Advantages and Uses of Annual Worth Analysis
For many engineering economic studies, the AW method is the best to use, when compared to PW, FW, and rate of return (Chapters 6). Since the AW value is the equivalent uniform annual worth of all estimated receipts and disbursements during the life cycle of the project or alternative, AW is easy to understand by any individual acquainted with annual amounts, for example, dollars per year. The AW value, which has the same interpretation as A used thus far, is the economic equivalent of the PW and FW values at the MARR for n years. All three can be easily determined from each other by the relation
The n in the factors is the number of years for equal-service comparison. This is the LCM or the stated study period of the PW or FW analysis. When all cash flow estimates are converted to an AW value, this value applies for every year of the life cycle and for each additional life cycle.
The annual worth method offers a prime computational and interpretation advantage because the AW value needs to be calculated for only one life cycle. The AW value determined over one life cycle is the AW for all future life cycles. Therefore, it is not necessary to use the LCM of lives to satisfy the equal-service requirement.
As with the PW method, there are three fundamental assumptions of the AW method that should be understood. When alternatives being compared have different lives, the AW method makes the assumptions that
1. The services provided are needed for at least the LCM of the lives of the alternatives.
2. The selected alternative will be repeated for succeeding life cycles in exactly the same manner as for the first life cycle.
3. All cash flows will have the same estimated values in every life cycle.
In practice, no assumption is precisely correct. If, in a particular evaluation, the first two assumptions are not reasonable, a study period must be established for the analysis. Note that for assumption 1, the length of time may be the indefinite future (forever). In the third assumption, all cash flows are expected to change exactly with the inflation (or deflation) rate. If this is not a reasonable assumption, new cash flow estimates must be made for each life cycle, and again a study period must be used.
In Example (4-3), National Homebuilders, Inc. evaluated cut-and-finish equipment from vendor A (6-year life) and vendor B (9-year life). The PW analysis used the LCM of 18 years. Consider only the vendor A option now. The diagram in Figure (5–1) shows the cash flows for all three life cycles (first cost $ -15,000; annual M&O costs $ -3500; salvage value $1000). Demonstrate the equivalence at i = 15% of PW over three life cycles and AW over one cycle. In Example (4-3), present worth for vendor A was calculated as PW = $ -45,036.
Figure (5-1): PW and AW values for three life cycles, Example (5-1).
Calculate the equivalent uniform annual worth value for all cash flows in the first life cycle.
When the same computation is performed on each succeeding life cycle, the AW value is
$ -7349. Now Equation (5-1) is applied to the PW value for 18 years.
The one-life-cycle AW value and the AW value based on 18 years are equal.