22. Criterion functions for optimization of vessel’s characteristics for commercial order, other asset or the property complex of the marine company, based on application of the economic criteria and value

The financial investment in the real assets of the marine companies from the economic point of view is innovative activity, and the economic model of the evaluation and the economic efficiency estimation among comparable variants of innovative strategy is the basis of the investments planning.
           The investments planning for the marine industrial activity includes the optimum choice of characteristics of the marine company’s real assets by the economic criteria and appropriate ones with view of financial or other limitations for optimum investment, in particular the determination of the optimum vessel characteristics by economic criteria for the contract commercial order.
           The examples of the choice of the commercial vessel characteristics in the property complex the shipping company for the commercial order with the aim of replenishment and renovation of the commercial fleet are considered earlier (Chapter 19). The necessity to adhere to the systematic approach and concepts of comparability of evaluated variants of the vessel, that is very important in marine industrial activity, is explained, considering, that characteristics of the marine company assets are functionally interconnected substantially.

22.1. Systematic approach in elaboration of the criterion functions for optimization of a commercial vessel or property complex of the marine company characteristics

It should be noted, that the property complex of the marine company functionally is a single whole, its elements are in many respects interconnected technologically and structurally, as well as the developed ocean resources.
           When the investments are estimated in compliance with the systematic approach concepts the functional integrity is among the methodological features of the marine company’s property complex in comparison with the investments estimation in other branches.
           Object of the project optimization by economic criterion is the real asset (for example, a commercial vessel) which can be evaluated as the isolated property complex or the working company. And applicability of the project optimization methods by the economic criterion depends on how accurately the properties of optimized object can be correlated with the properties of the isolated property complex of working marine company. To put it otherwise it matters what properties of the optimized object are more important: economic, functional or technological.
           Optimization of the project characteristics by economic criterion is the most effective approach for complex industrial objects for which, owing to the variety of properties – physical, technological and functional one property cannot be a generalized criterion, and the quantity of properties is transformed to economic quality which is a criterion.
           The economic criteria serve as index of efficiency and are determined by mathematical operations on the basic economical indexes: the annual income I, operation costs C, investments – market value MV or other value – with one definition or another, for example the value of a new asset of the marine company, the costs for manufacture of a real asset in market prices – reproduction cost RC.
           Unlike the annual income I and operation costs C which characterize distributed in time t economic flows of incomes, and expenses, and in economy are determined and summarized usually per a year, investments MV or RC have one–time or discrete character in time or can be transformed to an estimation of the present value index.
           The basic economical indexes and value (I, C, MV or RC) in them–selves do not reflect critical judgments, suitable for the choice of optimum decisions at a stage of designing, and are not criteria of a choice in optimization, but they serve to formulate the criteria which mathematically are determined by correlation of the basic indexes.
           It is impossible to determine, for example, if it is required or not to choose optimal characteristics of the marine company real asset by the criterion of minimization of the operation costs C taken separately from the indexes of: incomes I and investments MV or RC. With varied optimized characteristics it is required to analyze joint change of the basic economical indexes of the marine company asset.
           Mathematical operations on the basic indexes in formalizing of the criterion functions reflect critical judgments which are necessary to provide the compromise of advantages and disadvantages when optimizing project characteristics of the marine company’s property complex asset.
           The correlation between the applied economics and mathematics goes deep with the complexity of expert tasks. For wide consumption the estimation of serial objects can be carried out by the expert methods under the simplified adapted instructions.
           The applied economics and some sections of mathematics, such as theory of numbers and sequences, theory of the differential equations, probability theory etc., practically merge in case of estimation of complex objects which include: the functional property complexes of the industrial enterprises with the account the system analysis in time and prospects forecasting; the investment projects, including evaluation of strategy and intangible asset which estimation requires preliminary working out of corresponding economic model of the separate assets, durable and proportional to the enterprise as a whole, for example, marine commercial vessels or batches of vessels for the commercial order, where investments into their manufacture are elements of innovative strategy, etc.
           In process of globalization in the industry the convergence of mathematical and economic bases in an expert estimation will proceed.
           Formation of global economy should be correlated with the development of the technological pattern of the world, considering, that the core of the pattern is digital technologies. According to the given criterion the formation of the global economy will come by the end by the moment of change of the pattern, that is, when possibilities of the core development will be exhausted, and the basic direction of development will be changed.
           As digital technologies are aimed at the artificial intelligence modeling, probably the resource of the development directions will be exhausted and it is necessary to expect the change of the technological way when the intelligence will be technically sufficiently reproduced.
           By this time it will be possible to consider the formation of global economy finished which will be carried out through a digital model of public intelligence. And, possibly, this process will not take a long time, as dynamical processes of formation change can be observed.
           The greatest convergence of economy with mathematics will be implemented, when the control of digital processes in networks allows raising globally integration, and economic interaction will be carried out not pair wise, but integrally, that is, each enterprise will cooperate with all global set. The economy thus will become a mathematical model of global strategy, and monetary concepts will be displaced to consumption sphere.
           In modern market conditions, typical for the developed states and prior to globalization, investors are separated. At the same time in investment activity it is required to use criteria which are mathematical transformations on the basic economical indexes and allow operating investments with global orientation which is in the fact that that the general concept of efficiency and optimality for all investors are introduced by mathematical transformations on the basic indexes.
           Criteria of the optimality, allowing to separate the optimal project characteristics (or the range of the optimum solutions) from not optimum, are a way to use the economic criteria of efficiency which allow to arrange all compared project options in order of preference, that is, in other words the criterion of economic efficiency is a more general economic concept than the criterion of optimality, since it is not required to narrative all options by preference if there is a need to separate only optimum options. The criterion of optimality is a way to use of efficiency criterion.
           On the other hand, if to arrange the options by the criterion, then, in case of a limited quantity of options or in case of a limited range of definition of variables the optimum variants will be found as well.
           The criterion in the form of a criterion function f is defined depending on varied unknown characteristics of the marine company asset: variables X (that is a vector or a set of variables), parameters Y and data Z (constants).
           The set of variants of the resulted project characteristics investigated for the optimality, means a set of values of variables X (namely, values of vector), and each option is characterized by a certain value of this vector.
           The set of variables X is defined as a part of those independent values (that is, independent on each other, on parameters and constants) which substantially influence the criterion of the marine company’s property complex asset optimality.
           For example, to optimize economically the commercial vessel project characteristics, a certain value of the vector of variables X corresponds to each option among the compared, and the structure of the vector can include vessel characteristics varied by optimization (in particular, the displacement of commercial vessel, the deadweight, the load–carrying capacity, the tonnage and the power of main engine or the velocity).
           Working out of criterion function is inseparably linked and also is accompanied by classification of mathematical values in sets: variables X, parameters Y and data Z.
           While working out the criterion function f it is supposed, that the metrics is defined, for example, in the form of algorithm according to the influence of an independent values (X, Y or Z) on the criterion, and it is taken into account, that the structure of the criterion function which is based on classification of entering values, is developed by successive approximations. The estimation of influence of any entering value on the economic criterion can be made at each step, and working out of criterion function structure comes to end concurrently with performance of optimizing subject and, as a matter of fact, it is solution of this task.
           The set of parameters Y is introduced as a part of those independent values, where each of them separately does not influence substantially by the specified metrics on the optimality criterion in the form of criterion function f.
           For example, the unlimited quantity of economically insignificant for optimization of a commercial vessel design characteristics can be included into set of parameters, except those which are concern to variables X.
           For practical purposes the parameters can be taken structurally, let us assume, according to a technological prototype and can be considered invariable when making project optimization of variables by the economic criterion.
           According to system–based principles of project optimization by economic criteria the real asset as part of the marine company’s property complex methodologically should be defined as a single whole consisting of the parts. And when connecting the parts in the whole the dialectic principle of «quantity transition into quality» is carried out and the object as a single whole acquires new properties which were absent in parts. For example, if at stage of choice for the commercial order the cargo vessel optimized by economic criterion to consider as a set of two parts – a hull characterized by cargo capacity and a main engine (more exactly, a propulsive complex – a vessel’s «running gear») characterized by power, then, when connecting these two parts there appears a new property of the cargo vessel, in particular, carrying capacity which was absent in separate parts.
           It is an additional property arising in process of connection of parts of the real asset or the marine company’s property complex in a single whole that is a subject of the project optimization by economic criterion, instead of a set of the properties which are in the parts of the asset taken separately.
           It should be added, that determination of a complete object as a complex of parts in case of project optimization by economic criterion has a methodological rather the mechanical sense.
           Continuing an example concerning cargo vessel, the parts in methodological sense it should be defined more exactly as not a hull and an engine (and so on, with the account inexhaustibility of division), and not separate parts of the hull – a fore, an aft, sides, decks, bottom, bulkheads, details etc., but in each case as all the vessel as a whole, considered from the point of view of one part of methodology or another, that is, from the point of view of separate seaworthy properties and operational characteristics.
           In particular, with due account of design methodology the following characteristics can be considered as parts of commercial vessel: buoyancy, that is a commercial vessel as a whole from the point of view of useful physical property of buoyancy (seaworthy property), stability – all vessel from the point of view of physical property of stability, and further: unsinkability, controllability, marine propulsion, life time, manufacturability, etc.
           In other words, with due consideration of the systematic approach for the project optimization by economic criterion, the separate functional or technological properties referred for the asset as a whole should be considered as parts of real asset or marine company’s property complex.
           Since the optimized object is defined as a single whole of parts and its divisibility into parts is inexhaustible, there is a concept of a more general object, part of which is optimized object, and also there is a concept of inexhaustibility of induction, that is, methodological generalizations of optimized objects, by analogy to inexhaustibility of deduction – methodological divisions of objects into parts.
           For example, the shipping, the shipbuilding industry, the marine engineering, the marine industrial fishery etc. would be a more general object in project optimization by economic criterion, than a commercial vessel, in methodological sense.
           It should be noted, that representation of the marine company real asset optimized by economic criterion, as a whole of parts for dialectic definition of the objects properties absent in separate parts and appeared when connecting the parts, leads to definition of hierarchy of the economic models used for project optimization.
           Except the economic model of optimized object there supposed to be the models with more general objects, that is, the models of «top levels», as well as economic models of separate parts of  the optimized object, more exactly – the separate properties referred to an object as a whole, – the models of the «bottom levels». And as a result of the decision of more general, so–called external subjects of optimization of «top levels» are defined the data set Z (constants) which in subjects of «top levels» were optimized variables X are defined.
           It allows us to formulate the concept of options comparability in process of optimization of the project by the economic criterion, in other words, the concept of similarity of options compared when optimizing the real asset or the property complex of the marine company, that differ by characteristics X, and are similar by other characteristics.
           The concept of options comparability, which is the options similarity, means, that at the variables X range – the combinations of optimized object characteristics compared by the economic criterion – the data Z, which are determined as variables X in a more general subject of optimization remain unchanged and similar.
           It should be added, that in process of detailed elaboration of marine company’s property complex into parts and optimization of separate parts, that is in each case of the whole object considered from the point of view of a part of design methodology (the separate functional properties related to the object as a whole), variables X, which are determined in optimization of the whole object, become data Z in subjects of project optimization of «the bottom levels» for object’s parts.
           And the structure of variables X in subsystems (that is for a commercial vessel or another asset, estimated from the point of view of separate functional property) for subjects of «the bottom levels» is defined among the set of independent characteristics which in optimization of the whole object were parameters Y and were taken expertly, for example, according to a prototype.
           Thus, the criterion function f in project optimization of the marine company real asset by the economic criterion is defined depending on variables X, parameters Y and data Z. Thus the comparability of options compared by economic criterion that differ by the values of varied variables X is provided.
           The criterion function is formalized as an economic model of optimized object which is a sequence of dependences between variables X, parameters Y and data Z, on the one hand, and the basic economical indexes: the income I, the operation costs С and investments MV or RC, on the other hand.
           And any of the economic criteria used in optimization in the form of the criterion function f, is based on the correlation of the basic economical indexes – the income I, the operation costs С with the investments MV or RC.
           It’s worth mentioning, that the criterion function f is a mathematical generalization over the income I, the operation costs С and investments MV or RC and is defined depending on variables X, parameters Y and data Z of optimized object, since the basic economical indexes are defined depending on variables, parameters and data.
           It is necessary to add, that besides the specified economic indexes: I, С and MV or RC by which the economic criterion f depending on the values of vectors is defined: X, Y and Z, there are also generalized variables (intermediate values), dependent on X, Y and Z that are used in the structure of economic model during optimization.
           For example, if in case of vessel optimization the displacement empty DP and deadweight DW are referred to a number of independent variables X, the cargo displacement, which is the sum of deadweight and displacement empty D = DP + DW, does not enter in the structure of independent variables and is a generalized variable.
           It should be added, that for the applied purposes choose the set of independent variables X (vessel characteristics, other real asset or property complex of the marine company), varied in process of optimization by the economic criterion, it is reasonable to use practical recommendations in the form of the following properties of independent variable:
           – It substantially influences on the economic criterion of optimality;
           – It is not determined unequivocally by other characteristics which are independent variables;
           – It is ranged changeable, that is, it differs for comparable variants;
           – It has numerical measurement – it is expressed by a real number (that is, the discrete characteristics and non–numerical, as for example vessel class, shouldn’t be included in a set of the independent variables varied by optimization).
           Usually, when the specified practical recommendations are observed, the criterion function is continuous in the range of definition, smooth in mathematical sense and convex.
           The economic criterion functions which can be applied in optimization of vessel project characteristic, other real assets or marine company’s property complex are reviewed below without going into details. Besides, the examples of criterion functions practical use are shown in the form of graphs.

Test questions

1. Economic definition of the innovative marine industrial activity.
            2. Subject of the investments planning when choosing of optimal characteristics the marine company real asset.
            3. Object of optimization by the economic criterion.
            4. Basic economic indexes.
            5. Criteria of efficiency and the criterion of optimality.
            6. Ways of economic criteria transformation to the value.
            7.  The criterion of an economic optimality as a way of general and comparative efficiency indicators application.
            8. Criterion function and the economic model.
            9. Definition of the structure (set) of variables for optimization.
            10. Signs of the set of parameters.
            11. Systematic approach and comparability of options in case of optimization by the economic criterion.
            12. Definition of the data set (external data).
            13. Practical recommendations for definition of the independent variables set.

22.2. Economic criteria of characteristics optimization of vessel or property complex of the marine company for the commercial order, based on costs minimization

The criterion of the discounted costs (the specific costs as discounting of operation costs and investments by the discounting rate i) with the assumption of set life time T of the marine company real asset in the form of criterion function is defined as
.
           In other mathematical equations in definition of the criterion functions the symbols of variables X, parameters Y and data Z are omitted for brevity. Despite the fact that in symbols of indications of the arguments are omitted, all used indexes and economic criteria are functions of arguments X, Y and Z.
           The discounted costs is a minimized criterion of comparative efficiency, that is among the comparable variants of vessel characteristics for the commercial order or other marine company real asset from the set X the best is the option to which there corresponds the minimum value of the discounted costs.
           The economic criterion of the discounted costs means the present value of investments into the construction RC of a commercial vessel or an other real asset or the marine company’s property complex, which optimal characteristics are determined by this criterion, into the equipment of commercial vessel or replenishment of working assets of the marine company at a rate of OC and in productive operation of an asset – at a rate of cash flow of annual operation costs C. And in case of investing in manufacture of a new vessel or other asset of the marine company the discounted costs are defined in the form of criterion function as

.

(22.1)

The minimized criterion of the discounted costs can be named as a criterion of the present worth (value) also. But in view of terminology of economic methodology the «costs», instead of «worth (value)» is more correct, since the economic value index is a characteristic of investments into assets which in this case are in the commercial turnover– are on sale, transferred in rent, invested, pledged etc.
           The asset in turnover should be evaluated, as a rule, by two parties, and one of the investors has a concern in expenses, in one form or another connected with an asset, and the second one has a concern in incomes and profit. Therefore from the various points of view – both standard and methodological – it is not quite correct to call an index «the value» which is account only the expenses, as, for example, the criterion of the discounted costs.
           Besides application of the partial sums (22.1) from the formal–logic point the economic criteria and indexes of the present value can be defined by integrated summation. For example, the criterion of the discounted costs can be defined by integrated summation as
           ,
           where С(t) – the distributed in time intensity of operation costs cash flow.
           However, as in applied economics cash flows are usually summarized annually, it is preferable to determine the criteria by discrete summation of the discounted cash flows, instead of integration, in particular, because for integrated summation there will be difficulties when defining data – the distributed intensities of cash flows.
           With an assumption at a stage of project optimization by the economic criterion for the commercial order of a new vessel with the account the assumption of enough big life time T when , and also with the account the assumption that in the present prices the operation costs C do not vary in time the criterion function in the form of the present worth is defined as  and in the specified form usually is called the criterion of the discounted costs.
           When the system concepts of options comparability are observed, the criterion function can be applied for the project optimization of commercial vessel or other marine company asset in the form of the specific discounted costs – per unit of effect Q, that is as .
           For example, in case when the deadweight DW and the power of the main engine Ne are chosen as variables at a project optimization stage of a marine fishing vessel by economic criterion characteristics, the costs into manufacturing RC considerably exceed the expenses in equipment and supply – working assets (that is, if we neglect working assets OC as a part of optimality criterion), and the volume of annual catch as effect Q is defined, the criterion of the specific discounted costs transformed with the account listed assumptions on the basis of the economic criterion of discounted costs can be expressed as the criterion function:
           ,
and generally with the account the possibility of the commercial vessel order at the second–hand market
            .
           In the general subject of effective investments planning in the marine industrial activity, considering, that the commercial order for manufacturing of the vessel (that is, the purchase of commercial vessel from the manufacturer under the condition of branch transfer between shipbuilding and shipping) is a special case of the commercial order at the second–hand market when investments are estimated by the parties by the market value, the criterion component is not a reproduction cost RC of the commercial vessel or other real asset of the marine company, and the market value MV, irrespectively of age, even for a new vessel, differs from reproduction cost RC by the adjustment value by the economic obsolescence D₅(see paragraph 9) external influence taking into account the cause of the external influence wear explained as the parties difficulties to sell a newly manufactured vessel from a batch, shifted to the seller, and on the basis of the specific risks analysis (paragraph 18.2) for the option of purchase of the vessel at the second–hand market which is not a batch vessel with optimal characteristics.
           There is a dialectic interrelation between indexes: on the one hand, an estimation of difficulties in case of the purchase of a new vessel from a modern batches, on the other hand, clearing from certain risks which would arise in case of the purchase of the vessel at the second–hand market.
           As an example it is possible to present the criterion function in expanded form in order to determine the fishing vessel’s optimum characteristics by the economic criterion.
           The formula presented below for an illustrative example with use of the certain data and macro–economical indexes is the basic economic model of fishing vessel corresponding to a general form of the economic criterion of discounted costs (22.1), that is, the simplest model, suitable for the further detailed elaboration which, nevertheless, is formalized on the basis of systematic approach concepts application and reflects the influence of data, vessel characteristics, particulars and parameters for economical indexes and criterion:
           
thousand US dollars / tonne.
           Other criteria of economic efficiency and criterion functions considered below in the form of basic models in view of optimization by economic criteria of marine vessel characteristics for the commercial order have the similar expanded form.
           The form of criterion function of the specific discounted costs for an example of optimization of fishing vessel project characteristics, cargo vessel and for a choice of cargo vessel at the second–hand market is shown on charts (fig. 22.1–22.3).
           It should be explained, that the dependences of the basic indexes on variables are not considered in the given text though they are rather difficult when formalizing and data substantiation.
           In details the formalization of the dependences of the basic indexes on vessel characteristics is stated in the specialized literature on the economic optimization subject of marine commercial vessels characteristics [12].

And the economic model used in project optimization of the marine company real asset consists of dependences for determination of the basic indexes: , , , and also effect  and from the dependence of one criterion or another in the form of the criterion function on the basic indexes.

The basic indexes in themselves: the income I, the operation costs C and investments MV (or RC), – do not reflect critical judgments, suitable for a choice of optimum results in investment planning. For example, it is impossible to determine, whether it is necessary to reduce the operation costs C or not, since much depends on how the index of the income I thus will change.
           The concepts of efficiency, expediency and utility are introduced by mathematical operations on the basic indexes when formalizing of one economic criterion or another in the form of the criterion function, and judgments about economic efficiency depend on mathematical operations.
           For effective expert activity in applied economics good knowledge of mathematical analysis, including theory of numbers, exponential functions and their properties, differential and integral calculus, probability theory, and also mathematical statistics and computer science in the program of a university course for economists is required. It does not mean that the expert in the field of economy carries out mathematical derivations directly in his expert work, but it is required, that mathematical generalizations were competently used in the economic calculations and the expert was capable to reproduce the derivation of the used formulas.
           Besides the basic indexes the mathematical equations of criteria also include macroeconomic index of the discounting rate i which is an economic indicator of commercial risk and is usually estimated per year (in this sense the symbol i does not mean the mathematical imaginary unit).
           For innovative economy in the countries that mostly carry out the construction of new vessels and marine engineering, instead of the assets operation bought at the second–hand market, the limited values of risks according to the discounting rate i in a range from 0.05 to 0.25 (from 5 to 25 %) are characteristic.
           The criterion of the discounted costs exponential function of The Euler’ number (e = 2.71828283 ...) it is defined as
           .
           Assuming at a stage of commercial vessel project optimization or other asset of the marine company, that in the present prices the operation costs do not vary by years – C = const, the criterion function of the discounted costs can be presented as:

,

(22.2)

or  – on condition of discounting by exponential function of The Euler’ number.
           When formalizing the criterion function for the analysis of expediency of commercial vessel purchase at the second–hand market, in view of the fact that the reproduction cost RC of commercial vessel is not used as a part of specific discounted costs criterion, the market value MV is used with the account depreciation (see paragraph 8.1) by the formula
           .
            The economic advantages of not a new vessels operation, which value is less than the value of newly constructed vessels, are accompanied by the additional risks, and the expert decision concerning the comparative evaluation of economic advantages and additional risks is required.
           The minimized criterion of the required freight rate characterizes the income I per unit of effect Q, necessary for investments compensation for manufacture of the commercial vessel or other asset of the marine company or purchase at the second–hand market MV, for equipment OC (replenishment of the working assets), compensation of the operation costs C during the period of productive operation and the net operating income (or profit) for the rate corresponding to interests of the investor and equal, in particular, to the  macroeconomic index of total risks according the discounting rate i.
           The criterion of the required freight rate in the form of the criterion function is defined as

,

(22.3)

or for the discounting by the exponential function of The Euler’ number
           .
           Assuming for the commercial vessel or other real asset of the marine company, that in present prices the operating costs are constants – C_t=C=const , it is possible to represent the criterion of the required freight rate in the form of the criterion function as , that corresponds to the economic criterion considered above in the form of the specific discounted costs.

Test questions

1. Practical recommendations for determination of the set of independent variables definition.
            2. Criterion of the discounted costs (the formula derivation).
            3. Advantages of cash flows discrete summation.
            4. Transformation of the discounted costs criterion to the criterion of the resulted costs (the formula derivation).
            5. Application of discounting by exponential function of the Euler’ number in economic criteria (the formula derivation).
            6. Methodological assumptions in case of use the economic criteria for optimization of the vessel characteristics or other asset of the marine company.
            7. Criterion of internal rate of return (the formula derivation).
            8. Macroeconomic index of total risks according to the discounting rate and the real interest rate.
            9. Relative property of commercial vessel economic life time or other asset of the marine company with the account payback and the macroeconomic index of commercial risks.

 

22.3. Optimality criteria of commercial vessel project characteristics, assets or property complex of the marine company, based on an estimation of profitability indexes

The criterion function of the internal rate of return IRR is defined as

,

(22.4)

or for the discounting by the exponential function of The Euler’ number
           ,
           where Rv – is a reversion – the additional income from resale of the commercial vessel, other real asset or the property complex of the marine company at the second–hand market or for scrap at the end of productive operation.
           Assuming for commercial vessel, other asset or property complex of the marine company, that the net operating income in the present prices is constants – I_t-C_t=I-C=const , it is possible to present the criterion of the internal rate of return in the form of criterion function as

,

(22.5)

or  – for the discounting by the exponential function of The Euler’ number.
           If to assume that at a design stage the life time T is rather large, when , the influence Rvof the reversion on the economic criterion can be neglected.
           The index of the internal rate of return IRR which for new asset corresponds to the relation of the net operating income NOI of the productive operation of commercial vessel, other real asset or property complex of the marine company to the present value of investments , for project optimization is compared with the «real» interest rate.
           The relation of the rate of discounting i to the factor of discounting (1+i) , is used as a real interest rate, that is, the real interest rate means, figuratively speaking, «depreciated» for a year, that is, «discounted» rate of discounting i/(1+i).
           The economic criterion of the internal rate of return is a maximized index of general efficiency of the commercial vessel or other real asset.
           For new vessel, other real asset or the property complex of the marine company in case of sufficient life time with the account neglected of reversion Rv and with the account assumptions, that in present indexes the net operating income is constant – I_t-C_t=I-C=const, the criterion function in the form of criterion of internal rate of return is defined as or  – for the discounting by the exponential function of The Euler’ number.
           The form of the criterion function for an example of characteristics optimization for the commercial order of a new fishing vessel by the criterion of internal rate of return is shown at the charts: (fig. 22.4), for crude cargo vessel (fig. 22.5), for cargo vessel at the second–hand market (fig. 22.6).

For estimations when investing in the purchase at the second–hand market there is an expert problem of correlation of additional risks with planned indexes of efficiency, which for the second–hand market are substantially higher.
           And efficiency of investments at the second–hand market increases (fig. 22.6) in the relative value owing to the depreciation of the vessels or other assets over the time, and risks of investing thus grow.
           The estimation of growing risks balance and estimated indexes of efficiency is required. Apparently, in some cases it should be recommended to limit the efficiency with a view of decrease of investment risks.
           At the same time, there are companies which bought not new vessels on regular basis, and this activity with the account the ability of their managers to strategic planning, generally gave the positive results.
           It should be specified, that strategic planning usually is aimed at the reduction of risks in conditions when the basic branch activity involves commercial risks.

.

           

For example, if the source of income and profit is the purchase and use of not a new vessels before the decommission in the productive operation, the recommended object of innovative investment can be the development of shipbuilding, that, by the way, corresponds to the above mentioned example of Onassis’ activity, that is, the preferable object of investment is usually located in adjacent economic and branch space in relation to the basic industrial profile activity, to be exact, the preferable object of investment is an economic reflexion of branch activity.
           On the other hand, the strategic planning and investments management in other part of the activity is more difficult professional work than only determination of the general direction of investment.
           In particular, there is a need for estimation of proportions between investment and branch (industrial profile) activity, to be exact, planning of these proportions in the long term, up to a choice of characteristics and particulars, and also sequence of vessels planned to be constructed etc. if to continue the example.
           It should be noted, that economic life time T  of assets is a relative concept and it depends on total commercial risks i. It is possible to define, for example, the life time in relation to a payback period of investments T_R , which, in turn, is defined by the index of internal rate of return, that is T_R = 1/IRR, which correlated with macroeconomic index of risks – with the discounting rate i.
           In each task of estimation of the value and efficiency of investments the question of life time determination requires rather detailed studying. In case of the limited life time of the marine company real asset if assumption , is unacceptable, let us assume, if owing to economic stability the sum of commercial risks i is small, or the index of life time T is related to the expenditure of the limited resource, for example quotas of ocean biological resources, stocks of a deposit or fuel stocks in a single–use energy source etc., and for the specified reason the index of life time T is included into number of optimized variables X, then when determining the internal rate of return the relation of the present value of the profit cash flow p = NOI –f_m to the value of investments is taken as a maximized index of comparative efficiency, rather than the relation of the net operating income NOI to present value of investments MV+OC.
           Keeping in mind the infinite sequence of the cycle – the manufacture of the marine company asset through the investments MV, the equipment by means of working assets OC, the productive operation with extraction of the cash flow of net operating income NOI_t=I_t-C_t , recycling or resale at the second–hand market at the value corresponding to the reversion Rv, and multiply repetition of the specified cycle due to deductions from the net operating income for the replenishment of spent investments, then while determining the profit present values of cash flow it is required to subtract the value of so–called «the capitalized costs»  (MV+OC-Rv/(1+i)^T)/c(T,i), where c(T,i) – the factor of investments capitalization as a part of the criterion on the basis of a sequence estimation: vessel construction (or other real asset of the marine company) or purchase at the second–hand market, productive operation, recycling, reinvestment, remanufacturing and multiply repetition of the specified cycle, – is defined as c(T,i)=(1+i)^T/((1+i)^T-1) , or c(T,i)=e^i×T/(e^i×T-1) – for the discounting by the exponential function of The Euler’ number from the present value of cash flow of the net operating income

           The criterion of the internal rate of return determined with the account limited life time of the commercial vessel or other asset of the marine company on the basis of modeling of the profit cash flow, can be presented in the form of thecriterion function as

,

(22.7)

or for the discounting by the exponential function of The Euler’ number
            .
           Assuming for the commercial vessel or other real asset of the marine company, that in the present prices the net operating income is constant – , the criterion of the internal rate of return introduced with the account limited life time on the basis of modeling of the profit cash flow can be transformed as:

,

(22.8)

or for the discounting by the exponential function of The Euler’ number
           .

The criterion of the net present value NPV is a maximized index of efficiency.
           For commercial vessel, other real asset or property complex of the marine company at the manufacture stage, including designing and economic optimization of characteristics, the criterion of the net present value is determined in the form of the criterion function as

,

(22.9)

or for the discounting by the exponential function of The Euler’ number
.
           In the assumption, that – , the criterion of the net present value can be transformed to:

,

(22.10)

or for the discounting by the exponential function of The Euler’ number
.
The form of the criterion function for an example of fishing vessel optimization by the criterion of net present value is shown on the chart (fig. 22.7).

The criterion of the net present value defined with the account the limited life time of commercial vessel or other asset of the marine company on the basis of modeling of profit cash flow, it is possible to present in the form of the criterion function as:

,

(22.11)

or for the discounting by the exponential function of The Euler’ number
.
           Assuming for commercial vessel or for other real asset of the marine company, that in the present prices the net operating income is constant – , the criterion of the net present value introduced with the account of limited life time of real asset of the marine company on the basis of modeling of profit cash flow, can be transformed:

,

(22.12)

or for the discounting by the exponential function of The Euler’ number
.
           As for the possibility of use of the criteria which have been not expressed by economical indexes for optimization of characteristics, for the commercial order of vessel or other real asset of the marine company or when optimizing the investments into property complex, for example, the criteria of the minimized weight of commercial vessel structures or the minimized displacement, maximized cargo capacity or tonnage, operational speed, propulsive factor, carrying capacity, etc., it should be noted, that applicability of these or similar criteria should be estimated from positions of conformity of the results of characteristics optimization by these criteria which have not been expressed by the economical indexes, and results of optimization by a certain economic criterion.
           From the system point of view it is impossible to choose, for example, vessel characteristics only from the point of view of the minimum weight of the hull (let us suppose, in relation to cargo capacity). It is important at what price the weight of the hull is minimal. After all the unacceptable recommendation can appear result to make the hull of the excessively expensive material, though easy and strong (the titan, the carbon fiber–plastic, etc.).
           As for the application of optimality criterion, which is not an economic index, there supposed to be a general economic criterion in relation to which it is possible to judge about applicability of the «not economic» criterion then the specified general economic criterion is valid. Thus there is a question, why there is a need for the second criterion which has been not expressed economically.
           At the same time the criteria which have not been expressed by economic indexes can be applied to optimization of characteristics for the commercial order of marine engineering objects of separate kinds if the applicability of these criteria and their conformity to the general economic criterion is a settled result of the usual experience.

Test questions

1. Criterion of the internal rate of return for optimization of the commercial vessel or other asset of the marine company for the commercial order (the formula derivation).
            2. Criterion based on indexes of profit and capitalized costs with the account the limited life time of the commercial vessel.
            3. Economic criterion of the net present value (the formula derivation).
            4. Criterion of the net present value determined with the account the limited life time of the commercial vessel (the formula derivation).
            5. Possibility of application of the criteria which is not expressed by economic indexes for estimation of efficiency and for comparison of variants of investment in marine industrial activity.