I. INTRODUCTION

In Brazil, the former "Port Modernization Law", Law No. 8,630, of February 25, 1993, provided that private terminals could predominantly handle their own cargo, which was an inhibiting factor that significantly reduced the possibility of competition between public ports and private terminals. The current regulatory framework, Law No. 12,815, of June 5, 2013 ("New Law of Ports"), has expanded the possibilities of creating port infrastructure, freeing up the possibility of handling third-party cargo in Private Terminals (TUPs). Deregulation had the effect of a vertiginous growth in the number of TUPs, now in open competition with leases in public ports areas. Thereby, managers of public ports were forced to face a new market, leaving, to the past, the monopolistic position, in search of greater competitiveness and new revenues. The motto became efficiency, with the port tariff being a key factor for such success.

Port structures directly influence national navigation, impacting the product price for end customers. Therefore, when we talk about modernization and competition, we are also talking about adequate and reasonable port tariffs, which encourage the greatest possible movement within public ports, sustaining quality infrastructure, as the order of the day is to reduce the "Brazil Cost".

Given this background, the National Agency of Waterborne Transportation - ANTAQ, in 2019, issued Normative Resolution No. 32 (RN 32/2019) (ANTAQ, 2019), esforces a standardized tariff structure to the port authorities and a list of procedures for projects of review and adjustment of prices. Those rules created several new concepts, including: Tariff Modality, Required Revenue, Market Segmentation, Reference Period and Tariff Group.

Some highlights include article 15, which defines two procedural typologies: the tariff review, which may be extraordinary or ordinary, and the tariff readjustment. Article 16 informs elements of analysis, establishing a tariff review model based on the balance of projected revenues with the projected average costs of each service for the subsequent period. However, there is a lack of information: a mathematical-financial model and the nuances of this type of analysis.

The purpose of this work was the development of an application model with a hypothetical and general case study, using ANTAQ's rules contained in RN 32/2019, establishing the difference, in Brazil, between adjustment of tariffs and review of tariff, as well as analytical elements of economic-financial balance. The tariff modeling also seeks to elucidate a list of general principles for all those involved in the transportation services inside public ports, especially those provided by port authorities.

II. DEVELOPMENT

a) Price regulation in Brazilian public ports

"Price regulation" is understood, in Brazil, to be a regular government activity whose tool is a set of methodologies that determines a maximum or minimum price used by public utilities, carriers and service providers to charge its consumers for each product or service provided. Since such economic agents most often hold monopoly power, where the efficient price does not arise from a normal interaction between demand and supply, thus it is up to an independent agency to arbitrate the price. Therefore, it is a good method of replacing the competitive market, simulating its results.

Price formation is a central issue to regulation, as it concentrates questions about the operational cost distribution to consumers, including subsidies. Reconciling multiplayers interests are among the regulator's attributions.

Such rules are debated by the scholar Joana Paula Batista (BATISTA, 2005), in her book "Public Services Remuneration", discussing the applicable principles to the remuneration of public services. Deriving from the study, Table 1 is proposed, with some additions and adaptations of this part. The additions descend directly from RN 32/2019.

In Brazil, "tariff" is a type of price (and its ways of charging) regulated by an Agency or Federal Department. Also called "public price", as it is related to some state attribution. Usually used to deal with monopolies in the provision of essential infrastructure (transport, energy, telephony and sanitation). The regulated company's profit will not be so great that the consumer feels harmed, but it will not be so small that the entrepreneur feels uncomfortable (or discouraged) in investing high resources. It must be set at an adequate level to facilitate mortgages (therefore, it must be higher than market interest rates, or on the contrary, the loan must be subsidized by state banks) aimed at improving services or expanding infrastructure.

The port tariff, a concept created by Decree No. 24.508, of 1934, and by Law No. 3.421, of 1958, is the price offered by Brazilian port authorities for supplies within the respective public port under their commercial management. It consists of a price list, called, in industry jargon, "tariff table", through a metric (or form of tax incidence), called "tariff modality". The tariff table must be "public", with ample and prior knowledge of users (within a consolidated document). The value of the transaction is voluntarily assumed or provided by those who intend to use an available service, and it is not, therefore, a mandatory obligation arising from the legislation. It is carried out upon request, usually verbal, that is, on demand, without any kind of individual contract between the parties.

In terms of market structure, the port authority, manager of the public port (sometimes called "organized port") can be seen as a monopolist firm that discriminates N-Products, in addition to the following microeconomic characteristics: intensive in labor, sunk costs, economies of scale, barriers to entry, high fixed costs, low incentive to innovation, government participation in investments, extraordinary guarantees and a large presence of public goods. An alternative framework is also possible, such as a non-cooperative oligopoly, given that there are several ports in Brazil. However, we see some level of hegemony in certain types of cargo at certain ports, so that it is possible to model it as a monopoly, with a good dose of assertiveness, even if they face competition.

This market power has been decreasing since the 2010s, mainly due to the advent of new private terminals (there are more than 200 nowadays), but it is still predominant because relationships are often very complex inside the transportation area and "essential facilities". The simple entry of new providers is often not enough to reduce the market power of pre-existing agents. There are intangible aspects related to any business, such as loyalty, long-term relationships, trust between people and perception of quality. Another point is the idle capacity, where the local land transport infrastructure and the retroport areas also influence the choice of the embarkation or disembarkation port, as well as the offer of maritime routes by ship-owners.

In price regulation, there are several methods, but for the purposes of our work, we are going to work with two: Regulation by rate of return (cost pricing) and Regulation by ceiling price (price cap). That's what we'll see now.

b) Generic tariff review

In the Brazilian public ports, we define the Tariff Review as a procedure to evaluate and examine all costs and revenues of a regulated company, renegotiating a new level of profitability for future investments, without any prior indexes, in order to ensure balance of the original economic-financial framework (re-equilibrium). It can be regular (in cycles) or not (it is suggested that the first cycle is three years, and may be extended to four years in the second and five years in the third), depending on the contract (public-private partnership) signed with the port authority. In half of the cases, there is no contract, because companies belong to the federal government, which makes price regulation challenging, due to the lack of contractual obligations.

There are many review hypotheses; the most common is when a significant amount of new legal taxes or new investments (not originally foreseen in the "contract") is obligated by the Agency or Federal Government, generally for improving quality or expansion infrastructure. Existing prices will not be sufficient to cover all the news costs.

Until the mid-1980s, the most used method for tariff review in countries was price regulation according to the "cost of services", also called regulation by the internal "rate of return". The method was generalized from the North American experience started at the last century, with the regulation of monopolies. In other countries, there was no tradition of such regulation, as the service providers were, most of the time, government-owned (state-owned enterprise) - monopoly profit being appropriated by the State, as in Brazil.

From the perspective of US regulation, successful pricing is one that achieves the following main objectives:

• Avoids pricing below cost (including a "reasonable" return);

• avoids arbitrary profits;

• Facilitates agility in the process of defining and revising tariffs;

• Prevents misallocation of resources and inefficient production; and

• Establishes non-discriminatory or inappropriate prices among different types of consumers.

It seems to us that this perspective is appropriate to the Brazilian port sector, and is reflected in normative. Prices must remunerate total costs and contain a margin that provides a positive rate of return for investors.

Thus, the regulation by "rate of return" implies that, for example, a regular company providing a maritime access is authorized to set a toll fee in order to cover all the operating costs (which includes payment of employees, car fuel, machinery, expenses with water and electricity, equipment maintenance etc.), and the necessary loans for expanding the infrastructure, in addition to sustaining a reasonable profit based on investments and expenses.

In this example, the Regulator decides which expenses and investments are acceptable to compose the calculation, which is not a simple task, mainly because of information asymmetry, in which the firm always has more data than the regulator. At each period, based on accounting data, the depreciation policy and inflation in the period, tariff levels are set under certain market hypotheses. There may be negotiations on various aspects, in particular on what to do with the frustrated profit in the previous period compared to a forecast (for example, results can be compensated and included in the costs).

The regulated company's profit will not be so great that the consumer feels aggrieved, but it will not be so small that the entrepreneur feels uncomfortable (or without incentive) to invest high resources. The rate of return must be at an appropriate level to facilitate mortgages (therefore, it must be higher than market interest rate, or otherwise the loan must be subsidized by state-owned banks) aimed at improving services or expanding infrastructure.

To avoid excess profits, the Regulator, in general, determines the rate of return through a negotiation process with the service provider or representatives of the sector, listening to the group of affected users. In fact, the authority needs to pay attention to the market, i.e., to the rate that the business community is expecting (expectations is a central theme within the economy). A lower rate than expected generates less attractiveness for investments, reduces the value of the concession, auctions with few offers and low competition in the market dispute. In a kind of benchmarking regulation, the Regulator, when evaluating the review proposal, will be able to compare the project prices with similar ports, or even with the lowest known price, supposedly considered the most efficient.

The tariff review procedure is much more complex when there are several services provided by the firm, which is one of the objectives of this work, that is, a proposal for that. In this case, the definition of the different tariff levels requires apportionment of common costs (indirect and overhead) in order to obtain consistent relative prices that reflect efficient allocation.

In these more complex cases, there are three more general methods of apportionment formulas: i) according to the specific costs of which goods or services (as authorized by Law No. 8987, of 1995); ii) according to the income obtained by which goods or services; iii) according to the quantities of goods or services sold in the last period. All three are arbitrary to some degree (and the last two are circular, which can generate a vicious circle of errors) and can lead to inefficiencies and cross-subsidies.

The possible risk of unbalance is not enough to request an extraordinary tariff review; a real fact must have occurred, i.e., the "contract" must already be unbalanced. Therefore, the extraordinary tariff review does not take place at any time, only after an imbalance. There is some jurisprudence about that.

Furthermore, the re-equilibrium is not a discretionary act of the Regulator. He can only refuse granting you in one of the following situations:

• No real increase in charges;

• Occurrence of the event prior to the winning proposal (in cases of bids at auctions);

• Absence of a causal link between the events; and

• Bad management signs and guilt (intention) of the company for increasing his charges.

In case of port authorities that are government-owned, the lack of a contractual provision does not affect the application of the re-equilibrium model, because its foundation is not contractual, it is legal.

The Regulator should define an incentive-based regulation scheme that minimizes uncertainties and reduces information asymmetry, with a main driver of incentives for cost reduction during the tariff revisions period. During the intervals between tariff revisions, the Brazilian regulator applies a price-cap readjustment methodology.

In this model, a tariff cycle is imposed, which consists of the corresponding period of time between two ordinary tariff revisions, comprising a minimum period of 03 (three) years and a maximum of 05 (five) years, according to ANTAQ. It also informs that the first cycle, in existing contracts, begins with an extraordinary review. See Table 2 that the cycle starts with an extraordinary review.

First year, RN 32/2019 says that the extraordinary tariff revisions will be carried out at a request and promotion by the Regulator, ex officio. This will be the opportunity to contemplate the migration from the current tariff structure to the structure standardized by ANTAQ. Normally, every year or at the end of each Tariff Cycle, the Agency publishes calendars for companies in order to present their claims for annual readjustment or for an ordinary tariff review within a fixed period, which may coincide with the contract anniversary date.

Now it is finally necessary to state: applying the rate of return method is always difficult for Brazilian government agencies. This is explained below.

First, the regulation by rate-of-return method, given the complexity of its operation, is an appropriate method only when cost and demand conditions do not change significantly in short periods of time, i.e., when costs and demand are relatively stable. In the opposite situation, this process becomes much slower. In this condition, the cost and demand estimate is impaired for a medium period, say four or five years ahead, making it difficult to find the equilibrium parameters of the equation: what will be the Total Revenue and what will it be the Total Cost of the firm, remembering that the natural monopoly has that characteristic of subadditive cost: the more it produces, the lower the cost per unit. It seems to be the case in the Brazilian port sector, generally having annual incremental demand at a rate of less than 4% in most cases. Furthermore, it is known that variable costs in port authorities are substantially reduced when compared to fixed costs, a condition that inhibits the application of pricing techniques related to marginal cost, which also depends on knowledge of a more accurate demand curve (MONTEIRO, 2017).

Second, applying only regulation by rate of return, there are no incentives for the firm to seek efficiency, due all costs are passed on to consumers, and as companies' efforts to reduce costs do not increase their profits. The non-exogenous behavior of costs must be considered: the charging form affects the cost of production of the service. The doctrine shows us the existence of the Averch-Johnson effect (over investments).

Finally, the regulation by rate of return requires a lot of information to be submitted to, lacking a good deal of confidence um some of those.

However, the Cost of Service model still persists in Brazil, especially when we observe the presence of state-owned companies as service providers, or even private concessionaires, which is the model adopted by ANTAQ, with increments related to performance (productivity) and value (elasticity), as recommended by UNCTAD (1995).

c) Practical model of regular tariff review

In order to present projects, Article 16 of RN 32/2019 sets out a list of requirements to be attended by port authorities, as shown in Figure 1:

Fig. 1: Essential data for making a review project

If there are no demand or cost studies for the subsequent period, the same trend line in the previous period will be adopted and the same average costs and other non-tariff revenues for the subsequent period, month by month, of the preceding period. In the case of new tariff modalities, without previous invoicing, the port authority must present demand estimates (to be obtained directly from the users), and an initial estimated price, such as an original price.

As an objective function, the tariff review will assess, for a given port authority, the annual Operating Profit [OP] of each Tariff Group "j" or the sum "k" of them, in the following sequence: Initially, the Operating Profit of the current Tariff Structure will be evaluated, considering the Previous Reference Market of the port administration and then the new proposed Tariff Structure will be simulated, in the following scenarios (Table 3).

After analysis of scenarios, the current Tariff Structure and the proposed Tariff Structure will be characterized in one of the following situations: Balanced or Unbalanced. It will be considered Balanced, in general, the Tariff Structure k that provides a total Operating Profit equal to or greater than zero for the next twelve months. In this model, the Operating Profit level replaces the rate of return concept.

The scenarios indicate that the port tariff will have a ceiling price based on the composition of three dimensions: cost (expenses to deliver the product), performance (level of capacity and productivity) and value (marginal utility or consumer elasticity).

The model can be described in the following flowchart (Figures 2 and 3).

Fig. 2: Flowchart of a tariff review proposal. Vision 1 (tasks)

Fig. 3: Flowchart of a tariff review proposal. Vision 2 (phases)

Other indicators to be used for the evaluation of the proposal are the following:

Average Readjustment Index (ATI): percentage change in tariff collection, considering the previous moment. It's the user's vision; and

Average Tariff Effect (ATE): percentage change in total collection, considering the previous moment. It is the port's view.

The boundary conditions for the model's operation are as follows:

i. Cost accounting and tariff groups: standardization of the tariff structure in similar groups related to the cost objects of regulatory accounting;

ii. Reliable projection of demand for cargo handling: consideration of seasonality, cyclical patterns, likely entry and exit of competitors, new contracts;

iii. Disclosure of a tariff cycle calendar to increase predictability to users: Creation of a regular reference period and deadlines for companies to present their tariff review and readjustment project.

d) Extraordinary tariff reviews

An extraordinary tariff review will adopt the same methodology used in the ordinary review. However, according to the doctrine, the projects for extraordinary tariff reviews must identify the causal link responsible for the imbalance.

The instruction of requests for extraordinary tariff review shall inform the occurrence of an effective economic and financial imbalance, already manifested, or an economic and financial imbalance not yet manifested, if and only if the project considers an annual amortization of future investments in infrastructure to be covered by the tariff.

In these cases, requests for additional tariff revenues to cover capital expenditures on future investments in port infrastructure must be linked to a physical-financial schedule, agreed upon with the Regulator. When considering the use of some level of third-party capital, the non-governmental bank institution should not be remunerated through an interest rate above that normally practiced by the market.

The events giving rise to extraordinary review are (causal link):

• Increase or decrease in capacity;

• Exogenous variation of operating costs;

• Change in legislation or regulation that impacts business;

• Natural accidents and claims do not covered by insurance;

• Legal taxes change, except income tax;

• Strikes and riots.

III. CASE STUDY

In the following test, in order to simplify the demonstration, we will assume the existence of two tariff groups, as in Table 4, associated with two cost objects and respective tariff modalities. To simplify further, there will be no changes in the structure, keeping the tariff modalities for the next period, without additions or exclusions. We have two different moments: year A0 (year of start) and year A1 (year to be rebalanced). After evaluating the current equilibrium level, the goal is to find a new ceiling price for tariffs in the A1 period, at a new equilibrium level.

The costing method, for tariff purposes, was discussed in Technical Note No. 64/2017/GRP/SRG (ANTAQ, 2017c) and Technical Note No. 50/2017/GRP/SRG (ANTAQ, 2017b). It is a kind of Integral (full) Absorption Costing. However, Activity-Based Costing (ABC) method is also allowed, as a form of management improvement.

Absorption Costing is simple, suitable for mid-sized companies and provides a lot of information. It's a cost method that includes all manufacturing costs - direct materials, direct labour, and both variable and fixed overhead (indirect costs) - in unit product cost. Integral costing method is a principle whereby fixed as well as variable costs are allocated to the cost unit. On the other hand, absorption costing involves the appointment of overhead, which can be subjective. The resulting information can be misleading for management decision-making.

ANTAQ defends that the "main merit of the Integral Costing Method is the fact that all expenses incurred in an organization are taken into account, without exceptions. In it, we have the total recovery of all company expenses for the delivery of a given cost object. This results in more complete unit cost information. However, it differs from the conventional Absorption Method, as even the No-product cost (expenses, selling, administrative, lawyers, for example) are allocated to cost centers (or cost objects) - however, it has a very similar logic to that."

Using this method, costs that are assigned to cost objects can be divided into two categories: direct cost and indirect costs. Direct costs are those costs that can be specifically and exclusively identified with a particular cost object. In contrast, indirect cost cannot be exclusively with a given cost object.

ANTAQ mapped Nine Cost Objects for Brazilian port authorities, and transposes these objects into the tariff structure, because they are intimately connected with the tariff tables. Objects are the aggregation of different tariff modalities that have a high degree of affinity with each other regarding the products supplied or of type of users.

In the Integral Costing Method, the product offered by the company is responsible for absorbing all charges. Indirect costs must be allocated to the costing objects using apportionment criteria. ANTAQ assumes that there should be a proportional relationship between type of cost and the costing objects (indirect costs should be smaller compared to direct costs, for example).

The apportionment is carried out using indices that will direct the distribution of the Indirect Cost (and General Expenses) to the cost objects. Then, the percentage that the products consume of the adopted index is estimated. They then settle the overhead based on that percentage. All expenses related to the production and delivery effort are, therefore, distributed to all products or services offered. To reduce the arbitrariness of the Costing Method, there must be a cause and effect relationship between the distribution parameter and the volume of indirect cost. The variations that determine how the entity's resources are used by the costing objects must also be identified.

The hypothetical apportionment percentages to be used (both for the preceding and subsequent periods) in the case study are in Table 5:

The Operating Profit of -18.21%, as shown in Table 7 in Step 3, proves the unbalance in the current tariff structure.

IV. CONCLUSION

This study demonstrated a mathematical and economic model, based on efficient allocation costs, to be applied for tariff review by port authorities and all public ports - controlled by the federal government or even concessionaires (although concession contracts may contain their own specific rules). This proposal is being gradually implemented by the Agency during the years 2021 and 2022. As we see, it allows the search to various points of balance, to be tested by the company and negotiated with the Regulator, assisting in a price sensitivity analysis.

There are advantages and disadvantages.

Advantages: the profit of the port authority is monitored (a kind of "supervised freedom"), so that only the cost plus a certain percentage is paid by the consumers. In theory, this cost would fall, as the contract progresses in time, and the efficiency gains would be passed on to the consumer, preventing an arbitrary profit.

Disadvantages: As we guarantee a minimum rate of profit for the entrepreneur, it does not provide sufficient stimulus to increase efficiency, which is important in the face of technological changes. The inverse of the expected would then happen: the price, discounted for inflation, would rise over time, or the quality would fall. Therefore, it should be used together with other instruments, as a productivity factor (X Factor) within regular annual readjustments in a cycle logic.

The model presented here contributes to a reduction of uncertainties. Demonstrates something viable in efficiently allocating resources. It is flexible enough to be adopted by service providers, because it does not remove the possibility of a positive profit and of establishing a commercial policy aiming at maximizing total revenue. It also provides transparency and predictability to the market. To obtain the final price, other elements can be added to the cost, such as, for example, the perspective of added value to the consumer and productivity, a theme for the next paper.