Question

The State Highway Department is considering a bypass loop that is expected to save motorists $820,000 per year in gasoline and other automobile related expenses. However, local businesses will experience revenue losses estimated to bi_ The cost of the loop will be $9,000,000 (a) Calculate the conventional B/C ratio using an interest rate of 6% per year and a 20-year project period. (b) Calculate the conventional B/C ratio without considering the disbenefits. Is the project economically justified with and without considering the disbenefits?

Answer 1

To calculate the conventional benefit-cost (B/C) ratio, we need to compare the present value of the benefits to the present value of the costs. Let's go step by step:

Given:

Savings for motorists per year: $820,000

Cost of the loop: $9,000,000

Interest rate: 6% per year

Project period: 20 years

(a) Conventional B/C ratio with disbenefits:

To calculate the present value of the benefits and costs, we need to discount them to the present using the given interest rate.

1. Calculate the present value of the benefits:

Present Value of Benefits = Savings per year * Present Value factor for 20 years

Present Value of Benefits = $820,000 * (1 - (1 + 0.06)^(-20)) / 0.06

Present Value of Benefits ≈ $11,460,817.38

2. Calculate the present value of the costs:

Present Value of Costs = Cost of the loop

Present Value of Costs = $9,000,000

3. Calculate the conventional B/C ratio:

B/C ratio = Present Value of Benefits / Present Value of Costs

B/C ratio = $11,460,817.38 / $9,000,000

B/C ratio ≈ 1.27

Therefore, the conventional B/C ratio considering the disbenefits is approximately 1.27.

(b) Conventional B/C ratio without considering the disbenefits:

To calculate the B/C ratio without considering the disbenefits, we only consider the savings for motorists.

1. Calculate the present value of the benefits without disbenefits:

Present Value of Benefits = Savings per year * Present Value factor for 20 years

Present Value of Benefits = $820,000 * (1 - (1 + 0.06)^(-20)) / 0.06

Present Value of Benefits ≈ $11,460,817.38

2. Calculate the conventional B/C ratio without disbenefits:

B/C ratio = Present Value of Benefits / Present Value of Costs

B/C ratio = $11,460,817.38 / $9,000,000

B/C ratio ≈ 1.27

The project is economically justified both with and without considering the disbenefits since the B/C ratio is greater than 1 in both cases.