Sometimes I really feel the Dark Ages guild secrets still exist and well alive even nowadays as the most simple, practical and easy solutions had been hidden from approaching the topics.

Not overburden with excessive modesty is sure that “Time: The Economics Application” ought to surely have been among such things.

Just knowledge. “Time: The Economics Application”, by M.Kerjman

Time: The Economics Application
M. Kerjman
MIEAust CPEng (Reg)
Keywords: Environmental Management, Economics, IRR, NPV, Investment, Time, Prediction
ABSTRACT
What is time? This question has intrigued mystics and philosophers for centuries. Time changes both the quantity and quality of everything: scientists can study only what changes with time. Any change is a reflection on the interval of time upon which it occurs. Occurring upon a passage of time, changes in a matter identify the dynamism of a matter. Economics is a product of a human intelligence. This is an artificial process depending heavily on the natural resources and processes. Undertaking the most reasonable in certain circumstances solution concerning the efficiency of human activities constitutes the essence of economics. The appraisal of projects is a commonly used approach while making the choice of the most appropriate activity. The projects’ appraisal based on the method of cash flow analysis employs the internal rate of return (IRR) as a significant tool for the decision making.
Exploring the most rational pathways to solutions is the core content of this work.
THE NATURE OF INTERNAL RATE OF RETURN
The project yielding the higher level of NPV may appear more attractive in a business environment [1]. However, although the projects may require the same capital and yield the same benefit, the project with the lower IRR would be preferred as less intensive work could achieve the same result. Thus, the IRR is a dual measure for both productivity of capital sustaining the project and intensity of the activities proposed with that project. Both productivity and intensity are functions of time. So, IRR mathematically represents the grade of change occurring upon a passage of time in a project, which characterises the dynamism of project(s).
IRE. may simply be present as a function of the following economic performance measurements:
(1 +rY’- I = pv [2] = PV = f(n, l/r)
r* (1 +r)11 IFA(n,r) IFA(n,r)
and r = ?A(n,r) jJ
EAW = NPV / PV
IFA(n.r)
NPV=O =I=EAW*PV
IFA (n. r = IRR)
PV = I/EAW=I/(PV / NPV)
IFA(n. r IRR) IFA(nr)
U U U U U U
Ii IRR = f (NPV, 1/I, r, 1/n) I
NPV - Net Present Value, $; PV - Coefficient of Present Value of Annuity,
EAW- Equivalent Annual Worth, $ pa, I- Investment (capital cost), $,
r- Discount Rate, %, n- Duration of project, years.
Thus, the particular project is more productive then another in the case, where its NPV and discount
rate are higher and investment and duration are lower.
Let us assume, two projects to be compared, and that project 1 is the better one.
Concerning the dualism of IRR, in the case, where IRR1 > IRR2:
i1 (NPV7 / 2)- the most appropriate project has been indicated by higher ratio (NPV1/11): if projects had been equipped with the equal rates of return, the most cheap and the most beneficial project is the best one.
Therefore, if the project 1 is the most appropriate activity, the formula for projects’ appraisal should in general be present as:
>
11* IRR1* nI 12* I112 2
Benefit Cost Ratio (BCR) is one of the most important measurements. Obviously, the better
project has been equipped with higher BCR: NPV1* BCR1 > NPV2* BCR2, and formula can be re-written as:
fY1ir1* BCR1 > NY2i2 BCR2
IRR1* I* n1 IRR2* 12*n2
Levelised Cost of Production (LCP) indicates expenses being spent for one unit of production (LCP
= EXPENSES / quantity of the PRODUCED UNITS).
If other circumstances were the same, the project with lower LCP is the most appropriate:
For
NfY1II1*
mula 1:
BCR1 >
fY2j2
BCR2
Ii *IRI{ *
* LCP1
IdIRR * LCP2
The next step is the determination of IRR itself. As it was above mentioned [2],
(jr)’-1 =
r * (1 +r)11 IFA(n,r)
EAWNPV I PV
IFA (n, r)
NPVO z IEAW*PV
IFA (n, r = IRR)
PV = I/EAW=I/(NPV/PV)
IFA (n,r = IRR) IFA(n, r)
Let us assume, I / (NPV / PV 2 = C
IF (n,r)
[1-(IRR+1)11 ]/ IRR C
(IRR+1) (IRR+ 1) * IRR * C 1
(IRR+1)fl*(1IRR*C) 1
In(IRR+1)11 +In(1JRR*) 0
Ifl(IRR+1)rI in [1 I (1 * ]. It is undisputable for all values of IRR if
(1IRR* C)=O:
I Formula 2:
IRR = NPV /(I*pF 00%. For projects with indefinite life
I
IRR = r *( NPV / f
Thus, the projects with (NPV I ) BCR2
LCP IFA LCP2
BCR1> BCR2
LCP, LCP2
In order to employ the proper decision model which reflects the nature of the project(s), the necessary condition sustaining the distinctive feature of the passage of time called “the indefinite life of project” has been defined with the precise and simple mathematical quotation:
>
n / hr
Really, PVIFA(flr) = f (n, r), 0 [TOTAL COST]12
> [TOTAL REVENUE]2 * [QUANTITY PRODUCED]2 * r2* PVIFA2
[TOTAL COST]22 n2
Different projects have different r and n which define the nature of a particular project, and if the projects of indefinite life have been compared, the Universal Formula will have been used in a form:
[TOTAL REVENUE]1 * [QUANTITY PRODUCED]1 >
[TOTAL COST]12
> [TOTAL REVENUE]2 * [QUANTITY PRODUCED]2 [TOTAL COST]22
Estimating the most appropriate project can assume the values of such parameters as “Total Revenue” and “Total Cost” by taking the analogical data provided by the previously implemented projects.
The “ Quantity Produced” is a core of the activities suggested. This parameter is the most challenging, complex, and hard to predict variable. It is merely a function of the occurring in the particular moment of time demand of society on goods, services, generally speaking, on the development of certain processes which can fulfil that demand. Hence, the demand on development results from the existing in particular circumstances scarcity of the matters mentioned. And a scarcity itself is a socio - political aspect being important for the particular society during a particular interval of its history, which is a period of time.
Therefore, socio - political aspects constitute the decision rather, than pure mathematical calculations. So, the economics formulas would much more reliable work if they could be used to engineer the projects supposed to be implemented in exactly the same socio - political environment.
Altering upon a passage of time, the Total Revenue, Total Cost and Quantity Produced are inextricably linked and interacting parameters. The units of the currency are the dimension of the Total Revenue I Total Cost. The Quantity Produced (QP) has been present with the units of production being suggested with the project(s). In the case, where the projects resulting in different types of production have to be compared, the QP should eventually be present in a form of a “Present Market Value of the QP”. This can be achieved by multiplying the number of the units on the market price of a unit of production. Definitely, this type of a comparison appears to be more sophisticated: the prices of the different products vary upon a time dissimilarly. However, it would be possible to compare projects of a different type of production at any moment of time if the following this moment of time prices could be estimated. Hence, the QP may be present in a monetary form, and money, as usual, is a significant tool for the unification of the different products.
Any product, a pure natural resource or an artificial human-made merchandise, is a form of energy. Therefore, the main function of money is its intention to represent the variety of the forms of energy. Money is an artificial product which worth itself is equal to the energy being spent for producing the bank note, coin, cheque or electronic transaction. Practically, money is worth as much, as many units of other products may be obtained with a unit of a particular currency. Therefore, difference between the own price of money and its value is a socio - political variable challenging upon a time.
Factually, time, the universal process, characterizes a state of the energy. Time itself has been present with the state of the energy. A powerful economics tool, money is an artificial product of the human imagination, which dependence on the socio - political aspects makes the universality of money questionable. The duration of the project, that is time itself, has been inextricably linked with such parameters as NPV, IRR, r and I. Integrating all the above stated, the compact function brings out the complex relationship between past (I), present (r, IRR), future (NPV) as well as between real (I, r), presumable (NPV), imaginable (n, IRR), and may likely be used both while estimating the appropriate conditions to project’s implementation, and for modelling a multitude of different processes being challengeable upon a passage of time:
Process Implementation Predicament
(1 +
r)_(h1’r)
+
i
I
n(I + r)* I(N
PV/I) * (r/IRR)
-11
As it is clear from a mathematical description, the economic life of project doesn’t depend on value of money, but it does depend on the relativity existing between net present value and capital having initiated this project (I). Both NPV and I reflect the value of money.
CONCLUSIONS
Constructing the models prefers to deal with variables which can easily be quantified. As decisions concerning the best projects have been based on the socio - political considerations rather, than on pure economic formulas provided in a form of mathematical quotations, many nonquantiable aspects would have been avoided by making the appropriate assumptions. The longer a passage of time upon which the analogical data was collected and the shorter the length of the economic life of project - the higher probability of the assumptions’ occurring and more reliable result of a projects’ comparison. Thus, time is the most important factor for estimating the best project.
The economic life of project, that is a passage of time, is a function of the economic parameters of project being set by the author(s) of the project(s). Economic parameters of the project(s) quantify variables characterizing the project(s) activities, which take place during the economic life of this project. The project(s) activities would be achieved by spending the energy in different forms. Therefore, the economic life of the project is a function of the energy used to implement the project.
The activities of the project(s) have been described and measured with money. Money used to represent the energy being spent is a multifunctional abstract tool created by humans. Itself, it is a commodity depending heavily on the socio - political factors.
Therefore, under current never before seen pressure of a reality of a global ecological catastrophe, to what extent has money been appropriate to further substitute the energy itself?
The Time knows the answer.
ACKNOWLEDGMENT
I wish to express my debt of gratitude to Mr. N. L. Furman - for the mathematics knowledge I have gained, and to Mr. N.A. Rockliffe - for providing the access to a wide world of economics.
REFERENCES
[1] D. Salvatore, Managerial Economics In A Global Economy, McGraw - Hill, New York, p.598 (1996).
[2] M. Hirschey, J.L. Pappas, Managerial Economics, Harcout Brace Jovanovich College Publishers, Forth Worth, FL, the USA, p. 772 (1992).

I regret if something missed during operating copy-past commands.