Question

2. The construction cost of a parking facility on a local university campus is $200,000 Assume that maintenance will begin on the facility at the end of the third year of operation, and will increase by $500/year until the end of the useful life of the facility. Maintenance costs are expected to accrue to $2,000 during the third year of operation. If the interest rate is 7%, and the facility is expected to last 25 years, find the following (5 points): a) The present worth of the maintenance costs of the facility (2 points) b) The facility's annual maintenance costs. (2 points)

Answer 1

a) Present Worth of maintenance cost of the facility = $59,747.09

b) Annual maintenance cost = $172,500

year Discount Maintenance Discounted factor cost cost mino00 0.93458 0.87344 0.81630 0.76290 5 0.71299 6 0.66634 0.62275 8 0.58201 0.54393 0.50835 0.47509 0.44401 0.41496 0.38782 0.36245 0.33873 0.31657 0.29586 0.27651 0.25842 0.24151 22 0.22571 23 0.21095 0.19715 0.18425 Total 2,000.00 2,500.00 3,000.00 3,500.00 4,000.00 4,500.00 5,000.00 5,500.00 6,000.00 6,500.00 7,000.00 7,500.00 8,000.00 8,500.00 9,000.00 9,500.00 10,000.00 10,500.00 11,000.00 11,500.00 12,000.00 12,500.00 13,000.00 172,500.00 1,632.60 1,907.24 2,138.96 2,332.20 2,491.00 2,619.04 2,719.67 2,795.92 2,850.56 2,886.08 2,904.75 2,908.63 2,899.57 2,879.24 2,849.17 2,810.71 2,765.08 2,713.40 2,656.64 2,595.70 2,531.36 2,464.33 2,395.24 59,747.09

Formula for discount factor/ present value factor:

Present Value Factor = 7 (1 + i)

for example, for end of year 1:

PVF = 1/(1+.07)¹ = 0.93458

for end of year 2:

1/(1+.07)² = 0.87344

and so on...

Note that i have not rounded off any figures in the table.