Time value

The project cashflow discussed so far follows a pattern typical of E P projects a number of years of expenditure (giving rise to cash deficits) at the beginning of the project, followed by a series of cash surpluses. The annual cashflows need to be evaluated to incorporate the timing of the cash flows, to account for the effect of the time value of monef. The technique which allows the values of sums of money spent at different times to be consistently compared is called discounting. 

The cashflow discussed in Section 13.2 did not take account of the time value of money, and was therefore an undiscounted cashflow. The discounting technique discussed can now be applied to this cashflow to determine the present value of each annual cashflow at a specified reference date. 

Figure C 1.5.10. Nonnalized fluorescence intensity correlation function for a single terrylene molecule in p-terjDhenyl at 2 K. The solid line is tire tlieoretical curve. Regions of deviation from tire long-time value of unity due to photon antibunching (the finite lifetime of tire excited singlet state), Rabi oscillations (absorjDtion-stimulated emission cycles driven by tire laser field) and photon bunching (dark periods caused by intersystem crossing to tire triplet state) are indicated. Reproduced witli pennission from Plakhotnik et al [66], adapted from [118].

After identification of the elements that contain feet of particle trajectories the old time step values of F at the feet are found by interpolating (or extrapolating for boundary nodes) its old time step nodal values. In the example shown in Figure 3.6 the old time value of Fat the foot of the trajectory passing through A is found by interpolating its old nodal values within element (e). 

Toxicity studies (108—110) estabUshed tolerance levels and degrees of irritations, indicating that the eye is the area most sensitive to fluorine. Comprehensive animal studies (111—113) deterrnined a rat LC q value of 3500 ppm-min for a single 5-min exposure and of 5850 ppm-min for a 15-min exposure. A no-effect concentration corresponded to a concentration-time value of ca 15% of the LC q levels. 

Ref 91. Discounted cash-flow models account for use of capital, working capital, income taxes, time value of money, and operating expenses. Real after-tax return assumed to be 12.0%. Short-rotation model used for sycamore and poplar. Herbaceous model used for other species. Costs ia 1990 dollars. Dry tons. 

Cost. The catalytically active component(s) in many supported catalysts are expensive metals. By using a catalyst in which the active component is but a very small fraction of the weight of the total catalyst, lower costs can be achieved. As an example, hydrogenation of an aromatic nucleus requires the use of rhenium, rhodium, or mthenium. This can be accomplished with as fittie as 0.5 wt % of the metal finely dispersed on alumina or activated carbon. Furthermore, it is almost always easier to recover the metal from a spent supported catalyst bed than to attempt to separate a finely divided metal from a liquid product stream. If recovery is efficient, the actual cost of the catalyst is the time value of the cost of the metal less processing expenses, assuming a nondeclining market value for the metal. Precious metals used in catalytic processes are often leased. 

If money is borrowed, interest must be paid over the time period if money is loaned out, interest income is expected to accumulate. In other words, there is a time value associated with the money. Before money flows from different years can be combined, a compound interest factor must be employed to translate all of the flows to a common present time. The present is arbitrarily assumed often it is either the beginning of the venture or start of production. If future flows are translated backward toward the present, the discount factor is of the form (1 + i) , where i is the annual discount rate in decimal form (10% = 0.10) and n is the number of years involved in the translation. If past flows are translated in a forward direction, a factor of the same form is used, except that the exponent is positive. Discounting of the cash flows gives equivalent flows at a common time point and provides for the cost of capital. 

Payout time (PT), or payback period, is a measure of the time, usually in years, required to recover the investment in a scenario in which the time value of money is neglected. This can be represented by the general form... 

Time Value of Money A large part of business activity is based on money that can be loaned or Borrowed. When money is loaned, there is always a risk that it may not be returned. A sum of money called interest is the inducement offered to make the risk acceptable. When money is borrowed, interest is paid for the use of the money over a period of time. Conversely, when money is loaned, interest is received. 

These data may be evaluated by selecting different nominal overflow rates (equivalent to settling rates) for each of the detention-time values, and then plotting the suspended-solids concentrations for each nominal overflow rate (as a parameter) against the detention time. For a specified suspended-sohds concentration in the effluent, a cui ve of overflow rate versus detention time can be prepared from this plot and used for optimizing the design of the equipment. 

Once the bids are tabulated for specification compliance in the form of a chart for easy review by all others involved in the project, an overall evaluation should be made, factoring in energy cost, first cost, and time value of money using an established economic equation. Most companies have a standardized formula. If the data are available, total cost of ownership can be estimated, which for larger equipment is considered a good measure for evaluation. 

If the distribution curve is only known at a number of discrete time values, tj, then the mean is expressed by... 

The output from this operation is a single vector composed of time values and then the dependentvariablevalues.Weneedthemtobepairedinordertoplotthem.Thuswe first... 

For double acting pumps, single cylinder Q = (two times value for single acting) — 0.0204 d t,... 

This method, which is favored by many accountants today, takes into account the concept that money has a time value. This is because 2000 in 10 years time is not the same as 2000 now. Similarly, if a project earns 2000 in 10 years time this is not the same as 2000 spent now to help finance the project. If, instead of spending this 2000, it had been invested at compound interest, then in 10 years time it would have become a much larger... 

Historical average time values reflect what has happened rather than what should happen. 

Expenditure on corrosion prevention is an investment and appropriate accountancy techniques should be used to assess the true cost of any scheme. The main methods used to appraise investment projects are payback, annual rate of return and discounted cash flow (DCF). The last mentioned is the most appropriate technique since it is based on the principle that money has a time value. This means that a given sum of money available now is worth more than an equivalent sum at some future data, the difference in value depending on the rate of interest earned (discount rate) and the time interval. A full description of DCF is beyond the scope of this section, but this method of accounting can make a periodic maintenance scheme more attractive than if the time value of money were not considered. The concept is illustrated in general terms by considering a sum of money P invested at an... 

A consideration of the costs of the protective Schemes 1 and 3 given in Table 9.2 indicates that the latter is significantly more expensive than the former, and it is of interest, therefore, to apply the concept of the time value of money to these two schemes for 11 of steel processed. 

Thus it can be seen that although the aggregate cost indicates Scheme 1 to be the cheaper, it is the more expensive when account is taken of the time value of money. 

Methods of EGA using selective sorption, condensation of effluent gases, infrared absorption and thermoparticulate analysis have been reviewed by Lodding [144]. The use of simple gas burette systems should not be forgotten and an Orsat gas analysis apparatus can provide useful measurements in studies of the decomposition of formates [169]. Problems have been encountered in the determination of water released Kiss et al. [170—172] have measured the formation of this compound from infrared analyses of the acetylene evolved following reaction of water with calcium carbide. Kinetic data may be obtained by wet methods ammonia, determined by titration after absorption in an aqueous solution, has been used to measure a—time values for the decomposition of ammonium salts in a fluidized bed [173],... 

Characteristic features of a—time curves for reactions of solids are discussed with reference to Fig. 1, a generalized reduced-time plot in which time values have been scaled to t0.s = 1.00 when a = 0.5. A is an initial reaction, sometimes associated with the decomposition of impurities or unstable superficial material. B is the induction period, usually regarded as being terminated by the development of stable nuclei (often completed at a low value of a). C is the acceleratory period of growth of such nuclei, perhaps accompanied by further nucleation, and which extends to the... 

The reduced time method [in (ii), above] refers to the scaling of time values to facilitate the comparison. It is often convenient to use tT = 1.00... 

Jones et al. [73] have provided an alternative approach to the linearization of data using the tabulated reduced time values given by Sharp et al. [70]. The experimental data are expressed in the form ae as a function of (t/t0.s)ei where the subscript e refers to the experimental data. Three broadly equivalent methods of plotting can be used. 

Opposing reactions. Derive a kinetic equation for the system A P + Q that expresses the time dependence of 8, the shift in a concentration-jump experiment. Could 8 also be regarded as the difference between the timed value of [A] and the equilibrium value of [A] If so, what are the limitations on the ways in which A, P, and Q might be mixed ... 

Many reaction schemes with one or more intermediates have no closed-form solution for concentrations as a function of time. The best approach is to solve these differential equations numerically. The user specifies the reaction scheme, the initial concentrations, and the rate constants. The output consists of concentration-time values. The values calculated for a given model can be compared with the experimental data, and the rate constants or the model revised as needed. Methods to obtain numerical solutions will be given in the last section of this chapter. 

We turn now to situations for which the family of differential equations cannot be solved explicitly. They require numerical methods to generate concentration-time values. To achieve these solutions, the user specifies the initial concentrations, the rate... 

The simulated concentration-time values are displayed graphically in Fig. 5-1. These values could not have been obtained from analytical expressions. Most schemes that comprised a few steps can be handled by the Runge-Kutta methods, provided the time scales of the various steps are comparable. 

A graphical display of concentration-time values for three species in the following scheme ... 

The stopped-flow method generates ordinary kinetic data, presenting values of the property Y, as a function of time. At one time, values were read from a Polaroid photograph of the oscilloscope, but nowadays computer acquisition, presentation, and... 

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