ABSTRACT 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.

中文翻译：

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部分随机“油泵问题”中内部和外部收益率的分布

摘要 本文重新审视了一个经典的两期工程经济问题，即油泵问题，并一次为其现金流增加一个随机性。报告了外部收益率的内部和无条件累积概率密度函数的条件累积概率密度函数。分析结果通过蒙特卡罗模拟验证。提出了一个程序，通过使用项目接受的概率作为输出来评估项目的可取性。在数值示例中使用了两种比率的累积分布函数来说明如何计算项目的合意性或接受概率。结果表明，外部收益率的分布与内部收益率的分布产生相同的接受概率。本文对有关随机投资问题中收益率分布的文献进行了最新且详尽的回顾。审查还表明，油泵问题仍然是流行和广泛讨论的问题。