Question

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​ = ​$17,300,000

Operating and maintenance costs​ = ​$532,000 per year

Projected service life​ = 30 years

Savings in travel times and revenues generated from the tolls​ = ​$5,244,000 in the first year of operation and projected to increase by 2.75​% 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 ​$644,000 the first year and is also projected to increase at 2.75​% per year.

Assuming zero market​ (salvage) value at the end of 30 years and a MARR of 10​%per​ year, should the toll lanes be​constructed?

The conventional​ benefit-cost ratio of the project with PW is______​(Round to two decimal​ places.)

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

A.not be constructed

B. be constructed

Answer 1

Initial costs​ = ​$17,300,000

Operating and maintenance costs​ = ​$532,000 per year

Projected service life​ = 30 years

Savings = ​$5,244,000 in the first year and increase by 2.75​% per year

Additional societal health cost of ​$644,000 the first year increase at 2.75​% per year.

MARR = 10%

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 = ​$5,244,000 [1 – (1 + 0.0275) 30 (1 + 0.10) –30 ÷ 0.10 – 0.0275]

PW = $62,976,998.47

Step 2 – PW of all cost

Initial Cost = ​$17,300,000

PW of annual maintenance cost = ​$532,000 (P/A, 10%, 30)

PW of annual maintenance cost = ​$532,000 (9.42691) = $5,015,116.12

PW of Additional societal health cost

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

PW = ​$644,000 [1 – (1 + 0.0275) 30 (1 + 0.10) –30 ÷ 0.10 – 0.0275]

PW = $7,734,017.36

Total Cost = ​$17,300,000 + $5,015,116.12 + $7,734,017.36 = $30,049,133.48

Step 3 – Calculate B/C Ratio

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

B/C ratio = $62,976,998.47 ÷ $30,049,133.48

B/C Ratio = 2.09

The conventional​ benefit-cost ratio of the project with PW is 2.09.

According to the​ Benefit Cost ratio​ method, the toll lanes should

As the B/C Ratio is more than ONE

B. be constructed