The Economic Management of Physical Assets: The Practical Case of an Urban Passenger Transport Company in Portugal

Abstract

Organizations are increasingly concerned with new strategic guidelines and ways of managing physical assets to improve their competitiveness and sustainability. In this paper, we analyze the determinants of the economic management of physical assets in the specific case of a public passenger transport company located in one of the main cities of Portugal. Based on the case under analysis, it was possible to conclude that the economic management of physical assets is oriented by relevant indicators, including, for example, expenses associated with acquisition, maintenance, and operation. This paper provides a relevant contribution to monitoring and evaluating the life cycle of equipment, enabling more efficient and effective management of these physical assets for transport companies. We are convinced that the valuable results presented in this paper can open up new research avenues in the area of physical asset management.

1. Introduction

The dynamics of the worldwide market have led large industrial companies to become increasingly concerned with new strategic guidelines and ways of managing physical assets to improve their competitiveness in an increasingly demanding world where organizations are required to assume a decisive role in crucial agendas such as sustainable development. (For example, Ref. [1] argue that the introduction of Agenda 2030 and SDGs encouraged companies to play a central role in promoting sustainable development. On this topic, see also [2,3,4]). Their traditional problems have now been joined by issues such as those related to energy savings, maintenance, social responsibility, and the environment. Therefore, in today’s globalized economy, the survival of organizations depends on their capability to understand the changes taking place in the world and to have the ability to innovate.

For obvious reasons, public transport companies are strongly associated with sustainability, making urban passenger transport buses an important alternative to the use of individual transport. It should be noted that sustainable transport must be able to meet long-term and, simultaneously, environmental, social, and economic needs and impacts [5].

Similarly to any other company, industrial organizations, including public transport companies, must be financially viable. In this context, physical asset management assumes great importance, even having been recently considered to be one of the most important sources of competitive advantage for organizations [6]. They seek to improve the value of their assets by investing in asset management in order to obtain better returns for their business [7].

In this perspective, it is inferred that the use of a physical asset management system is one of the tools that enables companies to improve financial performance, decision-making processes, risk management, services and results, organizational reputation, and sustainability [8]. In fact, the literature shows that there is a strong linkage between physical asset management (PAM) and sustainability; in fact, the maximization of the asset’s life cycle represents less waste and, by consequence, increases sustainability. In this sense, Ref. [9] show that there are some PAM areas on which managers should focus in order to optimize costs, performance, and risk exposures concerning the physical assets and, therefore, enhance sustainability performance.

For [10], PAM is multidisciplinary and involves multifunctional processes, people, and technologies that contribute to the good performance of companies. It should be noted that the literature includes several studies that relate to the management of physical assets with a systematic and coordinated effort in terms of strategic, operational, and economic processes [6,11]. PAM also plays an important role in the management of the life cycle of an asset (LCA) as a whole, pursuing economic and physical performance [9]. (When determining the value of assets over their life cycle, it is important to have information about the different stages of their lives. Ref. [12] presents the stages of a physical asset’s life cycle from the moment the organization makes a decision about acquisition until Renewal/Withdrawal. Later, the author also presents the concept of life-cycle investment (LCI); this is a transition from life-cycle cost (LCC), which represents a change in the concept of cost, which is traditionally assumed to be a loss. The author also argues that when investing in assets, a question must be asked: “Will the value of the asset increase?” This increase can be seen in different ways, such as a reduction in product rejection or an increase in product production in manufacturing. On the other hand, it can be carried out through a renewal that can extend the life cycle of the product [2]).

The LCA of physical assets is indeed assumed to be crucial for many different companies, including transport companies. For example, Refs. [13,14] present and discuss a model for condition monitoring. Using data from the oil in the diesel engines of a fleet of urban buses, the authors study the evolution of degradation and develop a predictive maintenance policy for oil replacement. Based on the analysis of the oil condition, the intervals for oil replacement can be expanded, allowing increased availability. This exercise can be expanded to include other variables, and the model has the potential to be applied to other physical assets to achieve the best availability based on a condition monitoring policy.

Ref. [15] present an interesting study with the objective of applying new methods of econometric models to the LCA of physical assets. These authors highlight a method to evaluate asset depreciation using different variables, with an emphasis on investments in technology and sustainability.

Given the increasing interest in this subject and based on the scarcity of studies that explain the constructs that determine the economic management of physical assets, the objective of this paper is to contribute to the literature by analyzing these aspects in the specific case of the urban transport company in one of the biggest cities in Portugal. In this sense, it assesses, from a strictly economic point of view, the influence of exogenous variables on the cost of money, namely the inflation rate, the cost of money, and the costs associated with fuel, whose prices have undergone considerable changes, both positive and negative, over the years, presenting analysis models that make it possible to determine the influence of those variables on the time of sale and the size of the reserve fleet. (The value of money is directly linked to time, so it is correct to say that the longer the time of ownership of a physical asset, the greater the action of external agents or even the influence of macroeconomic factors in relation to the purchasing power of the specific currency. On the other hand, inflation is a determining factor in the relationship between money and time; there is a need to take into account the inflation rates to which capital is subject).

This paper is structured as follows: Section 2 presents a brief literature review regarding physical asset management; Section 3 presents the research methodology and the models; Section 4 presents the case study and discusses the estimated results; and Section 5 presents the main conclusions.

2. Literature Review: Physical Asset Management

Increased competition, deregulation, external pressures, and technological advances have encouraged companies to monetarize their investments and design new strategies that allow them to survive in the long term [16]. In this context, the management of physical assets has been gaining importance in the field of scientific research, with companies seeking to identify new competitive factors that make their investments profitable [17,18].

For [6], physical assets, also known as engineering assets, are important for creating tangible value for an organization, namely in transport services, electricity supply, water supply, construction, and mining, among other sectors. There is also a strong linkage between physical asset management (PAM) practices and the sustainability performance of companies. For example, using data collected from different organizations operating in six European countries, namely Greece, Poland, Slovakia, Slovenia, Sweden, and Turkey, Ref. [9] show that PAM practices positively influence sustainability performance outcomes, namely economic, environmental, and employee-related social performance. In the same perspective, using statistics and resorting to facts extracted from over 2800 journal articles, Ref. [19] present a systematic review regarding physical asset management as a key resource in achieving competitive advantage in the framework of sustainable development.

An adequate management of available resources also enables companies to obtain advantages over their competitors [16,20,21]. Indeed, companies can obtain important advantages when they prioritize the development of their resources through the management of physical assets, namely by determining the economic life of their equipment. This is also a reality for urban transport companies.

It should be noted that the maintenance management of passenger transport buses is a strategic activity to guarantee compliance with their life cycle, which implies combining management, technical, and economic actions in order to obtain high availability at rational costs [13,22]. In fact, poor maintenance management contributes to a significant financial cost [23].

The theoretical basis of this subject shows that the life-cycle cost (LCC) of an asset is the sum of all the capital expended to support the asset, from design and manufacture through operation until the end of its useful life. In other words, this concept represents the capital spent on supporting that asset, from its conception and manufacture through its operation until the end of its useful life [24]. We can also consider it a prediction of the future, and, as such, different methods are generally used to make cost estimates, such as activity-based costing (ABC). For [25], since ABC is crucial to activity-based LCA, some explanation of ABC is pertinent. ABC is a full-absorption costing method that is gaining more and more support over conventional methods.

In an ABC system, it is assumed that cost objects (products, services, and so forth) consume activities, while a conventional system assumes that cost objects consume resources. There are several implications of this difference, but the most important is that ABC acknowledges that one cannot manage costs; one can only manage what is being carried out, i.e., activities.

An ABC system utilizes drivers on several levels (unit, batch, product, and factory level), while a conventional system uses only unit-level characterizations called location bases, which, roughly speaking, are an arbitrary unit-level driver. Hence, ABC is much more accurate [25,26].

The LCC can be significantly higher than the initial investment value, and, in many cases, it is defined right at the design stage. (For example, Ref. [27] goes further and reinforces this idea, noting that from 70% to 90% of these total LCC costs are defined in the design and manufacturing phases). The initial investment costs are usually the most commonly used as a primary criterion and, sometimes, the only one in the purchase decision. Despite the obvious long-term benefits of LCC analysis, its adoption has been relatively slow. Possible reasons for this include the lack of standard or formal guidelines and the absence of reliable past data. The number of cross-case studies in the field of life-cycle costing is extremely low, and most of them are limited to a single industry [28,29]. (It should also be noted that, in order to support the life-cycle cost analysis, there are some standards and related documents that are good sources as guidelines for asset management, such as [30]), i.e., [31,32,33], which can be applied in any sector [34].

Ref. [35] illustrate how, throughout the life cycle of equipment, mastery of concepts and some economic calculation tools become essential for maintenance managers and organizations. However, the systematized study in this area remains underdeveloped, with the need to apply and create new equipment management models that can bring added value to companies in the sense of improving their productivity and quality of service, taking into account aspects of environmental sustainability, including quality, environment, safety, maintenance, and energy management standards [12]. It is also noted that many companies keep equipment in operation even when their operation is no longer economically viable because they do not follow their economic cycle, which has exogenous implications, namely in the size of the reserve fleet in the case of bus fleets (idem).

Ref. [36] refer to technological change as a motivator for replacing equipment. In scientific references, it is commonly assumed that technology continuously develops according to a well-defined function. On the other hand, [37] demonstrate that, combining continuous and discrete-time models, the equipment replacement period is shorter when the incorporated technology is greater.

According to [35], “the valuation of an asset is established by the expected future benefits of the cash flows referred to the present value, through a discount rate that reflects the risk of the decision”. Consequently, methods that consider the time value of money are the most suitable.

According to [38], the Equivalent Uniform Annual Cost method is adequate in the analysis of the company’s operational activities, with investments that can be repeated. The Equivalent Uniform Annual Cost method is similar to the value uniform annual equivalent, but the first makes a comparison between the costs of investment projects, while the second compares all cash flow components of the alternatives. By transforming all costs of the asset into equivalent annual costs with the application of a certain interest rate corresponding to the cost of capital on the investment or the minimum attractive rate, the objective is to determine in which year the lowest equivalent annual cost occurs, thus determining the ideal period of replacement of the depreciable asset, that is, its economic life.

In addition, the standardization of investment results for equivalent annual values means that the analysis of these results facilitates decision-making. The purpose of using this method is to determine in which year the lowest equivalent annual cost occurs, which indicates the best replacement period for the physical asset (idem).

The calculation of the equivalent annual cost is due to the use of the Capital Recovery Factor; it is through it that two or more investment opportunities can be compared and the ideal time to replace the equipment can be determined, taking into account information such as investment or acquisition value, resale value or residual value at the end of each year, operating costs, cost of capital, or the attractive minimum rate [39].

In this context, the literature identifies the following four main reasons that lead to equipment replacement [40]:

(i).

When the asset becomes inadequate for the activity;

(ii).

When the asset reaches the limit of its useful life;

(iii).

When the asset becomes obsolete due to technological advances;

(iv).

When more efficient methods prove to be more economical.

Within this replacement process, it is relevant to take into account the following aspects [12,41]:

-

The availability of new technologies;

-

Compliance with safety standards or other mandatory standards;

-

The availability of spare parts;

-

Obsolescence that may limit the asset’s use.

It is also important to note that specific calculation methods are available to determine when the asset should be replaced. For this purpose, several variables must be taken into account, such as acquisition value, assignment value, operating costs, maintenance costs, running costs, inflation rate, and capitalization rate. The values of most of these variables are obtained through historic valuation, with the exception of the assignment value. In this case, it will be necessary to obtain the market value for each specific piece of equipment, which may be difficult for several assets. As an alternative, various types of devaluation can be simulated, such as the following [12,41,42]:

-

Linear method of depreciation—the aging of the value of the equipment is constant over the years;

-

Sum-of-digits method—annual devaluation is non-linear;

-

Exponential method—the annual depreciation charge decreases over the life of the equipment.

Another additional method involves using the “useful life”, which defines that the life of an asset ends when its maintenance costs exceed the maintenance costs plus the capital amortization of equivalent new equipment. There are several methods for determining the economic cycle of replacing equipment. The most common ones are the following [12]:

-

The Uniform Annual Income Method;

-

The Total Average Cost Minimization Method;

-

The Total Average Cost Minimization Method with Present Value Reduction.

In turn, Ref. [43] proposes a policy for optimal replacement intervals for programming technical systems based only on the maintenance cost parameter: a system that is replaced by a new one as soon as the maintenance cost within a replacement cycle reaches or exceeds a certain level. Ref. [44] present a new approach to economic models for determining the most appropriate time for replacing equipment in services, which permits the evaluation of the life cycle of the equipment by the managers. Several studies consider the adoption of reliability parameters and maintenance costs to help evaluate more rational replacement decisions [44,45].

Ref. [46] adopted a model for a transit fleet replacement problem with various types of buses. However, many costs were highly oversimplified or not based on real data, and variability in vehicle characteristics uses market fluctuations that were not studied. The cost of replacing, remanufacturing, and rehabilitating a bus has been a focus of research by [47], as has the optimal allocation proposed by the Federal Transit Administration (FTA) of the United States of America (USA). Other lines of research have focused on statistical analyses of fleet data and on the relationships among age, utilization, and costs [48].

A numerical solution was proposed and illustrated by [49] using data from a given fleet. The authors considered a two-cycle replacement model, with decision variables based on the replacement age of the current fleet and the size of the new fleet. The optimal values for the decision variables can be found by minimizing the total discounted cost per unit of time or the equivalent income value.

Regarding predictive maintenance versus equipment replacement, and specifically oil analysis, some mathematical models and concepts have been used [12,13,14,22,24,41,44]. On the other hand, many studies have considered reliability parameters and maintenance costs to help evaluate more rational replacement decisions [13,14,22,24,44,45]. It should, however, be noted that there are other tools that may contribute to the development of a new vehicle replacement optimization model, such as fuzzy logic (Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical ways of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognizing, representing, manipulating, interpreting, and using data and information that are vague and lack certainty.) and Support Vector Machines (Support Vector Machines are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. SVMs are one of the most robust prediction methods, being based on statistical learning frameworks or VC theory) [24].

3. Research Methodology: Applied Models

It is essential to emphasize that wisdom is acquired in different ways, so scientific research seeks to be increasingly rigorous and acceptable since it is based on a rational process of the descriptive and explanatory power of facts and phenomena [35]. To analyze the determinants of the economic management of physical assets of the urban transport company under study [50], several authors have used econometric models for equipment replacement and their respective methods of measurement, namely [12,13,24,46,51].

However, the data used to analyze the economic life of the physical assets of the company under study were collected through the company’s own database (real data) and governmental statistical data platforms, namely the National Institute of Statistics (Instituto Nacional de Estatística-INE) and PORDATA.

The econometric models of equipment replacement and their optimization methods will be discussed below.

3.1. Economic Replacement Models

It is important to characterize the appropriate calculation methods for determining the most rational time for replacing physical assets, which can also be applied to the urban transport sector. For this purpose, it is necessary to take into account several variables [41]:

-

Acquisition cost (CA);

-

Assignment value (VC);

-

Exploration costs (CE);

-

Maintenance costs (CM);

-

Operating costs (CO);

-

Inflation rate (θ);

-

Capitalization rate (i).

The values of most of these variables are obtained through historical values, with the exception of the assignment value. In this case, it will be necessary to obtain the market value for each specific piece of equipment, which may prove difficult for many assets. Alternatively, various types of devaluation can be simulated, such as the following ones [41]:

-

Linear depreciation method;

-

Sum-of-digits method;

-

Exponential method.

3.2. Linear Depreciation Method

This method considers that the aging of the value of the equipment is constant over the years and is calculated as follows [41]:

$$d_l=\frac{CA-{VC}_n}{N}$$

(1)

where

dl	annual depreciation quota;
CA	acquisition cost;
VCn	residual value of equipment after N time periods;
N	lifetime corresponding to VCn;
l	l = 1, 2, 3 … n;
Vn	value of the equipment in a period n = 1, 2, 3 … N.

The value of the equipment, V_n, in a period n less than N is given by:

$$V_n=CA-l\times d$$

(2)

3.3. Sum-of-Digits Method

In this case, the annual devaluation is non-linear and is calculated as follows [41]:

$$d_l=2\times \frac{N-\left(l-1\right)}{N+1}\times \frac{CA-V{C}_n}{N}$$

(3)

where

dl	annual depreciation quota;
CA	acquisition cost;
N	lifetime corresponding to VCn;
VCn	residual value of equipment after N time periods;
l	l = 1, 2, 3 … N;
Vn	value of the equipment in a period n = 1, 2, 3 … N.

$$V_n=CA-d_l$$

(4)

3.4. Exponential Method

The exponential method applies a decreasing annual depreciation charge over the life of the equipment. The calculation formula is as follows [41]:

$$d_l=V{C}_{l-1}\times (1-\sqrt[N]{\frac{V{C}_n}{CA}})$$

(5)

where

dl	annual depreciation quota;
CA	acquisition cost;
N	lifetime corresponding to VCn;
VCn	residual value of equipment after N time periods;
l	l = 1, 2, 3 … N;
Vn	value of the equipment in a period n = 1, 2, 3 … N.

$$V_n=CA-d_l$$

(6)

The equipment can be replaced according to several criteria. First of all, there is the usual criterion corresponding to the “economic cycle”, which makes it possible to determine the optimal period that minimizes the average total costs of operation, maintenance, and capital immobilization. Another method used is the “useful life”, which defines that the life ends when its maintenance costs exceed the maintenance costs plus the capital amortization costs of equivalent new equipment. However, even though it is, in theory, possible to progress to the analysis of equipment replacement based on market depreciation values, two other types of variables should be taken into account, namely: the capitalization rate, denoted by i, and the inflation rate, denoted by θ. The apparent rate (i_A) updates the various values to the value of the present year (n). These rates are related as follows:

$$i_A=i+\theta +i\times \theta$$

(7)

where

• i_A—apparent rate.

3.5. Uniform Annual Income Method:

The Uniform Annual Income Method makes use of the following data [41]:

-

The equipment acquisition cost;

-

The assignment amounts (calculated according to the methods set out above);

-

The maintenance and operating costs over the years;

-

The apparent rate.

The Net Present Value in year n (NPVn) is calculated by:

$${NPV}_n=CA+\sum _{j=0}^n\frac{C{M_j+CO}_j}{{(1+i_A)}^j}-\frac{V_n}{{(1+i_A)}^n}$$

(8)

where

CA	acquisition cost;
CMj	maintenance costs in year j = 1, 2, 3 …. n;
COj	operating costs in year j = 1, 2, 3 …. n;
iA	apparent rate;
Vn	value of the equipment in a period n = 1, 2, 3 … N.

The Uniform Annual Income (UAI_n) is calculated as follows:

$${UAI}_n=\frac{i_A{(1+i_A)}^n}{{(1+i_A)}^n-1}\times \left(CA+{\sum }_{j=0}^n\frac{C{M_j+CO}_j}{{\left(1+i_A\right)}^j}-\frac{V_n}{{\left(1+i_A\right)}^n}\right),$$

(9)

$${UAI}_n=\frac{i_A{(1+i_A)}^n}{{(1+i_A)}^n-1}\times {VPL}_n$$

(10)

The lowest calculated Uniform Annual Income (UAI_n) value indicates the respective period (in multiples of years) during which the equipment ought to be replaced. This amount is equivalent to the annual minimum income of the equipment.

3.6. The Total Average Cost Minimization Method

The Total Average Cost Minimization Method (TACMM) makes it possible to determine the lowest average cost of ownership of the equipment and the respective year in which it occurs, which corresponds to the optimal time for replacement. Capital costs and the inflation rate are not considered. The calculation procedure is as follows [41]:

$$C_n^{\prime }=\frac{1}{n}{\sum }_{j=1}^n(C{M}_j+C{O}_j)$$

(11)

$$C_n^{″}=\frac{1}{n}(CA-V_n)$$

(12)

$$C_{n\left(MCMT\right)}^{}{=C_n^{\prime }+C_n^{″}=\min }_{\mathit{n}\in \left\{1,2,\dots ,\left.N\right\}\right.}\frac{1}{n}\left(CA-V_n+{\sum }_{j=1}^n(C{M}_j+C{O}_j)\right)$$

(13)

where

CA	acquisition cost;
CMj	maintenance costs in year j = 1, 2, 3 …. n;
COj	operating costs in year j = 1, 2, 3 …. n;
Vn	value of the equipment in a period n = 1, 2, 3 … N;
n	number of years n = 1, 2, 3 … n;
Cn(TACMM)	total average cost.

3.7. The Total Average Cost Minimization Method with Present Value Reduction

In this case, the calculation procedure is identical to the previous one, with the exception that capital costs and the inflation rate are considered. The various maintenance and disposal values are reduced over the years to their present value in accordance with the following procedure [41]:

$$C_n^{\prime }=\frac{1}{n}{\sum }_{j=1}^n(\frac{C{M}_j+C{O}_j}{{(1+i_A)}^j})$$

(14)

$$C_n^{″}=\frac{1}{n}(CA-\frac{V_n}{{\left(1+i_A\right)}^n})$$

(15)

$$C_{n(TACMM-PVR)}^{}{=C_n^{\prime }+C_n^{″}=\mathrm{m}\mathrm{i}\mathrm{n}}_{n\in \left\{1,2,\dots ,\left.N\right\}\right.}\frac{1}{n}\left(CA-\frac{V_n}{{\left(1+i_A\right)}^n}+{\sum }_{j=1}^n(\frac{C{M}_j+C{O}_j}{{(1+i_A)}^j})\right)$$

(16)

where

CA	acquisition cost;
CMj	maintenance costs in year j = 1, 2, 3 …. n;
COj	operating costs in year j = 1, 2, 3 …. n;
Vn	value of the equipment in a period n = 1, 2, 3 … n;
iA	apparent rate;
n	number of years n = 1, 2, 3 … n;
Cn(MCMT-RVP)	total average cost.

4. Case Study: The Replacement Time of an Urban Passenger Transport Company in Portugal

We address the methods for determining the replacement economic cycle in the practical case of a bus company (an urban transport company in one of the biggest cities in Portugal) based on a constant apparent rate, which enables the ability to understand its effect over the life cycle of equipment. For this purpose, an apparent rate of 8% was considered (used by the company, taking into account the experience of the professionals of this company). The Total Average Cost Minimization Method is not addressed due to the fact that it does not take into account the apparent rate, that is to say, it does not consider the capital costs and the inflation rate. This study was conducted on the same vehicles and in the same homogeneous groups. Accordingly, we present Vehicle X1 as an example, taking into account the two methods used to determine the economic cycle, which are presented in

Table 1. UAI_n constant apparent rate—X1.

Vehicles: X1												VC [EUR]	VPL [EUR Year n]	UAI [EUR Year n]
Year	Year j	CA [EUR]	ϕ [%]	i [%]	iA	iA [%]	π1 (1 + iA,j)	CM [EUR]	CO [EUR]	∑1 [EUR]	VP [EUR]	Meth. Exp.	Meth. Exp.	Meth. Exp.
1993	0	110.66 K	4%	4%	0.08	8%				110.66 K
1994	1		4%	4%	0.08	8%	1.08	0.98 K	11.22 K	12.20 K	121.94 K	87.74 K	34.20 K	36.99 K
1995	2		4%	4%	0.08	8%	1.08	1.02 K	10.71 K	11.73 K	131.97 K	69.57 K	62.40 K	35.07 K
1996	3		4%	4%	0.08	8%	1.08	1.12 K	10.46 K	11.58 K	141.12 K	55.16 K	85.96 K	33.45 K
1997	4		4%	4%	0.08	8%	1.08	1.27 K	10.48 K	11.76 K	149.71 K	43.74 K	105.97 K	32.11 K
1998	5		4%	4%	0.08	8%	1.08	1.49 K	10.76 K	12.25 K	157.99 K	34.68 K	123.31 K	31.01 K
1999	6		4%	4%	0.08	8%	1.08	1.77 K	11.31 K	13.07 K	166.15 K	27.50 K	138.65 K	30.14 K
2000	7		4%	4%	0.08	8%	1.08	2.10 K	12.12 K	14.22 K	174.37 K	21.80 K	152.56 K	29.46 K
2001	8		4%	4%	0.08	8%	1.08	2.50 K	13.19 K	15.69 K	182.74 K	17.29 K	165.45 K	28.97 K
2002	9		4%	4%	0.08	8%	1.08	2.95 K	14.53 K	17.48 K	191.37 K	13.71 K	177.66 K	28.63 K
2003	10		4%	4%	0.08	8%	1.08	3.64 K	15.54 K	19.18 K	200.13 K	10.87 K	189.26 K	28.41 K
2004	11		4%	4%	0.08	8%	1.08	3.91 K	18.46 K	22.37 K	209.57 K	8.62 K	200.95 K	28.37 K
2005	12		4%	4%	0.08	8%	1.08	5.97 K	20.75 K	26.72 K	219.99 K	6.83 K	213.16 K	28.52 K
2006	13		4%	4%	0.08	8%	1.08	5.13 K	22.01 K	27.15 K	229.78 K	5.42 K	224.36 K	28.64 K
2007	14		4%	4%	0.08	8%	1,08	5.40 K	21.73 K	27.13 K	238.83 K	4.30 K	234.53 K	28.71 K
2008	15		4%	4%	0.08	8%	1.08	6.06 K	26.30 K	32.37 K	248.81 K	3.41 K	245.40 K	28.95 K
2009	16		4%	4%	0.08	8%	1.08	7.05 K	17.92 K	24.97 K	255.93 K	2.70 K	253.22 K	28.90 K
2010	17		4%	4%	0.08	8%	1.08	10.06 K	17.99 K	28.05 K	263.32 K	2.14 K	261.18 K	28.94 K
2011	18		4%	4%	0.08	8%	1.08	8.61 K	21.46 K	30.07 K	270.64 K	1.70 K	268.95 K	29.02 K
2012	19		4%	4%	0.08	8%	1.08	6.38 K	27.52 K	33.90 K	278.28 K	1.35 K	276.93 K	29.17 K
2013	20		4%	4%	0.08	8%	1.08	8.72 K	25.96 K	34.68 K	285.50 K	1.07 K	284.44 K	29.32 K
2014	21		4%	4%	0.08	8%	1.08	9.36 K	26.83 K	36.19 K	292.47 K	0.85 K	291.63 K	29.47 K

Source: Calculated with data taken from [22].

and

Table 2. The Total Average Cost Minimization Method with Present Value Reduction with constant apparent rate—X1.

Vehicles: X1												C′ [EUR]	C″ [EUR Year n]
Year	Year j	CA [EUR]	ϕ [%]	i [%]	iA	iA [%]	π1 (1 + iA,j)	CM [EUR]	CO [EUR]	∑1 [EUR]	∑2 [EUR]	Meth. Exp.	Meth. Exp.
1993	0	110.66 K	4%	4%	0.08	8%				110.66 K
1994	1		4%	4%	0.08	8%	1.08	0.98 K	11.22 K	11.30 K	11.30 K	22.79 K	34.09 K
1995	2		4%	4%	0.08	8%	1.08	1.02 K	10.71 K	10.68 K	11.08 K	20.44 K	31.12 K
1996	3		4%	4%	0.08	8%	1.08	1.12 K	10.46 K	10.18 K	10.96 K	18.42 K	28.60 K
1997	4		4%	4%	0.08	8%	1.08	1.27 K	10.48 K	9.80 K	10.94 K	16.66 K	26.46 K
1998	5		4%	4%	0.08	8%	1.08	1.49 K	10.76 K	9.51 K	11.02 K	15.14 K	24.65 K
1999	6		4%	4%	0.08	8%	1.08	1.77 K	11.31 K	9.29 K	11.20 K	13.82 K	23.11 K
2000	7		4%	4%	0.08	8%	1.08	2.10 K	12.12 K	9.15 K	11.48 K	12.66 K	21.81 K
2001	8		4%	4%	0.08	8%	1.08	2.50 K	13.19 K	9.07 K	11.86 K	11.65 K	20.71 K
2002	9		4%	4%	0.08	8%	1.08	2.95 K	14.53 K	9.03 K	12.34 K	10.75 K	19.78 K
2003	10		4%	4%	0.08	8%	1.08	3.64 K	15.54 K	9.02 K	12.89 K	9.96 K	18.98 K
2004	11		4%	4%	0.08	8%	1.08	3.91 K	18.46 K	9.07 K	13.60 K	9.26 K	18.33 K
2005	12		4%	4%	0.08	8%	1.08	5.97 K	20.75 K	9.20 K	14.53 K	8.64 K	17.84 K
2006	13		4%	4%	0.08	8%	1.08	5.13 K	22.01 K	9.26 K	15.34 K	8.09 K	17.35 K
2007	14		4%	4%	0.08	8%	1.08	5.40 K	21.73 K	9.26 K	16.04 K	7.59 K	16.85 K
2008	15		4%	4%	0.08	8%	1.08	6.06 K	26.30 K	9.32 K	16.97 K	7.15 K	16.46 K
2009	16		4%	4%	0.08	8%	1.08	7.05 K	17.92 K	9.19 K	17.35 K	6.74 K	15.94 K
2010	17		4%	4%	0.08	8%	1.08	10.06 K	17.99 K	9.10 K	17.86 K	6.38 K	15.48 K
2011	18		4%	4%	0.08	8%	1.08	8.61 K	21.46 K	9.01 K	18.42 K	6.05 K	15.06 K
2012	19		4%	4%	0.08	8%	1.08	6.38 K	27.52 K	8.95 K	19.10 K	5.75 K	14.70 K
2013	20		4%	4%	0.08	8%	1.08	8.72 K	25.96 K	8.87 K	19.75 K	5.48 K	14.35 K
2014	21		4%	4%	0.08	8%	1.08	9.36 K	26.83 K	8.79 K	20.40 K	5.23 K	14.02 K

Source: Calculated with data taken from [22].

and Figure 1 and Figure 2, respectively. The data were taken from [22].

4.1. Replacement Models–the Constant Apparent Rate

4.1.1. Application of the Uniform Annual Income Method (UAI_n)

Table 1 illustrates the case of determining the replacement cycle of a bus whose acquisition, maintenance, and operation values are real values, considering an apparent constant rate of 8% (used by the company). The method used is the Uniform Annual Income.

It can be seen, through Table 1 and Figure 1, that the uniform annual income follows more linear values, that is to say, there is not such a sharp variation in values as when using capital costs and real inflation rates, existing, in this case, as a variation in the apparent rate. This situation leads to the conclusion that it is easier for the decision maker to define the most appropriate moment for replacing the equipment, as there is only one point where the uniform annual income is the minimum, with this point being well defined, leading the decision maker not to hesitate. However, it should be remembered that an apparent constant rate is being accepted, which, in reality, does not happen over the years. Consequently, this can lead to a less realistic decision.

4.1.2. Application of the Total Average Cost Minimization Method with Present Value Reduction

As mentioned above, it was also decided to study and present two examples of determining the economic cycle of replacing buses according to the Total Average Cost Minimization Method with Reduction to Present Value, using the data from the previous example.

Both Table 2 and Figure 2 show that the lowest average cost of ownership of the equipment is not attained, and the period in which it occurs is not clear. This should correspond to the most rational moment of replacement, given that the average cost of ownership continues to decrease and there is no inversion in the trajectory of the cost of ownership.

Table 3. Comparison of the two methods with constant apparent rate—X1.

Vehicles: X1											UAI [EUR Year n]	C″ [EUR Year 0]
Year	Year j	CA [EUR]	ϕ [%]	i [%]	iA	iA [%]	π1 (1 + iA,j)	CM [EUR]	CO [EUR]	∑1 [EUR]	Meth. Exp.	Meth. Exp.
1993	0	110.66 K	4%	4%	0.08	8%				110.66 K
1994	1		4%	4%	0.08	8%	1.08	0.98 K	11.22 K	12.20 K	36.99 K	34.09 K
1995	2		4%	4%	0.08	8%	1.08	1.02 K	10.71 K	11.73 K	35.07 K	31.12 K
1996	3		4%	4%	0.08	8%	1.08	1.12 K	10.46 K	11.58 K	33.45 K	28.60 K
1997	4		4%	4%	0.08	8%	1.08	1.27 K	10.48 K	11.76 K	32.11 K	26.46 K
1998	5		4%	4%	0.08	8%	1.08	1.49 K	10.76 K	12.25 K	31.01 K	24.65 K
1999	6		4%	4%	0.08	8%	1.08	1.77 K	11.31 K	13.07 K	30.14 K	23.11 K
2000	7		4%	4%	0.08	8%	1.08	2.10 K	12.12 K	14.22 K	29.46 K	21.81 K
2001	8		4%	4%	0.08	8%	1.08	2.50 K	13.19 K	15.69 K	28.97 K	20.71 K
2002	9		4%	4%	0.08	8%	1.08	2.95 K	14.53 K	17.48 K	28.63 K	19.78 K
2003	10		4%	4%	0.08	8%	1.08	3.64 K	15.54 K	19.18 K	28.41 K	18.98 K
2004	11		4%	4%	0.08	8%	1.08	3.91 K	18.46 K	22.37 K	28.37 K	18.33 K
2005	12		4%	4%	0.08	8%	1.08	5.97 K	20.75 K	26.72 K	28.52 K	17.84 K
2006	13		4%	4%	0.08	8%	1.08	5.13 K	22.01 K	27.15 K	28.64 K	17.35 K
2007	14		4%	4%	0.08	8%	1.08	5.40 K	21.73 K	27.13 K	28.71 K	16.85 K
2008	15		4%	4%	0.08	8%	1.08	6.06 K	26.30 K	32.37 K	28.95 K	16.46 K
2009	16		4%	4%	0.08	8%	1.08	7.05 K	17.92 K	24.97 K	28.90 K	15.94 K
2010	17		4%	4%	0.08	8%	1.08	10.06 K	17.99 K	28.05 K	28.94 K	15.48 K
2011	18		4%	4%	0.08	8%	1.08	8.61 K	21.46 K	30.07 K	29.02 K	15.06 K
2012	19		4%	4%	0.08	8%	1.08	6.38 K	27.52 K	33.90 K	29.17 K	14.70 K
2013	20		4%	4%	0.08	8%	1.08	8.72 K	25.96 K	34.68 K	29.32 K	14.35 K
2014	21		4%	4%	0.08	8%	1.08	9.36 K	26.83 K	36.19 K	29.47 K	14.02 K

illustrates the comparison of the two methods studied, where we can see that the Uniform Annual Income Method (UAI_n) indicates a replacement time of around 11 years (EUR 28.37 K); when employing the Total Average Cost Minimization Method with Present Value Reduction, we were unable to identify a replacement time.

4.2. The Influence of the Apparent Rate on Replacement Time

This section deals with the influence of the apparent rate in determining the bus replacement economic cycle in order to study its effect throughout its life cycle. As in the previous section, this study was carried out with the same vehicles and the same homogeneous groups previously used in order to facilitate their comparison.

Figure 3 shows the graph of the variation in inflation rates in Portugal over a period of 21 years, which corresponds to the study period for all models used (real data).

Figure 3 illustrates the variation in interest rates in Portugal over a period of 21 years.

Figure 4 illustrates the variation in capitalization rates in Portugal over a period of 21 years.

Finally, the evolution or variation in the apparent rate for the same time interval resulting from the two preceding variables is illustrated (Figure 5).

In

Table 4. The decrease in the apparent rate—Uniform Annual Income (X1).

Vehicles: X1												VC [EUR]	VPL [EUR Year n]	UAI [EUR Year n]
Year	Year j	CA [EUR]	ϕ [%]	i [%]	iA	iA [%]	π1 (1 + iA,j)	CM [EUR]	CO [EUR]	∑1 [EUR]	VP [EUR]	Meth. Exp.	Meth. Exp.	Meth. Exp. <
1993	0	110.66 K	4%	4%	0.08	8%				110.66 K
1994	1		4%	4%	0.08	8%	1.08	1.00 K	10.00 K	11.00 K	120.85 K	87.91 K	32.94 K	35.56 K
1995	2		4%	4%	0.08	8%	1.08	1.05 K	11.00 K	12.05 K	131.25 K	70.11 K	61.14 K	34.16 K
1996	3		4%	4%	0.08	8%	1.08	1.10 K	12.00 K	13.10 K	141.84 K	56.13 K	85.71 K	32.98 K
1997	4		4%	4%	0.07	7%	1.07	1.15 K	13.00 K	14.15 K	152.63 K	45.11 K	107.52 K	31.98 K
1998	5		4%	4%	0.07	7%	1.07	1.20 K	14.00 K	15.20 K	163.52 K	36.39 K	127.13 K	31.11 K
1999	6		3%	3%	0.07	7%	1.07	1.25 K	15.00 K	16.25 K	174.80 K	29.48 K	145.32 K	30.41 K
2000	7		3%	3%	0.07	7%	1.07	1.30 K	16.00 K	17.30 K	186.2 K	23.97 K	162.25 K	29.80 K
2001	8		3%	3%	0.07	7%	1.07	1.35 K	17.00 K	18.35 K	197.90 K	19.56 K	178.33 K	29.29 K
2002	9		3%	3%	0.06	6%	1.06	1.40 K	18.00 K	19.40 K	209.87 K	16.03 K	193.84 K	28.87 K
2003	10		3%	3%	0.06	6%	1.06	1.45 K	19.00 K	20.45 K	222.17 K	13.19 K	208.99 K	28.52 K
2004	11		3%	3%	0.06	6%	1.06	1.50 K	20.00 K	21.50 K	234.85 K	10.89 K	223.96 K	28.23 K
2005	12		3%	3%	0.06	6%	1.06	1.55 K	21.00 K	22.55 K	247.96 K	9.03 K	238.93 K	28.00 K
2006	13		3%	3%	0.05	5%	1.05	1.60 K	22.00 K	23.60 K	261.54 K	7.51 K	254.03 K	27.82 K
2007	14		3%	3%	0.05	5%	1.05	1.65 K	23.00 K	24.65 K	275.67 K	6.28 K	269.39 K	27.68 K
2008	15		3%	3%	0.05	5%	1.05	1.70 K	24.00 K	25.70 K	290.41 K	5.27 K	285.14 K	27.59 K
2009	16		2%	2%	0.05	5%	1.05	1.75 K	25.00 K	26.75 K	305.83 K	4.44 K	301.40 K	27.53 K
2010	17		2%	2%	0.05	5%	1.05	1.80 K	26.00 K	27.80 K	322.03 K	3.75 K	318.28 K	27.50 K
2011	18		2%	2%	0.04	4%	1.04	1.85 K	27.00 K	28.85 K	339.08 K	3.18 K	335.89 K	27.51 K
2012	19		2%	2%	0.04	4%	1.04	1.90 K	28.00 K	29.90 K	357.09 K	2.71 K	354.38 K	27.54 K
2013	20		2%	2%	0.04	4%	1.04	1.95 K	29.00 K	30.95 K	376.18 K	2.32 K	373.86 K	27.61 K
2014	21		2%	2%	0.04	4%	1.04	2.00 K	30.00 K	32.00 K	396.46 K	1.99 K	394.47 K	27.69 K

Source: Calculated with data taken from [22].

and Figure 6, it is possible to verify the influence of the apparent rate in the calculation of the uniform annual income, taking into account the decrease in the apparent rate that occurred during the period from 1993 to 2014.

Table 4 and Figure 6 indicate the replacement to occur at the 17-year point. It can also be seen that the value of the uniform annual rent is EUR 27.50 K.

In

Table 5. The apparent rate increase—Uniform Annual Income (Bus X1).

Vehicles: X1												VC [EUR]		VPL [EUR Year n]	UAI [EUR Year n]
Year	Year j	CA [EUR]	ϕ [%]	i [%]	iA	iA [%]	π1 (1 + iA,j)	CM [EUR]	CO [EUR]	∑1 [EUR]	VP [EUR]	Mét. S. Díg.	Meth. Exp.	Meth. Exp.	Meth. Exp. >
1993	0	110.66 K	4%	4%	0.08	8%				110.66 K
1994	1		4%	4%	0.08	8%	1.08	1.00 K	10.00 K	11.00 K	120.81 K	95.16 K	87.57 K	33.24 K	36.02 K
1995	2		4%	4%	0.09	9%	1.09	1.05 K	11.00 K	12.05 K	131.01 K	81.32 K	69.04 K	61.97 K	35.03 K
1996	3		4%	4%	0.09	9%	1.09	1.10 K	12.00 K	13.10 K	141.13 K	69.03 K	54.22 K	86.91 K	34.20 K
1997	4		4%	4%	0.09	9%	1.09	1.15 K	13.00 K	14.15 K	151.04 K	58.21 K	42.42 K	108.62 K	33.52 K
1998	5		5%	5%	0.09	9%	1.09	1.20 K	14.00 K	15.20 K	160.71 K	48.74 K	33.06 K	127.65 K	32.99 K
1999	6		5%	5%	0.09	9%	1.09	1.25 K	15.00 K	16.25 K	169.82 K	40.52 K	25.66 K	144.16 K	32.53 K
2000	7		5%	5%	0.10	10%	1.10	1.30 K	16.00 K	17.30 K	178.53 K	33.43 K	19.85 K	158.68 K	32.19 K
2001	8		5%	5%	0.10	10%	1.10	1.35 K	17.00 K	18.35 K	186.69 K	27.37 K	15.29 K	171.39 K	31.93 K
2002	9		5%	5%	0.10	10%	1.10	1.40 K	18.00 K	19.40 K	194.25 K	22.22 K	11.74 K	182.51 K	31.74 K
2003	10		5%	5%	0.10	10%	1.10	1.45 K	19.00 K	20.45 K	201.19 K	17.89 K	8.98 K	192.22 K	31.62 K
2004	11		5%	5%	0.10	10%	1.10	1.50 K	20.00 K	21.50 K	207.49 K	14.27 K	6.84 K	200.65 K	31.55 K
2005	12		5%	5%	0.11	11%	1.11	1.55 K	21.00 K	22.55 K	213.13 K	11.27 K	5.19 K	207.94 K	31.53 K
2006	13		5%	5%	0.11	11%	1.11	1.60 K	22.00 K	23.60 K	218.12 K	8.81 K	3.92 K	214.20 K	31.54 K
2007	14		5%	5%	0.11	11%	1.11	1.65 K	23.00 K	24.65 K	222.47 K	6.81 K	2.95 K	219.52 K	31.59 K
2008	15		6%	6%	0.11	11%	1.11	1.70 K	24.00 K	25.70 K	226.20 K	5.21 K	2.22 K	223.98 K	31.67 K
2009	16		6%	6%	0.12	12%	1.12	1.75 K	25.00 K	26.75 K	229.33 K	3.92 K	1.66 K	227.67 K	31.77 K
2010	17		6%	6%	0.12	12%	1.12	1.80 K	26.00 K	27.80 K	231.89 K	2.92 K	1.23 K	230.65 K	31.89 K
2011	18		6%	6%	0.12	12%	1.12	1.85 K	27.00 K	28.85 K	233.92 K	2.13 K	0.92 K	233.00 K	32.02 K
2012	19		6%	6%	0.12	12%	1.12	1.90 K	28.00 K	29.90 K	235.45 K	1.53 K	0.68 K	234.78 K	32.16 K
2013	20		6%	6%	0.12	12%	1.12	1.95 K	29.00 K	30.95 K	236.53 K	1.08 K	0.50 K	236.03 K	32.32 K
2014	21		6%	6%	0.13	13%	1.13	2.00 K	30.00 K	32.00 K	237.20 K	0.75 K	0.37 K	236.83 K	32.48 K

Source: Calculated with data taken from [22].

and Figure 7, it is possible to verify the influence of the apparent rate in the calculation of the UAI, taking into account the increase in the apparent rate over a period of 21 years.

Table 5 and Figure 7 show that the replacement is located at the 12-year point, taking into account the increase in the inflation rate over the years, which consequently increases the apparent rate. It can also be proven that the value of the uniform annual rent is EUR 31.53 K and that the increase in the apparent rate substantially increases the value of the uniform annual rent of a bus.

In turn, Figure 8 shows the considerable influence of the apparent rate on the econometric models of substitution. It can also be seen that the increase or decrease in the apparent rate over the years causes the replacement point to vary. The same figure shows that the replacement point can vary by 5 years; that is to say, the replacement point is 12 years if there is an increase in the apparent rate over the years. If not, if a depreciation of the same rate is considered, then the replacement point is located at 18 years. As already mentioned above, the increase in the uniform annual rent of the bus is also notorious. Accordingly, it can be said that the replacement period varies considerably with the apparent rate, which influences the result and the final decision of the manager. It should also be noted that, usually, taxes are fixed (see, for example [39,41]). In this paper, the authors consider apparent rate variables with the objective of making the model as close to reality as possible.

5. Conclusions

In this paper, we analyze the determinants of the economic management of physical assets in the specific case of an urban passenger transport company in one of the biggest cities in Portugal. Given the difficulty in encountering research that explains the impact of the factors that govern the economic management of physical assets in organizations, it was decided to carry out a qualitative study with a practical case, which involved the analysis of models designed to calculate the replacement year of this type of urban transport asset.

During the initial phase of the research, connection points were built between the models and the methods that they reflect, as well as the determinants that influence the economic management of a company’s physical assets, including urban transport.

Then, it was possible to conclude that the economic management of physical assets is oriented by relevant indicators, including, for example, the costs associated with acquisition, maintenance, and operation. This paper makes a relevant contribution to monitoring the life cycle of equipment, enabling a more efficient and effective management of the physical assets of urban passenger transport companies. Furthermore, by confirming, for the first time, the importance of certain specific factors for the economic management of physical assets in the case of an urban passenger transport company, we make an important contribution to the literature on the subject.

However, it is also important to emphasize that the facts presented in this study are not the only ones that affect the economic management of physical assets. There is a need to carry out future research with the aim of contributing to the promotion of a more accessible and understandable management of physical assets. We must also draw attention to the fact that an evident limitation of this study lies in the fact that we are only dealing with one specific case. Therefore, it is suggested that, in the future, more case studies be carried out on equipment replacement models, identifying possible correlations between certain determinants within the scope of forecast models that are suitable for the management of physical assets, especially for other transport companies. Therefore, we believe that this paper can open up new research avenues in the area of physical asset management.