1. Background

The Ministry of Transport and Communications wanted, through the railway reform, for the users of railway infrastructure to a greater extent pay for the services provided. This was intended to make it clear that railways are to a greater extent a commercial activity and not public administration – something that requires a business-oriented relationship between the infrastructure manager and the train operating companies. This implies that the services provided by the infrastructure manager are, to a greater extent than previously, subject to purchase and sale.

2 Pricing of freight terminals

For freight terminals, the regulation has introduced a two-part division, namely the ability to operate trains to/from the terminal (access service) and terminal operations as such (priority service).

This report concerns only the access service.

Access services in an “extended” sense mean the use of arrival/departure tracks, loading/unloading tracks, and environmental facilities. Pricing here shall be in accordance with marginal cost. The cost driver in this context is assumed to be the number of trains to/from the terminal. Bane NOR has two alternatives regarding who shall be invoiced for payments for access to the terminal; namely the terminal operator or the train operating companies.

The Norwegian National Rail Administration has not had a financial model suitable for cost allocation for this type of service. Therefore, “standard figures” have been used based on infrastructure costs at Alnabru and Ganddal in 2015. This results in an annual cost of NOK 650 per metre of track for intermodal/wagonload terminals, excluding tied-up capital. For timber terminals, the costs will be significantly lower. Reference is made to section 4.4 regarding the result of Bane NOR’s calculations.

As a starting point, a distinction is made between intermodal/wagonload terminals and timber terminals. Due to its size, Alnabru is suitable for a separate assessment. For port tracks and sidings, Bane NOR will enter into separate agreements with the track owner.

Table 1: Terminal grouping

Bane NOR SF will calculate marginal costs for intermodal terminals and timber terminals respectively, but each individual terminal will be priced separately based on these calculations; reference is made to sections 4.2 and 4.3.

1: There are also private timber terminals.

3 Estimation of unit costs

As described in section 2, the cost basis is limited. This makes the calculations uncertain.

Access to freight terminals is calculated based on marginal costs, where alternative models have been tested. The mathematical exposition is described in Annex 1. The models used estimate cost elasticity, and the variants test whether the elasticity is constant or varies with production volume. For calculation of marginal costs, the model variant that provides the best fit and/or the most significant parameters is used.

4 Results

4.1 Summary of costs

Table 2 shows calculated costs for operation and maintenance of the intermodal terminals. The costs are calculated based on a standard rate per track metre per year. The rate is calculated at NOK 650 per track metre per year based on the costs at Alnabru and Ganddal.

Table 2: Summary of costs – Intermodal/wagonload terminals

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In the marginal cost calculations, only costs related to arrival/departure tracks and loading tracks are included.

The same has been done for the timber terminals owned by Bane NOR. Based on best professional judgement, the rate per track metre has been set at approximately 20% of the rate for intermodal terminals. Table 3 shows the calculated costs for the various timber terminals.

Table 3: Summary of costs – Timber terminals

4.2 Calculation of marginal costs – intermodal/wagonload terminals

As the cost is defined, the regression analysis will in reality show how the need for the number of track metres varies with traffic volume measured in number of trains. Three variants of a “double log” cost model have been used. This is described in more detail in Annex 1. The variants distinguish between how costs increase relative to increased production:

• Model A: The percentage increase in costs is constant with increasing production
• Model B: The percentage increase either increases or decreases with increasing production
• Model C: The percentage increase can both increase and decrease with increasing production

Table 4 shows the result of the statistical (econometric) calculations related to access costs.

Table 4: Regression results – Intermodal terminals – Figures in parentheses show standard deviation 

Although Model B and C have higher R2 values and thus explain the variation better, the estimated parameters are not significantly different from zero (0). Model C also lacks economic meaning, as it results in negative marginal costs. Model A yields significant parameters, and it is proposed that this model be used. It provides a constant cost elasticity of 0.39; that is, when the number of trains increases by 10%, costs increase by 3.9%. This implies economies of scale in the access service, and that marginal costs are 39% of average costs. Table 5 shows the number of trains, marginal cost, and potential revenue for the intermodal terminals.

Table 5: Access and service costs per unit and potential revenue – Intermodal terminals 

As the variations are quite large and the number of observations is relatively small, it is proposed that an average marginal cost be used for the timber terminals, and this lies between 15 and 25 NOK. The price is therefore set at NOK 20 per call.

Table 9: Prices and revenues – Timber terminals

5 Price adjustment mechanisms

Bane NOR SF provides that prices are adjusted periodically, as well as in the event of significant changes.

Table 10: Price adjustments

6 Bibliography

[1] Bane NOR SF, “Report 2016‑1: Service catalogue part 1,” 2016.

[2] Ministry of Transport and Communications, “Railway Regulation,” 20 12 2016. [Internet]. Available: https://lovdata.no/dokument/LTI/forskrift/2016-12-20-1771

[3] European Commission, “EU 2015/909 – On provisions for the calculation of costs directly incurred as a result of railway operations,” 12 06 2015. [Internet]. Available: http://eur-lex.europa.eu/legal-content/DA/TXT/PDF/?uri=CELEX:32015R0909&from=EN.

[4] European Parliament, “2012/34/EU – On the establishment of a single European railway area,” 21 11 2012. [Internet]. Available: https://www.regjeringen.no/globalassets/upload/sd/vedlegg/jernbane/hoering_02122013/hdirective212.pdf.

[5] K. Sydsæter and B. Thalberg, Mathematical formula collection, Oslo: Dreyers Forlag, 1976.

[6] Ministry of Transport and Communications, “Report to the Storting no. 27 (2014–2015) – On the right track,” 05 12 2015. [Internet]. Available: https://www.regjeringen.no/no/dokumenter/meld.-st.-27-2014-2015/id2411094/?ch=1&q=.

[7] Ministry of Transport and Communications, “Proposition to the Storting no. 52 (1999–2000) On NSB Gardermobanen AS and follow‑up of NOU 1999: 28 The Gardermoen project. Evaluation of planning and implementation,” 2000. [Internet]. Available: https://www.regjeringen.no/no/dokumenter/stprp-nr-52-1999-2000-/id203026/.

[8] Ministry of Transport and Communications, “Proposition to the Storting no. 64 (1996–97) On certain matters under road purposes and railway purposes,” 13 5 1997. [Internet]. Available: https://www.regjeringen.no/no/dokumenter/stprp-nr-64-1996-97-/id201411/.

[9] Norwegian National Rail Administration, “Stabling Eastern Norway – Main report,” Norwegian National Rail Administration, 2016.

7 Annexes 

7.1 Annex: Description of the mathematical approach used

7.1.1 Production function

The produced good or service is described as a transformation of input factors such as labour, materials, and capital. This is typically described as a mathematical function. The production function defines the optimal production process given the technology that is available.

(1)$X=f\left(v\right)$

where:

X = quantity produced of a good or service
v = vector of input factors$(v=v_1,v_2,\dots ,v_n)$

If function (1) is continuously differentiable and v consists of cost‑effective input factors, there will be a dual relationship between (1) and a cost function.

7.1.2  Costs

Costs are linked to the consumption of input factors and the prices of these. 

$\text{(2)}B\left(X\right)=q\cdot v\left(X\right)=\sum _{i=2}^n{q}_i\cdot v_i\left(X\right)$

where:

$q_i$= price of input factor no. i

$v_i$= consumption of input factor no. i

7.1.3 Marginal cost criterion

The marginal cost criterion follows from economic welfare theory, which concludes that welfare optimum is achieved when there is perfect competition with full information to all parties. The producer will then maximise profit (π) with respect to the production volume:

$\text{(3)}\pi \left(X\right)=pX-B\left(X\right)$

The maximum is found by setting the derivative of (3) with respect to X equal to 0 (zero), i.e.:

$\text{(4)}p=B^{\text{'}}\left(X\right)$

Double‑log

Double‑log functions also imply that the natural logarithms of both cost (B) and production volume (X) are used. 

$\text{(5)}\ln B(X,s)=a+\sum _{i=1}^n{\theta }_i\cdot \ln \left(X\right){}^i$

When n = 1, the function is a Cobb–Douglas variant with constant cost elasticity. If n = 2, cost elasticity either increases or decreases with respect to production volume. If n = 3, cost elasticity may both increase and decrease with respect to production volume.

7.1.5 Calculation of cost elasticity

The following is based on standard rules for differentiation and elasticities; see [5]. By applying these, cost elasticity and thereby marginal cost can be calculated. Cost elasticity is given by (6).

Cost elasticity [Double‑log]

7.2 Annex: Result tables

where:
ei   = cost elasticity model no. i
MCi   = marginal cost model no. i