Economic justification of laboratory automation

PurposeThis study aims to analyze the effects of variations in annual real interest rates in the assessment of the techno-economic feasibility of a hybrid renewable energy system (HRES) for an off-grid community.Design/methodology/approachHybrid Optimization of Multiple Energy Resources (HOMER) software is used to propose an HRES for Abadam community in northern Nigeria. The HRES was designed to meet the basic needs of the community over a 25-year project lifespan. Based on the available energy resources in the community, photovoltaic (PV), wind turbine, diesel generator and battery were suggested for integration to serve the load requirements.FindingsWhen the annual real interest rates were taken as 10 and 8 per cent, the total amount of total energy fraction from PV, wind turbine and the diesel generator is 28, 57 and 15 per cent, respectively. At these interest rates, wind turbines contributed more energy across all months than other energy resources. The energy resource distribution for 0, 2,4 and 6 per cent annual real interest rates have a similar pattern, but PV contributed a majority of the energy.Practical implicationsThis study has used annual real interest and inflation rates dynamic behavior to determine optimal HRES for remote communities. Hence, its analysis will equip decision-makers with the necessary information for accurate planning.Originality/valueThe results of this study can be used to plan and design HRES infrastructure for off-grid communities around the world.

This study aimed to develop a commercial concept for transforming farms into wellness tourist destinations. The proposed scenario involved the renovation of a hayrack into a highend tourist accommodation, comprising relaxation rooms with panoramic glass walls and the renovation of the barns, as well as an outdoor swimming pond. The research methods includeddescription, compilation, and synthesis to explore the legislation in Slovenia related to investment performance and trends in wellness tourism to support the realisation of the proposed investment. Furthermore, the study used the method of financial estimation of investment using cost-benefit analysis to facilitate the transition. Four datasets were used for the estimation: investment income, investment costs, end value of the investment, and annual interest rate. The estimated investment cost was €530,000 and the total estimated revenue was €192,720, with total costs amounting to 50% of the total income, as well as an annual cash flow of €96,360, which was used in the assessment of the investment return period. According to the findings, the investment return period is 15 years with the lowest annual cash flow and interest rate of 3.5%. However, caution is advised due to uncertainties in the long-term costs of raw materials and energy.

Investing decisions require the valuation of investments and the determination of yields on investments. Necessary for the valuation and yield determination are the financial mathematics that involve the time value of money. With these mathematics, future cash flows can be translated to a value in the present, a value today can be converted into a value at some future point in time, and the yield on an investment can be computed. Keywords: time value of money; simple interest; compound interest; interest on accumulated interest; interest on interest; growth rate; return; arithmetic average return; geometric average return; compound average annual return; true return; annual percentage rate; continuous compounding; discount factor; ordinary annuity; future value annuity factor; present value annuity factor; loan amortization; perpetuity; annuity due; deferred annuity; nominal interest rate; annual percentage rate; effective annual rate; loan amortization; fully amortizing loan; amortization; balloon payments; yield; internal rate of return

Interest rates considerations in cash flows are fundamental concepts in finance, real estate, insurance, accounting and other areas of business administration. The assumption that future rates are fixed and known with certainty at the beginning of an investment, is a restrictive and theoretical assumption that is not obtainable in real situations. A more realistic approach would be, to report the expected future value and its variance for a given return process. This paper derives formulae for the mean and variance of future values for a single cash flow and sequences of cash flows when returns processes are randomly and independently distributed. Numerical examples are given to illustrate the magnitude of the change from the fixed rate of return process to stochastic (random) rate of return processes. Keywords: Stochastic, Cash flow, Rate of returns, future value

Using a Markov-induced decomposition of time in the labor force, we compute means, standard deviations, and other distributional characteristics of the present value of years of labor force activity. We also provide bootstrap estimates of the mean present value and the corresponding standard deviations of sample means. This paper combines years of future labor force activity, decomposed with a Markov process, with discounting that activity to the present, whereas previous literature has analyzed only undiscounted years of activity.A worker at exact age x, given activity status, sex and education, receives $1 for each future year in the labor force. The present value of this stream, which is assumed to grow at rate g and to be discounted at the interest rate r, is a random variable, since it depends on future labor market realizations and mortality experience. Letting NDR be the net discount rate, (r – g)/(1 + g), we define this random variable to be PVA (a, x, NDR) when the person begins active and PVA (i, x, NDR) when commencing inactive. We assume that future labor force activity status follows the usual Markov or increment-decrement model. In arranging these random variables into the row random vector PVA (x, NDR)′ ≡ PVA (a, x, NDR), PVA (i, x, NDR), we provide a recursion for its probability mass function (often abbreviated "pmf" below), which we show to be computationally intractable. Next, we indicate how we may nevertheless estimate the probability mass function. We then provide a computationally useful recursion for its expected value E [PVA (x, NDR)′]. These expected values have been tabulated in the United Kingdom, where they are associated with the Ogden Tables. From another point of view, E [PVA (x, NDR)′] is a generalization of the worklife expectancy since , the familiar worklife expectancies when NDR = 0. The same concepts apply to flows of $1 while in the inactive state, and our computationally feasible recursion covers it as well.It is well known that a person's worklife expectancy does not provide enough information to accurately compute the associated present value, since worklife will on average be allocated over future years in a particular pattern dictated by the underlying Markov model. Skoog and Ciecka (2006) took up a graphic way to perform this allocation. Other papers (Skoog and Ciecka, 2001a, 2001b and 2002) pointed out the intrinsic variability of the random variables YAx,a and YAx,i (years of activity starting active and inactive) around their respective means. The present paper brings these two ideas together, adds an extension of a recursion and decomposition found in Skoog (2002), to address what must surely be among the most natural and interesting questions for forensic economists: (1) What does the mean of the present value random variable, correctly calculated with the Markov-induced decomposition, look like at various NDR's? (2) What is the size of the standard error of the estimated mean of the present value random variable at various NDR's? (3) What does the present value distribution look like at different net discount rates? While the so-called Ogden Tables have asked about the first and second questions in the context of British data and a single NDR, it will be helpful to have these tables calculated for American data based on labor force participation and various NDR's. The third question has not even been previously asked. This is surprising; in the age of Daubert we feel that displaying variation as standard errors is important. Perhaps the lack of attention to this question has occurred because of the technical difficulties highlighted in this paper. We suggest another reason, however. Many forensic economists have implicitly understood or assumed that what we carefully define as the present value random variable instead meant expected present value. Questions about variability have not arisen because the discourse simply did not allow it. Our intuition about the variability comes from observing that, when the NDR is zero, present value is years of activity, whose pmf has been tabulated. We expect the same variability for the present value random variable when the NDR exceeds zero, but pulled leftward and shrunk, due to discounting.Beyond this introduction, the paper is organized as follows. Sections II and III contain notation to capture the probability structure and timing (of payments) convention used in the paper. Section IV deals with the intractable present value recursion for the present value function. On a first reading, this section may be skimmed to more quickly arrive at Sections V and VI containing mean recursions and tabular results, respectively. The paper concludes with a brief discussion of the Ogden Tables in Section VII and some final thoughts about the present value random variable and its expected value in Section VIII.We let Zx denote the state of our worker (referred to in the masculine) at exact age x, so that Zx = a or Zx = i. TA – 1 (where TA is "terminal age" or "truncation age") is an age at which all transitions occurring ½ of a year later are to the death state; this is illustrated as age 110 below. As in our previous work, we assume that transitions occur at midpoints, so that for the next half-year at least, he continues in the same state he occupied at age x. At age x + ½, the first transition occurs, which we formalize by defining the "increment" random variables Zx,.5, depending on the state occupied at age x: In the same way, and, generally,Let t ≥ 0 refer to any (not necessarily integer or half integer) number of years beyond age x, and let Zx (t) be the random state occupied at this age, x+t, defined out of the increments in (1a)–(1d). We construct a random variable which is left continuous and constant between half integers, and it changes on the half integer whenever the labor force status changes. The stochastic structure of Zx (t) depends on the initial state of Zx and is induced by the probabilities . We can convert the function Zx(t), which takes on values of a, i and d, to a function which equals one for all time when in the active state, by use of the commonly used indicator function I[ Zx (t)=a ], defined as: for any event E, IE= 1 whenever the event E is true.Our earlier work focused on YAx, the years of additional labor force activity, starting at age x in state m. Evidently If we indicate both age x and the initial state, a or i, in our notation, we can express this last equality as Despite equation (3), this model is essentially discrete. A truly continuous model would posit instantaneous forces of increment, decrement and mortality, and payments would grow and be discounted with instantaneous forces. We take this model up elsewhere, but note here that in continuous time the "construction" of Zx (t) would not be required, simplifying the development above.We need to specify when earnings are paid, how they are discounted, and how they grow. We are motivated by the fact that our transitions will be observed once per year, but compensation is paid much more frequently, rarely daily or annually, but more often bi-weekly, semi-monthly or monthly. In the case of monthly payments, the average of the payment points of 1/12, 2/12,…, 12/12 of a year is 6.5 months or 13/24 of a year. Consequently assuming one payment is made at the midpoint of 12/24 introduces a very modest acceleration of 1/24 of a year.We allow for an age-earnings curve by including the sequence {aej} for appropriate indices j relative to the base earnings level for age x, although much forensic practice, and our tabulated tables, will set {aej} to unity. We follow standard forensic economic practice and assume that earnings grow at rate g and are discounted at rate r; these may be taken as either both nominal or both real. Since the effects of r and g separately enter the present value through the net discount rate, we use the relationsIn light of the timing issue between payments and transitions, and consistent with the convention adopted in our previous work, we continue to assume that transitions take place at mid-period. Our first inclination is to consider the possibility of assuming that payments are made when transitions take place, i.e. at mid-periods. There is one asymmetry, namely, that we begin at an exact age, x, and the first transition is after ½ of a period, followed thereafter at periods one year apart. To fix ideas, assume the worker is active at x. Then $.5 is earned between x and x+.5. Assume that the transition at x+.5 is active to active, so (i) $.5 is earned for the activity in [x+.5, x+1) and (ii) $.5 is earned in [x+1,x+1.5). We define two allocation conventions below: Convention A assumes that (i) $.5 is paid at x+.5, ½ of a period before the mid-point of the interval [x+.5, x+1.5) while (ii) another $.5 is paid at x+1.5, ½ of a period after the mid-point of the interval [x+.5, x+1.5). This convention splits payments for the interval into two pieces. Additionally, the transition which took place at age x –.5, and which is responsible for the activity in [x, x+.5), results in $.5 being paid at x+.5, so all future work at x and beyond is paid in the future.Convention B would put the entire payment at x+1, the mid-point of the [x+.5, x+1.5) interval. In this case, payments occur at exact ages, different points from transitions. Convention B requires that the payment for [x, x+.5) was made at x along with the payment for activity in [x–.5, x), and that these payments took place the instant before attaining age x, so that references to the present value of payments at exact age x start at age x+.5, with its associated one year interval [x+.5, x+1.5).The present value random variables associated with Convention A are: andOn Convention B, the expression on the right hand side does not depend on the initial state, although the distribution of I[Zx,j = a] does, so that we have:The equations (6) display the source of the randomness in the present value random variable, and provide the suggestion for how we will need to go about computing the probability mass function which summarizes its randomness. Recalling the connection of I[Zx,j = a|Zx = m] and Zx (t) emphasizes that any individual worker would have experienced a sample path of future labor market activity, which could be very short or very long, and so could have experienced a small or large present value of future compensation. We have a choice in studying the probability mass function of (6)—we could either attempt to discover its recursive structure, as we have done with the related random variables, or we could use (6) to generate a large number of realizations via simulation. We will start with the former and discern the necessity of doing the latter. We also have a choice of allocation methods. The theoretical and empirical work that follows utilizes Convention A.Equations (6) will be seen as new for most forensic economists and actuaries, who have slipped into the habit of thinking about the present value random variable as a number. By taking the mathematical expectations of the left hand sides in (6) and computing or estimating E{I[Zx.j= a|Zx= m]}on the right hand sides, they have been referring to the expected present value rather than the present value of the revenue stream. Nowhere has this emphasis been more pronounced than in actuarial science, where the notation for the random variable representing the payment of $1 per year for life is not typically distinguished from its expectation, ax. We will take up this point again in Section V.This section, as it describes the probability mass function of the present value function, should also help to fix ideas introduced in the notation of the previous section. Let us assume that TA, the truncation age, is 111. The last transition is at age 109.5, and everyone who survives this last transition, governed by either ap109a or ip109a, is dead at 110.5.1 The probability mass function for any age and initial condition is the function which assigns probabilities to each possible value of the present value random variable. We can do this from first principles. We will work with Convention A and starting active. There are two possibilities: at 109.5, the transition is to active, resulting in payments at 109.5 and 110.5, or the transition is to the inactive or dead states, resulting in no payment. In any case, for the first half of the interval, the beginning state of activity is continued (i.e., from age 109 to 109.5). There is a payoff for this half period of .5, which grows and is discounted over this interval, resulting in a present value contribution of .5β regardless of the transition. We generically define the probability mass function by the symbols px, m(pv), where the subscripts are the beginning age and state, m, the pv arguments are all possible values of the present value, and the value of the function (its range) at each of these pv values in the domain is the probability of that value of the present value occurring. Here, the pmf is Had we started inactive, there would be only one .5β term, and we would either realize a present value of .5β.5β3 or nothing. The pmf is We notice that the domain of p109,a (•) is, for the small NDR's encountered in practice (1% to 3%, say) "essentially" .5 and 1.5, which is exactly the domain encountered when β = 1 and the present value is counting years of activity. Similarly, the domain of p109,i (•) is, for these small NDR's encountered in practice "essentially" 0 and 1, again exactly the domain encountered when β = 1 and the present value is counting years of activity. These domains are exactly 0,.5β,.5β.5β3, β + .5β3 and do not overlap.2Moving back to age 108, we can begin to see the domains interleave and escalate. Starting active at x = 108, there will be .5β realized at least. If we go active, we will receive another .5β, and be active at 109. We can then use the two present values associated with p109,a(•), discounted by β2 since it is one year in the future, to complete this half of the pmf. Alternatively, we could go inactive at 108, contributing .5β and 0 at 108.5, and leaving us with β2 times the possibilities entailed in p109,i(•). Doing the accounting, showing how each of the two potential contributions for each transition contribute, and then grouping, gives us: The number of distinct points in the domain has doubled; let us define it as D109,a = {β+ β3+ .5β5, β + .5β3,. 5β + .5β3 + .5β5,.5β}. The 4 distinct points are essentially 2.5, 1.5 and .5, with there being now two distinct but slightly different ways to realize about 1.5. This problem will become worse when we get to 107, and will increase exponentially.For inactives at age 108 we have The number of distinct points in this domain has doubled, which we again define as D108,i = {.5β3 + .5β5,.5β + .5β3,.5β3 + .5β5,0}. The domain is essentially 2, 1 and 0, and there are now two distinct but slightly different ways to realize about 1. Again, this problem will become worse when we get to 107, and will increase exponentially thereafter. In fact, Figures 1a, 1b, 2a, and 2b show the general recursion, from which the age x – 1 = 107 domain elements and their corresponding probabilities evolve from their age x = 108 counterparts.The general pattern is now clear. Starting at 107, with three transitions left (at 107.5, 108.5, and 109.5), there are in each of the domains of D107,a and D107,j. Binomial coefficients capture the number of ways in which each of the essential values occurs, there being 3+1=4 such essential values for each domain of 8 points. The domains of D107,a and D107,i are non-overlapping, being essentially on half-integers and integers, respectively, although this distinction will blur as the number of periods less than the terminal age, three above, increases. The link between the domains and ranges one year apart is indicated in Figures 1a and 2a, holds in general, and expresses the recursion of the present value function.This recursion, although true, provides only insight into the mathematical structure and cannot be exploited for computational purposes, unless β = 1, in which case the number of distinct points in the domain does not increase exponentially, but equals (TA – x). For a person age x, the number of distinct points, 2(TA – x−1), becomes a number which is impossible to compute and store: at age 50, 2111–50–1= 260 = 250210, and 250 megabytes of information will never be computable. We state this as thePresent Value Function Properties and Recursion: The present value functions px,a (•) and px,i (•) for a person exact age x will contain 2(TA– x–1) distinct possible values (points in the domains Dx,a and Dx,i, respectively). These arise from 2(TA –x)− 1 sample paths, giving rise to (TA – x) essential values, which arise from grouping of the distinct values together the of While computationally the domain of follows from the domains of and by use of the where the first half of Dx,a = .5β .5β + β2 and the second half of = .5β + β2 defined above, and the same is for the first half of = + .5β + β2 and the second half of = + + β2 The ranges of follow from the ranges of (•) and (•) by to the transition probabilities a a and a i and i as indicated in Figures 1a and Figures and light of the and computational of the present value function, it that there would be a useful and recursion to be The next section such a recursion for the of the present value random be the or mathematical expectations of the probability mass functions defined We now in exactly the same way as we did for and the present value functions in the active state, the new present value functions and which $1 for each year in the inactive These are not to be as but their the which which is enough Additionally, the of these present values gives a standard in both states, while and are of the value of an for all years while inactive have in or when there is no labor force will the present value and expected present value of years of The present values are defined much like for years of activity. We use only the Convention A and so only equations corresponding to its timing We allow for a different rate and a different age earnings with the symbols and will be where we that, we to these probability mass we should to these functions and their domains from given in now the equations for the mean value which will be into below. We consider The present value of all future activity, starting active, will have the first of which is a payment ½ of a year from age x, the ½ year discount β on the $1 for ½ of a period, and the .5, by the age earnings would typically be to 1 for age x). Next, there is a transition resulting in active, which at x + ½, then by our Convention .5 of this is paid then .5 must again be discounted back to x by and it with probability so that its expected value while .5 is paid 1 year and so will be in the present value The payments will occur at and and their present value, as of x+1, the transition at x + ½ is to active, and is the x + ½ transition is to inactive. These with probabilities and so that the expected present value at is + we need to these values back to age x, which requires discounting for two half by of are where in we are counting rather than activity. may be into where their structure becomes the equations gives each its in and the to denote the of could be with B results in which we as the Value labor force participation follows the Markov the expected present value of each base x) $1 of and is given by the of = B + + when starting active, and by the when starting inactive. The expected present value of each base x) $1 in the inactive state is given by the when starting active, and by the when starting are in 1. While by a the computational use of the time in the We need some value for at some age on the right hand side to be to use the equation to simply and quickly all previous values The natural age would to TA – 1, since at that age, only ½ year of life activity, one receives payment for .5 years discounted by active at and 0 with The same is when is and discounted at inactive at TA 1 and to start the recursion we have the If TA 1 is taken to be because of the values of and between x = and x = the values in are to either the choice of TA 1 or the values for Our present value or like the Ogden are calculated with no age earnings i.e. with = for all x. that it is to age earnings with = = 1 into the β = = 1 so that B = and = the recursion to = + + this is the same recursion which + + E and with no since it follows that = where is the of expected time in the right state, given that one has started at age x in the left we have that in this case the of the expected present values on the and the interest rate, for any initial and final and is continuous is from the recursion, and is Consequently the function is continuous as g and r, and the is well from the theoretical of as an extension of a well known function its the equality is useful in a computational for exact expression for the provides computational when the entire probability mass function is by as it must be when its general from its are being In this case, the question will arise as to a sample size is large enough to be that the of large has taken By the for the and the with known via the recursion, one can for the of sample the mean is not a sample size is there is no need to the for a the with a sample size in the of which would be in for one exact Since B and the recursion may be as (not to = results in the The information in recursion may be in a that the more familiar to forensic by of the age and for x, and and that this may be continued to x – x we the second equation into the first results in while the third expression we as in Skoog (2002), the as: of the are probabilities that a worker in the state by the left state at age x will be in the state by the right at age x + This is by for and is the in = on the right hand side are to which are each with an interesting economic The first the flows in age (x, is the in we have where the second payment and the first payment of .5 from two transitions are second the flows in transition (x, resulting from the grouping of in is The first in is the second payment made at x+.5 from the transition. The in the capture the two payments of .5 from the x+.5, transitions. In both the half period discount B are on and since and over a number of of the this the of x in in equation We provide tables which may be used with between for the or when are as of the for as of this is found in the of and In such a case, the so calculated would be by a interest In most state the period is between on which no discounting or is and future which are discounted to present value. In such a case, where the flows are either an would be or an extension of these tables would need to be For assuming that no more than years between the and the for a case where the is known to have to the the probabilities of being active and inactive in each of the years could be in a or out mortality would be in state death where would not be probabilities be useful in of and in the for a – average In any the tables with or such will provide both a on present value as well as a of the underlying variation about the expected present value which forensic economists Since the present value is in the NDR, the tables a to the question about how present value would with a small increase or in the 1 some characteristics of for x = Convention A for active age-earnings of This for the expected present value, present value, standard and the and points of the present value pmf at NDR's of 0, 1 is based on sample at each age x. present in 1, follow from the mathematical and (1) present value with (2) present value with and (3) As with life and in in expected present values become for in the the of the 1 less about present value (1) age, the standard of the present value random variable with the Figures show present value at age for NDR = 0, and – standard deviations with NDR's are in these which have the same of in to In at the standard

16 - Engineering Economics

Real-world tax systems distort investment and financing decisions. Therefore, taxes are integrated into capital budgeting models. However, these models use very simplified tax bases. Investors typically assume tax bases to be equal to cash flows less depreciation allowances. We analyse the investment incentives resulting from such a simplified tax planning. The analysis is based on a stochastic business simulation model applying empirical data from different industries. Using Monte Carlo simulations, we cover a wide variety of business developments. We show that using cash flows minus depreciation allowances as a tax base generates deviations compared to investment planning with a detailed tax base in accordance with current tax laws. The anticipated NPVs or future values of companies can be too high or too low, depending on the company's legal structure and industry. Using only cash flows as a tax base leads to an anticipated future value which is always too high. But these deviations are small compared to incorrect forecasts of interest rates or tax rates. For example, if the income tax is reduced to 37%, while the anticipated tax rate is 42%, or if the interest rate increases by 3 percent points, the future value and the deviation are much higher compared to tax base-induced deviations. Hence, investors should pay more attention to the forecast of interest rates and tax rates, as opposed to reproducing a more detailed tax base of investment projects.

Comment

If the historical average annual real interest rate is m > 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year? Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process dr(t) = alpha[m - r(t)]dt kdw(t), where w is a standard Wiener process. Then we prove that the long run rate of interest is r_infinity = m-k^2/2alpha^2. This confirms the Weitzman-Gollier principle that the volatility and the persistence of interest rates lower long run discounting. We fit the OU model to historical data across 14 countries covering 87 to 318 years and estimate the average short rate m and the long run rate r_infinity for each country. The data corroborate that, when doing cost benefit analysis, the long run rate of discount should be taken to be substantially less than the average short run rate observed over a very long history.

Economic analysis of power generation from floating solar chimney power plant

Stability in the Present Value Assessment of Lost Earnings Abstract This article recommends a uniform methodology and a benchmark for assessing present value awards for future lost earnings in personal injury litigation. basis of this recommendation is the remarkable stability, over successive periods of loss and across occupations, of the relative difference between the average annual after-tax interest rate on short-term Treasury securities and the average annual growth rate in after-tax earnings. stability of this relationship is consistent with economic and financial theories and is strongly supported by empirical evidence from 1952 through 1982. Introduction desire to adopt a uniform methodology and the need to establish guidelines for assessing present value awards for future lost earnings in personal injury litigation have been widely recognized in the literature and by the courts. Numerous articles have addressed the issues in determining the proper present value of lost earnings. Several of these articles have concentrated on the appropriate interest rate to use in discounting future lost earnings to present value [e.g., 5, 10, 17, 18, 20, 23]. Other articles have suggested benchmarks for assessing awards based on the historical relationship between interest rates and growth rates in earnings [e.g., 4, 7, 15, 16, 22, 24, 25]. Despite this attention, there is no consensus among economists or the courts regarding the best approach to employ in determining present value awards for lost earnings. Methodologies and benchmarks adopted and/or advocated by different courts for assessing these awards have varied dramatically [e.g., 1, 2, 3, 8, 13, 21]. After reviewing much of the literature and many of the court cases pertaining to this issue, the Supreme Court recently called for a study, stating, The legislative branch of the federal government is far better equipped than we are to perform a comprehensive economic analysis and to fashion the proper general rule[21, p. 2557]. In this article the authors report the results of a comprehensive and integrated study of the assessment of present value awards for lost earnings from 1952 through 1982. Thousands of present value awards (awards that would have allowed replication of actual after-tax lost earnings) were calculated for 454 industrial classifications for various periods of loss. This analysis suggests both a relatively simple methodology and a benchmark to use in assessing present value awards for lost earnings for the many cases in which the plaintiff's lost earnings stream is expected to equal the earnings over the period of loss of the average worker in a given occupation. Background current practice in personal injury litigation is to award plaintiffs a present sum of money as compensation for future lost earnings. intention is to make the plaintiff whole in the sense that the award allows the plaintiff, through investment in relatively safe securities, to replicate over time the lost after-tax earnings stream. amount of such an award depends ultimately on the relative difference, over the period of loss, between the after-tax rate of interest the plaintiff is expected to earn through investing the award and the rate of growth in after-tax earnings expected in the plaintiff's pre-injury occupation. This relative difference, which is defined and explained below, will be referred to as the discount or net interest rate. A number of economists have recently argued that the net discount rate is relatively stable over time because both the interest rate and the growth rate in earnings are positively correlated with the rate of price inflation[e.g., 4, 15, 16, 24]. Several authors have advocated using net discount rates, based on historical observations of interest and growth in earnings rates, in assessing awards for lost earnings. …

The use of an inter-temporally constant discount rate or cost of capital is a strong assumption in many ex ante models of finance and in applied procedures such as capital budgeting. We investigate how robust this assumption is by analysing the implications of allowing the cost of capital to vary stochastically over time. We use the Feynman–Kac functional to demonstrate how there will, in general, be systematic differences between present values computed on the assumption that the currently prevailing cost of capital will last indefinitely into the future and present values determined by discounting cash flows at the expected costs of capital that apply up until the point in time at which cash flows are to be received. Our analysis is based on three interpretations of the Feynman–Kac functional. The first assumes that the cost of capital evolves in terms of a state variable characterised by an Uhlenbeck and Ornstein (“On the Theory of the Brownian Motion.” Physical Review 36(5): 823–841) process. The second and third interpretations of the Feynman–Kac functional are based on the continuous time branching process. The first of these assumes that the state variable tends to drift upwards over time, whilst the second assumes that there is no drift in the state variable. Our analysis shows that for all three stochastic processes there are significant differences between present values computed under the assumption that the currently prevailing cost of capital will last indefinitely into the future and present values determined by discounting cash flows at the expected costs of capital that apply up until the point in time at which cash flows are to be received. Comparisons are also made with the environmental economics literature where similar problems have been addressed by invoking a ‘gamma discounting’ methodology.

Lambrinos and Harmon (1989) empirically evaluate two methods that have been used to estimate economic damages. The two approaches they evaluate are the offset approach and the augmented offset approach. The augmented offset approach is adjusted by an age-earnings factor. The estimated present values using each approach are calculated and then evaluated by comparing them with the present values of actual worker earnings drawn from the Panel Study on Income Dynamics (PSID). Discussing their comparison of estimated present values using the offset and augmented offset methods with the calculated present values using the PSID longitudinal survey earnings data, the authors state that both methods underestimate the loss ... (p. 737). The use of an inappropriately low interest rate to discount PSID earnings could cause both methods of estimation to underestimate the loss. If an inappropriately low interest rate is used to discount actual PSID earnings, the resulting lump-sum awards will be higher than if higher interest rates were used. The resulting higher calculated lump-sum awards for actual PSID earnings would cause the estimated awards using both the offset and augmented offset methods to be low in comparison. The authors state that the rate chose for discounting the workers' actual earnings from 1971 through 1983 is the nontaxable municipal bond yield average from 1961 through 1970, 4.10 (p. 735).(1) It can be argued that the use of the average municipal bond yield from 1961 through 1970 to discount actual 1971 through 1983 earnings is inappropriate. To the extent that interest rates rise with inflation, it is likely that the discount rate would be higher if one rolled-over short-term instruments rather than invested in long-term bonds in an environment of rising inflation. Returns from a portfolio of long-term bonds do not change as interest rates rise. Thus, while Lambrinos and Harmon state that Because this period spans three full business cycles, the results are not likely to reflect the influence of a particular stage of the business cycle, (p. 738) they overlook an important postwar event-the rise of inflation in the 1970's. The authors, constrained by data availability, used the period 1971 through 1983 to compare the estimated present values using the offset and augmented offset approaches with present values using actual PSID earnings. Table 1 shows that this 13 year period (1971 through 1983) exhibited higher inflation, wage growth, and interest rates than the 1961 through 1970 decade that preceded it. Recall that Lambrinos and Harmon used the 1961 through 1970 period to calculate the average municipal bond yield which they used to discount actual PSID earnings. Table 1 A Comparison of the 1961 through 1970 and 1971 through 1983 periods* 1961-1970 1971-1983 (percent) percent annual average inflation rate 2.7 7.5 annual average rate of wage change 4.0 6.8 annual average Treasury bill rate 4.6 7.9 annual average municipal bond rate 4.1 7.3 * The inflation rate is for the consumer price index. The rate of wage change is for total private average weekly earnings. The Treasury bill rate is for 9 through 12 month issues for 1961 through 1970 and one year issues for 1971 through 1983. The municipal bond rate is the S&P high grade series. See: Economic Report of the President and the Federal Reserve Bulletin. The use of short-term Treasury instruments to reduce exposure to inflation risk would have resulted in a higher discount rate. That is, the discount rate employed by the authors based on the 1961 through 1970 period was lower than would have been the case if interest rates that prevailed on short-term instruments during the 1971 through 1983 period had been used. …

Stochastic bio-economic optimization of pond size for intensive commercial production of whiteleg shrimp Litopenaeus vannamei

Mathematical modeling of the tubular solar still (TSS) has been carried out. The MATLAB code has been developed for calculating the performance parameters like tubular glass cover temperature, rectangular basin liner temperature, basin water temperature, and productivity and efficiency. The results obtained from mathematical modeling has been compared with the benchmark results of experimental work of various research work related to present study for the validation of present work . Different heat transfer coefficients have been calculated on hourly basis. Heat transfer coefficient values increase from minimum at early in the morning and reaches the maximum at afternoon then it starts decreasing near the evening time. The maximum evaporative heat transfer coefficient, convective heat transfer coefficient, and radiative heat transfer coefficient are 33.28 W m 2 ∘ C , 2.90 W m 2 ∘ C , and 6.49 W m 2 ∘ C , respectively. Evaporative heat transfer coefficient is dominating amongst others. Basin water temperature and hourly yield of TSS have been calculated for 1 cm, 2 cm, 3 cm, and 4 cm water depth, respectively. The tubular glass cover temperature and basin water temperature for different climatic zone of India have been calculated. Various cities such as Nagpur, Chennai, Jaipur, Srinagar, and Guwahati are considered for studying the effect on tubular glass cover temperature, water temperature stored in rectangular basin liner, hourly yield for these geographical locations of India. The tubular glass cover temperature for three absorptivity values 0.04, 0.08, and 0.16 (of glass materials) has also been calculated. As a result, 5.8 kg of fresh water cumulative yield have been obtained from 6 am to 6 pm for whole day. From the economic analysis study of TSS, it is found that cost for producing fresh water per kg depend on annual interest rate. Higher value of interest rate results in higher cost for producing fresh water. In the study, annual rate considered are 5%, 10%, and 15% for which cost of producing fresh water are 0.255, 0.521, and 0.786 $ / k g , respectively. Efficiency of TSS increases from morning and reaches maximum at the noon when solar intensity is highest for a day then it starts decreasing toward the end of day in the evening. The maximum thermal efficiency of TSS is 43.78% at 12 noon where solar intensity is maximum for the day. The maximum exergy efficiency obtained at 11 am is 50.88% then it decreases as the temperature and solar intensity decreases with the time.