Introduction
In this document, the findings of a benefit-cost analysis that was carried out by JET Corporation to determine whether or not it would be feasible to construct two dams—Dam #1, which is located in the southwest region of Georgia, and Dam #2, which is situated in North Carolina—are presented. A significant contribution the research makes is that it helps facilitate the selection of a project based on its economic feasibility (Venkataraman & Pinto, 2023).
In the context of this investigation, the benefit-to-cost ratio serves as the deciding element. A figure greater than 1.0 indicates that the benefits outweigh the drawbacks. For the purpose of calculating benefit-cost ratios, several benefit categories and expenditures associated with each project have been defined and simulated.
Problem Analysis
Dam #1 exhibited a mode ratio of 1.53, and Dam #2 had a mode ratio of 1.50, which is somewhat lower, suggesting that both projects may be economically viable.
For Dam #1:
- Minimum Scenario: 1.12.
- Mode Scenario: 1.53.
- Maximum Scenario: 1.53.
For Dam #2:
- Minimum Scenario: 1.14.
- Mode Scenario: 1.50.
- Maximum Scenario: 1.48.
To gain a deeper understanding and incorporate variability, we simulated 10,000 benefit-cost ratios for each project. These simulations were based on a triangular distribution of the estimated benefits and costs, reflecting the uncertainty inherent in such large-scale projects. For Dam #1, the simulations resulted in the following statistical measures:
- Mean benefit-cost ratio: 1.43.
- Standard deviation: 0.15.
The histogram for Dam #1’s benefit-cost ratio simulations exhibited a normal distribution, indicating that the ratios likely cluster around the mean (Fig. 1). For Dam #2, the simulations yielded:
- Mean benefit-cost ratio: 1.41.
- Standard deviation: 0.15.
Similarly, the histogram for Dam #2 also suggested an approximately normal distribution, albeit with slight skewness, indicating the presence of higher outliers (Fig. 1).
Visualizations
The Chi-Squared Test
For the purpose of determining whether or not the simulated ratios of Dam #1 were adequately defined by a normal distribution, a Chi-squared Goodness-of-fit test was carried out. 108.20 is the value of the Chi-squared statistic, and the P-value is somewhere around 0.00000236, according to the findings of the tested hypothesis. Given this, it is reasonable to conclude that the null hypothesis, which states that the benefit-cost ratio of Dam #1 follows a normal distribution, should be rejected. To determine the extent to which the observed frequencies depart from the predicted frequencies under the hypothesized theoretical distribution, the chi-squared test statistic is used. When the value of Chi-squared increases, the amount of the variance likewise increases.
The P-value indicates the likelihood of encountering a Chi-squared statistic that is equally or more extreme than the one computed on the assumption that the theoretical distribution is accurate. The P-value is much less than 0.05 in this instance, indicating that the simulated data for ?1 do not conform to the normal distribution and would not be expected by chance alone.
Hence, with the test, we would reject the null hypothesis that the benefit-cost ratio for Dam #1 follows a normal distribution at the conventional 0.05 significance level. This implies that although the distribution of ?1 appears to follow a standard pattern at first glance, it may not be statistically representative of a normal distribution, and alternative distributions may offer a better approximation. The observed outcome may be attributed to the dataset’s attributes or the chi-squared test’s susceptibility to substantial sample sizes. Upon completing the statistical calculations, we shall compute the possibility that ?1 will surpass ?2.
DataFrame 1. The probability that ?1 will be greater than ?2, based on the simulations, is 53.18%.
Recommendation
The simulation findings indicate that Dam #1 (?1) exhibits a somewhat greater mean benefit-cost ratio than Dam #2 (?2). Both ratios have quite comparable measurements of central tendency and variability in their distributions. In contrast, Dam #1’s distribution is less skewed to the right, as indicated by its skewness, suggesting fewer very high ratios than in Dam #2. Furthermore, based on the probabilities, it is highly probable that both initiatives will have a benefit-to-cost ratio exceeding 1, hence indicating economic feasibility.
However, the chance that ?1 is bigger than ?2 is slightly greater than 50 percent, suggesting that the likelihood that Dam #1 will have a higher benefit-cost ratio than Dam #2 is just marginally greater. After examining the variables above and Dam #1’s significantly better mean benefit-cost ratio and lower skewness, it is possible to suggest that Dam #1 is superior to Dam #2 due to its marginally greater economic feasibility. However, the benefit-cost ratio does not capture other aspects of the decision, such as strategic significance, environmental impacts, and compatibility with the project’s business objectives.
Conclusion
Dam #1 produced a mean ratio that was somewhat superior to that of Dam #2, and it also exhibited a less skewed distribution. This combination of characteristics indicates that Dam #1 is more predictable and less prone to experiencing extreme occurrences. Furthermore, it is projected that, on average, Dam #1 will have a better benefit-cost ratio than Dam #2, indicating that Dam #1 is somewhat preferred over Dam #2. Other considerations that ought to inform the eventual decision include the environmental impact, the implications for society, and the extent to which the option aligns with the organization’s long-term goals. In conclusion, although the quantitative analysis shows that Dam #1 has a marginal edge in the benefit-cost ratio, the top choice for JET Corporation should be influenced by both qualitative and quantitative factors.
Reference
Venkataraman, R. R., & Pinto, J. K. (2023). Cost and value management in projects. John Wiley & Sons.