Multi Pool, Multi Cost Object Allocation: Reciprocal Allocation

Reciprocal allocation attempts to consider all possible consumption and allocates each overhead cost pool to all other pools, cost objects, and even itself. It is considered by some to be the most precise method for multi pool, multi cost object allocation. However, this method is by far the most complex and suffers in terms of understandability, credibility, and usefulness.

Note that there are now forty four pathways for cost flows instead of the original twenty eight in direct, simple allocation. Remember also that all cost in the cost pools must ultimately flow to the cost objects. The fact that cost pools in reciprocal allocation can allocate to themselves means that there is cost left in the cost pools after one iteration.

Cost allocation computer systems can handle this by running the allocation again and again until the cost left in the pools is essentially zero. U.S. Customs, now Customs and Border Protection and part of Homeland Security Department, once had a cost allocation computer system that handled allocation in this manner. They would start running the allocations when they left in the evening and the job would be finished by morning.

Mathematically, the allocation can also be viewed as solving for a series of simultaneous linear equations. The solution requires creation of a system of “n” equations in “n” unknowns where:

Matrix [D] Represents Fraction of Services Consumed

Matrix [E] Represents the Vector of Service Costs

Matrix [B]T is the Transpose of the Reciprocal Cost Vector

Once this is established the allocations can be calculated as: [E] = [B]T[D]

The Real Problem With Reciprocal Allocation

The difficulty and time to calculate reciprocal allocation is bad enough. Its biggest problem, however, is the difficulty that user managers have in understanding the allocations. I’ve been in organizations with reciprocal allocation that refer to the costing system as accounting’s “black box.” This is to say that the derivation of the number is a mystery.

This misses one of the major benefits of allocation. Managers receiving an allocation can target driver reduction as a method to lower costs for which they are accountable. For example, an allocation based on square footage gives managers the incentive to reduce their square footage.

See the step down blog for an experience of mine in this exact case. I should also mention that the organization freed up thousands of square feet. They were able to consolidate work spaces to reduce janitorial services and utilities and saved millions of dollars.

Prior to allocation by square footage there was no reason for managers to critically examine their occupied space. In fact the incentive was to occupy every space in case it might be needed in the future. The result was that there was not any unoccupied space in the entire organization.

Understanding the cost of facility space and making occupiers accountable produced significant changes in behavior. Besides saving cost the freed up space also eliminated the need for capital expenditures to build new buildings in the future.