Present worth determination

Work sheet for presenting discounted-cash flow, present-value, and net-present-worth determinations ... 

Verink s equation for determining the present worth (PW) for different economic design situations using straight-line depreciation were written as ... 

It is often necessary to determine the amount of money which must be available at the present time in order to have a certain amount accumulated at some definite time in the future. Because the element of time is involved, interest must be taken into consideration. The present worth (or present value) of a... 

In Eq. (5), S represents the amouht available after n interest periods if the initial principal is P and the discrete compound-interest rate is i. Therefore, the present worth can be determined by merely rearranging Eq. (5). 

Example 4 Determination of present worth and discount. A bond has a maturity value of 1000 and is paying discrete compound interest at an effective annual rate of 3 percent. Determine the following at a time four years before the bond reaches maturity value ... 

For the conditions of Prob. 9, determine the present worth at time zero for each of the three types of payments. 

In the preceding treatment of discounted cash flow, the procedure has involved the determination of an index or interest rate which discounts the annual cash flows to a zero present value when properly compared to the initial investment. This index gives the rate of return which includes the profit on the project, payoff of the investment, and normal interest on the investment. A related approach, known as the method of net present worth (or net present value or venture worth), substitutes the cost of capital at an interest rate i for the... 

To illustrate the method for determining net present worth, consider the example presented in Table 1 for the case where the value of capital to the company is at an interest rate of 15 percent. Under these conditions, the present value of the cash flows is 127,000 and the initial investment is 110,000. Thus, the net present worth of the project is... 

It is quite possible to compare a series of alternative investments by each of the profitability measures outlined in the early part of this chapter and find that different alternatives would be recommended depending on the evaluation technique used. If there is any question as to which method should be used for a final determination, net present worth should be chosen, as this will be the most likely to maximize the future worth of the company. 

For investments 2 and 3, the present values of the cash flows to the projects are determined from the first two equations under part (c) of this problem, with i 0.15. The resulting net present worth are ... 

The preceding example clearly shows that inflation effects can be important in determining returns on investment. The best strategy for handling such effects is to use the discounted-cash-flow or present-worth method for reporting returns on investment with the results based on the after-tax situation. This method of reporting can be handled easily and effectively by use of an appropri-... 

Calculate the net present worth (NPW)for the inorganic chemicals plant. Step 3 determined undiscounted NCFs. To determine the net present worth, NPW, it is necessary to determine the discounted NCF for each year in the project life and then their sum. The discounted NCF for year k is the product of the discount factor (1 /[I + i ]k) and the undiscounted NCF. The discounted NCFs for the various years, and their sum the NPW, are as follows ... 

Present worth of an annuity, 228 definition of 225-226 factors for, 223n., 236-237 method for determining depreciation, 285... 

Many properties other than those presented will determine the eventual worth of an agent in a desalting process. Among these are the stability in water, the solubility in water and salt solutions, the rates of nucleation and growth and the nature of the hydrate crystals, and the cost of the agent. 

Each company and each economist has one or more ways of determining profitability by economic analysis. It is not the purpose of this book to elaborate on these. Excellent books on chemical engineering economy are listed in the Additional Selected References. However, three of the more popular methods will be discussed (1) return on investment, (2) pay-out time, (3) project present worth. To proceed with the economic analysis, net or new earnings must first be determined from selling price less costs. 

To illustrate, consider the problem summarized in Table 3. There are three risky, independent, end-of-year cash flows the means and variances of their respective probability functions are given in columns (2) and (3) of Table 3. Project life, N, is also a random variable, with probability mass function as shown in columns (6) and (7) of the table. A 10% discount rate is assumed. Determination of the expected present worth, based on Eq. 17, is summarized in the table. Here, fXp = — 82.64. The variance of present worth, 0-2, based on Eqs. 18 and 19, may be shown to be... 

Step 3 Determine the figure of meat (rate of return or present worth, for example) for each combination of factors. One trial consists of one calculation of the figure of merit. 

The model determines the type and sizes of facilities to be added/removed and when so that the present worth of all capacity changes is minimized while meeting forecasted demand. Examples of such classical and static models can be found in Manne (1967) and Freidenfelds (1981), while a good review on classical capacity expansion models can be found in Luss (1982). 

Early in this section, only two sums of money were considered, one at the beginning, called present worth, P, and one at the end, called future worth, F. One of these was referred to as the single payment. The two were related by equations involving the interest rate/period and the number of periods that interest was applied. The use of compound interest to determine sums earlier in time (e.g., present worth) that are equivalent to a later, larger sum (e.g., future worth) was referred to as discounting. Factors such as 1/(1 + /)" are called discount factors. The concepts in the previous section can be extended to a veiy common situation, called the annuity, where instead of a single payment, a series of equal payments is made at equal time intervals. Annuities also involve discounting and discount factors. 

The present worth of an annuity, P, is the amount of money at the present time that if invested at a compound interest rate will yield the amount of the annuity, F, at a future time. This is useful for determining the periodic payments that can be made over a specified number of years in the future from an annuity. 

Annuity equations relating F and the periodic payments. A, are converted to equations relating P to A by combining them with Eq. (17.12) for discrete interest or Eq. (17.20) for continuous interest. This is often referred to as discounting the amount of the annuity to determine its present worth. In Table 17.7, under periodic interest, the discrete uniform-series sinking-fund deposit factor becomes the discrete uniform-series capital-recovery facte in the following manner ... 

Note that we have determined the equivalent present worth of all future cash flow, including the yearly maintenance and operating costs and the salvage value of the air-conditioning unit. In the preceding analysis, the negative si indicates cost, and because alternative B has a lower present cost, we choose alternative B. 

It incorporates the concept of present worth for evaluating future expenditure and the procedure of life cycle cost analysis (LCCA). The basic factors required for LCCA are as follows (a) initial cost of pavement structure (b) cost of future overlays, major maintenance or reconstruction, or other interventions (c) time, in years, from initial construction up to each intervention (d) salvage value of the structure at the end of the analysis period (e) interest rate and (f) determination of the analysis period. 

The trial present-worth calculations that equal the net cash flow total are those that are used to determine the ROI. 

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