Probability Distribution Function of the Internal Rate of Return for Short-Term Projects with Some Random Cash Flows and Extensions

Literature Critique
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By: First Name M.I. Last Name
Sarper, H., Palak, G., Chacon, R. P., and Fraser, M. J. (2010). Probability Distribution Function
of The Internal Rate of Return for Short-Term Projects with Some Random Cash Flows and Extensions. The Engineering Economist: A journal Devoted to the Problems of Capital Investment, 55 (4): 350-378
This article discusses a report on the closed-form probability density function (pdf) and associated expressions. The expressions in this article include the internal rate of return (IRR) in one and two-period pure and simplified probabilistic engineering problems. Developing the probability density function for the IRR can help economists and financial analysts to make decisions on different projects. It follows that this paper analyses the outcome from a study on the pdf of “The Internal Rate of Return for Short-Term Projects with Some Random Cash Flows and Extensions”.
The study was completed by setting the interest rate i that ensured cash inflows of an investment was equal to cash outflows of the investment. The study considered that the pdf for the IRR is sensible if multiple root problems are solved efficiently and the re-investment at the IRR assumption is suitable. Thus, the projects used were simple and pure investments in order to avoid complications arising from multiple roots and cash flow sign changes.
The investigation tackled one-period and two-period problems. The one-period project had an initial investment of A0 at time zero and a positive net cash flow of A1. The variable i was the random IRR. The one-period project considered that if at least one of the cash flows had pdf, then i would also have a pdf. It is notable that A1 is usually greater A0, but the analysis considered the possibility of A0 being less than A1. The two-period project used an initial time of zero, an investment of A0 and positive cash flows of A1 and A2.
In order to complete an efficient investigation, the study conducted an up to date literature review on the idea of randomness of IRR. The foundation was based on studies completed by previous authors. This included both positive and negative responses to opinions from different authors. Consequently, an equation that solved the present worth P, the variance, and the expected value of P emerged. The analysis from the literature review established that the IRR was the interest rate with a present worth P that is equal to zero. Furthermore, the analysis established that the pdf for IRR is found by solving for the pdf of P for various values of i to determine the cumulative distribution of IRR then deriving the pdf of R.
In this study, the projects derived the pdf for IRR using the exponential and the uniform distributions. The pdf derived in the study included the one-period and two-period problems. The cumulative distribution function for the two problems were obtained and use...