The reciprocal method (also known as the algebraic method) provides the most accurate service department allocation technique by fully recognizing mutual services between service departments. Unlike the direct and step-down methods, which either ignore or partially account for inter-service support, the reciprocal method treats all service departments as both providers and receivers of services until all costs are allocated to operating departments.

How it works

The method involves setting up and solving simultaneous equations to reflect the reciprocal services. Once the total adjusted costs of each service department are computed (including the services they receive from each other), the costs are allocated to the operating departments using the usual cost drivers.

Key features

Recognizes all inter-service department interactions
Uses mathematical equations to distribute costs accurately
Most precise but also the most complex method

Example: Assume a company has the following departments:

Service departments:

Human Resources (HR): $60,000
Information Technology (IT): $40,000

Operating departments:

Department A
Department B

Department	Number of Employees	Number of Computers
HR	10	20
IT	50	20
Dept A	100	100
Dept B	150	100

Let’s allocate HR costs based on the number of employees and IT costs based on the number of computers. Note that we need to ignore the cost drivers in the department itself (i.e. number of computers n IT) because we need to allocate the service department costs to the other departments.

Step 1: Calculate allocation percentages

HR Cost Allocation (based on employees):

Recipient Dept	Employees	Proportion
IT	50	50 / 300 = 16.67%
Dept A	100	100 / 300 = 33.33%
Dept B	150	150 / 300 = 50.00%
Total	300	100%

The above means that the total $IT Cost$ to be allocated to the operational departments is the $$40, 000 + 16.67% of HR Costs$ . This will be translated into an equation in the next step.

IT Cost Allocation (based on computers):

Recipient Dept	Computers	Proportion
HR	20	20 / 220 = 9.10%
Dept A	100	100 / 220 = 45.45%
Dept B	100	100 / 220 = 45.45%
Total	220	100%

The above means that the total $HR Cost$ to be allocated to the operational departments is the $$60, 000 + 9.10% of IT Costs$ . This will be translated into an equation in the next step.

Step 2: Set up the equations

Let:

$HR = Total cost of HR including IT’s allocation to HR$

$IT = Total cost of IT including HR’s allocation to IT$

From the allocation logic above:

$HR = 60, 000 + (9.10% \times IT)$

$IT = 40, 000 + (16.67% \times HR)$

Step 3: Solve the equations

Substitute the first equation (HR) into the second (IT):

$IT IT IT IT - 0.01517 IT 0.98483 IT IT = 40, 000 + 0.1667 (60, 000 + 0.0910 IT) = 40, 000 + (0.1667 \times 60, 000) + (0.1667 \times 0.0910 IT) = 40, 000 + 10, 002 + 0.01517 IT = 50, 002 = 50, 002 = 50, 772$

Substitute back to solve for H:

$HR = 60, 000 + (9.10% \times IT) = 60, 000 + (9.10% \times 50, 772) = 60, 000 + 4, 620 = 64, 620$

Step 4: Calculate the interdepartment costs

HR (Total Cost = $64,620) Allocated Based on Employees using the original allocation rates in Step 1:

To IT: 0.1667 × 64,620 = $10,772
To Dept A: 0.3333 × 64,620 = $21,538
To Dept B: 0.5000 × 64,620 = $32,310

Notice that if you add the IT share of the HR costs amounting to $10,772, it results in the total IT costs IT Costs we have computed in Step 3 amounting to $50,772.

IT (Total Cost = $50,772) Allocated Based on Computers using the original allocation rates in Step 1:

To HR: 0.0910 × 50,772 = $4,620
To Dept A: 0.4545 × 50,772 = $23,076
To Dept B: 0.4545 × 50,772 = $23,076

Notice that if you add the HR share of the IT costs amounting to $4,620, it results in the total HR costs we have computed in Step 3 amounting to $64,620.

Step 5: Final allocated costs to operating departments:

Department	From HR	From IT	Total
Dept A	$21,538	$23,076	$44,614
Dept B	$32,310	$23,076	$55,386
Total			$100,000

The total overhead costs allocated to the operational departments should still be $100,000.

Benefits of the reciprocal method

Most accurate method for reflecting true cost relationships
Fully incorporates mutual support between service departments
Provides better cost transparency and basis for pricing or budgeting decisions

Limitations of the reciprocal method

Mathematically complex; requires solving equations or matrix algebra
Difficult to implement without software support
May be impractical for organizations with many service departments

Reciprocal method of allocation

Fully recognizes mutual services between service departments
Uses simultaneous equations to allocate costs
Most accurate, but most complex allocation method

How it works

Set up equations for each service department’s total cost (including services received)
Solve equations to find adjusted service department costs
Allocate final costs to operating departments using appropriate cost drivers

Key features

Accounts for all inter-service department interactions
Requires mathematical (algebraic) solutions
Highest precision among allocation methods

Example process

Identify cost drivers for each service department (e.g., employees for HR, computers for IT)
Calculate allocation percentages, excluding self-service
Set up and solve equations:
- HR = direct HR cost + % of IT cost
- IT = direct IT cost + % of HR cost
Allocate adjusted service department costs to operating departments using calculated percentages

Benefits of the reciprocal method

Most accurate reflection of true cost relationships
Fully incorporates mutual support between service departments
Improves cost transparency for pricing and budgeting

Limitations of the reciprocal method

Mathematically complex; requires solving simultaneous equations
Difficult to apply manually for many service departments
Often needs software for practical implementation

Next | 4.4.1 Supply chain management

Allocation of service department costs: reciprocal method

Reciprocal method of allocation