Question

Suppose that you are working for the state highway department. The state turnpike is in poor shape, with large potholes and crumbling shoulders that slow down traffic and pose an accident risk. The governor has charged you with the task of considering whether the state should invest in repairing this road, assuming it will last for 100 years.

The data for the project is indicated in the Table below. Note that all values are in nominal dollar terms (actual market values).

Benefit and Cost:                        

Making improvements will require the following inputs:

1. Initial cost: 1 million bags of asphalt, $100/bag;
2. Initial cost: 1 million hours of construction labor (500 workers for 2,000 hours each), at $20/hour
3. $10 million per year in the future for maintenance costs

There are two main benefits to these road improvements:

1. Driving time for producers (trucks) and consumers will be reduced by 500,000 hours per year. Hourly value is $19/hour.
2. The road will be safer, resulting in five fewer fatalities per year. The estimated life value (using wages) is $8.7 million/life.

                                                        

Question 1: What is the net present value of the investment at 5%, 7%, and 10%? Should the project be undertaken?

Question 2: Now assume that the maintenance cost is increasing at the rate of 5% per year in nominal terms. Hourly value of the reduced driving time is rising at 2% per year in nominal terms. Life values increase by 1% per year in nominal terms. The inflation rate is 2% per annum. All annual values accrue at the end of each year. Assume the nominal discount rate is 7%.

1. What is the real discount rate?
2. What is the Net Annual Worth (annualized net benefit) of this project?
3. What is the net present value? Should the project be undertaken?

Answer 1

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