Question

9-41 A do-nothing and two mutually exclusive alterna- tives are being considered for reducing traffic con- gestion. User benefits come from reduced congestion once the project is complete, while user disbenefits are due to increased congestion during construction. The interest rate is 8%, and the life of each alterna- tive is 15 years. Which alternative should be chosen? Alternative A User benefits ($M/yr) 2.1 User disbenefits ($M) 1.2 First cost ($M) 6.9 Operations and maintenance ($M/yr) 0.75 B 2.6 2.1 9.9 0.825 (a) Use the benefit-cost ratio. (b) Use the modified benefit-cost ratio. (c) Use the public/government version of the B/C ratio. (d) Assume these numbers apply to a private firm and use a present worth index. (e) Are your recommendations for (a) through (d) consistent? Which measure gives the largest value? Why?

Answer 1

ANSWER Given the table hlor . : Alternative user - benefits 2.1 osct.dis benefits la first cost ($H) Gia operations and 0.75 I. Malutenaire Conlar Now, we can find out benefit- cost satio (BCR] 2.! 9.9 0.825 a) . * Annual ulooth Clixstow cost] = y 4/1.08 +---+Y/1.08456-4 v = $0.806M] * Annual worth Cuscs dis benefits] : y' W11.08+ --- + /6034 12 [y!= $ 0.14MB Ble= (2.100.14) 10.75 +0.806) lolas Hodified Bl= (2.120.14-0.75) 0.806 341-377) © Modified -- benefit cas't satio Annual worth (first cost) ay »/1.037....tulighet aa y = $1.467 ..

* Annual worth losed-dis benefits] ay'. y! 11.08t -. +'7602969= 2.1 'se'$0.2511? . ; Ble: 2.6- 0.25 modifiedol - Modified ble 2.6-0.05-0825 0.825+1:16 / - ) 2.1881 ? (06 = 323) - * © publicl goverment bession of the olea ratio The houerment should select project B as it benefits overweighs the cost associated with the project Hoke ever its BCR as well as modified BCR both ateşl. The goverment most select the project where the. Purpose is well being of the public. * * * Yes, these numbers apply to private firm as well - The calculations above performed by calculated the present value of cash flows out the Complete project life * - xes, the recommendations are consistent by both the methods, Modified BCR gives the highest value as compared- to BCR method. at