Reciprocal Method

The reciprocal method allocates support-department costs to operating departments by fully recognizing the mutual services provided among all support departments. For example, the reciprocal method fully incorporates the engineering services provided by the Engineering and Production Control Department to the Materials Management Department and the material-handling services provided by the Materials Management Department to the Engineering and Production Control Department.

Exhibit 16-6 presents one way to understand the reciprocal method as an extension of the step-down method. First, Engineering and Production Control Department budgeted costs are allocated to all other departments, including the Materials Management Support Department (Materials Management, 30%; Machining, 50%; Assembly, 20%). The budgeted costs of the Materials Management Department then total $354,000 ($264,000+$90,000 from the first-round allocation), as in Exhibit 16-5. The $354,000 is then allocated to all other departments that the Materials Management Department supports, including the Engineering and Production Control Support Department—Engineering and Production Control, 10%; Machining, 20%; and Assembly, 70% (see Exhibit 16-3). The Engineering and Production Control Department budgeted costs that had been brought down to $0 now have $35,400 from the Materials Management Department allocation. Engineering and Production Control Department costs are again reallocated to all other departments (Materials Management, 30%; Machining, 50%; Assembly, 20%) as previously allocated. Now the Materials Management Department budgeted costs that had been brought down to $0 have $10,620 from the Engineering and Production Control Department allocations. Materials Management Department costs are again reallocated to all departments (Engineering and Production Control, 10%; Machining, 20%; and Assembly, 70%) as previously allocated. Successive rounds result in smaller and smaller amounts being allocated to and reallocated from the support departments until eventually all support-department costs are allocated to the Machining Department and the Assembly Department.

Exhibit 16-6

Reciprocal Method of Allocating Support-Department Costs Using Repeated Iterations at Robinson Company for 2020

Spreadsheet screenshot shows the reciprocal method of allocating support-department costs under repeated iterations at Robinson Company for 2020.

Details of the five allocations are as follows:

  1. Budgeted costs before any interdepartment cost allocation

    • Engineering and production control: $300,000

    • Materials management: $264,000

    • Machining department: $329,000

    • Assembly department: $227,000

    • Total: $1,120,000

  2. 1st Allocation of Engineering and production Control

    • Engineering and production control: (300,000)

    • Materials management (3 tenths): 90,000

    • Machining department (5 tenths): 150,000

    • Assembly department (2 tenths): 60,000

  3. 1st Allocation of Materials Management

    • Engineering and production control (1 tenth): 35,400

    • Materials management: (354,000) in parentheses

    • Machining department (2 tenths): 70,800

    • Assembly department (7 tenths): 247,800

  4. 2nd Allocation of Engineering and production Control

    • Engineering and production control: (35,400) in parentheses

    • Materials management (3 tenths): 10,620

    • Machining department (5 tenths): 17,700

    • Assembly department (2 tenths): 7,080

  5. 2nd Allocation of Materials Management

    • Engineering and production control (1 tenth): 1,062

    • Materials management: (10,620) in parentheses

    • Machining department (2 tenths): 2,124

    • Assembly department (7 tenths): 7,434

  6. 3rd Allocation of Engineering and production Control (3/10,5/10,2/10)

    • Engineering and production control: (1,062) in parentheses

    • Materials management (3 tenths): 319

    • Machining department (5 tenths): 531

    • Assembly department (2 tenths): 212

  7. 3rd Allocation of Materials Management

    • Engineering and production control (1 tenth): 32

    • Materials management: (319) in parentheses

    • Machining department (2 tenths): 63

    • Assembly department (7 tenths): 224

  8. 4th Allocation of Engineering and production Control

    • Engineering and production control: (32) in parentheses

    • Materials management (3 tenths): 10

    • Machining department (5 tenths): 16

    • Assembly department (2 tenths): 6

  9. 4th Allocation of Materials Management

    • Engineering and production control (1 tenth): 1

    • Materials management: (10) in parentheses

    • Machining department (2 tenths): 2

    • Assembly department (7 tenths): 7

  10. 5th Allocation of Engineering and production Control

    • Engineering and production control: (1) in parentheses

    • Materials management (3 tenths): 0

    • Machining department (5 tenths): 1

    • Assembly department (2 tenths): 0

  11. Total budgeted overhead of operating departments

    • Engineering and production control: $0

    • Materials management: $0

    • Machining department: $570,237

    • Assembly department: $549.763

    • Total: $1,120,000

Note: Total support department amounts allocated and reallocated

An alternative way to implement the reciprocal method is to formulate and solve linear equations. This implementation requires three steps.

  1. Step 1: EXPRESS SUPPORT-DEPARTMENT BUDGETED COSTS AND RECIPROCAL RELATIONSHIPS IN THE FORM OF LINEAR EQUATIONS. Let EPC be the complete reciprocated costs of the Engineering and Production Control Department and MM be the complete reciprocated costs of the Materials Management Department. Complete reciprocated costs are support department costs plus any interdepartmental cost allocations. We express the data in Exhibit 16-3 as:

(1)

EPC=$300,000+0.1 MM

(2)

MM=$264,000+0.3 EPC  

  1. The 0.1 MM term in equation 1 is the budgeted percentage of the Materials Management Department services used by the Engineering and Production Control Department. The 0.3 EPC term in equation 2 is the budgeted percentage of Engineering and Production Control Department services used by the Materials Management Department. Complete reciprocated costs in equations 1 and 2 are also called artificial costs of the support departments.
  1. Step 2: SOLVE THE SET OF LINEAR EQUATIONS TO OBTAIN THE COMPLETE RECIPROCATED BUDGETED COSTS OF EACH SUPPORT DEPARTMENT. Substituting equation 1 into 2:

MM=$264,000+[0.3 ($300,000+0.1 MM)]MM=$264,000+$90,000+0.03 MM0.97 MM=$354,000MM=$364,949  

  1. Substituting this into equation 1:

EPC=$300,000+0.1 ($364,949)EPC=$300,000+$36,495=$336,495  

  1. The complete reciprocated costs or artificial costs are budgeted to be $364,949 for the Materials Management Department and $336,495 for the Engineering and Production Control Department. The complete-reciprocated-cost figures also appear at the bottom of Exhibit 16-6 as the total amounts allocated and reallocated from the Materials Management Department and the Engineering and Production Control Department. When there are more than two support departments with reciprocal relationships, software programs help calculate the complete reciprocated costs of each support department. Because the calculations involve finding the inverse of a matrix, the reciprocal method is also sometimes referred to as the matrix method.*
  1. Step 3: ALLOCATE THE COMPLETE RECIPROCATED BUDGETED COSTS OF EACH SUPPORT DEPARTMENT TO ALL OTHER DEPARTMENTS (BOTH SUPPORT DEPARTMENTS AND OPERATING DEPARTMENTS) ON THE BASIS OF THE BUDGETED USAGE PERCENTAGES (BASED ON TOTAL UNITS OF SERVICE PROVIDED TO ALL DEPARTMENTS). Consider the Materials Management Department. The complete reciprocated budgeted costs of $364,949 are allocated as follows:
<p>A table shows how the complete reciprocated budgeted costs are allocated</p>

The table depicts how the complete reciprocated budgeted costs are allocated. The details of the table are as follows:

1. To engineering and production control department, one-tenth times 364,949 dollars: 36,495 dollars

2. To machining department, two-tenths times 364,949 dollars: 72,990 dollars

3. To assembly department, seven-tenths times 364,949 dollars: 255,464 dollars

4. Total: 364,949 dollars

  1. Similarly, the $336,495 in reciprocated budgeted costs of the Engineering and Production Control Department are allocated to the Materials Management Department (3/10), Machining Department (5/10), and Assembly Department (2/10).

Exhibit 16-7 presents summary data based on the reciprocal method.

Exhibit 16-7

Reciprocal Method of Allocating Support-Department Costs Using Linear Equations at Robinson Company for 2020

Flow diagram shows the Reciprocal Method of allocating support- department costs using linear equations at Robinson Company for 2020.
Spreadsheet screenshot shows the various allocation costs for support departments and operating departments.

Details of the spreadsheet are as follows:

  1. Support department

    Engineering and Production Control

    • Budgeted overhead costs before any interdepartment cost allocations: $300,000

    • Allocation of engineering and production Control: (336,495) in parentheses

    • Allocation of materials management (one tenth): 36,495

    • Total budgeted overhead of operating departments: $0

    Materials management

    • Budgeted overhead costs before any interdepartment cost allocations: $264,000

    • Allocation of engineering and production Control (three tenths): 100,949

    • Allocation of materials management: (364,949)

    • Total budgeted overhead of operating departments: $0

  2. Operating Department

    Machining:

    • Budgeted overhead costs before any interdepartment cost allocations: $329,000

    • Allocation of engineering and production Control (five tenths): 168,247

    • Allocation of materials management (two tenths): 72,990

    • Total budgeted overhead of operating departments: $570,237

    Assembly:

    • Budgeted overhead costs before any interdepartment cost allocations: $227,000

    • Allocation of engineering and production control (two tenths): 67,299

    • Allocation of materials management (seven tenths): 255,464

    • Total budgeted overhead of operating departments: $549,763

  3. Total budgeted overhead of operating departments: $1,120,000

Note 1: Base is $120,000 (sum of $36,000, 60,000, and 24,000), so $36,000 divided by $120,000 gives the fraction 3 by 10, $60,000 divided by $120,000 gives the fraction 5 by 10, and $24,000 divided by $120,000 gives the fraction 2 by 10.

Note 2: Base is 4,000 hours (sum of 400, 800, and 2,800), so 400 divided by 4,000 gives the fraction 1 by 10, 800 divided by 4,000 gives the fraction 2 by 10, and2,800 divided by 4,000 gives the fraction 7 by 10.

Robinson’s $701,444 complete reciprocated budgeted costs of the support departments exceed the budgeted amount of $564,000.

<p>A table shows how reciprocated budgeted costs of the support departments exceed the budgeted amount</p>

The table depicts complete reciprocated budgeted costs, budgeted costs, and the difference for the engineering and production control department and the materials management department, as well as the totals. The details of the table are as follows:

1. Engineering and production control department

2. Materials management department

3. Total

Each support department’s complete reciprocated budgeted cost is greater than the budgeted amount because it takes into account that support costs are allocated to all departments using its services and not just to operating departments. This step ensures that the reciprocal method fully recognizes all interrelationships among support departments, as well as relationships between support and operating departments. The difference between complete reciprocated budgeted costs and budgeted costs for each support department reflects the costs allocated among support departments. The total budgeted costs allocated to the operating departments under the reciprocal method are still only $564,000 ($168,247+$67,299 allocated from the Engineering and Production Control Department and $72,990+$255,464 allocated from the Materials Management Department, see Exhibit 16-7).