12. A do-nothing and two mutually exclusive alternatives are being considered fo
ID: 370082 • Letter: 1
Question
12. A do-nothing and two mutually exclusive alternatives are being considered for reducing traffic congestion,User benefits come from reduced congestion once the project is complete, while user dis-benefits are due to increased congestion during construction. The interest rate is 9%, and the life of each alternative is 15 years, which alternative should be chosen? User benefits (SM/r) User dis-benefits ($M) First cost ($M) Operations and maintenance LSM/yr) 2.1 1.2 6.9 0.75 2.6 2.1 9.9 0.825 use the benefit-cost ratio Use the modified benefit-cost ratio a. b.Explanation / Answer
a) Capital recovery factor (A/P,9%,15) = 0.1241 (taken from MARR table)
Using Benefit-cost ratio,
B-C ratio of alternative A = AW(B-D) / (CR + AW(O&M)) = (2.1-1.2*0.1241) / (6.9*0.1241+0.75) = 1.215
B-C ratio of alternative B = AW(B-D) / (CR + AW(O&M)) = (2.6-2.1*0.1241) / (9.9*0.1241+0.825) = 1.139
B-C ratio of both alternatives is greater than 1, however it is higher for alternative A, so it should be undertaken.
b)
Modified B-C ratio of A = AW(B-D-O&M) / CR = (2.1-1.2*0.1241 - 0.75) / (6.9*0.1241) = 1.403
Modified B-C ratio of B = AW(B-D-O&M) / CR = (2.6-2.1*0.1241 - 0.825) / (9.9*0.1241) = 1.233
Modified B-C ratio of alternative A is higher, therefore it should be undertaken.
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