Analytical Techniques in Public Administration - Statistics Project Example

Statistics Analytical Techniques in Public Administration A. Background This study uses the concept of sensitivity analysis and theNet Present Value in the two options with measures of uncertainties. Sensitivity analysis is a decision making tool, which in this case, applies the Net Present Value in the assessment of risk between option AS and Option B. In the two decision scenarios, the future is full of inherent uncertainty, regardless of the costs and benefits analysis or the risk and timing analysis, based on the various assumptions. It is vital to evaluate the uncertainties and their effect on the decisions that the Baltimore Mayor will arrive at in choosing between the two options. This project applies sensitivity analysis as the major technique for the decision making. The significance of the sensitivity analysis has to be taken into consideration, and practically implemented with the calculation of the Net present values of the two options. B. Analysis of Prior Estimates Before the major decisions are arrived at, this study explores two fundamental forms of sensitivity analysis, the cost and benefit and the net present value of option A and B, with and without discounting. 1. Cost and Benefit Analysis The Benefit-cost analysis is the difference between the benefits and the total cost of an option. From the available data, the total benefits of Option A of the Baltimore Chamber of Business are a total of US$ 186,800,000. The corresponding value of costs is US$500,571,150.This shows that the costs exceed the benefits of option A. As for option B, the total benefits amount to US$ $433,272,000, while the total cost amounts to US$240,000,000. The cost of Option B is therefore less than its Benefits. The second option (Option B) is a better choice considering the aspect of cost and benefit analysis. 2. Net Present Value The time-value-of-money is the value that money holds temporarily at any given time. Is payment is made at the present time; there is an opportunity to obtain a discount. On the other hand, payments made at later times are higher because discounting does not apply. Net present values of the project are taken as the difference between the benefits (B) and the costs (C). In option A, the Net present value is obtained as follows: NPV (A) = B - C NPV (A) = $186,800,000 - $500,571,150 NPV (A) = -$313771150  By applying a discount of 30%, the NPV of option A is obtained as follows: NPV (A) = -$313771150 – (30/100) * -$313,771,150  NPV (A) -$407,902,495 The Net Present Value of Option B is calculated as: NPV (B) = B – C NPV (B) = $433,272,000 - $240,000,000 NPV (B) = $193272000 Applying a discount of 30%, the NPV of project B reduces as follows: NPV (B) =$193,272,000 – 10/ 100 * $193,272,000 NPV (B) = $135,290,400 In the two prior estimates, Analysis of option A by the Baltimore Chamber of Business shows higher NPV for option B than option A, whether discounting is applied or not. The analysis of the Net Present Value predicts that Option B will continue to exhibit higher values than A. The strength of the Cost – Benefit analysis is that it is simple and straight forward. It is more accurate in the estimation of the value of the business. It however has a weakness in the sense that it cannot be adjusted through the discounting process. In the case of the NPV estimation method, the net present value of the project option can be adjusted by varying the discounts given to the market. The limitation of the Net Present Value estimation method is that the discount rates are not constant; hence the prediction is less accurate than the Cost - Benefit analysis. C. Reconciliation Analysis 1. Assessment of Assumptions of Prior Analyses In the prior analyses of the options for Baltimore Chamber of Business, the expected Value of the NPV is taken as the mean value of the possible results from the weights of their probabilities. The probabilities represent the discounts provided for the calculation of the expected (estimated) values. In that regard, the scenarios, the NPVs and the corresponding probabilities are estimated as presented below: Table 1: Sensitivity Analyses Scenario NPV Probability NPV * Probability 1 $1000m 0.0 0 2 $1100m 0.02 $22M 3 $1200m 0.04 $48m 4 $1300m 0.06 $78m 5 $1400m 0.08 $112m 6 $1500m 0.10 $150m Expected Value: $410m Figure 1: Sensitivity Analyses 2. Revised Model The model for computation of the expected NPV of the two options is adjusted through a special optimization model. The optimization involves the application of the assumption of less discount rate. The revised model is thus presented below. NPV = V + D * A Where V is the initial Net Present Value, D is the discounting rate and A is the fixed cost of the option. The optimized model gives the present values of the two options as follows: Option A: NPV (A) = -313,771,150 + (10 / 100) * 100,000,000 = -$303771150 Option B: NPV (B) = 193,272,000 + (10 / 100) * 100,000,000 = $203,272,000 3. Sensitivity Analyses The first sensitivity analysis test is carried out for the two options using two assumptions, including the discounting rate and the variation of life of the light rail line after its construction Option A: Discount Rate The variation in the discount rates considers discounts between 0% 1nd 10 %. The sensitivity Analysis of the option generates the expected net present values as shown below: Table 2: Sensitivity Analysis for Option A: Discount Rates Scenario NPV Discount Discounted NPV 1 ($303,771,150) 0 ($303,771,150) 2 ($303,771,150) 0.01 ($303,801,527) 3 ($303,801,527) 0.02 ($303,862,287) 4 ($303,862,287) 0.03 ($303,953,446) 5 ($303,953,446) 0.04 ($304,075,027) 6 ($304,075,027) 0.05 ($304,227,065) 7 ($304,227,065) 0.06 ($304,409,601) 8 ($304,409,601) 0.07 ($304,622,688) 9 ($304,622,688) 0.08 ($304,866,386) 10 ($304,866,386) 0.09 ($305,140,766) Figure 2: NPV vs Discount Rates (Option A) The greatest NPV for option A in the sensitivity analysis is -$303,771,150, while the least sensitivity analysis is -$305,140,766. For any slight change in the discount rate, there is a great negative change in the NPV of option A. Option B: Discount Rate The sensitivity analysis for option B with the assumption of discount rate is presented in table 3 below and figure 3 below. Table 3: Sensitivity Analysis for Option B: Discount Rates Scenario NPV Discount NPV * Probability 1 203,272,000 0 $203,272,000 2 $203,272,000 0.01 $203,292,327 3 $203,292,327 0.02 $203,332,986 4 $203,332,986 0.03 $203,393,986 5 $203,393,986 0.04 $203,475,343 6 $203,475,343 0.05 $203,577,081 7 $203,577,081 0.06 $203,699,227 8 $203,699,227 0.07 $203,841,817 9 $203,841,817 0.08 $204,004,890 10 $204,004,890 0.09 $204,188,494 11 $204,188,494 0.1 $204,392,683 Figure 3: NPV vs Discount Rates (Option A) The least NPV for option B is make sure you address how changes in assumptions change the final NPV is $203,272,000, and the greatest NPV is $204,392,683. For any slight change in the discount rate in option B, there is a great positive growth in the NPV values. D. Additional Factors for Consideration Apart from the sensitivity analysis forms used in this study, discount and NPV, other forms can be used to test for the sensitivity in line with the discount rate and the expected (estimated) values. Other sensitivity analysis forms in this include the exploration of the factors relating to the Value changes. Rates used for Wage The value of risks related to the option Time value related to the option The economic multiplier impact of the scheme Impacts of the Environment There is need for the research to include at least three additional forms of sensitivity analysis especially in option A that has negative NPVs. Likewise, for the contentious measures applied in the sensitivity analysis, the use of multiple sensitivity test is necessary, because the cost or benefit analysis represents a large part of the total costs and benefit of the projects (Sudret, 2008). E. Conclusions and Recommendations For the mayor and the committee of the Baltimore Chamber of Business, the study presents the decision options between A and B, advising the adoption and implementation of the second option (B). This is because of the positive growth of the Net Present Values in the sensitivity analysis with and without the application of discount rates. In the entire life of the building of the new Light Rail line in Baltimore, the NPV of option A continuously drops significantly, and is not suitable as an investment option as projected by the revised model. It is recommended that the committee adopts option B, and also consider including more factors in the sensitivity analysis for the future, other than discount and the NPV. References Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions}, Reliability Engineering & System Safety 93(7): 96-97. Read More