Question

#1

Toll lanes on a section of the​ I-40 freeway are being considered in order to reduce traffic congestion and travel times.

Since this is a government​ project, the​ B-C ratio method must be applied in the evaluation. The following are cost and other​ estimates:

-Construction costs​=​$17,200,000

Operating and maintenance costs​ =​$521,000 per year

Projected service life​ =24 years

Savings in travel times and revenues generated from the tolls​ =​$5,152,000 in the first year of operation and projected to increase by 2.5% per year due to the projected annual increase in traffic. In​ addition, environmental analysis estimates that the project will result in increased noise and air pollution that will cause an additional societal health cost of $552,000 the first year and is also projected to increase at 2.5% per year.Assuming zero market​ (salvage) value at the end of 24 years and a MARR of 9​% per​ year, should the toll lanes be constructed?

a). The conventional​ benefit-cost ratio of the project with PW is_______

b). According to the​ B-C ratio​ method, the toll lanes should be constructed or not?

Answer 1

Initial costs​ = $17,200,000

Operating and maintenance costs​ = $521,000 per year

Projected service life​ = 24 years

Savings = $5,152,000 in the first year and increase by 2.5​% per year

Additional societal health cost of $552,000 the first year increase at 2.5​% per year.

MARR = 9%

Calculating the conventional benefit cost ratio using Present Worth.

Conventional Benefit cost ratio = PW of Benefits ÷ Initial Cost + PW of all costs

Step 1 – PW of Benefits

PW = A1 [1 – (1+g) N (1+i) –N ÷ i – g]

PW = $5,152,000 [1 – (1 + 0.025) 24 (1 + 0.09) –24 ÷ 0.09 – 0.025]

PW = $61,139,822.59

Step 2 – PW of all maintenance cost

PW of annual maintenance cost = $521,000 (P/A, 9%, 24)

PW of annual maintenance cost = $521,000 (9.70661) = $5,057,143.81

Step – 3

PW of Additional societal health cost

PW = A1 [1 – (1+g) N (1+i) –N ÷ i – g]

PW = $552,000 [1 – (1 + 0.025) 24 (1 + 0.09) –24 ÷ 0.09 – 0.025]

PW = $6,550,695.28

Step 4

Calculate Net Benefit

Net Benefit = $61,139,822.59 – $6,550,695.28 = $54,589,127.31

Step 5

Calculate total Cost

Total Cost = $17,200,000 + $5,057,143.81 = $22,257,143.81

Step 6 – Calculate B/C Ratio

B/C ratio = PW of all Benefits ÷ PW of all Costs

B/C ratio = $54,589,127.31 ÷ $22,257,143.81

B/C Ratio = 2.45

The conventional​ benefit-cost ratio of the project with PW is 2.45.

According to the​ B-C ratio​ method, the toll lanes should

As the B/C Ratio is more than ONE

B. be constructed