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without ZIP+4) ranks the lowest in overall NPV, but somewhat higher (4th) in NPV with low ZIP+4 usage. Option A (single-line) ranks the lowest in NPV with low ZIP+4 usage.

The dominance of option D (automatic conversion) can also be illustrated by plotting the cumulative probability distributions of NPV for each option. As shown in figure 14, for any value of NPV (incremental over option F (cancel]), the probability is greatest for option D. For example, for an NPV of $1 billion, the probability is about 0.9 or 90 percent that option D will exceed that NPV (cumulative probability of about 0.1), about 0.75 that option A will exceed, about 0.7 that option B will exceed, and only 0.5 (or 50 percent) that option C will exceed $1 billion.

Because option D dominants all other options under all conditions of uncertainty, option D is stochastically dominant.

Supplemental sensitivity analysis. The basic models built in three uncertainties (ZIP+4 usage, savings rate, multi-line performance rate). A supplemental analysis was conducted to check the sensitivity of NPV results to changes in the purchase price of the multi-line OCR or the number of multi-line OCR units.

The results, summarized in figure 15, showed that an increase in multi-line OCR purchase price from $850,000 to $970,000 would have very little effect on NPV. The effect would be to reduce NPV by about $0.02 and 0.03 billion. Likewise, an increase in the number of multi-line OCR units from 403 to 439 (as estimated by GAO to be required if the entire Phase 11 procurement was switched from single- to multi-line OCRs) would cost about an additional $34.9 million (41 units x 850,000/unit), which is less than the $40.3 million cost of a $120,000 price increase for 403 machines. Therefore, the effect

on NPV again would be very little.

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