Question

A DOT is performing a benefit-cost analysis of a new highway using an analysis period of 40 years as part the required environmental impact assessment of the project. The section of highway is estimated to have a construction cost $220 million dollars. The public benefit in reduced travel time and economic development around the highway is estimated to be $17 million per year for the first 5 years, then decrease by 3% per year for the remainder of the 40 year analysis period as congestion grows and economic development slows. The public disbenefit is estimated to be $2 million dollars in year 0 due to additional congestion and pollution during construction, then average $160,000 per year over the 40-year project life in environmental costs due to increased runoff and vehicle emissions. Using an interest rate of 4%, determine the benefit-cost ratio for this project using public/government version of the B/C ratio. Express your answer to two decimal places.

Answer 1

Given,

Analysis Period = 40 years

Total Cost Estimated = $220 million = Present Value (PV) cost

The benefits:

$17 million for first 5 years and decreases further by 3% for the remaining years

The disbenefits:

$2 million in the year 0

$160,000 per year for all the years.

Discount factor = 4%

Now with the given data, we have to calculate the Present value (PV) of Net benefits using the following formulae:

Net Benefits = Benefits - Disbenefits

PV of Net benefits = Net benefits x Discount factor

Interest rate is given as 4%.

Hence the discount factor can be calculated as (1+4%)-year = (1+0.04)-year = (1.04)-year

For year 0, (1.04)-0 = 1

For year 1, (1.04)-1 = 0.9616 and so on.

I have used MS-Excel to calculate all the values. The cost values are entered in millions.

I have entered the years, benefits and disbenefits. It calculates the net benefits, discount factor and PV of net benefits.

$17 million is entered as benefit for first 5 years.

It decreases at 3%

So for year 6, benefit = 17 - (17 x 0.03) = 16.49

For year 7, benefit = 16.49 - (16.49 x 0.03) = 16 and so on.

$2 million is entered as disbenefit for year 0.

$0.16 million is enteres as disbenefit for all years from year 1 to year 40.

Total PV of Net Benefits = Sum of all PV of Net Benefits

B/C Ratio = PV of Net Benefits / PV of Construction Costs

= 248/220 = 1.13

Therefore B/C ratio for this project = 1.13