Project, present-worth method

Project Present Worth Method. This method recognizes the time value of money and is more widely used by economists and accountants in presenting profitability reports to management, particularly when two processes require close comparison. Engineers should have an understanding of this method. 

The sum of these discounted NCEs over the life of the project is the project s net present worth. The project with the highest positive net present worth would be the one selected. The discount rate used in Eq. (18.5) is the firm s marginal acceptable rate of return (MARR) for anticipated projects or its hurdle rate. Note that the discount rate is expressed on an after-tax basis to be consistent with the NCF. Also, when comparing projects via the present worth method, all projects must have equal... 

The internal rate of return method is a special case of the present worth method. With the IRR, the net present worth of each project first is arbitrarily set equal to zero, with the discount rate kept as an independent variable. Then, each NPW equation is solved (via an iterative procedure) for the unique discount rate/intemal rate of return that yields an NPW of zero. The project with the highest positive IRR would be the one selected. 

Related Calculations. The difference between the two internal rates of returns is so small that, on a purely economic basis, the projects are virtually indistinguishable. By contrast, the difference in the projects net present worths (see Example 18.5) is large enough to make the textile fibers expansion the clear choice for funding. As with the net present worth method, the internal rate of return procedure cannot be used unless the lifetimes of the competing projects are equal. 

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. 

The present worth method compares all of a project s estimated expenditures to all of its estimated revenues and other benefits at a reference time called the present (/ = 0). For a particular interest rate, if the present value of the revenues and other benefits exceeds the present value of the expenses, the project is considered acceptable. The present worth of alternative j with cash flows that last of n periods of time at i% interest per period is... 

The annual worth method converts all cash flows to an equivalent uniform series of equal annual payments. As in the present worth method, if the annual worth of the revenues is greater them the annual worth of the costs for the specified interest rate, then the project is acceptable. The annual worth of alternative j and i percent rate of interest per period, which lasts for n periods, is... 

The future worth (FW) method is comparable to the present worth method except that the comparison between the project s estimated expenditures and benefits occurs at a reference time called the future (t = F). As in present worth analysis, in future worth analysis a project is acceptable at a particular interest rate if the future value of the revenues and other benefits exceeds the future value of the expenses. Likewise, the preferred alternative, given equal future benefits, would be the alternative with the lowest future costs. 

The annualized capital cost (ACC) is the product of the CRF and TCC and represents the total instaUed equipment cost distributed over the lifetime of the project. The ACC reflects the cost associated with the initial capital outlay over the depreciable life of the system. Although investment and operating costs can be accounted for in other ways such as present-worth analysis, the capital recovery method is preferred because of its simplicity and versatUity. This is especiaUy true when comparing somewhat similar systems having different depreciable lives. In such decisions, there are usuaUy other considerations besides economic, but if all other factors are equal, the alternative with the lowest total annualized cost should be the most viable. 

Discounted cashflow (DCF). This method recognizes that 1,000 income in five years time is worth less than 1,000 receivable this year. The use of DCF in appraising two or more competing projects offers two methods of assessment the net present value (NPV) or DCF rate of return. 

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... 

Income-tax effects can be included properly in all the profitability methods discussed in this chapter by using appropriate definitions of terms, such as those presented in Table 4. The methods of discounted-cash-flow rate of return and present worth are limited to consideration of cash income and cash outgo over the life of the project. Thus, depreciation, as a cost, does not enter directly into the calculations except as it may affect income taxes. 

In the present worth (or discounted cash flow) method, each annual net cash flow for a project is discounted to the beginning of the project (year zero), in order to express all cash flows on the same basis. This discounting is done via the following equation ... 

Even so, the EUAR method is best suited to those situations where (as in this case) the undiscounted net cash flows are constant. However, when they are not constant, each NCF must be discounted back to year zero, summed, and annualized by multiplying it by the CRF. Finally, this annualized NCF must be added to the capital recovery cost. By the time the analyst has done all of this, he or she could just as well have calculated the net present worths or internal rates of return of the competing projects. 

A commonly used profitability index in conjunction with the NPV method shows how closely a project has met the criterion of economic performance. This index is known as the present value ratio (PVR) or present worth ratio (PWR), and is defined as... 

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