Which Is Not True Of The Various Methods Of Allocating Service Department Costs?

While service departments generally aren't involved in the direct production of appurtenances or services, they play an integral role in enabling an system's operations. Yet ofttimes the prospect of allocating service department costs can lead to feelings of frustration or dread in bookkeeping practitioners and students.

An authentic, clear understanding of service department costs is valuable in several ways. First and foremost, service department costs are used to determine the full cost of a product. They're likewise valuable for rationing demand for internal services—if no cost is charged for a service, for example, the service may be overconsumed past operating departments. In addition, they make it possible to assess the department'due south operational efficiency. If the internal cost for a service is greater than the cost charged by an external supplier, the service department could be considered for elimination.

There are three methods for allocating service department costs: directly, sequential, and reciprocal. The showtime footstep of each method is to classify each organizational unit as either an operating or service department. Operating departments directly produce or distribute the company's output, such every bit machining and assembly departments. Service departments provide services and support to operating departments as well equally other back up departments. Examples include homo resources and information systems departments.

The problem in allocating service section costs is complicated by multiple-department relationships, where each service section 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 accurateness because of how they approach this problem.

The direct method allocates costs to the operating departments directly, with no allocations to the other service departments. The method is like shooting fish in a barrel to implement, but it ignores the fact that other service departments require services from each other, so it's less accurate.

The sequential method (also known as the step-down method), allocates costs to operating departments and other service departments sequentially, just only in one direction. At that place is no set gild in the sequence used: One mutual technique is to brainstorm with the service department that incurs the about costs supporting other service departments and work downward to the department with the least costs. In one case a service department'south cost is allocated out, even so, no portion of its cost is allocated dorsum to it from other service departments. This method partially recognizes other service departments, which makes information technology more authentic than the direct method.

The reciprocal method fully recognizes the other service departments by allowing reallocations back to each service department. Every bit such, information technology's more than difficult to calculate merely also more accurate than the other methods.

The direct method was used nearly in practice until the 1970s, when the Cost Bookkeeping Standards Board (CASB) established a standard for service department cost allocation. The exposure draft for Toll Accounting Standard (CAS) 418, "Allotment of direct and indirect costs," initially specified the reciprocal method. But according to Robert Kaplan and Anthony Atkinson in Advanced Management Accounting, defense force contractors complained that "they had neither the expertise nor the computational ability to implement the method," and thus the sequential method was specified as a reasonable alternative to the reciprocal method.

The straight method was allowed, but but if the allocations could be considered reasonably close to the allocations resulting from the sequential method. CAS 418 stipulates that "the allocation of indirect cost pools which do good one another may be accomplished by the use of (i) the cross-allocation (reciprocal) method, (2) the sequential method, or another method the results of which judge that achieved past either of the methods [listed previously]" (CAS 9904.418.50).

Today, cost accounting textbooks draw the reciprocal method with simple examples that involve repeated iterations or simultaneous equations (or both) to model the cost of each department. In a simple example with two service departments and two operating departments, merely four simultaneous equations are needed and tin be hands solved by hand. When more than 2 service departments are involved, accounting textbooks recommend the use of simultaneous equations, matrix algebra, and a figurer to solve the equations. Unfortunately, students and financial managers discover the use of matrix algebra to exist quite a challenge.

Fortunately, at that place is at present an culling 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 adding selection eliminates the demand to manually reallocate service department costs through multiple iterations (or through simultaneous equations using matrix algebra). This method is an bonny alternative to explain and solve the service department toll allocation trouble and should make the reciprocal method more accessible to managers.

THE RECIPROCAL METHOD

Consider an example using two service departments, S1 and S2, and two operating departments, P1 and P2. Each service department provides services to the other 3 departments. The $100 directly toll 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 directly toll of $xl is allocated using 1,000 car hours, with 500, 100, and 400 car hours consumed by S1, P1, and P2, respectively (see Figure i).

To illustrate the methods, it'south convenient to catechumen the resource allotment bases from hours consumed by each department to percentages of the total base for each service department (see Figure ii). To keep it simple, neither S1 nor S2 consumes its ain services.

Repeated Iterations

Effigy iii shows the reciprocal method with repeated iterations. Service department costs are reallocated back to the service departments for several rounds until the reallocated costs are reduced to virtually-zero amounts. In the first round, S1's toll is allocated to S2, P1, and P2 using the allocation percentages for S1 shown in row 8 of Figure ii, and S2's direct toll of $twoscore and its newly allocated cost of $twenty from S1 are allocated to S1, P1, and P2 using the percentages shown for S2 in row ix.

In the second circular, S1'due south cost of $30 (prison cell C14) is allocated and reallocated, resulting in a balance of $3 in S1 (jail cell C15). 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).

Although allocating and reallocating service section costs through multiple rounds successfully recognizes the reciprocal relationships of these departments, this method is tedious and impractical when there are many service departments.

Matrix Algebra

A more refined approach uses simultaneous equations and matrix algebra to model the reciprocal relationships and allocate the service department costs without the need for multiple rounds of reallocations. In this method, linear equations are created for the allocated costs of each department using the percentages in rows 8 and 9 of Figure 2. The 4 equations are:

P1 = 0.5(S1) + 0.1(S2)
P2 = 0.3(S1) + 0.4(S2)
S1 = 0.5(S2) + 100
S2 = 0.ii(S1) + xl

Equations 1 and ii draw the allocated costs to P1 and P2. P1'due south allocated cost is fifty% of S1'south price and 10% of S2's cost, and P2's allocated cost is 30% of S1's cost and xl% of S2's price. Equations 3 and 4 draw the "reciprocated costs" of S1 and S2. S1's reciprocated cost is 50% of S2 and its ain direct toll of $100, and S2's reciprocated cost is xx% of S1'south price and its own direct cost of $40.

Solving the four simultaneous equations by hand is relatively easy, but as the number of departments grows, it's user-friendly to use matrix algebra and a computer to find the solution. In matrix notation, the equation for the simultaneous equations is AX = B, where A is a 4-by-iv matrix of the coefficients from the simultaneous equations, Ten is the costs allocated to the departments, and B is the costs allocated from the service departments. Multiplying both sides of the equation by the changed of A results in the solution, X = A-1B.

Excel has assortment functions that tin be used to do the matrix inversion (MINVERSE) and multiplication (MMULT). In Figure iv, the coefficient matrix is cells C28:F31, the inverted coefficient matrix is cells C34:F37, and the allocated costs are shown in cells G34:G37. Note that the costs allocated to P1 and P2 are the same as derived by the reciprocal method with multiple iterations. Only like nosotros said before, practitioners and students often resist the use of matrix algebra because they perceive it to be too difficult.

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.

The Iterative Calculation Option

Equally we've noted, the problem with the reciprocal method with repeated iterations is the number of rounds required and increased complexity when many more than departments are involved. Our simple example with 2 departments took half-dozen rounds. This quickly becomes unwieldy when the number of rounds needed is much larger. Our alternative method uses Excel's "iterative adding choice" and a template for the price allocations to accept Excel itself calculate a larger number of rounds.

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

To enable this option, go to the Formula category of the Excel Options dialog. (In Excel 2013, go to File, Options, Formula.) In the Calculations section, select the "Enable iterative calculations" checkbox. The default settings for the number of iterations and precision are sufficient for the purposes hither.

Once the iterative calculation choice is enabled, prison cell formulas tin can exist used in the template to make the cost allocations (come across Figure 5). Get-go create formulas to compute the "reciprocated cost" of S1 and S2. The reciprocated toll of S1 is equal to S1's direct cost + cost allocated to S1 from other service departments. The reciprocated toll of S2 is S2's direct cost + cost allocated to S2 from other service departments. Then classify the reciprocated costs to the other departments.

Figure 6 shows what this would look like using our example. The reciprocated toll of S1 is the directly cost of S1 ($100) and the cost allocated to S1 from S2 ($33). Thus, the formula in jail cell C40 of the spreadsheet is =–C5–C41. Likewise, the reciprocated cost of S2 is S2's direct cost of $xl and the cost allocated from S2 to S1 ($27). The formula in cell D41 of the spreadsheet is =–D5–D40. (Entering these formulas volition result in a "circular fault" warning message unless the iterative adding option is enabled.) The negative values of these reciprocated costs suggest that these costs are beingness allocated out of S1 and S2.

The remaining cells in the template are computed by multiplying the reciprocated costs (cells C40 and D41) by the percentages in rows 8 and ix of Figure 2. Multiply S1's reciprocated cost of $133 by the percentages shown in the row for S1 (20%, l%, xxx%). The spreadsheet formulas in cells D40, E40, and F40 are =C40*D8, =C40*E8, and =C40*F8. Likewise, multiply S2's reciprocated cost of $67 by the percentages shown in the row for S2 (50%, ten%, twoscore%). The spreadsheet formulas in cells C41, E41, and F41, are =D41*C9, =D41*E9, and =D41*F9. The positive signs for these costs indicate that the reciprocated costs were allocated into the departments. The reciprocated costs of S1 and S2, and the costs allocated to P1 and P2, are the aforementioned as calculated by the other methods.

A SIMPLER Arroyo

There are some drawbacks to this option. The reciprocal method that uses simultaneous equations and matrix algebra provides additional information that isn't bachelor from our suggested method. For example, the coefficients in the main diagonal of the inverted coefficient matrix (the "reciprocated factors") can be used to compute the total variable costs avoided when considering the outsourcing of service departments. Considering this information isn't bachelor from the alternative method described hither, the simultaneous equation method that uses matrix algebra is necessary if such information is needed.

But the reciprocated costs of S1 and S2 can exist converted into internal prices by dividing by the allocation bases used for S1 and S2. The internal price of S1 is $0.27 per DLH ($133.three/500 hours), and the internal price of S2 is $0.07 per automobile hour ($66.7/1,000 hours). Assuming that all costs in the analysis are variable, these prices may then be compared to external prices for the aforementioned service from external suppliers and used as benchmarks to evaluate the efficiency of the internal service departments.

Despite those shortcomings, fiscal managers should find the reciprocal method much more than accessible using this approach. Like the defence force 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. It requires simultaneous equations, a coefficient matrix, matrix inversion, and matrix multiplication to get the cost allocations. Fifty-fifty when using Excel for the matrix functions, the method is still resisted past students whose eyes frequently glaze over when the apply of matrix algebra is discussed—non to mention the added complexity involved in using matrix (i.east., array) formulas in Excel. And using the sequential method with repeated iterations is very boring. No one wants to gear up upward a spreadsheet with many rounds of toll allocations. Excel's iterative calculation option makes the reciprocal method much easier and quicker.

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David Christensen, CMA, Ph.D., is a professor of accounting at Southern Utah Academy in Cedar Urban center, Utah. He also is a fellow member of IMA'southward Table salt Lake Area Chapter. He tin exist reached at christensend@suu.edu.

Paul Schneider is a lecturer of accounting at Southern Utah Academy. He can be reached at paulschneider@suu.edu.