Since Q and K are correlated as shown in Eq. 4, the cash flow CF, like the launch requirement UP, depends only on the capital growth function K. A common method for weighing the costs and benefits over the life of a project is by evaluating the present discounted value (PDV) of its net cash flow. PDV is also commonly denoted as “net present value” (NPV). Mathematically, the goal is to maximize the objective function (15) Future computer simulations should use the nonapproximate form of PDV and should also discount both the “research and development” (RND) and “initialization” (INT) costs of the project. Both RND and INT will be spread over a period of time. They clearly begin before start of flight operation and will likely continue through a major portion of the flight operations. When choosing between alternative production paths, PDV is one of the critical considerations. PDV must be positive for a project to be attractive. However, given two projects with positive PDV's, it might be that the project with the highest PDV also has the highest capital investment requirement. If the capital investment required is greater than can be funded then the project with the lower PDV might be pursued instead. Also, the project with the greatest PDV of two or more alternative projects might also have the greatest risk associated with it. Again, one of the alternative projects with a positive PDV might be preferred. To reiterate, our objectives are to formalize one possible approach to the PDV analysis of a bootstrapped space industry, define relevant numerical values for one example or tutorial case of a lunar-based bootstrapped industry, to explore the operation of the analytic model for that example, and finally to encourage more analytical work on PDV and related topics such as risk analysis and specific engineering models. Within this framework, the three approaches to space industrialization differ only quantitively, not qualitatively. All can be analyzed with the equations above simply by varying the constituent functions (Fig. 2). In general, increases in the complexity of the forms assumed for these functions and their interrelationships lead to greater uncertainty and mathematical difficulty in evaluating the mass and cash flows. OBSTACLES TO THE EVALUATION OF BOOTSTRAPPING In order to evaluate bootstrapping, it is important to know the general form of K. By definition, the capital stock is nondecreasing. Moreover, since the ability to manufacture equipment in space depends on the amount of machinery already there, the capital stock will probably increase exponentially at first. Eventually, this growth must slow down so that capacity can be diverted to production of the final output, Q. where r is the discount rate, T is the “time horizon” (which may be infinite), RND is the cost of research and development, and INT is the cost associated with initializing the system. Equation 9 is an approximation to PDV (or NPV) which is satisfactory for low discount rates. The exact form is
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