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Mathematical model of sales and lease back mechanism

Mathematical model of sales and lease back mechanism
photo: Archives/Railway
04 / 05 / 2021

In a previous article, we clarified the commitment of the capital of rail carriers. We wrote that the liberalisation of the railways led to the emergence of private operators, which led to a loss of competitiveness of state railways, which were forced to slim down the balance sheet. In today's article, we will bring the various European national railway and their practices of slimming down the balance sheet after market liberalisation, while at the same time point to the steps they have taken in this area and also to those that could have historically done better.

Liberalisation of railways in Europe

After the liberalisation of the railways mentioned in the last article, the company began to be divided into passenger and freight. Examples include German Deutsche Bahn, Swedish Green Cargo or Slovak ZSSK Cargo. Most European lands continue in a model where the operation of passenger and freight transport is integrated within a single holding, with cost synergies expected to result. However, some European countries have decided to divide passenger and freight transport into two independent organisations. This division leads to a loss of cost synergies, but blocks the flow of cross-subsidies between freight and passenger transport.

We will now look at a few European countries and owners where private operators have not become dominant rail operators from other countries. Deutsche Bahn became the owner of the dominant British (2007), Danish (2001) and Dutch (2000) freight carrier. Austrian ÖBB became the new owner of the freight carriers of our Hungarian neighbours in 2008. Of the 45% shareholding, the Swedish dominant freight carrier Green Cargo became the owner of Norwegian freight carriers. Only if we look at the privatisation of estonian railways in 2001 and the first phase of British privatisation in 1996 have private consortia become the new owners.


Case study

In a case study, we'll show you the mathematical model of the sales and lease back mechanism. This model works by selling their fleet to the private sector and then renting back wagons from the private sector. This is more advantageous for state railways because they do not use the entire fleet, only some of its percentage, but they have to maintain the entire fleet and therefore only the number of wagons they use from the private sector, paying only rent.

From the theory, we move on to practice, where, in x's sample case study, we will bring the sale of the unnamed state fleet closer to the private sector, where state railways and the private sector will conclude a contract for 7 years. State railways sell 45,000 wagons, whose average age is 43 years, at a cost of € 360,000,000, using only 60% of the total number of wagons sold. The private sector leases back 27,000 wagons to state railways for €15/day/wagon. You can notice individual losses and gains in the chart.


The study shows that with year-on-year inflation of 2.6%, the profit of state railways will increase by approximately 2 million euros. It is therefore more advantageous for state railways to sell their fleet and to lease back only the required number of wagons.

 In the next article, we will move a step further and show the case study in practice.