Shared service allocations are rarely one-way. IT supports HR, HR supports IT; a sales manager is also a salesperson. When a pool is spread across receivers that include the pool's own owner, some of the cost comes back to where it started. This is reciprocal or self-referential allocation, and there are two standard ways to solve it.
The example
A sales manager pool of 120,000 is spread across three reps by salary. One of those reps, R-101, is also the manager, so R-101's share flows straight back into the manager pool.
| Rep | Salary | Share |
|---|---|---|
| R-101 (the manager) | 145,000 | 0.402778 |
| R-102 | 118,000 | 0.327778 |
| R-103 | 97,000 | 0.269444 |
| Total | 360,000 | 1.000000 |
Each time the pool is spread, 40.28% of it returns.
Method 1: iterative
Spread the pool, collect what came back, spread that, and repeat a fixed number of times. After each pass the returning amount is smaller: 120,000 × 0.402778 after the first pass, then that amount × 0.402778 again, and so on.
After five passes:
| Receiver | Allocated |
|---|---|
| R-102 | 65,162.31 |
| R-103 | 53,565.63 |
| Still in the manager pool | 1,272.06 |
| Total | 120,000.00 |
The iterative method is easy to explain and to audit pass by pass. Its weakness is the remainder: 1,272.06 is still circulating after five passes. More passes shrink it, and the design has to say where the last of it goes.
Method 2: algebraic
Solve the circle in one step. If a fraction s of every pass returns, the total eventually spread to an outside receiver with share r is:
amount = pool × r / (1 − s)
For R-102: 120,000 × 0.327778 / (1 − 0.402778) = 65,860.47 For R-103: 120,000 × 0.269444 / (1 − 0.402778) = 54,139.53
| Receiver | Allocated |
|---|---|
| R-102 | 65,860.47 |
| R-103 | 54,139.53 |
| Still in the manager pool | 0.00 |
| Total | 120,000.00 |
Nothing is left over. The algebraic method gives the exact answer the iterative method approaches as the number of passes grows.
Which to choose
| Iterative | Algebraic | |
|---|---|---|
| Result | Close to exact; a remainder is left | Exact |
| Explaining it | One pass at a time | One formula, or a matrix for many departments |
| Best for | Teams used to step-by-step schedules; few passes needed | Many interlinked departments; exact chargebacks |
Both are legitimate. The important things are that the choice is made per allocation step, written down, and that the remainder under the iterative method has a named destination rather than silently disappearing. Either way, the result should reconcile to the 120,000 that went in.
Where this shows up
- IT, HR, finance and facilities charging each other before charging the business.
- Managers who are also producers, as in this example.
- Support departments in hospitals that serve each other before serving clinical departments.
In each case, ignoring the circle understates the cost of the departments that consume the most shared services, and overstates it for everyone else.