A do-nothing and two mutually exclusive alternatives are being considered for reducing traffic congestion. User benifits 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 alternative is 5 years. Which alternative should be chosen?Alternative A BUser benefits ($M/yr) 2.1 2.6User disbenefits ($M) 1.2 2.1First cost ($M) 6.9 9.9O&M ($M/yr) 0.75 0.825(a) Use the benefit-cost ratio.(b) Use the public/government version of the B/C ratio. Please show me a full step by step solution.

A) DO nothing is selected ( BCR for both alternatives ≤ 1 )

B) Do nothing is to be selected ( government BCR fr both alternatives ≤ 1 )

Explanation:

A) using the benefit-cost ratio to determine which alternative to be chosen

Benefit cost ratio = PW of benefits / ( first cost + PW of O&M costs )

Benefit cost ratio for Alternative ( A )

= (2.1 (user benefits) * P/A ( interest rate , life of alternative ) / ( 6.9 + 0.75 * P/A ( interest rate, life of alternative )

= ( 2.1 * P/A ( 8% , 5 ) / ( 6.9 + 0.75 * P/A ( 8%,5 )

= (2.1 * 3.9927) / ( 6.9 + 0.75 * 3.9927 )

= 8.38 ( approximately ) / 9.89 ( approximately ) = 0.85

Benefit cost  ratio for Alternative ( B )

= (2.6 ( user benefits ) * P/A (8%,5)  / ( 9.9 + 0.825 * P/A(8%,5)

= ( 2.6 * 3.9927 ) / ( 9.9 + 0.825 * 3.9927 )

= 10.38 / 9.9 + 3.29

= 0.79  

note : P/A ( 8%,5 ) value is gotten from the P/A factor table

B) using public/government version of the B/C ratio

Government BCR = ( PW of benefits - PW of dis-benefits ) / ( first cost + PW of O&M costs )

For Alternative A = ( 2.1 - 1.2 )* P/A(8%,5) / ( 6.9 + 0.75 * P/A(8%,5) )

= (0.9 * 3.9927) / ( 6.9 + 2.99)

= 3.59 / 9.89 = 0.36

For Alternative B = ( 2.6 -2.1 ) * P/A ( 8%,5) / ( 9.9 + 0.825 * P/A(8%,5) )

= ( 0.5 * 3.9927) / ( 9.9 + 3.29 )

= 0.15