Calculate Full Costs Using the Reciprocal Method on an Example

2024/09/11
Jérôme Keller
Calculate Full Costs Using the Reciprocal Method on an Example

In this article, we offer you a comprehensive example of Full Cost calculations for marketed Services. To do this, the reciprocal method for allocating Costs applies to auxiliary and primary Analysis Centers.

To learn more about the Direct, Step-down, and Reciprocal Methods, see the article: Distribute Direct and Indirect Costs to Analysis Centers.

EuroTrans Logistics, a fictional road transport company in Europe, offers a range of innovative services supported by its departments: administration, finance, sales, IT, and human resources. With an annual turnover of 500 million euros, EuroTrans Logistics stands out for its operational efficiency and its ability to meet the diverse needs of its customers.

5 Services Offered by EuroTrans Logistics

EuroTrans Logistics provides comprehensive and reliable transport and logistics solutions, tailored to the varied needs of its customers across Europe:

General Goods Transport

Main service that ensures the delivery of various goods throughout Europe with exemplary punctuality and reliability

Hazardous Materials Transport

Specialized in the handling and safe transport of hazardous materials, complying with all European regulations

Logistics and Warehousing

Offers complete storage and inventory management solutions, enabling fast and efficient distribution

Express Transport

Accelerated delivery service for urgent shipments, guaranteeing very short delivery times

Fleet Management and Maintenance

Provides fleet management and preventive maintenance services to optimize the lifespan and performance of vehicles.

Analysis Centers: 2 Primary and 5 Auxiliary

EuroTrans Logistics uses a management model focused on cost efficiency and resource optimization. To do this, the company is divided into several analysis centers, each with its initial costs, specific to them and therefore before any allocation:

Auxiliary Centers

  • Administrative: 10 million €
  • Financial: 8 million €
  • IT: 6 million €
  • Human Resources: 4 million €
  • Maintenance: 60 million €

Primary Centers

  • Sales: 12 million €
  • Transport: 400 million €

If you want to know how to identify your Primary and Auxiliary Centers, we recommend consulting: Identify your Primary and Auxiliary Centers from the Value Chain of your organization.

Consumption between Centers

The table below shows in percentage how much each Analysis Center consumes from other Analysis Centers. Here is how to read this table:

Each row represents a consuming analysis center, that is, the center that receives costs from other centers. For example, if we look at the "Administrative" row, it indicates the costs that this center consumes from other centers (for example, 10% of the costs of the Financial Center are consumed by the Administrative Center).

Each column represents a supplying analysis center, that is, the center that allocates part of its costs to other centers. For example, the "Financial" column shows how the costs of the Financial Center are distributed to other centers (for example, 10% of the costs of the Financial Center are allocated to the Administrative Center).

Analysis CentersAdministrative (%)Financial (%)Sales (%)IT (%)HR (%)Maintenance (%)Transport (%)
Administrative-10-2010--
Financial10--2510--
IT2025--10--
HR1010-10---
Maintenance1510-1010--
Transport (Primary)1520-2540100-
Sales (Primary)3025-1020--

Calculate Full Costs: Set Up and Solve Mathematical Equations

To solve full costs including reciprocal parts, we use mathematical equations for each cost center.

1. Define the Equations

For each Auxiliary Center, we define an equation that includes reciprocal allocations by taking the initial costs and consumption rates:

  • Administrative Center (A): A = 10,000,000 + 0.10*F + 0.20*I + 0.10*HR
  • Financial Center (F): F = 8,000,000 + 0.10*A + 0.25*I + 0.10*HR
  • IT Center (I): I = 6,000,000 + 0.20*A + 0.25*F + 0.10*HR
  • Human Resources Center (HR): HR = 4,000,000 + 0.10*A + 0.10*F + 0.10*I
  • Maintenance Center (M): M = 60,000,000 + 0.15*A + 0.10*F + 0.10*I + 0.10*HR

For each Primary Center, we have:

  • Sales Center (V): V = 12,000,000 + 0.30*A + 0.25*F + 0.10*I + 0.20*HR
  • Transport Center (T): T = 400,000,000 + 0.15*A + 0.20*F + 0.25*I + 0.40*HR + 1*M

2. Solve the System

By solving the System of Equations, we obtain the Full Costs for the Auxiliary Centers:

  • Administrative Center (A): A = 14.81 million €
  • Financial Center (F): F = 13.59 million €
  • IT Center (I): I = 13.17 million €
  • Human Resources Center (HR): HR = 8.16 million €
  • Maintenance Center (M): M = 65.71 million €

And for the Primary Centers, the calculations give us:

  • Sales Center (V): V = 22.79 million €
  • Transport Center (T): T = 477.21 million €

Consumption of Primary Centers and Full Costs of Services

The first table below shows in percentage the consumption of Primary Analysis Centers by the 5 Services provided to customers. The second table shows the Full Costs of these Services by allocating the Full Costs of the Primary Centers according to their consumption:

ServicesSales Center (%)Transport Center (%)
General Goods Transport3050
Hazardous Materials Transport1010
Logistics and Warehousing2010
Express Transport2020
Fleet Management and Maintenance2010
ServicesFull Cost
General Goods Transport250.07 million €
Hazardous Materials Transport51.13 million €
Logistics and Warehousing73.76 million €
Express Transport102.27 million €
Fleet Management and Maintenance73.76 million €

Simplify Everything: Model Your Full Costs with Easy Orga

With only 7 Centers, these calculations are already complex, time-consuming, and error-prone: imagine modeling 50 centers and 200 services!

With Easy Orga, you no longer have to do any calculations, everything is simpler: create a model, add the centers and services, establish the relationships, consume the centers and add the initial costs... And that's it! You can then view and analyze the Consumption and Full Costs

Consumption of analysis centers by the reciprocal allocation method
Zoom on the Consumption of the Sales center by the reciprocal allocation method
Zoom on the Consumption of the Transport center by the reciprocal allocation method
Zoom on the Full Costs of the Sales center by the reciprocal allocation method
Zoom on the Full Costs of the Transport center by the reciprocal allocation method