9-41 A do-nothing and two mutually exclusive alterna- tives are being considered

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 construc- tion. The interest rate is 8%, and the life of each altenative is 15 years. Which altermative should be chosen? Alternative A B User benefits (SM/yr) User disbenefits (SM) First cost (SM) Operations and maintenance (SM/yr) 2.1 2.6 1.2 2.1 6.9 9.9 0.75 0.825 (a) Use the benefit-cost ratio. (b) Use the modified benefit-cost ratio.

Explanation / Answer

Alternative A:

Since both User disbenefits and first cost are on a present worth basis, we must convert them into annual worth basis.

Annual worth (First cost) = y

y/1.08 + .... + y/1.0815 = 6.9

y = $0.806M

Annual worth (User disbenefits) = y'

y'/1.08 + .... + y'/1.0815 = 1.2

y' = $0.14M

B/C = (2.1 - 0.14)/(0.75 + 0.806) = 1.195

modified B/C = (2.1 - 0.14 - 0.75)/0.806 = 1.377

Alternative B:

Since both User disbenefits and first cost are on a present worth basis, we must convert them into annual worth basis.

Annual worth (First cost) = y

y/1.08 + .... + y/1.0815 = 9.9

y = $1.16M

Annual worth (User disbenefits) = y'

y'/1.08 + .... + y'/1.0815 = 2.1

y' = $0.25M

B/C = (2.6 - 0.25)/(0.825 + 1.16) = 1.188

modified B/C = (2.6 - 0.25 - 0.825)/1.16 = 1.323

Alternative A must be chosen in both the cases when B/C is used or modified B/C is used. (Higher B/C in comparison to Alternative B)

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