Life Cycle Cost versus Life Cycle Investment – A new Approach

Abstract

The paper proposes a model for the life cycle of physical assets that includes the maintenance policy, because it has direct implications on the equipment's Return On Investment (ROI) and Life Cycle Cost; the developed model can be applied to any type of physical asset. The model is called Life Cycle Investment (LCI) instead of the traditional Life Cycle Cost (LCC). The paper proposes a new methodology based on the modified economic life cycle and lifespan methods by including the maintenance policy using maintenance Key Performance Indicators (KPI), namely Availability, based on the Mean Time Between Failures (MTBF) and the Mean Time To Repair (MTTR). The benefits (profits) that result from the asset's Availability must be balanced with the initial investment and the variable maintenance investment along its life, which has relation with the maintenance policy and the ROI.

Full text

Life Cycle Cost versus Life Cycle Investment – A new approach
JOSÉ TORRES FARINHA1,2, HUGO NOGUEIRA RAPOSO1,2, DIEGO GALAR3
1CEMMPRE - Centre for Mechanical Engineering, Materials and Processes, Univ. of Coimbra,
PORTUGAL
2ISEC/IPC - Polytechnic Institute of Coimbra, PORTUGAL
3LTU - Luleå University of Technology, SWEDEN
Abstract: - The paper proposes a model for the life cycle of physical assets that includes the maintenance
policy, because it has direct implications on the equipment’s Return On Investment (ROI) and Life Cycle
Cost; the developed model can be applied to any type of physical asset. The model is called Life Cycle
Investment (LCI) instead of the traditional Life Cycle Cost (LCC). The paper proposes a new methodology
based on the modified economic life cycle and lifespan methods by including the maintenance policy using
maintenance Key Performance Indicators (KPI), namely Availability, based on the Mean Time Between
Failures (MTBF) and the Mean Time To Repair (MTTR). The benefits (profits) that result from the asset’s
Availability must be balanced with the initial investment and the variable maintenance investment along
its life, which has relation with the maintenance policy and the ROI.
Key-Words: - Physical Assets; Life Cycle Cost; LCC; Life Cycle Investment; ROI
Received: June 5, 2020. Revised: November 27, 2020. Accepted: December 22, 2020.
Published: December 28, 2020.
1 Introduction
This paper presents a global approach to the life cycle
of physical assets structured in two parts: The first
one analyses the management of assets’ global life
cycle, from acquisition to withdrawal, usually called
Life Cycle Cost (LCC); The second presents a new
approach to assets’ financial life cycle, based on
econometric models, called Life Cycle Investment
(LCI).
With the accelerated growth of the
implementation of ISO5500X standards, as well as
the maintenance norms, the importance of analysing
carefully the asset’s life cycle becomes a very
relevant issue.
About this subject Farinha [9] presents an
integrated approach of physical asset management
emphasizing tools to manage the entire life cycle,
comprising the following times and steps:
t1 - Decision for acquisition;
t2 - Terms of reference;
t3 - Market consultation;
t4 – Acquisition;
t5 – Commissioning;
t6 - Starting production / starting maintenance;
t7 - Economic / lifespan;
t8 - Renewal / withdrawal.
The author also shows the relations between the
life cycle of physical assets, ISO 5500X standards
(55000, 55001, 55002) and some maintenance
standards, for example, NP4492 and others
associated norms [9]. Figure 1 represents Farinha’s
graphical approach to the life cycle of physical assets
including the standards.
Figure 1 – Times of a physical asset life cycle
As Figure 1 shows, to guarantee the
service/production of the physical asset from
acquisition to withdrawal, there is a continuous
negative financial movement. Interestingly, however,
the acquisition financial value is called investment,
but the maintenance financial values along physical
asset life cycle are called costs! Because of this
contradiction, this paper uses the LCI instead of LCC.
In fact, without ongoing investment along an asset’s
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life cycle to support an adequate maintenance policy,
it is not possible to guarantee the availability of the
asset to meet its productive function. The
econometric models used to evaluate the LCI
consider all costs and benefits, from initial
investment to withdrawal, including all the variables
investments (usually called costs) to guarantee their
normal functioning and Availability.
The paper is structured as follows:
 Section 2 synthesizes some relevant
literature on an asset’s life cycle and
maintenance policies;
 Section 3 describes a global vision of a
physical asset’s life cycle and explains the
life cycle cost versus the life cycle
investment;
 Section 4 presents a simulation;
 Section 5 offers the conclusions.
2 State of the Art on Asset’s Life Cycle
and Maintenance Policies
Physical asset management is attracting increasing
attention, especially after the publication of ISO
5500X standards (ISO 55000, ISO 55001, ISO
55002) and PAS 55. According to ISO 55000, the
asset life is the period from “asset creation to asset
end-of-life,” and the life cycle corresponds to “the
stages involved in the management of an asset”.
Woodward [1] says that “the life cycle cost of an item
is the sum of all funds expended in support of the item
from its conception and fabrication through its
operation to the end of its useful life”. To this he adds,
“Life cycle costing is concerned with optimizing
value for money in the ownership of physical assets
by taking into consideration all the cost factors
relating to the asset during its operational life”.
According to Goh & Sun [2], “the history of the
application of Life Cycle Costing (LCC) began in the
UK in the late 1950’s.” The authors conclude that
“major improvements are necessary to make LCC
comparable with common economic evaluation
methods (e.g. benefit-to-cost ratio, net benefits and
savings-to-investment ratio, for capital investment
analysis related to buildings)”. Lindholm & Suomala
[3] state that “Life Cycle Costing (LCC) is a way of
thinking where attention is paid to the total costs that
occur during a product’s entire life cycle”. The
authors say that “an essential feature of LCC is cost
monitoring during a product’s life cycle”. By the
same way, Estevan & Schaefer [4] argue that, “Life
1 http://information.mcgsol.com/calculate-life-cycle-
cost-of-equipment, accessed on 2019.08.02
cycle costing is a powerful technique that supports
the analytical processes by which managers can make
the most cost-effective decisions on options
presented to them at differing life cycle stages and at
different levels of the life cycle cost estimate”.
The United States Department of Energy (USDE)
has a comprehensive life cycle cost definition: “the
sum of all direct, indirect, recurring, nonrecurring,
and other related costs incurred in the planning,
design, development, procurement, production,
operations and maintenance, support,
recapitalization, and final disposition of real property
over its anticipated life span for every aspect of the
program, regardless of funding source.”1.
Schuh, Jussen & Optehostert [5] relate that, in the
life cycle of products, “relevant information which
can be used to assess the subsequent maintenance
costs are requirements for product life cycle, e.g.
service costs according to Total Cost of Ownership
(TCO) as well as serviceability and maintainability of
the product. Furthermore, organizational framework
conditions for the service are defined in the planning
phase.”
Spickova & Myskova [7] say that “The main goal
of the Life Cycle Costing approach is to optimize life
cycle costs of the assets or investment project without
loss their performance”, and the main costs of LCC
are the following: investment (acquisition) costs;
operation costs; maintenance costs; renewal costs;
disposal (retirement) costs.
According to Kianian et al. [6], “Life Cycle
Costing (LCC) was initially used by US Defence
Department to seek optimal costs for acquiring,
owing and operating an equipment during its useful
life (also including any disposal costs)”. The same
authors emphasize that “these cost calculation
methods usually do not include the three performance
parameters (quality, productivity and availability) of
the Overall Equipment Efficiency (OEE) measure, or
lost profit, although Life Cycle Profit (LCP) were
introduced already 1983 in literature”.
Bengtsson & Kurdve [8] present an LCC analysis
of machining equipment in a Swedish company and
discuss the Life Cycle Profit (LCP). The authors state
that a company with a low LCC, does not necessarily
have a high Life Cycle Profit (LCP). LCC is centred
on the costs; however, if the asset’s owner is a
company, the LCC must be analysed simultaneously
with the benefits, i.e., the physical assets’ production
results, suggesting that the asset’s life cycle must be
seen from an investment point of view. The authors
also present theory on LCC and LCP; they add that,
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“there are a number of different options in working
to achieve a high LCP” - “reducing LCC can be one
option; however, sometimes it might be of value to
increase LCC in order to reduce or eliminate losses
that will increase LCP more than the increases in
LCC”.
In his recent book, Farinha [9] presents a global
view of the life cycle of physical assets, including
some tools to manage their entire life cycle,
integrating the ISO 5500X, as well as the relations
between maintenance policies and the LCC.
According to Ljiljana, Dragutin & Zelimir [10],
“Asset Management is a relatively new discipline
that provides methods and tools for effective
management of Physical Assets to maximize their
utilization during entire Life Cycle. Asset
Management evolved from Maintenance
Management to provide a holistic approach to
manage the life of a physical asset. This management
is important for the performance of any organization,
particularly Physical Asset intensive organizations”.
Today, it is recognized that asset governance is a key
point for leading role in the development and
implement asset management in the company and it
is evidence in PAS 55 and the ISO 55000 standards.
Katicic, Lisjak & Dulcic [13] say that physical
asset management evolved from maintenance
management to provide a holistic view for the
management of the life of physical assets. The
authors also mention that physical asset governance
is a key point in the development and implementation
of asset management in the ISO 5500X standards.
Stimie & Vlok [11] propose a mechanism that can
assist Physical Asset Management (PAM)
practitioners and academics with the early detection
and management of PAM Strategy Execution Failure
(PAMSEF). The mechanism, a “Physical Asset
Management Strategy Execution Enforcement
Mechanism” (PAMSEEM), is a double–loop
feedback system consisting of four iterative phases,
four major decisions, and a number of
implementation processes or steps.
The relevance of evaluating the life cycle of
physical assets managed by Eicher [12] in the
following way: “Investing in hospital infrastructure
is not just a financing activity. It is important to
consider the whole life cycle of an asset. For
example, it is necessary to think about the operating
life of an asset before building it, because this can
influence investment costs and follow-up costs
substantially”.
Banyani & Then [14] present a study showing
how physical facilities management can be perceived
at different levels of maturity based on personal
judgement. They note the lack of a tool to assess
maturity levels and propose an Integrated Feeder
Factors Framework (I3F) as a yardstick. In the same
way, Volker, Telli & Ligtvoet [15] mention that an
asset management system for the transportation
sector requires system-level performance measures,
models, and interoperable databases used by asset
groups to make evidence-based decisions.
In the area of passenger urban transport, Hugo et
al. [16], [17] discuss the relations between some
maintenance KPIs, like MTTR, MTBF and
availability, and the dimension of the reserve fleet.
They use the Return On Investment (ROI) as the KPI
to evaluate the relations between maintenance policy
and the economic results.
According to the Center for Transportation
Research and Education (CTRE), transportation
agencies could benefit from the adoption of asset
management principles. CTRE presents a guide to
support transportation organizations in their
implementation of a physical asset management
program. It also presents a guide to the various levels
of the transportation organization’s maturity in
undertaking the activities comprising the asset
management framework. The levels of maturity
presented are as follows [18]:
 Organizational goals and objectives;
 Inventory of pavements, bridges, and other
major infrastructure assets;
 Knowledge of the age, condition, and
deterioration of these assets;
 Availability of information to undertake life
cycle cost analysis for all major asset types
and asset classes;
 Information to undertake risk management
analysis at the enterprise and program level;
 Information to develop the organization’s
financial plan to support investment;
 Development of investment strategies to
manage the network for its whole life.
LCC is a commonly used concept mentioned in
several standards, like the ISO 15663-1, Petroleum
and natural gas industries — Life cycle costing - Part
1: Methodology. The work of Pais et al. [19] is in line
with [9], as they include a diagnostic model on the
state of organizations to help the implementation of
ISO 55001.
Farinha [20] presents some econometric models
to evaluate the LCC, including the withdrawal time
for medical equipment.
Raposo et al. [21], [22] and [23] discuss the
application of econometric models to LCC in an
urban bus fleet based on maintenance costs, as well
as their importance in a good management policy.
The models include the influence of internal rate of
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return, as well as the price of fuel to the withdrawal
time. These authors also discuss the influence of
maintenance policy, namely the condition
monitoring, in the LCC and the dimension of the fleet
reserve.
Asiedu & Gu [24] present an interesting life cycle
cost analysis approach related to Life Cycle
Assessment (LCA). The authors say LCA
corresponds to a framework for the study of the
impact of products and processes on the environment,
and LCA is an environmental and energy audit that
focuses on the entire life cycle of a product from raw
material acquisition to withdrawal, including the
environmental emission.
Durairaj, Nee & Tan [25] review some
methodological approaches; they outline a
framework for a tool to evaluate eco-costs and
present a cost effective eco-design for any product, in
the ambit of a circular economy.
Kloepffer [26] emphasizes a model
corresponding to a life cycle sustainability
assessment (LCSA), that is the sum of the Life Cycle
Assessment (LCA), plus the Life Cycle Cost (LCC),
plus the Social Life Cycle Assessment (SLCA).
Sarma & Adeli [27] emphasizes the relevance of
LCC evaluation in all areas where physical assets are
key. In the same way, Frangopol & Liu [28] present
a paper on maintenance and the management of civil
infrastructure based on condition monitoring,
including LCC. They note that most existing
maintenance systems are based on the LCC
minimization, and they may not correspond to long-
term structural performance.
Toniolo [29] presents some dimensions of
sustainability addressed in international standards
using a life cycle perspective. The objective of the
standards is to support LCA professionals in
identifying for each specific situation the standards
that ought to be used and the methods required to
support the life cycle concepts beyond the
environmental aspects.
Favi, Campi and Germani [30] offer a
comparative life cycle assessment of metal arc
welding technologies using engineering design
documentation. They do not evaluate the
maintenance area but they refer to it as an important
variable.
Hugo et al. [16] and [17] demonstrate how a
condition monitoring maintenance policy based on
oil analysis influence the availability of urban buses.
Moubray [31] describes the importance of
condition monitoring techniques and tools to increase
the availability and the extending an asset’s life
cycle.
Rao [32] presents some important condition
monitoring techniques and tools, including an
analysis of cost-effective benefits.
Davies [33], in his book describes some
techniques and tools for condition monitoring. The
book emphasizes the economic justification and
benefits of condition monitoring. It also discusses the
variable investment in condition monitoring along
the asset’s life.
Nilsson & Bertling [34] present two case studies
of life cycle cost analysis for wind power systems
using condition monitoring. The authors demonstrate
that using condition monitoring results in improved
maintenance planning; investing in these types of
maintenance leads to increased availability and
increased electricity production.
Fonseca, Farinha, and Barbosa [35] present a
methodology, based on ant algorithm, demonstrating
that in the maintenance management of any asset,
both the policy and the maintenance logistics are keys
to maximize the investment in the asset’s life cycle.
Shina & Jun [36] propose a general approach to a
condition monitoring-based maintenance policy
addressing several aspects of condition-based
maintenance: definitions, related international
standards, procedures, and techniques.
Wang [37] suggests a prognosis model for wear
prediction based on oil monitoring; the author reports
the development of a wear prediction model based on
stochastic filtering and hidden Markov theory.
Simões et al. [38] present a state of the art hidden
Markov model for predictive maintenance of Diesel
engines, demonstrating the importance of investment
in a maintenance policy based on oil analysis to
maximize buses’ availability, to maximize the
number of passengers transported, and minimize the
reserve fleet.
Yam et al. [39] propose an intelligent predictive
decision support system for Condition-Based
Maintenance (CBM). The authors develop an
intelligent predictive decision support system for
CBM, adding the capability of intelligent condition-
based fault diagnosis and the capacity to predict the
trend of equipment deterioration. The approach was
used as input to an integrated maintenance
management system to pre-plan and pre-schedule
maintenance work, to reduce inventory costs for
spare parts, to cut down unplanned forced outage, and
to minimize the risk of catastrophic failure. The
success of the approach demonstrates the importance
of investing in the right maintenance policy to
maximize the equipment’s life cycle.
Lebold et al. [40] review vibration analysis
methods for gearbox diagnostics and prognostics. In
fact, almost all equipment has vibrations; so,
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vibration analysis is one of the most important
techniques to maximize the life cycle of assets.
Aherwar & Khalid [41] review vibration analysis
technique for gearbox diagnosis. Vibration signal
analysis is widely used in the detection of faults in
rotating machinery. The authors relate the
importance of the maintenance policy to the
equipment’s life cycle.
Tchomeni & Alugongo [42] present an
experimental diagnosis of multiple faults on a rotor-
stator system using Fast Fourier Transform and
wavelet scalogram, researching multiple fault
detection for a rotating shaft using a time-frequency
method; this approach permits to maximize the life
cycle of this type of equipment.
LCC can be seen from the perspective of the
consumer or investor. For the first, it signifies a cost;
for the second, it represents an initial investment and
a variable investment along the equipment’s life
cycle. For the first, it follows the asset’s use and the
maintenance policy recommended by the
manufacturer; for the second, it tries to maximize the
production capacity of the asset by investing in
maintenance policies (i.e., condition monitoring,
predictive maintenance, among others) that permit
the investment to be maximized.
If “the life cycle cost of an item is the sum of all
funds expended in support of the item from its
conception and fabrication through its operation to
the end of its useful life” [1], then, determining the
LCC is an impossible exercise for the end user,
because the person who purchases the equipment
only knows the selling value and monetary values
ahead.
The production income and the investment in
maintenance must have the objective of maximizing
availability, but the traditional LCC concept does not
use these last two variables, as seen in [1]. The main
variable companies can manage to improve
equipment profitability is maintenance. The right
maintenance strategy will increase the asset’s
availability and, consequently, its profitability.
Other relevant approach can be found in [43].
3 Physical Assets’ Life Cycle Analysis
3.1 Life Cycle Cost
There are several ways to evaluate the LCC; two of
these are the lifespan and the economic life cycle.
3.1.1 Lifespan
The lifespan ends when the maintenance costs
overpass the maintenance costs plus the capital
amortization of a new equivalent asset [9]. To
calculate the lifespan, it is necessary to collect the
historical cost data of the asset, as shown in Table 1
and Figure 2. In this theoretical example, the
equipment reaches the end of its useful life after six
years. Usually, the lifespan is longer than the
economic life cycle.
To analyse the lifespan, the following variables
should be considered:
 Initial investment - acquisition value;
 Exploration – functioning and maintenance;
 Cessation value.
Table 1 - Determining the lifespan of a physical asset
Figure 2 - Graph for analysis of lifespan
3.1.2 Economic Life Cycle
The end of economic life is the most rational time to
withdraw an asset, minimizing the average total cost
of operation, maintenance and capital
immobilization. The economic life cycle method
usually requires the conversion of all the financial
movements of the physical asset to reach the present
value, expressed by the Formula (1):



 (1)
where PV is the present value,
Ft is the financial movement, and
IRR is the internal rate of return.
The following variables are considered in the
analysis of the life cycle of a physical asset:
 Initial Investment (acquisition value) - II
 Functioning Present Value – FPV
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 Maintenance Present Value – MPV
 Benefit Present Value - BPV
In the traditional approach of the economic life cycle,
under the concept of LCC, the benefits are considered
null, as shown in Table 2.
The final global result (GRn) in year n (BPVn-ATCn)
can be represented by Formula (2):



 


 


 (2)
where Bj is the value of benefit in year j,
Fj is the value of functioning in year j, and
Mj is the value of maintenance in year j.
Table 2 and Figures 3 and 4 show the simulation of
an initial investment with variable costs of
functioning and maintenance over 20 years. The
interest rate considered is 25%. The variables
mentioned in the table, corresponding to the
preceding considerations, are the following:
 Time
 Initial Investment - II
 Functioning Present Value - FPV
 Maintenance Present Value - MPV
 Accumulated Total Costs -
(ATC=FPV+MPV)
 Benefit Present Value - BPV
 Accumulated Total Benefits - ATB
Table 2 – Values of investment and functioning
As can be seen, the final result of this approach has a
negative financial movement, because it is based only
on the costs.
About this subject, the references [9], [16] and [17]
are very relevant.
Figure 3 – Investment, functioning and maintenance
Figure 4 – Investment, functioning and maintenance
3.2 Life Cycle Investment
Investment and costs generally mean different things:
the initial cost of a physical asset is called investment,
but the remaining values along its life are usually
called costs. It is important to clarify these concepts
and to name the initial cost the initial investment and
to name the remaining values along time as variable
investments. This, in turn, suggests the need to
change the acronym LCC to LCI (Life Cycle
Investment) if the asset is used for industrial
production.
Some maintenance KPI must be considered in
industrial production companies, because the
expected productivity of the equipment depends on
them, namely the Availability.
The profits (benefits) are directly related with
Availability: The benefits must be calculated
considering that the equipment need downtime for
maintenance, and the downtime duration is directly
related to the maintenance policy, measured through
the Mean Time To Repair (MTTR) - the lower MTTR
the maximum Availability.
The non-productive time necessary to perform
maintenance, both planned and non-planned,
depends on the maintenance policy, including the
following options:
 Planned maintenance
o Scheduled
o Condition monitoring
 Predictive
 Non-planned maintenance
The variable that usually measures the
maintenance downtime is the Time To Repair (TTR),
generally evaluated by its mean, i.e., the MTTR. The
time of good functioning is usually called the Time
Between Failures (TBF), usually evaluated by its
mean, i.e., the Mean Time Between Failures
(MTBF). Based on these two KPI, the Availability
can be calculated using Formula (3):
Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Initial Investment (II) -1200
Functioning -200 -200.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00
Present Value (FPV) -160.00 -160.00 -128.00 -102.40 -81.92 -65.54 -52.43 -41.94 -33.55 -26.84 -21.47 -17.18 -13.74 -11.00 -8.80 -7.04 -5.63 -4.50 -3.60 -2.88
Accumulated FPV -1360.00 -1520.00 -1648.00 -1750.40 -1832.32 -1897.86 -1950.28 -1992.23 -2025.78 -2052.63 -2074.10 -2091.28 -2105.02 -2116.02 -2124.82 -2131.85 -2137.48 -2141.99 -2145.59 -2148.47
Maintenance -500 -500.00 -550.00 -605.00 -665.50 -732.05 -805.26 -885.78 -974.36 -1071.79 -1178.97 -1296.87 -1426.56 -1569.21 -1726.14 -1898.75 -2088.62 -2297.49 -2527.24 -2779.96 -3057.95
Present Value (MPV) -400.00 -352.00 -309.76 -272.59 -239.88 -211.09 -185.76 -163.47 -143.85 -126.59 -111.40 -98.03 -86.27 -75.92 -66.81 -58.79 -51.73 -45.53 -40.06 -35.26
Accumulated MPV -400.00 -752.00 -1061.76 -1334.35 -1574.23 -1785.32 -1971.08 -2134.55 -2278.41 -2405.00 -2516.40 -2614.43 -2700.70 -2776.61 -2843.42 -2902.21 -2953.94 -2999.47 -3039.53 -3074.79
Accumulated Total Costs (ATC=FPV+MPV) -1760.00 -2272.00 -2709.76 -3084.75 -3406.55 -3683.18 -3921.37 -4126.78 -4304.19 -4457.62 -4590.50 -4705.71 -4805.72 -4892.63 -4968.24 -5034.06 -5091.43 -5141.46 -5185.12 -5223.26
Benefit 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Present Value (BPV) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Accumulated Total Benefits (ATB) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
ATB+ATC -1760.00 -2272.00 -2709.76 -3084.75 -3406.55 -3683.18 -3921.37 -4126.78 -4304.19 -4457.62 -4590.50 -4705.71 -4805.72 -4892.63 -4968.24 -5034.06 -5091.43 -5141.46 -5185.12 -5223.26
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Volume 15, 2020

 
 (3)
However, when there is a fault, there may be a
time interval between the fault communication and
the technician intervention. This time is usually
called Waiting Time (WT), generally evaluated by its
mean, i.e., Mean Waiting Time (MWT). If this
variable is considered in Formula (3), the new
Availability evaluation, at time j, is done by Formula
(4):

 (4)
Under this perspective, the Formula (2) can be
upgraded to include Availability, that is multiplied by
the total benefits (Bj), because the useful time for
production only happens when the physical asset has
Availability. The Formula (5) includes this new
variable:



 


 



 


 


 (5)
where Bj is the value of benefit in year j
Aj is the availability in year j
Fj is the value of functioning in year j
Mj is the value of maintenance in year j
Nj is the value of non-production in year j
and
Ij is the value of the physical asset in year j
If the variable Aj from Formula (4) is inserted into
Formula (5), this results in Formula (6):




 



 


 


 



 (6)
In addition, if we consider the values of non-
production related to the unavailability of the
physical asset, the variable Nj may be evaluated using
the Formula (7):
 
 (7)
By substituting the variable Nj of Formula (7) into
Formula (6), we get:




 


 



  



 



 (8)
Formula (8) includes the initial investment and the
variable maintenance annual investments along the
asset’s life, giving the global result that a company
may expect from the asset’s life cycle from an
investment perspective.
4 Case Study Simulation
This section uses the developed models to
demonstrate the importance of availability (based on
the maintenance policy) in the LCI of a physical
asset.
The next simulation considers an investment in a
maintenance policy from which it is expected a
positive return.
However, instead of this simulation, it can be done
any type of simulation, where the Global Result can
be any other: the model presented in the preceding
section is general, being possible to use it to support
any decision about the best combination between
physical asset Availability and investment,
considering the maintenance policy to reach the
desired Availability.
Table 3 and Figures 5 and 6 consider the
following values:
 Internal rate of return: 0.25
 Availability: 0.82
The variables mentioned in the table,
corresponding to the preceding considerations, are as
follows:
 Time
 Initial investment present value (IIPV)
 Functioning present value (FPV)
 Maintenance present value (MPV)
 Non-production present value (NPPV)
 Benefit present value (BPV)
Based on these values and using Equation (5), a
positive cycle of results can be observed from the 4th
year to the 16th year.
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2020.15.75
José Torres Farinha,
Hugo Nogueira Raposo, Diego Galar
E-ISSN: 2224-2856
749
Volume 15, 2020

Table 3 – Values of investment, functioning and benefits,
with A=0.82
Figure 5 – Values of investment, functioning and benefits,
according to Table 3
Figure 6 – Annual financial results of physical asset
investment, according to Table 3
Table 4 and Figures 7 and 8 consider the same
values as Table 3, but with a higher value for
availability: 0.89. Based on these values, a higher
positive cycle of results can be observed from the 4th
year to the 20th year – an increase of four years.
Table 4 – Values of investment, several costs, and
benefits, with A=0.89
Figure 7 – Annual financial results of physical asset
investment, according to Table 4
Figure 8 – Annual financial results of physical asset
investment, according to Table 4
As can be seen, maintaining all the other values
and conditions of Table 3, i.e., values of acquisition,
functioning, maintenance, and benefits, and with
little increase in availability, i.e., from 0.82 to 0.89,
the profits (benefits) of the physical asset
immediately increase by four years. This
demonstrates the importance of investment in a good
maintenance policy and the need to consider the
concept of LCI instead of LCC.
5 Conclusions
Physical assets are very important investments, that
must be carefully analysed, in order to evaluate
which is the best maintenance policy for them, to
reach the best Availability, as well as the best time to
withdrawal. The paper presents an econometric
model to make this evaluation, as well as a simulation
with two situations of Availability.
As result it is proposed to change the traditional
Life Cycle Cost (LCC) analysis concept to the Life
Cycle Investment (LCI) analysis. The objective is to
emphasize the importance of KPI related to the
Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Initial Investment (II) -1200
II Present Value (IIPV) - Return -1200 -960.00 -768.00 -614.40 -491.52 -393.22 -314.57 -251.66 -201.33 -161.06 -128.85 -103.08 - 82.46 -65.97 - 52.78 -42.22 - 33.78 -27.02 - 21.62 -17.29 - 13.84
Functioning (F) -150 -150.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00
Present Value (FPV) -120.00 -160.00 -128.00 -102.40 -81.92 -65.54 -52.43 -41.94 -33.55 -26.84 -21.47 -17.18 -13.74 -11.00 -8.80 -7.04 -5.63 -4.50 -3.60 -2.88
Accumulated FPV -1320.00 -1480.00 -1608.00 -1710.40 -1792.32 -1857.86 -1910.28 -1952.23 -1985.78 -2012.63 -2034.10 -2051.28 -2065.02 -2076.02 -2084.82 -2091.85 -2097.48 -2101.99 -2105.59 -2108.47
Maintenance (M) -250 -250.00 -300.00 -360.00 -432.00 -518.40 -622.08 -746.50 -895.80 -1074.95 -1289.95 -1547.93 -1857.52 -2229.03 -2674.83 -3209.80 -3851.76 -4622.11 -5546.53 -6655.83 -7987.00
Present Value (MPV) -200.00 -192.00 -184.32 -176.95 -169.87 -163.07 -156.55 -150.29 -144.28 -138.51 -132.97 -127.65 -122.54 -117.64 -112.93 -108.42 -104.08 -99.92 - 95.92 -92.08
Accumulated MPV -200.00 - 392.00 -576.32 - 753.27 -923.14 -1086.21 -1242.76 -1393.05 -1537.33 -1675.84 -1808.80 -1936.45 -2058.99 -2176.63 -2289.57 -2397.99 -2502.07 -2601.98 -2697.90 -2789.99
Non Production (NP) -250 -250.00 -300.00 -360.00 -432.00 -518.40 -622.08 -746.50 -895.80 -1074.95 -1289.95 -1547.93 -1857.52 -2229.03 -2674.83 -3209.80 -3851.76 -4622.11 -5546.53 -6655.83 -7987.00
Present Value (NPPV) -200.00 -192.00 -184.32 -176.95 -169.87 -163.07 -156.55 -150.29 -144.28 -138.51 -132.97 -127.65 -122.54 -117.64 -112.93 -108.42 -104.08 -99.92 - 95.92 -92.08
Accumulated NPPV -200.00 -392.00 -576.32 -753.27 -923.14 -1086.21 -1242.76 -1393.05 -1537.33 -1675.84 -1808.80 -1936.45 -2058.99 -2176.63 -2289.57 -2397.99 -2502.07 -2601.98 -2697.90 -2789.99
Accumulated Total Costs - 1720.00 -2264.00 -2760.64 -3216.93 -3638.59 -4030.28 -4395.81 -4738.33 -5060.44 -5364.30 -5651.71 -5924.18 -6183.01 -6429.29 -6663.95 -6887.82 -7101.61 -7305.95 -7501.40 -7688.45
Benefit (B) 2500 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18 2049.18
Present Value (BPV) 1639.34 1311.48 1049.18 839.34 671.48 537.18 429.74 343.80 275.04 220.03 176.02 140.82 112.65 90.12 72.10 57.68 46.14 36.91 29.53 23.63
Accumulated Benefits BPV 1639.34 2950.82 4000.00 4839.34 5510.82 6048.00 6477.74 6821.54 7096.58 7316.61 7492.63 7633.45 7746.10 7836.23 7908.32 7966.00 8012.15 8049.06 8078.59 8102.22
BPV+FPV+MPV+NPPV+IIPV -1280.66 -513.18 39.36 422.41 672.23 817.72 881.93 883.21 836.13 752.31 640.92 509.26 363.09 206.94 44.37 - 121.82 -289.47 - 456.89 -622.80 -786.23
Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Initial Investment (II) -1200
II Present Value (IIPV) - Return -1200 -960.00 -768.00 -614.40 -491.52 -393.22 -314.57 -251.66 -201.33 -161.06 -128.85 -103.08 -82.46 -65.97 -52.78 - 42.22 -33.78 - 27.02 -21.62 - 17.29 -13.84
Functioning (F) -150 -150.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00 -250.00
Present Value (FPV) -120.00 -160.00 -128.00 -102.40 -81.92 -65.54 -52.43 -41.94 -33.55 -26.84 -21.47 -17.18 -13.74 -11.00 -8.80 -7.04 -5.63 -4.50 -3.60 -2.88
Accumulated FPV -1320.00 -1480.00 -1608.00 -1710.40 -1792.32 -1857.86 -1910.28 -1952.23 -1985.78 -2012.63 -2034.10 -2051.28 -2065.02 -2076.02 -2084.82 -2091.85 -2097.48 -2101.99 -2105.59 -2108.47
Maintenance (M) -250 -250.00 -300.00 -360.00 - 432.00 - 518.40 -622.08 - 746.50 - 895.80 -1074.95 -1289.95 -1547.93 -1857.52 -2229.03 -2674.83 -3209.80 -3851.76 -4622.11 -5546.53 -6655.83 -7987.00
Present Value (MPV) -200.00 -192.00 -184.32 -176.95 -169.87 -163.07 -156.55 -150.29 -144.28 -138.51 -132.97 -127.65 -122.54 -117.64 -112.93 -108.42 -104.08 -99.92 -95.92 -92.08
Accumulated MPV -200.00 - 392.00 - 576.32 -753.27 - 923.14 -1086.21 -1242.76 -1393.05 -1537.33 -1675.84 -1808.80 -1936.45 -2058.99 -2176.63 -2289.57 -2397.99 -2502.07 -2601.98 -2697.90 -2789.99
Non Production (NP) -250 -250.00 -300.00 -360.00 -432.00 -518.40 -622.08 -746.50 -895.80 -1074.95 -1289.95 -1547.93 -1857.52 -2229.03 -2674.83 -3209.80 -3851.76 -4622.11 -5546.53 -6655.83 -7987.00
Present Value (NPPV) -200.00 -192.00 -184.32 -176.95 -169.87 -163.07 -156.55 -150.29 -144.28 -138.51 -132.97 -127.65 -122.54 -117.64 -112.93 -108.42 -104.08 -99.92 -95.92 - 92.08
Accumulated NPPV - 200.00 - 392.00 -576.32 - 753.27 - 923.14 -1086.21 -1242.76 -1393.05 -1537.33 -1675.84 -1808.80 -1936.45 -2058.99 -2176.63 -2289.57 -2397.99 -2502.07 -2601.98 -2697.90 -2789.99
Accumulated Total Costs - 1720.00 -2264.00 -2760.64 -3216.93 -3638.59 -4030.28 -4395.81 -4738.33 -5060.44 -5364.30 -5651.71 -5924.18 -6183.01 -6429.29 -6663.95 -6887.82 -7101.61 -7305.95 -7501.40 -7688.45
Benefit (B) 2500 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14 2232.14
Present Value (BPV) 1785.71 1428.57 1142.86 914.29 731.43 585.14 468.11 374.49 299.59 239.67 191.74 153.39 122.71 98.17 78.54 62.83 50.26 40.21 32.17 25.73
Accumulated Benefits BPV 1785.71 3214.29 4357.14 5271.43 6002.86 6588.00 7056.11 7430.61 7730.20 7969.87 8161.61 8315.00 8437.72 8535.89 8614.43 8677.25 8727.52 8767.73 8799.90 8825.63
BPV+FPV+MPV+NPPV+IIPV -1134.29 -249.71 396.50 854.49 1164.26 1357.72 1460.30 1492.27 1469.76 1405.57 1309.91 1190.82 1054.71 906.60 750.47 589.43 425.90 261.78 98.50 - 62.81
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2020.15.75
José Torres Farinha,
Hugo Nogueira Raposo, Diego Galar
E-ISSN: 2224-2856
750
Volume 15, 2020

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their Availability and, by consequence, their profits.
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DOI: 10.37394/23203.2020.15.75
José Torres Farinha,
Hugo Nogueira Raposo, Diego Galar
E-ISSN: 2224-2856
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Volume 15, 2020

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