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 User benefits ($M/yr) 2.1 2.6 User disbenefits ($M) 1.2 2.1 First cost ($M) 6.9 9.9 Operations and maintenance ($M/yr) 0.750.825 (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

(a)

Benefit-Cost Ratio (BCR) = PW of benefits / (First cost + PW of O&M costs)

BCR, Alternative A = [2.1 x P/A(8%, 5)] / [6.9 + 0.75 x P/A(8%, 5)]

= (2.1 x 3.9927**) / [6.9 + 0.75 x 3.9927**]

= 8.38 / (6.9 + 2.99)

= 8.38 / 9.89

= 0.85

BCR, Alternative B = [2.6 x P/A(8%, 5)] / [9.9 + 0.825 x P/A(8%, 5)]

= (2.6 x 3.9927**) / [9.9 + 0.825 x 3.9927**]

= 10.38 / (9.9 + 3.29)

= 10.38 / 13.19

= 0.79

Since BCR is less than 1 for both alternatives, Do Nothing is to be selected.

(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.

(c)

Public/Government BCR = (PW of benefits - PW of disbenefits) / (First cost + PW of O&M costs)

Public/Government BCR, Alternative A = [(2.1 - 1.2) x P/A(8%, 5)] / [6.9 + 0.75 x P/A(8%, 5)]

= (0.9 x 3.9927**) / [6.9 + 0.75 x 3.9927**]

= 3.59 / (6.9 + 2.99)

= 3.59 / 9.89

= 0.36

Public/Government BCR, Alternative B = [(2.6 - 2.1) x P/A(8%, 5)] / [9.9 + 0.825 x P/A(8%, 5)]

= (0.5 x 3.9927**) / [9.9 + 0.825 x 3.9927**]

= 2.00 / (9.9 + 3.29)

= 2.00 / 13.19

= 0.15

Since Public/Government BCR is less than 1 for both alternatives, Do Nothing is to be selected.