**By**** Steve McAdams***
Published in the September 2011 issue of *Today’s Facility Manager

Recently, politicians and the media have been selling the value of life cycle costing (LCC) as a cure for the U.S. government’s budget conundrum. Although this idea has merit, it is certainly not new.

LCC has been used with significant results in facilities design, operations, and management for many generations. However, it is critical for facility managers (fms) to understand all of the assumptions necessary for the process as well as the impact on the analysis, especially if the initial assumptions are inaccurate. Using sensitivity analysis in conjunction with an LCC comparison can help mitigate the risks in the decision process.

### Decoding Basic LCC Methodology

Before discussing sensitivity analyses, a brief summary of basic LCC development is warranted. LCC is considered the total expense incurred throughout the life cycle of a component or system being evaluated. It is comprised of an initial capital cost and annual recurring costs converted to a single lump sum value.

This conversion has two significant stages. First, the annual cost is escalated to the anticipated year of occurrence using assumed escalation rates. Then the escalated cost is discounted to “today’s dollars” using a discount rate. The discounted cost is considered the present value or the actual cost in “today’s dollars.”

Chart 1 identifies the basic approach using a baseline annual cost of $1 as an example.

The sum of the discounted costs over the five year period is $4.59, which is the lump sum value of the annual recurring costs in “today’s dollars” (present value). This cost is then added to the present value of the capital costs to estimate the LCC.

The $1 baseline was used in the Chart 1 example to identify the Uniform Present Value (UPV) factor as well. The UPV factor is multiplied by the annual recurring cost to calculate the present value as shown below:

*Present Value = Baseline annual cost x UPV factor*

Therefore, in the aforementioned example, the UPV factor is equal to 4.59 ($4.59/$1). This is referred to as a “uniform” present value factor, because it is applied when the same baseline cost and escalation rate are used for each year. The following formula can also be used to calculate the UPV factor.

(The UPV factor will be used later in this article to simplify the math.)

When the escalation rate is anticipated to change on an annual non-uniform basis, a spreadsheet can be used to calculate and sum the annual discounted cost.

### LCC Sensitivity Analysis

The changes in the assumptions needed for developing LCC can have a significant impact on the results, which can limit the confidence in selecting the appropriate alternative. By performing sensitivity analyses that challenge the initial assumptions, a greater understanding of the specific sensitivity of an assumption can be gained.

Consider the following example where a new technology, Equipment B, can reduce annual operating costs by 10% compared to Technology A, but has a capital cost premium of nearly 100%. Beginning with an initial energy escalation rate of 2%, an LCC comparison between the two alternatives is developed as follows:

Based upon the assumptions in Chart 2, the UPV (2%) factor equals 17.53 and the LCC of the two components is developed below:

**Equipment A: $75,000 + $1,000 x 17.53 + $45,000 x 17.53 = $881,000
Equipment B: $140,000 + $1,000 x 17.53 + $40,500 x 17.53 = $872,000**

In this scenario, Equipment B (the new technology) has a slightly lower LCC by approximately 1%. However, the question remains as to whether or not this is a great enough difference to generate a conclusive result. A sensitivity analysis can be developed to assist in this decision.

The two assumptions in this example that have the most uncertainty are the energy cost escalation rate and the capital cost. Therefore, the sensitivity analyses will focus on various escalation rates and capital cost contingencies.

To test the assumption of a 2% energy cost escalation the analysis is re-run for escalation rates between 0% and 4%. Chart 3 identifies the resulting LCC for each technology (the lower LCC is shaded).

Equipment B has the lowest LCC, except when the energy cost escalation is less than 1%. Essentially, provided that energy rates continue to increase, Technology B will maintain a slight economic advantage over Technology A.

### Capital Cost Contingencies

The next step is to identify sensitivity with regard to capital cost contingencies. The capital cost estimates are increased between 5% and 20% to determine the impact on the resulting LCC for each technology as noted in Chart 4.

Technology B will have a lower LCC, provided the capital costs are within 15% of the estimates used within the analysis.

The two sensitivity analyses frame the economic conditions for which Technology B will provide favorable economics as follows:

**Energy cost assumptions: Energy rates increase greater than 1% average
Capital cost contingency: Capital cost estimates are within 15% of actual costs**

### Coming To Conclusions

A more complicated and advanced matrix can be developed to address both assumptions simultaneously and provide even further assistance in understanding the impact of changes in the initial assumptions. However, for this example the data included throughout this article will be used to develop an initial conclusion.

Even though under the initial comparison Technology B has a minimal (1%) LCC advantage when performing the sensitivity analysis on the various assumptions, Technology B appears to be a safer selection than perhaps initially considered. If fms can assume energy costs will increase in the future an average of at least 1% annually, then the focus becomes whether the capital cost estimate will be within 15% of the construction costs. A more detailed or second cost estimate would further mitigate this risk and substantiate the conclusion of selecting Technology B.

An LCC comparison can be an extremely valuable tool in determining the economic advantages of multiple options. However, with the multiple assumptions needed, it is critical for fms to recognize the sensitivities associated with each assumption prior to developing a final decision. A sensitivity analysis to determine a confidence range for the option with the lowest LCC will assist fms in there efforts to determine the economic risk.

*McAdams, P.E., C.E.M., is an associate at RMF Engineering. With 20 years of industry experience, he leads RMF’s master planning group, which specializes in developing strategies for utility systems, infrastructure growth, and energy. The group advises clients on investing in systems and infrastructure, for the long- and short-term, outlining the best strategies to employ when beginning a project in order to maximize investment, efficiency, and sustainability.*

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