This paper presents a model to address the uncertainty inherent in replacement problems, whereby a firm must select between mutually exclusive projects of unequal lifespans by applying the Kelly criterion (which is not well known to the engineering economics community) within a binomial lattice option-pricing environment. Assuming that only the interest rate, among many factors, is uncertain, Brown and Davis performed an economic analysis of this problem by employing a real option-pricing method and argued that their model yields results opposite to those yielded by the traditional approach. However, the results yielded by the model proposed herein are consistent with those by the traditional approach, unlike Brown and Davis's model. The conclusion is that since the investment time horizon is infinite, a firm rationale pertaining to the selection of the best method for the investment problem of such types does not exist.
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