Present Worth Analysis of Equal-Life Alternatives
The PW comparison of alternatives with equal lives is straightforward. The present worth P is renamed PW of the alternative. The present worth method is quite popular in industry because all future costs and revenues are transformed to equivalent monetary units NOW; that is, all future cash flows are converted (discounted) to present amounts (e.g., dollars) at a specific rate of return, which is the MARR. This makes it very simple to determine which alternative has the best economic advantage. The required conditions and evaluation procedure are as follows:
If the alternatives have the same capacities for the same time period (life), the equal-service requirement is met. Calculate the PW value at the stated MARR for each alternative.
For mutually exclusive (ME) alternatives, whether they are revenue or cost alternatives, the following guidelines are applied to justify a single project or to select one from several alternatives.
One alternative: If PW ≥ 0, the requested MARR is met or exceeded and the alternative is economically justified.
Two or more alternatives: Select the alternative with the PW that is numerically largest, that is, less negative or more positive. This indicates a lower PW of cost for cost alternatives or a larger PW of net cash flows for revenue alternatives.
Note that the guideline to select one alternative with the lowest cost or highest revenue uses the criterion of numerically largest. This is not the absolute value of the PW amount, because the sign matters. The selections below correctly apply the guideline for two alternatives A and B.
For independent projects, each PW is considered separately, that is, compared with the DN project, which always has PW = 0. The selection guideline is as follows:
One or more independent projects: Select all projects with PW ≥ 0 at the MARR.
The independent projects must have positive and negative cash fl ows to obtain a PW value that can exceed zero; that is, they must be revenue projects.
A university lab is a research contractor to NASA for in-space fuel cell systems that are hydrogenand methanol based. During lab research, three equal-service machines need to be evaluated economically. Perform the present worth analysis with the costs shown below. The MARR is 10% per year.
These are cost alternatives. The salvage values are considered a “negative” cost, so a + sign precedes them. (If it costs money to dispose of an asset, the estimated disposal cost has a - sign.) The PW of each machine is calculated at i = 10% for n = 8 years. Use subscripts E , G , and S .
The solar-powered machine is selected since the PW of its costs is the lowest; it has the numerically largest PW value.
As discussed in the introduction to this chapter, ultrapure water (UPW) is an expensive commodity for the semiconductor industry. With the options of seawater or groundwater sources, it is a good idea to determine if one system is more economical than the other. Use a MARR of 12% per year and the present worth method to select one of the systems.
An important first calculation is the cost of UPW per year. The general relation and estimated costs for the two options are as follows:
Calculate the PW at i = 12% per year and select the option with the lower cost (larger PW value). In $1 million units:
Based on this present worth analysis, the seawater option is cheaper by $2.52 M.