Please do not copy past an answer from a previous chegg expert, this is a differ
ID: 1190949 • Letter: P
Question
Please do not copy past an answer from a previous chegg expert, this is a different question with a 20 year life span.
The state of Minnesota is considering building a highway through undeveloped wilderness. The construction will take 1 year and the construction costs are estimated at $10 million. The annual routine maintenance costs are expected to be $1 million per year. The relevant interest rate is 5%. The expected estimated annual benefits to the public and environment are $2 million per year. Assume an 20 year project life.
a. Find the PV of the Costs of this project.
b. the PV of the benefits of this project.
c. the PV of the Benefits – PV of the Costs.
d. Find the annual value of benefits which generates a zero net present value.
e. Assuming an infinite project life, find the increase in annual routine maintenance costs that make the NPV = 0.
Explanation / Answer
a. Present value of costs -
10 million + Present value of all maintenance costs
To calculate the present value of all maintenance costs, P[{1-(1/1+0.05)^t}/0.05] = 1[{1-(1/1.05)^20}/0.05]
=$12.46 million
So, present value of costs = 10 + 12.46 = $22.46 million
b. PV of benefits = PV of total benefits of $2million per year for 20 years
Similar to the first part, using the annuity formula: $24.92 million
c. PV of benefits - PV of costs = $2.46 million
d. For generating a net present value of zero, we assume that the PV of benefits would be equal to the PV of costs which is $22.46million
Using the reverse of the annuity formula, we want to calculate the new annual benefit which comes out to be $1.8million
e. For an infinite project life, we assume that the annuity formula gets reduced to C/r where C is the annual cost and r is the rate of interest.
Therefore, 10+ C/0.05 = 2/0.05 (Assuming that the benefits still remain the same per year)
which yields C = $1.5million per year. Therefore, the annual increase in maintenance cost would be 1.5-1 = $0.5 million dollars.