Question

You are a design engineer working for the Turnpike Authority. Your client has asked you to re-evaluate the economic feasibility of two alternative toll bridge designs that you assessed previously. Both alternatives are expected to have a useful life of 25 years. Also, for both designs, it is assumed that major rehabilitation of each bridge will be required during Year 15 of the useful life. Further, inflation is expected to average about 3% annually during the project life but will vary within a reasonable range with a mean value of 3% and a standard deviation of 0.5%. The Turnpike Authority would like to earn a return of 7%. Therefore, the total project discount rate is about 10% depending upon the actual inflation year to year.

Alternative 1 is a lower initial cost option but restricts traffic across the bridge and thus does not optimize toll revenue. Alternative 1 has initial capital cost of $1,000,000 and starting at the end of Year 1 is expected to generate toll revenue each year ranging from $75,000 to $135,000 with a most likely annual value of $125,000 until the end of its useful life. Major rehabilitation during Year 15 is expected to cost between $175,000 and $300,000 with a most likely value of $200,000.

Alternative # 2 is more expensive but generates greater toll revenues each year. Alternative 2 has initial capital cost of $1,300,000 and starting at the end of Year 1 is expected to generate toll revenue each year ranging from $85,000 to $175,000 with a most likely annual value of $150,000 until the end of its useful life. Major rehabilitation during Year 15 is expected to cost between $175,000 and $300,000 with a most likely value of $250,000.

Answer the following questions regarding these alternatives:

2. What is minimum and maximum Net Present Value of the annual toll revenue in Year 13 for each alternative (Only evaluate the toll revenue alone for Year 13) ?

Answer 1

Since, revenue for year 13 alone is required to be calculated therefore npv will not be calculated.

However, following will be the minimum toll revenue alone for year 13 in case of alternative 1 will be $75000xpvif(13,10%)

= $75000x0.2897 = $21727.5

maximum npv of revenue for year 13 alone in case of alternative 1 will be $135000x0.2897 = $39109.5

minimum npv of toll revenue for year 2013 alone in case of alternative 2 will be $85000x0.2897

= $24624.5

maximum npv of toll revenue for year 2013 alone in case of alternative 2 will be $175000x0.2897

= $50697.5