## Distribution of the internal and external rates of return in a partially stochastic oil pump problem

#### journal contribution

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This article revisits a classic two-period engineering economy problem known as the oil pump problem and adds randomness to its cash flows one at a time. Conditional cumulative probability density functions of the internal and unconditional cumulative probability density functions of the external rates of return are reported. The analytical results are verified with Monte Carlo simulation. A procedure is proposed to assess project desirability by using the probability of project acceptance as the output. The cumulative distribution functions of both rates are used in numerical examples to illustrate how project desirability or acceptance probabilities can be calculated. It is shown that the distribution of the external rate of return yields the same probability of acceptance as the distribution of the internal rate of return. This article provides an up-to-date and exhaustive review of the literature on the distribution of the rate of return in stochastic investment problems. The review also shows that the oil pump problem is still popular and widely discussed.