LIFE CYCLE COST ANALYSIS–A CASE STUDY
 Long-term operating costs can manifest themselves in facilities in a variety of ways. The most visible and notorious is simple deferred maintenance, where systems, equipment and materials are not taken care of and they age or fail prematurely. The normal excuse is that the organization does not have the resources, in either labor or dollars, to perform the expected levels of upkeep. Other costs are less visible and more parasitic such as energy and operating costs.
Example: Air Handling Units
Consider the selection between two air handling units. A 10 percent discount rate, a twenty-four year life cycle, and a differential energy rate escalation of 2 percent per year are assumed. Other relevant data are:
|
Alternative 1 |
Alternative 2 |
| Type of Cost |
Energy Efficient |
Economy |
| Initial cost |
$15,000 |
$10,000 |
| Energy (annual) |
1,800 |
2,200 |
| Maintenance (annual) |
500 |
800 |
| Useful life |
12 years |
8 years |
The solution begins by converting all annual or recurring costs to the present time. Using the present worth annuity factor
(Table 1 (PDF - 21 KB),
the recurring costs of maintenance would be:
Alternative One: maintenance (present worth) = $500 x (8.985) = $4,492
Alternative Two: maintenance (present worth) = $800 x (8.985) = $7,188
According to
Table 2 (PDF - 24 KB),
the present worth of the energy costs for each alternative would be:
Alternative One: energy (escal. @ 2%) = $1800 x (10.668) = $19,202
Alternative Two: energy (escal. @ 2%) = $2200 x (10.668) = $23,470
Replacement or nonrecurring costs are considered next. When one or more alternatives have a shorter or longer life than the life cycle specified, an adjustment for the unequal life is necessary. If the life of an alternative is shorter than the project's life cycle, the item continues to be replaced until the life cycle is reached. On the other hand, if the item life is longer than the specified life cycle, then a terminal or salvage value for the item is recognized at the end of the life cycle. This treatment, using the present worth factors in
Table 3 (PDF - 25 KB),
is illustrated as follows:
Alternative Two: replacement (n = 8) = $10,000 x (0.4665) = $4,665
Alternative One: replacement (n = 12) = $15,000 x (0.3186) = $4,779
Alternative Two: replacement (n = 16) = $10,000 x (0.2176) = $2,176
The salvage value for both systems equals zero since they both complete replacement cycles at the end of the twenty-four year life cycle. A summary of present worth life cycle costs follows:
|
Alternative 1 |
Alternative 2 |
| Type of Cost |
Energy Efficient |
Economy |
| Initial cost |
$15,000 |
$10,000 |
| Maintenance (recurring) cost |
4,492 |
7,188 |
| Energy (recurring) cost |
19,202 |
23,470 |
| Replacement (nonrecurring), year 8 |
0 |
4,665 |
| Replacement (nonrecurring), year 12 |
4,779 |
0 |
| Replacement (nonrecurring), year 16 |
0 |
2,176 |
| Salvage, year 24 |
0 |
0 |
| Total present worth life cycle costs |
$43,473 |
$47,499 |
The first alternative should be selected based on this life cycle cost analysis.
To simplify the above example, a uniform worksheet (using the present worth method) is presented in Figure 1. Each cost element for the second example is entered on the present worth format worksheet. This worksheet is divided into three major categories. The upper third is devoted to initial costs. In this example, the purchase cost is listed for each air-handler alternative. Note that the estimated cost and the present worth cost are the same for the initial cost category. The total initial cost for each alternative is then determined and recorded in the appropriate place on the form.
The middle third of the worksheet is used for recording replacement and salvage values. In this example, replacement costs occur at years eight and sixteen for the economy air handler and year twelve for the performance air handler. These values are listed under the estimated cost column of the worksheet. To calculate the present worth of replacement costs, the present worth (single amount) factor must be obtained for years eight, twelve, and sixteen from
Table 3 (PDF - 25 KB)
under the column headed "10 Percent," which is the discount rate of this example. Once these factors are obtained, the estimated cost of repair is simply multiplied by the appropriate factor to arrive at the present-worth equivalent cost. For example, 10,000 x 0.4665 = 4,665 is the present worth for the year eight replacement cost for the economy air handier. The total replacement and salvage present worth cost is then determined and recorded in the appropriate place on the worksheet.
Figure 1: Life Cycle Cost Worksheet
The final third of the worksheet records annual costs such as maintenance and energy costs. In this example, maintenance and energy costs are listed for each alternative. To convert these estimated annual costs to an equivalent present-worth cost, the present worth annuity factor must be obtained from
Table 1 (PDF - 21 KB).
For electrical energy costs, the fuel is anticipated to escalate by 2 percent per year. Therefore, referring to
Table 2 (PDF - 24 KB),
under the "2 Percent" column heading for a 10 percent discount rate and a twenty-four-year life cycle, the factor is 10.668. Multiplying this factor by the estimated annual energy cost for each alternative yields the equivalent present- worth cost. For example, the performance air handler = 1,800 x 10.668 = $19,202. Other annual costs are calculated similarly. The total annual present worth cost is then determined and recorded in the appropriate place on the form.
The total present worth life cycle cost for each air handler is established by totaling the initial, replacement/salvage, and annual operating costs. Using life cycle costing, one can see that although the performance air handler was the most expensive initially, it costs much less to operate. These calculations show that, over its life, the performance air handler will save $4,026 over the economy air handler.
- Stephen Kirk
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