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The basic methodology employed was to develop probabilistic cash flow models for each of the decision options (except for the split procurement options, which were analyzed by interpolating from results of other options).

A decision tree was developed for each option. The tree included the uncertainties discussed previously, as applicable to each specific option, and a cash flow valuation measured by rate of return (ROI) and net present value (NPV) discounted at 15 percent, as illustrated conceptually in figure A-1. The uncertainties (i.e., ZIP+4 usage, savings rate, multi-line OCR performance rate) were treated as continuous random variables. The continuous random distributions were approximated by the Pearson-Tukey

approximation which uses values of the variable at three discrete points:

95 percentiles. three percentiles,

Pearson-Tukey assigns probabilities as shown in figure A-2.

of

0.185,

0.63,

and

the 5,

50, and

0.185

to these

Simplified schematic models for options A, B, C, D, and E are shown in figures A-3 through A-7. The full models are shown in appendix B.

The models were run on an IBM Personal Computer using Lotus 1-2-3 and proprietary software.

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