It requires simultaneous equations, a coefficient matrix, matrix inversion, and matrix multiplication to get the cost allocations. No one wants to set up a spreadsheet with many rounds of cost allocations. Excel’s iterative calculation option makes the reciprocal method much easier and quicker. The reciprocal method of cost allocation uses simultaneous equations to capture and allocate 100% of service center (interdepartmental) costs. The disadvantages of the reciprocal method are that it is complicated, and may not justify the effort required for additional accuracy. Today, cost accounting textbooks describe the reciprocal method with simple examples that involve repeated iterations or simultaneous equations (or both) to model the cost of each department.

Service department costs are reallocated back to the service departments for several rounds until the reallocated costs are reduced to near-zero amounts. To overcome this problem, a method known as reciprocal method is used which fully recognizes interdepartmental services and provides greater exactness in allocating the cost of a service departments to other departments. The reciprocal method uses the simultaneous equations technique and is therefore also referred to as simultaneous equations method and algebraic method of departmental cost allocation.

## Matrix Algebra

The allocation of service department costs is incomplete if the method used for cost allocation ignores or does not give full recognition to interdepartmental services. Interdepartmental services are services that two or more service departments provide to each other. For example, consider a case where service department A provides service to service department B, and in turn, department B provides service to department A. The Step-down Method allocates costs to both operational departments and service centers.

If the internal cost for a service is greater than the price charged by an external supplier, the service department could be considered for elimination. The direct method was used most in practice until the 1970s, when the Cost Accounting Standards Board (CASB) established a standard for service department cost allocation. The exposure draft for Cost Accounting Standard (CAS) 418, “Allocation of direct and indirect costs,” initially specified the reciprocal method. The reciprocal method fully recognizes the other service departments by allowing reallocations back to each service department. As such, it’s more difficult to calculate but also more accurate than the other methods.

The default settings for the number of iterations and precision are sufficient for the purposes here.

Fortunately, there is now an alternative solution using the iterative calculation option in Excel (or any spreadsheet software with similar functionality) to calculate the reciprocal method more easily. Using a simple example, we’ll show how the iterative calculation option eliminates the need to manually reallocate service department costs through multiple iterations (or through simultaneous equations using matrix algebra). This method is an attractive alternative to explain and solve the service department cost allocation problem and should make the reciprocal method more accessible to managers. Despite those shortcomings, financial managers should find the reciprocal method much more accessible using this approach. Like the defense contractors that balked at the CASB’s recommendation to use the reciprocal method, many students today find the simultaneous equations method using matrix algebra too difficult to implement.

## Reciprocal Method Cost Allocation: Advantages and Examples

This process continues through multiple rounds until the balance in S1 is immaterial. We stopped at the sixth round, where the balance of S1 was $0.0003 (cell C23). Since maintenance costs are allocated to administration and administration cost is allocated to maintenance — things get interesting. You will need to determine the TOTAL cost being allocated to both the Administration and Maintenance Departments first. The costs allocated to S1 and S2 are termed “reciprocated costs.” They are greater than the direct costs of S1 and S2 because costs are reallocated back to S1 and S2.

- Unfortunately, students and financial managers find the use of matrix algebra to be quite a challenge.
- This method does not allocate costs to other service centers, and, as such, is both the easiest to apply and the least accurate of the three methods.
- The major advantage of reciprocal or algebraic method is that it fully takes into account the interdepartmental services.
- The reciprocal method uses the simultaneous equations technique and is therefore also referred to as simultaneous equations method and algebraic method of departmental cost allocation.
- The method is also the most accurate method of cost allocation available to accountants.

With the iterative calculation option enabled, Excel will allow circular references in formulas. A circular reference is when the formula in a cell refers to other cells that in turn refer to the original cell. Normally, Excel can’t automatically calculate a formula like that because it would by default keep recalculating indefinitely—almost like a basic go-to loop in programming that never ends. The iterative calculation option lets you put a limit on the number of times Excel recalculates the formula.

## Reciprocal method definition

The $100 direct cost of S1 is allocated using 500 direct labor hours, with 100, 250, and 150 direct labor hours consumed by S2, P1, and P2, respectively. S2’s direct cost of $40 is allocated using 1,000 machine hours, with 500, 100, and 400 machine hours consumed by S1, P1, and P2, respectively (see Figure 1). The direct method allocates costs to the operating departments directly, with no allocations to the other service departments. The method is easy to implement, but it ignores the fact that other service departments require services from each other, so it’s less accurate.

- The $100 direct cost of S1 is allocated using 500 direct labor hours, with 100, 250, and 150 direct labor hours consumed by S2, P1, and P2, respectively.
- Consider an example using two service departments, S1 and S2, and two operating departments, P1 and P2.
- As we’ve noted, the problem with the reciprocal method with repeated iterations is the number of rounds required and increased complexity when many more departments are involved.
- This means service department costs are allocated to and from the other service departments.

The reciprocal method uses simultaneous equations to allocate the costs incurred by service departments to other departments; allocations are also made between the service departments. The method is rarely used, since there are somewhat less accurate methods available that require fewer calculations. The problem in allocating service department costs is complicated by multiple-department relationships, where each service department may provide service to all of the other departments, including other service departments and itself. The three service cost-allocation methods vary in terms of ease and accuracy because of how they approach this problem. The major advantage of reciprocal or algebraic method is that it fully takes into account the interdepartmental services.

## Advantages and disadvantages of reciprocal or algebraic method

In a simple example with two service departments and two operating departments, only four simultaneous equations are needed and can be easily solved by hand. When more than two service departments are involved, accounting textbooks recommend the use of simultaneous equations, matrix algebra, and a computer to solve the equations. Unfortunately, students and financial managers find the use of matrix algebra to be quite a challenge.

Costs may be allocated between service departments which is useful because it provides insight into overhead costs. The method is also the most accurate method of cost allocation available to accountants. Additionally, it is thorough, and it allows quick comparison of company departments. P1’s allocated cost is 50% of S1’s cost and 10% of S2’s cost, and P2’s allocated cost is 30% of S1’s cost and 40% of S2’s cost. S1’s reciprocated cost is 50% of S2 and its own direct cost of $100, and S2’s reciprocated cost is 20% of S1’s cost and its own direct cost of $40.

Although allocating and reallocating service department costs through multiple rounds successfully recognizes the reciprocal relationships of these departments, this method is tedious and impractical when there are many service departments. In the reciprocal method, the relationship between the service departments is recognized. This means service department costs are allocated to and from the other service departments.

It is therefore considered a more accurate method than direct and step method for departmental cost allocation. The reciprocal method of cost allocation uses algebra to capture and allocate 100% of service center (interdepartmental) costs. The mathematical tool required to perform the reciprocal allocation method is called simultaneous equations. The three methods of cost allocation are the direct method, the step method, and the reciprocal method. The reciprocal method is also called the simultaneous equations method or the algebraic method of departmental cost allocation.