station division: 696,123 dollars

Exhibit 16-8

Alternative Methods of Allocating Corporate Support-Department Costs to Operating Divisions of Computer Horizons: Dual-Rate Method

Details of the spreadsheet are as follows:

Allocation method: Direct method
1. Corporate support department: Legal department
  - Fixed costs: $360,000
  - Legal: (360,000) in parentheses
  - Fixed support dept. cost allocated to operating divisions: $0
  - Variable costs: $200,000
  - Legal: (200,000)
  - Variable support dept. cost allocated to operating divisions: $0
2. Corporate support department: Personnel department
  - Fixed costs: $475,000
  - Personnel: (475,000) in parentheses
  - Fixed support dept. cost allocated to operating divisions: $0
  - Variable costs: $600,000
  - Legal: (600,000)
  - Variable support dept. cost allocated to operating divisions: $0
3. Operating Division: Laptop division
  - Legal (1,500 divided 2,250): $240,000
  - Personnel (22,500 divided by 47,500): 225,000
  - Fixed support dept. cost allocated to operating divisions: $465,000
  - Legal (400 divided by 1,600): $50,000
  - Personnel (26,600 divided by 38,000): 420,000
  - Variable support dept. cost allocated to operating divisions: $470,000
4. Operating Division: Work station department
  - Legal (750 divided 2,250): $120,000
  - Personnel (25,000 divided by 47,500): 250,000
  - Fixed support dept. cost allocated to operating divisions: $370,000
  - Total Fixed support dept. cost allocated to operating divisions: $835,000
  - Legal (1,200 divided by 1,600): $150,000
  - Personnel (11,400 divided by 38,000): 180,000
  - Variable support dept. cost allocated to operating divisions: $330,000
  - Total Variable support dept. cost allocated to operating divisions: $800,000
Allocation method: Step down method
1. Corporate support department: Legal department
  - Fixed costs: $360,000
  - Legal: (360,000) in parentheses
  - Fixed support dept. cost allocated to operating divisions: $0
  - Variable costs: $200,000
  - Legal: (200,000)
  - Variable support dept. cost allocated to operating divisions: $0
2. Corporate support department: Personnel department
  - Fixed costs: $475,000
  - Legal (250 divided by 2,500): 36,000
  - Personnel: (511,000) in parentheses
  - Fixed support dept. cost allocated to operating divisions: $0
  - Variable costs: $600,000
  - Legal (400 divided by 2,000): 40,000
  - Personnel: (640,000) in parentheses
  - Variable support dept. cost allocated to operating divisions: $0
3. Operating Division: Laptop division
  - Legal (1,500 divided 2,500): $216,000
  - Personnel (22,500 divided by 47,500): 225,000
  - Fixed support dept. cost allocated to operating divisions: $465,000
  - Legal (400 divided by 1,600): $50,000
  - Personnel (22,500 divided by 47,500): 242,053
  - Variable support department cost allocated to operating divisions: $458,053
4. Operating Division: Work station department
  - Legal (750 divided 2,500): $108,000
  - Personnel (25,000 divided by 47,500): 268,947
  - Fixed support dept. cost allocated to operating divisions: $376,947
  - Total Fixed support dept. cost allocated to operating divisions: $835,000
  - Legal (1,200 divided by 2,000): $120,000
  - Personnel (11,400 divided by 38,000): 192,000
  - Variable support dept. cost allocated to operating divisions: $312,000
  - Total Variable support dept. cost allocated to operating divisions: $800,000
Allocation method: Reciprocal method
1. Corporate support department: Legal department
  - Fixed costs: $360,000
  - Legal: (385,678) in parentheses
  - Personnel (2,500 divided by 50,000): 25,678
  - Fixed support dept. cost allocated to operating divisions: $0
  - Variable costs: $200,000
  - Legal: (232,323)
  - Personnel (2,000 divided by 40,000): 32,323
  - Variable support dept. cost allocated to operating divisions: $0
2. Corporate support department: Personnel department
  - Fixed costs: $475,000
  - Legal (250 divided by 2,500): 38,568
  - Personnel: (513,568) in parentheses
  - Fixed support dept. cost allocated to operating divisions: $0
  - Variable costs: $600,000
  - Legal (400 divided by 2,000): 46,465
  - Personnel: (646,465) in parentheses
  - Variable support dept. cost allocated to operating divisions: $0
3. Operating Division: Laptop division
  - Legal (1,500 divided 2,500): $231,407
  - Personnel (22,500 divided by 50,000): 231,106
  - Fixed support dept. cost allocated to operating divisions: $462,513
  - Legal (400 divided by 2,000): $46,465
  - Personnel (26,600 divided by 40,000): 429,899
  - Variable support department cost allocated to operating divisions: $476,364
4. Operating Division: Work station department
  - Legal (750 divided 2,500): $115,703
  - Personnel (25,000 divided by 50,000): 256,784
  - Fixed support dept. cost allocated to operating divisions: $372,487
  - Total Fixed support dept. cost allocated to operating divisions: $835,000
  - Legal (1,200 divided by 2,000): $139,393
  - Personnel (11,400 divided by 40,000): 184,243
  - Variable support dept. cost allocated to operating divisions: $323,636
  - Total Variable support dept. cost allocated to operating divisions: $800,000

Note: Calculation for the legal and personnel fixed costs of reciprocal method are as follows:

Fixed costs:

Letting LF equal to Legal department fixed costs, and PF equal to Personnel department fixed costs, the simultaneous equations for the reciprocal method for fixed costs are:

LF equals $360,000 plus 0.05 PF
PF equals $475,000 plus 0.10 LF
LF equals $360,000 plus 0.05 times the sum of $475,000 and 0.10 LF
LF equals $385,678
PF equals $475,000 plus 0.10 times $385,678 which equals $513,568

Variable costs:

Letting LV equal to Legal department variable costs, and PV equal to Personnel department variable costs, the simultaneous equations for the reciprocal method for variable costs are:

LV equals $200,000 plus 0.05 PV
PV equals $600,000 plus 0.20 LV
LV equals $200,000 plus 0.05 times the sum of $600,000 and 0.20 LV
LV equals $232,323
PV equals $600,000 plus 0.20 times $232,323 which equals $646,465