Allocation of service department costs: reciprocal method

Reciprocal method of allocation

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.

Example: Reciprocal allocation of HR and IT costs

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.

Watch out: when you compute allocation percentages, exclude the department’s own cost driver count - for example, don’t count IT’s own 20 computers when allocating IT costs. You’re only distributing cost to the departments that actually receive the service, which under the reciprocal method includes the other service department.

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 $\text{IT cost}$ to be allocated to the operational departments is the $\$40,000+16.67\%\text{ of HR costs}$. 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%

Note: 20 / 220 actually computes to 9.09%; it’s nudged up to 9.10% here so the three allocation percentages add up to exactly 100%.

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

Step 2: Set up the equations

Let:

$$\text{HR}=\text{Total cost of HR including IT’s allocation to HR}$$

$$\text{IT}=\text{Total cost of IT including HR’s allocation to IT}$$

From the allocation logic above:

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

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

Step 3: Solve the equations

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

$$\begin{array}{rl}\text{IT}& =40,000+0.1667(60,000+0.0910\text{ IT})\\ \text{IT}& =40,000+(0.1667\times 60,000)+(0.1667\times 0.0910\text{ IT})\\ \text{IT}& =40,000+10,002+0.01517\text{ IT}\\ \text{IT}-0.01517\text{ IT}& =50,002\\ 0.98483\text{IT}& =50,002\\ \text{IT}& =50,772\end{array}$$

Substitute back to solve for HR:

$$\begin{array}{rl}\text{HR}& =60,000+(9.10\%\times \text{IT})\\ & =60,000+(9.10\%\times 50,772)\\ & =60,000+4,620\\ & =64,620\end{array}$$

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

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

These reciprocal shares reconcile back to Step 3: IT’s $10,772 share of HR plus the original $40,000 gives IT’s solved total of $50,772, and HR’s $4,620 share of IT plus the original $60,000 gives HR’s solved total of $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.

For comparison, the direct method - which ignores HR and IT’s mutual usage entirely - would allocate about $44,000 to Dept A and $56,000 to Dept B from this same data. The reciprocal method shifts roughly $600 from Dept B to Dept A once each service department’s reliance on the other is recognized.

Watch out: the solved totals from Step 3 (HR = $64,620 and IT = $50,772) add up to $115,392 - more than the $100,000 actually spent. That’s because those totals include the reciprocal transfers between HR and IT, which never leave the service-department system. Only the amounts that land in Dept A and Dept B are real costs leaving the service departments, and those still total $100,000. When you work through Step 4, always multiply the Step 1 percentages by the solved totals ($64,620 and $50,772) - not by the original $60,000 and $40,000 - or you’ll understate the allocation.

Benefits of the reciprocal method

• Most accurate method for reflecting true cost relationships
• Fully incorporates mutual support between service departments
• Recognizes all inter-service department interactions using mathematical equations
• 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