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17 4.5 Analyze/Interpret Results value) and 75 percent probabilities. The figure indicates that Alternative B has a lower NPV than Alternative A at both prob- Regardless of whether deterministic or probabilistic life-cycle ability levels. costs are computed, the results must be analyzed and inter- Suppose that Alternative A had a slightly lower mean NPV preted carefully to evaluate the cost-effectiveness of a pavement ($1.608 million instead of $1.611 million) and a more dis- strategy. Because the outputs of each computational approach persed distribution, as shown in Figure 12. In such a case, the are different, the ways in which they are evaluated and inter- tails of the frequency distribution curves should be evaluated preted also are different. for any potential cost-associated risks. The distribution curves shown in Figure 12 indicate clear differences in the forecasted 4.5.1 Analysis of Deterministic NPV at the tails. For Alternative A, there is potential for a cost Life-Cycle Cost Results underrun if the true NPV is low (say, less than $1.45 million). This opportunity for cost savings is called upside risk. If, on the In the analysis of deterministic results, the percent differ- other hand, the true NPV is high (say, greater than $1.75 mil- ence in life-cycle costs of alternatives is computed. The cost- lion), there is a potential for a cost overrun associated with effectiveness of alternatives is established by comparing the Alternative A. This chance for financial loss is called down- percent difference against some established threshold require- side risk. ment. Since the agency has to take other financial considera- In the cumulative distributions shown in Figure 13, it can tions into account, such as the cost feasibility of alternatives, be seen that there is a 10 percent probability that the NPV of available funding levels, and the impact on overall system Alternative A will be less than that of Alternative B by as needs, the decision to eliminate or further evaluate an alterna- much as $26,000. At the other end of the spectrum, there is tive is made after the evaluation of pertinent economic criteria. a 10 percent probability that Alternative A will exceed the Chapter 5 discusses the evaluation of alternatives using eco- cost of Alternative B by up to $41,000. Although many agen- nomic factors. cies may find this information insufficient for identifying the most cost-effective strategy, to some risk-averse agencies it 4.5.2 Analysis of Probabilistic may provide enough assurance that the allocated budget is best served by choosing Alternative B. In other words, there Life-Cycle Cost Results is a greater risk of the true cost of Alternative A exceeding the In the analysis of probabilistic results, the likelihood of an cost of Alternative B. alternative's cost-effectiveness is evaluated with those of other alternatives. This can be accomplished by risk assessment of 4.5.3 Reevaluate Strategies forecasted NPV distributions. This approach involves comparing NPV distributions of dif- In the final step of the LCCA process, information result- ferent alternatives at a specified level of probability. A proba- ing from the LCCA is reevaluated to determine if any modi- bility level between 75 and 85 percent will provide reliable fications to the alternative strategies are warranted, prior to estimates. Figure 11 shows the cumulative probability distribu- making a final decision on which alternative to use. Such tions of NPV for two alternative strategies at 50 percent (mean adjustments may entail changes to the original structure or 100% 90% 80% Cumulative Probability 70% 60% 50% 40% 30% 20% 10% 0% 1200 1300 1400 1500 1600 1700 1800 1900 2000 NPV, $1000 Alternative A Alternative B 50 percent probability 75 percent probability Figure 11. NPV frequency distributions for alternative strategies A and B.
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18 200 Alternative B 180 Alternative A Mean = $1,600,344 Mean = $1,611,702 Std Dev = $89,996 Std Dev = $100,190 160 140 Frequency 120 100 80 60 40 20 0 1200 1300 1400 1500 1600 1700 1800 1900 2000 NPV, $1000 Alternative A Alternative B Figure 12. Risk assessment--NPV frequency distributions. rehabilitation treatment, revisions to the maintenance of traf- variables. A correlation coefficient of +1 indicates that two vari- fic plans, reductions in construction periods, or changes in ables are perfectly related in a positive linear sense, while a future M&R activities. value of -1 indicates perfect negative correlation. Values closer Probabilistic sensitivity analysis can provide insight on the to zero indicate poor or no correlation, and other intermedi- refinement of strategies. This technique uses correlation analy- ate values indicate partial correlation. sis and tornado plots to show the impacts of key input param- In this example, the NPV of the pavement alternative is pos- eters on life-cycle costs. Inputs found to be driving the LCCA itively correlated with cost factors while negatively correlated results can be scrutinized to determine if actions can be taken with the discount factor and pavement service-life estimates. to improve cost-effectiveness. The initial construction cost appears to be the dominating fac- Figure 14 presents an example showing the correlation tor influencing NPV, followed by the initial life of the original coefficients of factors influencing the NPV of a pavement pavement. In other words, to reduce the NPV of this pave- alternative. The correlation coefficient is a statistical measure ment alternative, a strategy to reduce initial construction cost that indicates the strength of the linear association between two would be more effective than other possible strategies. 100% 90% Alternative B Alternative A $1,711,000 $1,752,000 Cumulative Probability 80% 70% 60% - $41,000 50% Upside Risk (opportunity 40% for cost savings) 30% $26,000 20% Alternative A Alternative B 10% $1,463,000 $1,489,000 0% 1200 1300 1400 1500 1600 1700 1800 1900 2000 NPV, $1000 Alternative A Alternative B Figure 13. Risk assessment--NPV cumulative distributions.
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19 Initial Const. Cost 0.60 Initial Const. Life -0.35 First Rehab Cost 0.25 Discount -0.22 First Rehab Life -0.20 Second Rehab Cost 0.12 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 Correlation Coefficient Figure 14. Correlation coefficients of factors affecting the NPV of a particular pavement strategy.